make test1 "MAXIMA=`pwd`/src/saved_maxima `pwd`/src/" make[1]: Entering directory `/home/wfs/cvs/maxima' date Sun May 6 01:10:22 CDT 2001 (cd doc ; /home/wfs/cvs/maxima/src/saved_maxima /home/wfs/cvs/maxima/src/ -dir `pwd`/../src/ -load "tests.lisp" < /dev/null ) GCL (GNU Common Lisp) Version(2.4.0) Sun May 6 01:05:49 CDT 2001 Licensed under GNU Library General Public License Contains Enhancements by W. Schelter Testing rtest1.mac /* ********************** Problem 1. *************** */ %Input is (FMAKUNBOUND(f), KILL(FUNCTIONS, VALUES, ARRAYS)) The result is DONE ..Which was correct /* ********************** Problem 2. *************** */ %Input is 2 F(X) := Y + X The result is 2 F(X) := Y + X ..Which was correct /* ********************** Problem 3. *************** */ %Input is F(2) The result is Y + 4 ..Which was correct /* ********************** Problem 4. *************** */ %Input is EV(F(2), Y : 7) The result is 11 ..Which was correct /* ********************** Problem 5. *************** */ %Input is 2 F(X) := 1 + SIN (X) The result is 2 F(X) := 1 + SIN (X) ..Which was correct /* ********************** Problem 6. *************** */ %Input is F(1 + X) The result is 2 SIN (X + 1) + 1 ..Which was correct /* ********************** Problem 7. *************** */ %Input is G(Y, Z) := 3 Y + F(Z) The result is G(Y, Z) := 3 Y + F(Z) ..Which was correct /* ********************** Problem 8. *************** */ %Input is EV(G(Z + 2 Y, - 0.5), Y : 7) The result is 3 (Z + 14) + 1.22984884706593 Using ratsimp RAT replaced 1.22984886 by 1953//1588 = 1.229848866498741 RAT replaced 1.22984884706593 by 1953//1588 = 1.229848866498741 ..Which was correct /* ********************** Problem 9. *************** */ %Input is I H(N) := SUM(I X , I, 0, N) The result is I H(N) := SUM(I X , I, 0, N) ..Which was correct /* ********************** Problem 10. *************** */ %Input is FUNCTIONS The result is [F(X), G(Y, Z), H(N)] ..Which was correct /* ********************** Problem 11. *************** */ %Input is T (X) := RATEXPAND(2 X T (X) - T (X)) N N - 1 N - 2 The result is T (X) := RATEXPAND(2 X T (X) - T (X)) N N - 1 N - 2 ..Which was correct /* ********************** Problem 12. *************** */ %Input is T (X) := 1 0 The result is T (X) := 1 0 ..Which was correct /* ********************** Problem 13. *************** */ %Input is T (X) := X 1 The result is T (X) := X 1 ..Which was correct /* ********************** Problem 14. *************** */ %Input is T (Y) 4 The result is 4 2 8 Y - 8 Y + 1 ..Which was correct /* ********************** Problem 15. *************** */ %Input is G (X) := SUM(EV(X), I, N, 2 + N) N The result is G (X) := SUM(EV(X), I, N, 2 + N) N ..Which was correct /* ********************** Problem 16. *************** */ %Input is H(N, X) := SUM(EV(X), I, N, 2 + N) The result is H(N, X) := SUM(EV(X), I, N, 2 + N) ..Which was correct /* ********************** Problem 17. *************** */ %Input is 2 G (I ) 2 The result is 2 3 I ..Which was correct /* ********************** Problem 18. *************** */ %Input is 2 H(2, I ) The result is 29 ..Which was correct /* ********************** Problem 19. *************** */ %Input is 2 N DIFF((X - 1) , X, N) P (X) := RATSIMP(---------------------) N N 2 N! The result is 2 N DIFF((X - 1) , X, N) P (X) := RATSIMP(---------------------) N N 2 N! ..Which was correct /* ********************** Problem 20. *************** */ %Input is 2 N DIFF((X - 1) , X, N) Q(N, X) := RATSIMP(---------------------) N 2 N! The result is 2 N DIFF((X - 1) , X, N) Q(N, X) := RATSIMP(---------------------) N 2 N! ..Which was correct /* ********************** Problem 21. *************** */ %Input is P 2 The result is 2 3 X - 1 LAMBDA([X], --------) 2 ..Which was correct /* ********************** Problem 22. *************** */ %Input is P (1 + Y) 2 The result is 2 3 (Y + 1) - 1 -------------- 2 ..Which was correct /* ********************** Problem 23. *************** */ %Input is Q(2, Y) The result is 2 3 Y - 1 -------- 2 ..Which was correct /* ********************** Problem 24. *************** */ %Input is P (5) 2 The result is 37 ..Which was correct /* ********************** Problem 25. *************** */ %Input is J I F (X, Y) := Y + X I, J The result is J I F (X, Y) := Y + X I, J ..Which was correct /* ********************** Problem 26. *************** */ %Input is G(FUN, A, B) := PRINT(FUN, " applied to ", A, " and ", B, " is ", FUN(A, B)) The result is G(FUN, A, B) := PRINT(FUN, " applied to ", A, " and ", B, " is ", FUN(A, B)) ..Which was correct /* ********************** Problem 27. *************** */ %Input is G(F , SIN(%PI), 2 C) 2, 1 2 LAMBDA([X, Y], Y + X ) applied to 0 and 2 C is 2 C The result is 2 C ..Which was correct /* ********************** Problem 28. *************** */ %Input is ROMBERG(SIN(y), y, 1, %PI) The result is 1.540302306426815 ..Which was correct Congratulations: No differences! Testing rtest1a.mac /* ********************** Problem 1. *************** */ %Input is (USE_FAST_ARRAYS : TRUE, ARRAY(bil, 3)) The result is #(NIL NIL NIL NIL) ..Which was correct /* ********************** Problem 2. *************** */ %Input is bil 1 The result is FALSE ..Which was correct /* ********************** Problem 3. *************** */ %Input is bil : 3 1 The result is 3 ..Which was correct /* ********************** Problem 4. *************** */ %Input is bil 1 The result is 3 ..Which was correct /* ********************** Problem 5. *************** */ %Input is LISTARRAY(bil) The result is [FALSE, 3, FALSE, FALSE] ..Which was correct /* ********************** Problem 6. *************** */ %Input is ARRAYINFO(bil) The result is [DECLARED, 1, [3]] ..Which was correct /* ********************** Problem 7. *************** */ %Input is ha : 2 1 The result is 2 ..Which was correct /* ********************** Problem 8. *************** */ %Input is ha 3 The result is FALSE ..Which was correct /* ********************** Problem 9. *************** */ %Input is ARRAYINFO(ha) The result is [HASH_TABLE, 1, 1] ..Which was correct /* ********************** Problem 10. *************** */ %Input is USE_FAST_ARRAYS : FALSE The result is FALSE ..Which was correct /* ********************** Problem 11. *************** */ %Input is ARRAY(bil1, 3) The result is bil1 ..Which was correct /* ********************** Problem 12. *************** */ %Input is bil1 2 The result is bil1 2 ..Which was correct /* ********************** Problem 13. *************** */ %Input is bil1 : 3 2 The result is 3 ..Which was correct /* ********************** Problem 14. *************** */ %Input is bil1 2 The result is 3 ..Which was correct /* ********************** Problem 15. *************** */ %Input is LISTARRAY(bil1) The result is [#####, #####, 3, #####] ..Which was correct /* ********************** Problem 16. *************** */ %Input is ARRAYINFO(bil1) The result is [DECLARED, 1, [3]] ..Which was correct /* ********************** Problem 17. *************** */ %Input is oldha : 8 1 The result is 8 ..Which was correct /* ********************** Problem 18. *************** */ %Input is oldha 2 The result is oldha 2 ..Which was correct /* ********************** Problem 19. *************** */ %Input is ARRAYINFO(oldha) The result is [HASHED, 1, [1]] ..Which was correct /* ********************** Problem 20. *************** */ %Input is USE_FAST_ARRAYS : TRUE The result is TRUE ..Which was correct /* ********************** Problem 21. *************** */ %Input is bilx := n bilx n n - 1 The result is bilx := n bilx n n - 1 ..Which was correct /* ********************** Problem 22. *************** */ %Input is bilx : 1 0 The result is 1 ..Which was correct /* ********************** Problem 23. *************** */ %Input is bilx 3 The result is 6 ..Which was correct Congratulations: No differences! Testing rtest2.mac /* ********************** Problem 1. *************** */ %Input is KILL(FUNCTIONS, ARRAYS, VALUES) The result is DONE ..Which was correct /* ********************** Problem 2. *************** */ %Input is USE_FAST_ARRAYS : FALSE The result is FALSE ..Which was correct /* ********************** Problem 3. *************** */ %Input is A := N A N N - 1 The result is A := N A N N - 1 ..Which was correct /* ********************** Problem 4. *************** */ %Input is A : 1 0 The result is 1 ..Which was correct /* ********************** Problem 5. *************** */ %Input is A 5 The result is 120 ..Which was correct /* ********************** Problem 6. *************** */ %Input is A := N N The result is A := N N ..Which was correct /* ********************** Problem 7. *************** */ %Input is A 6 The result is 6 ..Which was correct /* ********************** Problem 8. *************** */ %Input is A 4 The result is 24 ..Which was correct /* ********************** Problem 9. *************** */ %Input is (USE_FAST_ARRAYS : TRUE, KILL(A)) The result is DONE ..Which was correct /* ********************** Problem 10. *************** */ %Input is 2 2 2 LAMBDA([X, Y, Z], Z + Y + X ) The result is 2 2 2 LAMBDA([X, Y, Z], Z + Y + X ) ..Which was correct /* ********************** Problem 11. *************** */ %Input is %(1, 2, A) The result is 2 A + 5 ..Which was correct /* ********************** Problem 12. *************** */ %Input is A + 2 + 1 The result is A + 3 ..Which was correct /* ********************** Problem 13. *************** */ %Input is 2 Y EXP : [X , -, - 2] 3 The result is 2 Y [X , -, - 2] 3 ..Which was correct /* ********************** Problem 14. *************** */ %Input is % X 1 The result is 3 X ..Which was correct /* ********************** Problem 15. *************** */ %Input is [A, EXP, %] The result is 2 Y 3 [A, [X , -, - 2], X ] 3 ..Which was correct /* ********************** Problem 16. *************** */ %Input is M : MATRIX([A, 0], [B, 1]) The result is [ A 0 ] [ ] [ B 1 ] ..Which was correct /* ********************** Problem 17. *************** */ %Input is 2 M The result is [ 2 ] [ A 0 ] [ ] [ 2 ] [ B 1 ] ..Which was correct /* ********************** Problem 18. *************** */ %Input is EXP : M . M The result is [ 2 ] [ A 0 ] [ ] [ A B + B 1 ] ..Which was correct /* ********************** Problem 19. *************** */ %Input is M M 1, 1 The result is [ 2 ] [ A 0 ] [ ] [ A B A ] ..Which was correct /* ********************** Problem 20. *************** */ %Input is 1 - EXP + % The result is [ 1 1 ] [ ] [ 1 - B A ] ..Which was correct /* ********************** Problem 21. *************** */ %Input is <- 1> M The result is [ 1 ] [ - 0 ] [ A ] [ ] [ B ] [ - - 1 ] [ A ] ..Which was correct /* ********************** Problem 22. *************** */ %Input is [X, Y] . M The result is [ B Y + A X Y ] ..Which was correct /* ********************** Problem 23. *************** */ %Input is MATRIX([A, B, C], [D, E, F], [G, H, I]) The result is [ A B C ] [ ] [ D E F ] [ ] [ G H I ] ..Which was correct /* ********************** Problem 24. *************** */ %Input is <2> % The result is [ 2 ] [ C G + B D + A C H + B E + A B C I + B F + A C ] [ ] [ 2 ] [ F G + D E + A D F H + E + B D F I + E F + C D ] [ ] [ 2 ] [ G I + D H + A G H I + E H + B G I + F H + C G ] ..Which was correct /* ********************** Problem 25. *************** */ %Input is 2 EXP : 1 + X = Y The result is 2 X + 1 = Y ..Which was correct /* ********************** Problem 26. *************** */ %Input is X - 1 = 1 + 2 Y The result is X - 1 = 2 Y + 1 ..Which was correct /* ********************** Problem 27. *************** */ %Input is % + EXP The result is 2 2 X = Y + 2 Y + 1 ..Which was correct /* ********************** Problem 28. *************** */ %Input is EXP --- Y The result is X + 1 ----- = Y Y ..Which was correct /* ********************** Problem 29. *************** */ %Input is 1 - % The result is Y 1 ----- = - X + 1 Y ..Which was correct /* ********************** Problem 30. *************** */ %Input is FIB := IF N = 1 OR N = 2 THEN 1 ELSE FIB + FIB N N - 2 N - 1 The result is FIB := IF N = 1 OR N = 2 THEN 1 ELSE FIB + FIB N N - 2 N - 1 ..Which was correct /* ********************** Problem 31. *************** */ %Input is FIB + FIB 2 1 The result is 2 ..Which was correct /* ********************** Problem 32. *************** */ %Input is FIB 3 The result is 2 ..Which was correct /* ********************** Problem 33. *************** */ %Input is FIB 5 The result is 5 ..Which was correct /* ********************** Problem 34. *************** */ %Input is ETA(MU, NU) := IF MU = NU THEN MU ELSE (IF MU > NU THEN MU - NU ELSE NU + MU) The result is ETA(MU, NU) := IF MU = NU THEN MU ELSE (IF MU > NU THEN MU - NU ELSE NU + MU) ..Which was correct /* ********************** Problem 35. *************** */ %Input is ETA(5, 6) The result is 11 ..Which was correct /* ********************** Problem 36. *************** */ %Input is ETA(ETA(7, 7), ETA(1, 2)) The result is 4 ..Which was correct /* ********************** Problem 37. *************** */ %Input is IF NOT 5 >= 2 AND 6 <= 5 OR 1 + 4 > 3 THEN A ELSE B The result is A ..Which was correct /* ********************** Problem 38. *************** */ %Input is KILL(F) The result is DONE ..Which was correct /* ********************** Problem 39. *************** */ %Input is HESSIAN(F) := BLOCK([DFXX, DFXY, DFXZ, DFYY, DFYZ, DFZZ], DFXX : DIFF(F, X, 2), DFXY : DIFF(F, X, 1, Y, 1), DFXZ : DIFF(F, X, 1, Z, 1), DFYY : DIFF(F, Y, 2), DFYZ : DIFF(F, Y, 1, Z, 1), DFZZ : DIFF(F, Z, 2), DETERMINANT(MATRIX([DFXX, DFXY, DFXZ], [DFXY, DFYY, DFYZ], [DFXZ, DFYZ, DFZZ]))) The result is HESSIAN(F) := BLOCK([DFXX, DFXY, DFXZ, DFYY, DFYZ, DFZZ], DFXX : DIFF(F, X, 2), DFXY : DIFF(F, X, 1, Y, 1), DFXZ : DIFF(F, X, 1, Z, 1), DFYY : DIFF(F, Y, 2), DFYZ : DIFF(F, Y, 1, Z, 1), DFZZ : DIFF(F, Z, 2), DETERMINANT(MATRIX([DFXX, DFXY, DFXZ], [DFXY, DFYY, DFYZ], [DFXZ, DFYZ, DFZZ]))) ..Which was correct /* ********************** Problem 40. *************** */ %Input is KILL(X, Y, Z) The result is DONE ..Which was correct /* ********************** Problem 41. *************** */ %Input is 3 3 HESSIAN(Y - 3 A X Y Z + X ) The result is 2 2 3 2 3 - 3 A Y (9 A X Z + 18 A Y ) - 27 A X Y Z - 54 A X ..Which was correct /* ********************** Problem 42. *************** */ %Input is 2 SUBST(1, Z, QUOTIENT(%, - 54 A )) The result is 3 3 Y + A X Y + X ..Which was correct /* ********************** Problem 43. *************** */ %Input is F(X) := BLOCK([A, Y], LOCAL(A), Y : 4, A : X, DISPLAY(A )) Y Y The result is F(X) := BLOCK([A, Y], LOCAL(A), Y : 4, A : X, DISPLAY(A )) Y Y ..Which was correct /* ********************** Problem 44. *************** */ %Input is Y : 2 The result is 2 ..Which was correct /* ********************** Problem 45. *************** */ %Input is A : 0 2 + Y The result is 0 ..Which was correct /* ********************** Problem 46. *************** */ %Input is F(9) A = 9 4 The result is DONE ..Which was correct /* ********************** Problem 47. *************** */ %Input is A 2 + Y The result is 0 ..Which was correct Congratulations: No differences! Testing rtest3.mac /* ********************** Problem 1. *************** */ %Input is KILL(ALL) The result is DONE ..Which was correct /* ********************** Problem 2. *************** */ %Input is FOR A FROM - 3 STEP 7 THRU 26 DO LDISPLAY(A) (E1) A = - 3 (E2) A = 4 (E3) A = 11 (E4) A = 18 (E5) A = 25 The result is DONE ..Which was correct /* ********************** Problem 3. *************** */ %Input is S : 0 The result is 0 ..Which was correct /* ********************** Problem 4. *************** */ %Input is FOR I WHILE I <= 10 DO S : I + S The result is DONE ..Which was correct /* ********************** Problem 5. *************** */ %Input is S The result is 55 ..Which was correct /* ********************** Problem 6. *************** */ %Input is SERIES : 1 The result is 1 ..Which was correct /* ********************** Problem 7. *************** */ %Input is TERM : EXP(SIN(X)) The result is SIN(X) %E ..Which was correct /* ********************** Problem 8. *************** */ %Input is DIFF(TERM, X) FOR P UNLESS P > 7 DO (TERM : -------------, P P SERIES : SUBST(X = 0, TERM) X + SERIES) The result is DONE ..Which was correct /* ********************** Problem 9. *************** */ %Input is SERIES The result is 7 6 5 4 2 X X X X X -- - --- - -- - -- + -- + X + 1 90 240 15 8 2 ..Which was correct /* ********************** Problem 10. *************** */ %Input is POLY : 0 The result is 0 ..Which was correct /* ********************** Problem 11. *************** */ %Input is J FOR I THRU 5 DO (FOR J FROM I STEP - 1 THRU 1 DO POLY : I X + POLY) The result is DONE ..Which was correct /* ********************** Problem 12. *************** */ %Input is POLY The result is 5 4 3 2 5 X + 9 X + 12 X + 14 X + 15 X ..Which was correct /* ********************** Problem 13. *************** */ %Input is GUESS : - 3.0 The result is - 3.0 ..Which was correct /* ********************** Problem 14. *************** */ %Input is 10 FOR I THRU 10 DO (GUESS : SUBST(GUESS, X, 0.5 (-- + X)), X ! 2 ! IF !GUESS - 10! < 5.0E-5 THEN RETURN(GUESS)) The result is - 3.162280701754386 ..Which was correct /* ********************** Problem 15. *************** */ %Input is FOR COUNT FROM 2 NEXT 3 COUNT THRU 20 DO LDISPLAY(COUNT) (E6) COUNT = 2 (E7) COUNT = 6 (E8) COUNT = 18 The result is DONE ..Which was correct /* ********************** Problem 16. *************** */ %Input is X : 1000 The result is 1000 ..Which was correct /* ********************** Problem 17. *************** */ %Input is 5 THRU 10 WHILE X # 0 DO X : 0.5 (- + X) X The result is DONE ..Which was correct /* ********************** Problem 18. *************** */ %Input is X The result is 2.282429035887867 Using ratsimp RAT replaced 2.28242904 by 6352//2783 = 2.282429033417176 RAT replaced 2.282429035887867 by 6352//2783 = 2.282429033417176 ..Which was correct /* ********************** Problem 19. *************** */ %Input is REMVALUE(X) The result is [X] ..Which was correct /* ********************** Problem 20. *************** */ %Input is NEWTON(F, GUESS) := BLOCK([NUMER, Y], LOCAL(F, DF, X, GUESS), NUMER : TRUE, DEFINE(DF(X), DIFF(F(X), X)), DO (Y : DF(GUESS), IF Y = 0 THEN ERROR("derivative at", GUESS, "is zero"), F(GUESS) GUESS : GUESS - --------, IF ABS(F(GUESS)) < 5.0E-6 THEN RETURN(GUESS))) Y The result is NEWTON(F, GUESS) := BLOCK([NUMER, Y], LOCAL(F, DF, X, GUESS), NUMER : TRUE, DEFINE(DF(X), DIFF(F(X), X)), DO (Y : DF(GUESS), IF Y = 0 THEN ERROR("derivative at", GUESS, "is zero"), F(GUESS) GUESS : GUESS - --------, IF ABS(F(GUESS)) < 5.0E-6 THEN RETURN(GUESS))) Y ..Which was correct /* ********************** Problem 21. *************** */ %Input is 2 SQR(X) := X - 5.0 The result is 2 SQR(X) := X - 5.0 ..Which was correct /* ********************** Problem 22. *************** */ %Input is NEWTON(SQR, 1000) The result is 2.236068027062195 ..Which was correct /* ********************** Problem 23. *************** */ %Input is FOR F IN [LOG, RHO, ATAN] DO LDISP(F(1.0)) (E9) 0.0 (E10) RHO(1.0) (E11) 0.78539816339745 The result is DONE ..Which was correct /* ********************** Problem 24. *************** */ %Input is EV(CONCAT(E, LINENUM - 1), NUMER) The result is E10 ..Which was correct /* ********************** Problem 25. *************** */ %Input is KILL(FUNCTIONS, VALUES, ARRAYS) The result is DONE ..Which was correct /* ********************** Problem 26. *************** */ %Input is DONE The result is DONE ..Which was correct /* ********************** Problem 27. *************** */ %Input is EXP : DIFF(X F(X), X) The result is d X (-- (F(X))) + F(X) dX ..Which was correct /* ********************** Problem 28. *************** */ %Input is F(X) := SIN(X) The result is F(X) := SIN(X) ..Which was correct /* ********************** Problem 29. *************** */ %Input is EV(EXP, DIFF) The result is SIN(X) + X COS(X) ..Which was correct /* ********************** Problem 30. *************** */ %Input is X The result is X ..Which was correct /* ********************** Problem 31. *************** */ %Input is X : 3 The result is 3 ..Which was correct /* ********************** Problem 32. *************** */ %Input is X The result is 3 ..Which was correct /* ********************** Problem 33. *************** */ %Input is 'X The result is X ..Which was correct /* ********************** Problem 34. *************** */ %Input is 2 F(X) := X The result is 2 F(X) := X ..Which was correct /* ********************** Problem 35. *************** */ %Input is F(2) The result is F(2) ..Which was correct /* ********************** Problem 36. *************** */ %Input is EV(%, F) The result is 4 ..Which was correct /* ********************** Problem 37. *************** */ %Input is '(F(2)) The result is F(2) ..Which was correct /* ********************** Problem 38. *************** */ %Input is F(2) The result is 4 ..Which was correct /* ********************** Problem 39. *************** */ %Input is SUM(I!, I, 1, 4) The result is 33 ..Which was correct /* ********************** Problem 40. *************** */ %Input is 4 ==== \ >I! / ==== I = 1 The result is 4 ==== \ >I! / ==== I = 1 ..Which was correct /* ********************** Problem 41. *************** */ %Input is REMVALUE(X) The result is [X] ..Which was correct /* ********************** Problem 42. *************** */ %Input is B / [ I F(X) dX ] / A The result is B / [ 2 I X dX ] / A ..Which was correct /* ********************** Problem 43. *************** */ %Input is 2 FOR I THRU 5 DO S : I + S The result is DONE ..Which was correct /* ********************** Problem 44. *************** */ %Input is EXP : S The result is S + 55 Using ratsimp Using ratsimp ..Which was correct /* ********************** Problem 45. *************** */ %Input is EV(%, S : 0) The result is 55 ..Which was correct /* ********************** Problem 46. *************** */ %Input is EV(EXP) The result is S + 110 Using ratsimp Using ratsimp ..Which was correct /* ********************** Problem 47. *************** */ %Input is N ==== \ EXP : >G(I) / ==== I = 0 The result is N ==== \ >G(I) / ==== I = 0 ..Which was correct /* ********************** Problem 48. *************** */ %Input is Z Z %E The result is Z Z %E ..Which was correct /* ********************** Problem 49. *************** */ %Input is 2 EV(%, Z : X ) The result is 2 2 X X %E ..Which was correct /* ********************** Problem 50. *************** */ %Input is 2 SUBST(X , Z, EXP) The result is N ==== \ >G(I) / ==== I = 0 ..Which was correct /* ********************** Problem 51. *************** */ %Input is A : % The result is N ==== \ >G(I) / ==== I = 0 ..Which was correct /* ********************** Problem 52. *************** */ %Input is 1 + A The result is N ==== \ >G(I) + 1 / ==== I = 0 ..Which was correct /* ********************** Problem 53. *************** */ %Input is KILL(A, Y) The result is DONE ..Which was correct /* ********************** Problem 54. *************** */ %Input is A The result is A ..Which was correct /* ********************** Problem 55. *************** */ %Input is DECLARE(INTEGRATE, NOUN) The result is DONE ..Which was correct /* ********************** Problem 56. *************** */ %Input is / [ 2 I Y dY ] / The result is / [ 2 I Y dY ] / ..Which was correct /* ********************** Problem 57. *************** */ %Input is 2 INTEGRATE(Y , Y) The result is 3 Y -- 3 ..Which was correct /* ********************** Problem 58. *************** */ %Input is F(Y) := DIFF(Y LOG(Y), Y, 2) The result is F(Y) := DIFF(Y LOG(Y), Y, 2) ..Which was correct /* ********************** Problem 59. *************** */ %Input is 1 F(Y) := - Y The result is 1 F(Y) := - Y ..Which was correct /* ********************** Problem 60. *************** */ %Input is C10 The result is C10 ..Which was correct /* ********************** Problem 61. *************** */ %Input is 3 (Y + X) The result is 3 (Y + X) ..Which was correct /* ********************** Problem 62. *************** */ %Input is DIFF(%, X) The result is 2 3 (Y + X) ..Which was correct /* ********************** Problem 63. *************** */ %Input is 2 Y : 1 + X The result is 2 X + 1 ..Which was correct /* ********************** Problem 64. *************** */ %Input is KILL(ALL) The result is DONE ..Which was correct /* ********************** Problem 65. *************** */ %Input is X 2 EV(%E SIN (X), EXPONENTIALIZE) The result is X %I X - %I X 2 %E (%E - %E ) - ------------------------ 4 ..Which was correct /* ********************** Problem 66. *************** */ %Input is INTEGRATE(%, X) The result is (2 %I + 1) X (1 - 2 %I) X %E %E X -------------- + -------------- - 2 %E 2 %I + 1 1 - 2 %I - --------------------------------------- 4 Using ratsimp ..Which was correct /* ********************** Problem 67. *************** */ %Input is EV(%, DEMOIVRE) The result is X X %E (%I SIN(2 X) + COS(2 X)) %E (COS(2 X) - %I SIN(2 X)) X ---------------------------- + ---------------------------- - 2 %E 2 %I + 1 1 - 2 %I - ------------------------------------------------------------------- 4 Using ratsimp ..Which was correct /* ********************** Problem 68. *************** */ %Input is ANS : EV(%, RATEXPAND) The result is X X X %E SIN(2 X) %E COS(2 X) %E - ------------ - ------------ + --- 5 10 2 ..Which was correct /* ********************** Problem 69. *************** */ %Input is EV(ANS, X : 1, NUMER) - EV(ANS, X : 0, NUMER) The result is 0.57791601820424 ..Which was correct /* ********************** Problem 70. *************** */ %Input is BLOCK([FPPREC : 35], EV(ANS, X : 1, BFLOAT) - EV(ANS, X : 0, BFLOAT)) The result is 5.7791601820424019599988308251707781B-1 Using ratsimpRAT replaced 5.779160182042402B-1 by 1858/3215 = 5.779160186625195B-1 RAT replaced 5.779160182042402B-1 by 1858/3215 = 5.779160186625195B-1 ..Which was correct /* ********************** Problem 71. *************** */ %Input is X 2 INTEGRATE(%E SIN (X), X) The result is X X X 2 %E SIN(2 X) + %E COS(2 X) - 5 %E - ------------------------------------- 10 Using ratsimp ..Which was correct /* ********************** Problem 72. *************** */ %Input is TRIGREDUCE(%) The result is X X X 2 %E SIN(2 X) + %E COS(2 X) - 5 %E - ------------------------------------- 10 Using ratsimp ..Which was correct /* ********************** Problem 73. *************** */ %Input is EV(% - ANS, RATSIMP) The result is 0 ..Which was correct /* ********************** Problem 74. *************** */ %Input is EV(SIN(X), %EMODE) The result is SIN(X) ..Which was correct /* ********************** Problem 75. *************** */ %Input is %PI %PI TAN(---) + SIN(---) 6 12 The result is %PI 1 SIN(---) + ------- 12 SQRT(3) ..Which was correct /* ********************** Problem 76. *************** */ %Input is EV(%, NUMER) The result is 0.83616931429215 ..Which was correct /* ********************** Problem 77. *************** */ %Input is SIN(1) The result is SIN(1) ..Which was correct /* ********************** Problem 78. *************** */ %Input is EV(SIN(1), NUMER) The result is 0.8414709848079 ..Which was correct /* ********************** Problem 79. *************** */ %Input is 1 2 BETA(-, -) 2 5 The result is 1 2 BETA(-, -) 2 5 ..Which was correct /* ********************** Problem 80. *************** */ %Input is EV(%, NUMER) The result is 3.67909265499715 ..Which was correct /* ********************** Problem 81. *************** */ %Input is DIFF(ATANH(SQRT(X)), X) The result is 1 ----------------- 2 (1 - X) SQRT(X) ..Which was correct /* ********************** Problem 82. *************** */ %Input is FPPREC : 25 The result is 25 ..Which was correct /* ********************** Problem 83. *************** */ %Input is SIN(5.0B-1) The result is 7.41875087617627074653449B-190 Using ratsimpRAT replaced PQUOTIENT by zero -- an error. Quitting. To debug this try DEBUGMODE(TRUE);) Caused a error break: rtest3.mac Testing rtest4.mac /* ********************** Problem 1. *************** */ %Input is KILL(FUNCTIONS, ARRAYS, VALUES) The result is DONE ..Which was correct /* ********************** Problem 2. *************** */ %Input is EV(SIN(X), EXPONENTIALIZE) The result is %I X - %I X %I (%E - %E ) - ---------------------- 2 ..Which was correct /* ********************** Problem 3. *************** */ %Input is SIN(X) TAYLOR(------, X, 0, 4) X The result is 2 4 X X 1 - -- + --- + . . . 6 120 ..Which was correct /* ********************** Problem 4. *************** */ %Input is 2 2 2 2 EV(COS (X) - SIN (X), SIN (X) = 1 - COS (X)) The result is 2 2 COS (X) - 1 ..Which was correct /* ********************** Problem 5. *************** */ %Input is 2 (SQRT(2.25) + SQRT(- 4)) The result is 2 (2 %I + 1.5) ..Which was correct /* ********************** Problem 6. *************** */ %Input is EXPAND(%) The result is 6.0 %I - 1.75 ..Which was correct /* ********************** Problem 7. *************** */ %Input is EXPAND(SQRT(2 %I)) The result is 1/4 (- 1) SQRT(2) ..Which was correct /* ********************** Problem 8. *************** */ %Input is KILL(ALL) The result is DONE ..Which was correct /* ********************** Problem 9. *************** */ %Input is d 2 -- (SIN(W)) + (1 + W) + COS(Y) + SIN(X) dW The result is d 2 COS(Y) + SIN(X) + -- (SIN(W)) + (W + 1) dW ..Which was correct /* ********************** Problem 10. *************** */ %Input is EV(%, SIN, EXPAND, DIFF, X = 2, Y = 1) The result is 2 COS(W) + W + 2 W + COS(1) + 1.909297426825682 ..Which was correct /* ********************** Problem 11. *************** */ %Input is EV(Y + X, X : Y + A, Y : 2) The result is Y + A + 2 ..Which was correct /* ********************** Problem 12. *************** */ %Input is 3 d 2 2 ------ (X + X Y + Y ) 2 dX dY The result is 3 d 2 2 ------ (Y + X Y + X ) 2 dX dY ..Which was correct /* ********************** Problem 13. *************** */ %Input is EV(%, DIFF) The result is 0 ..Which was correct /* ********************** Problem 14. *************** */ %Input is EXP : 2 X - 3 Y = 3 The result is 2 X - 3 Y = 3 ..Which was correct /* ********************** Problem 15. *************** */ %Input is 2 Y - 3 X = - 4 The result is 2 Y - 3 X = - 4 ..Which was correct /* ********************** Problem 16. *************** */ %Input is SOLVE([EXP, %]) The result is 1 6 [[Y = - -, X = -]] 5 5 ..Which was correct /* ********************** Problem 17. *************** */ %Input is EV(EXP, %) The result is 3 = 3 ..Which was correct /* ********************** Problem 18. *************** */ %Input is 1 1 - + X > GAMMA(-) X 2 The result is 1 X + - > SQRT(%PI) X ..Which was correct /* ********************** Problem 19. *************** */ %Input is 1 EV(%, NUMER, X = -) 2 The result is 2.5 > 1.772453850905516 ..Which was correct /* ********************** Problem 20. *************** */ %Input is EV(%, PRED) The result is TRUE ..Which was correct /* ********************** Problem 21. *************** */ %Input is ZEROEQUIV(SIN(2 X) - 2 SIN(X) COS(X), X) The result is TRUE ..Which was correct /* ********************** Problem 22. *************** */ %Input is X ZEROEQUIV(X + %E , X) The result is FALSE ..Which was correct /* ********************** Problem 23. *************** */ %Input is ZEROEQUIV(- LOG(B) - LOG(A) + LOG(A B), A) The result is DONTKNOW ..Which was correct /* ********************** Problem 24. *************** */ %Input is 1 3 2 (-------- - --------) 4 3 (Y + X) (Z + Y) The result is 1 3 2 (-------- - --------) 4 3 (Y + X) (Z + Y) ..Which was correct /* ********************** Problem 25. *************** */ %Input is EXPAND(%, 2, 0) The result is 6 9 1 - ----------------- + -------- + -------- 4 3 6 8 (Y + X) (Z + Y) (Z + Y) (Y + X) ..Which was correct /* ********************** Problem 26. *************** */ %Input is EXPAND(A . (F + C . (E + D) + B)) The result is A . F + A . C . E + A . C . D + A . B ..Which was correct /* ********************** Problem 27. *************** */ %Input is 3 EXPAND((1 + X) ) The result is 3 2 X + 3 X + 3 X + 1 ..Which was correct /* ********************** Problem 28. *************** */ %Input is 7 EXP : (1 + X) The result is 7 (X + 1) ..Which was correct /* ********************** Problem 29. *************** */ %Input is EXPAND(%) The result is 7 6 5 4 3 2 X + 7 X + 21 X + 35 X + 35 X + 21 X + 7 X + 1 ..Which was correct /* ********************** Problem 30. *************** */ %Input is EXPAND(EXP, 7, 7) The result is 7 6 5 4 3 2 X + 7 X + 21 X + 35 X + 35 X + 21 X + 7 X + 1 ..Which was correct /* ********************** Problem 31. *************** */ %Input is 2 EV(A (C + B) + A (C + B), EXPOP : 1) The result is 2 A (C + B) + A C + A B ..Which was correct /* ********************** Problem 32. *************** */ %Input is 3 RATEXPAND((2 X - 3 Y) ) The result is 3 2 2 3 - 27 Y + 54 X Y - 36 X Y + 8 X ..Which was correct /* ********************** Problem 33. *************** */ %Input is 1 X - 1 EXP : ----- + -------- X - 1 2 (1 + X) The result is X - 1 1 -------- + ----- 2 X - 1 (X + 1) ..Which was correct /* ********************** Problem 34. *************** */ %Input is EXPAND(%) The result is X 1 1 ------------ - ------------ + ----- 2 2 X - 1 X + 2 X + 1 X + 2 X + 1 ..Which was correct /* ********************** Problem 35. *************** */ %Input is RATEXPAND(EXP) The result is 2 2 X 2 --------------- + --------------- 3 2 3 2 X + X - X - 1 X + X - X - 1 ..Which was correct /* ********************** Problem 36. *************** */ %Input is 2 2 X (1 + LOG(X)) - LOG (X) SIN(------) = %E 2 X + X The result is 2 2 X (LOG(X) + 1) - LOG (X) SIN(------) = %E 2 X + X ..Which was correct /* ********************** Problem 37. *************** */ %Input is RATSIMP(%) The result is 1 2 SIN(-----) = %E X X + 1 ..Which was correct /* ********************** Problem 38. *************** */ %Input is A A + B X + B (- - X) B The result is A B X + B (- - X) + A B ..Which was correct /* ********************** Problem 39. *************** */ %Input is RATSIMP(%) The result is 2 A ..Which was correct /* ********************** Problem 40. *************** */ %Input is 3/2 (X - 1) - (1 + X) SQRT(X - 1) -------------------------------- SQRT(X - 1) -------------------------------- SQRT(1 + X) The result is 3/2 (X - 1) - SQRT(X - 1) (X + 1) -------------------------------- SQRT(X - 1) SQRT(X + 1) ..Which was correct /* ********************** Problem 41. *************** */ %Input is RATSIMP(%) The result is 2 - ----------- SQRT(X + 1) ..Which was correct /* ********************** Problem 42. *************** */ %Input is 1/A + A EV(X , RATSIMPEXPONS) The result is 2 A + 1 ------ A X ..Which was correct /* ********************** Problem 43. *************** */ %Input is 2 A (LOG(X + X ) - LOG(X)) ----------------------- A/2 LOG(1 + X) The result is 2 A (LOG(X + X) - LOG(X)) ----------------------- A/2 LOG(X + 1) ..Which was correct /* ********************** Problem 44. *************** */ %Input is RADCAN(%) The result is A/2 LOG(X + 1) ..Which was correct /* ********************** Problem 45. *************** */ %Input is X 2 X LOG(1 + 2 A + A ) -------------------- X LOG(1 + A ) The result is 2 X X LOG(A + 2 A + 1) -------------------- X LOG(A + 1) ..Which was correct /* ********************** Problem 46. *************** */ %Input is RADCAN(%) The result is 2 ..Which was correct /* ********************** Problem 47. *************** */ %Input is X %E - 1 --------- X/2 1 + %E The result is X %E - 1 --------- X/2 %E + 1 ..Which was correct /* ********************** Problem 48. *************** */ %Input is RADCAN(%) The result is X/2 %E - 1 ..Which was correct /* ********************** Problem 49. *************** */ %Input is KILL(ALL) The result is DONE ..Which was correct /* ********************** Problem 50. *************** */ %Input is B A B A COMBINE(- + - + - + -) Y Y X X The result is B + A B + A ----- + ----- Y X ..Which was correct /* ********************** Problem 51. *************** */ %Input is - F(X) 1 X -------- - ----- + -------- 3 X - Y 2 (X - Y) (X - Y) The result is 1 X F(X) - ----- + -------- - -------- X - Y 2 3 (X - Y) (X - Y) ..Which was correct /* ********************** Problem 52. *************** */ %Input is 3 MULTTHRU((X - Y) , %) The result is 2 - (X - Y) + X (X - Y) - F(X) ..Which was correct /* ********************** Problem 53. *************** */ %Input is RATEXPAND(%) The result is 2 - Y + X Y - F(X) ..Which was correct /* ********************** Problem 54. *************** */ %Input is 2 10 2 (A B) + 2 A B S + (B + A) S ------------------------------- 2 A B S The result is 10 2 2 2 (B + A) S + 2 A B S + A B ------------------------------ 2 A B S ..Which was correct /* ********************** Problem 55. *************** */ %Input is MULTTHRU(%) The result is 10 2 A B (B + A) - + --- + --------- S 2 A B S ..Which was correct /* ********************** Problem 56. *************** */ %Input is MULTTHRU(A . (F + C . (E + D) + B)) The result is A . F + A . C . (E + D) + A . B ..Which was correct /* ********************** Problem 57. *************** */ %Input is 20 - X 1 (2 + X) - 2 Y --------- + --------- + --------------- 20 19 20 (Y + X) (Y + X) (Y + X) The result is 20 1 (X + 2) - 2 Y X --------- + --------------- - --------- 19 20 20 (Y + X) (Y + X) (Y + X) ..Which was correct /* ********************** Problem 58. *************** */ %Input is XTHRU(%) The result is 20 (X + 2) - Y ------------- 20 (Y + X) ..Which was correct /* ********************** Problem 59. *************** */ %Input is 1 2 2 -------- - ----- + ----- 2 1 + X 2 + X (1 + X) The result is 2 2 1 ----- - ----- + -------- X + 2 X + 1 2 (X + 1) ..Which was correct /* ********************** Problem 60. *************** */ %Input is RATSIMP(%) The result is X - ------------------- 3 2 X + 4 X + 5 X + 2 ..Which was correct /* ********************** Problem 61. *************** */ %Input is PARTFRAC(%, X) The result is 2 2 1 ----- - ----- + -------- X + 2 X + 1 2 (X + 1) ..Which was correct /* ********************** Problem 62. *************** */ %Input is 63 FACTOR(2 - 1) The result is 2 7 73 127 337 92737 649657 ..Which was correct /* ********************** Problem 63. *************** */ %Input is 2 FACTOR(- 8 Y - 4 X + Z (2 Y + X)) The result is (2 Y + X) (Z - 2) (Z + 2) ..Which was correct /* ********************** Problem 64. *************** */ %Input is 2 2 2 2 2 - 1 - 2 X - X + Y + 2 X Y + X Y The result is 2 2 2 2 2 X Y + 2 X Y + Y - X - 2 X - 1 ..Which was correct /* ********************** Problem 65. *************** */ %Input is % -- 36 BLOCK([DONTFACTOR : [X]], FACTOR(------------)) 2 1 + 2 Y + Y The result is 2 (X + 2 X + 1) (Y - 1) ---------------------- 36 (Y + 1) ..Which was correct /* ********************** Problem 66. *************** */ %Input is 3 X FACTOR(1 + %E ) The result is X 2 X X (%E + 1) (%E - %E + 1) ..Which was correct /* ********************** Problem 67. *************** */ %Input is 4 2 FACTOR(1 + X , A - 2) The result is 2 2 (X - A X + 1) (X + A X + 1) ..Which was correct /* ********************** Problem 68. *************** */ %Input is 2 2 2 2 2 3 FACTOR(- Y Z - X Z + X Y + X ) The result is 2 - (Y + X) (Z - X) (Z + X) ..Which was correct /* ********************** Problem 69. *************** */ %Input is 2 + X ----- 3 + X ----- B + X -------- 2 (C + X) The result is X + 2 ------------------------ 2 (X + 3) (X + B) (X + C) ..Which was correct /* ********************** Problem 70. *************** */ %Input is RATSIMP(%) The result is 4 3 2 2 (X + 2)/(X + (2 C + B + 3) X + (C + (2 B + 6) C + 3 B) X 2 2 + ((B + 3) C + 6 B C) X + 3 B C ) ..Which was correct /* ********************** Problem 71. *************** */ %Input is PARTFRAC(%, X) The result is 2 4 3 2 2 - (C - 4 C - B + 6)/((C + (- 2 B - 6) C + (B + 12 B + 9) C 2 2 C - 2 + (- 6 B - 18 B) C + 9 B ) (X + C)) - --------------------------------- 2 2 (C + (- B - 3) C + 3 B) (X + C) B - 2 + ------------------------------------------------- 2 2 3 2 ((B - 3) C + (6 B - 2 B ) C + B - 3 B ) (X + B) 1 - ---------------------------------------------- 2 ((B - 3) C + (18 - 6 B) C + 9 B - 27) (X + 3) Using ratsimp Polynomial quotient is not exact -- an error. Quitting. To debug this try DEBUGMODE(TRUE);) Caused a error break: rtest4.mac Testing rtest5.mac /* ********************** Problem 1. *************** */ %Input is KILL(ALL) The result is DONE ..Which was correct /* ********************** Problem 2. *************** */ %Input is PARTITION(2 A X F(X), X) The result is [2 A, X F(X)] ..Which was correct /* ********************** Problem 3. *************** */ %Input is PARTITION(B + A, X) The result is [B + A, 0] ..Which was correct /* ********************** Problem 4. *************** */ %Input is 2 (2 A LOG(Y) + A LOG(X)) The result is 2 (2 A LOG(Y) + A LOG(X)) ..Which was correct /* ********************** Problem 5. *************** */ %Input is LOGCONTRACT(%) The result is 2 4 A LOG(X Y ) ..Which was correct /* ********************** Problem 6. *************** */ %Input is LOGCONTRACT(LOG(SQRT(1 + X) - SQRT(X)) + LOG(SQRT(X) + SQRT(1 + X))) The result is 0 ..Which was correct /* ********************** Problem 7. *************** */ %Input is ROOTSCONMODE : FALSE The result is FALSE ..Which was correct /* ********************** Problem 8. *************** */ %Input is 1/2 3/2 ROOTSCONTRACT(X Y ) The result is 3 SQRT(X Y ) ..Which was correct /* ********************** Problem 9. *************** */ %Input is 1/2 1/4 ROOTSCONTRACT(X Y ) The result is 1/4 SQRT(X) Y ..Which was correct /* ********************** Problem 10. *************** */ %Input is ROOTSCONMODE : TRUE The result is TRUE ..Which was correct /* ********************** Problem 11. *************** */ %Input is 1/2 1/4 ROOTSCONTRACT(X Y ) The result is SQRT(X SQRT(Y)) Using ratsimp ..Which was correct /* ********************** Problem 12. *************** */ %Input is 1/2 1/3 ROOTSCONTRACT(X Y ) The result is 1/3 SQRT(X) Y ..Which was correct /* ********************** Problem 13. *************** */ %Input is ROOTSCONMODE : ALL The result is ALL ..Which was correct /* ********************** Problem 14. *************** */ %Input is 1/2 1/4 ROOTSCONTRACT(X Y ) The result is 2 1/4 (X Y) Using ratsimp ..Which was correct /* ********************** Problem 15. *************** */ %Input is 1/2 1/3 ROOTSCONTRACT(X Y ) The result is 3 2 1/6 (X Y ) Using ratsimp ..Which was correct /* ********************** Problem 16. *************** */ %Input is ROOTSCONMODE : FALSE The result is FALSE ..Which was correct /* ********************** Problem 17. *************** */ %Input is ROOTSCONTRACT(SQRT(SQRT(X) + SQRT(1 + X)) SQRT(SQRT(1 + X) - SQRT(X))) The result is 1 ..Which was correct /* ********************** Problem 18. *************** */ %Input is ROOTSCONMODE : TRUE The result is TRUE ..Which was correct /* ********************** Problem 19. *************** */ %Input is 1/4 ROOTSCONTRACT(SQRT(5 + SQRT(5)) - 5 SQRT(1 + SQRT(5))) The result is 0 ..Which was correct /* ********************** Problem 20. *************** */ %Input is KILL(F, G, H, X, Y) The result is DONE ..Which was correct /* ********************** Problem 21. *************** */ %Input is 2 3 DIFF(2 X + X + SIN(X), X) The result is 2 COS(X) + 3 X + 4 X ..Which was correct /* ********************** Problem 22. *************** */ %Input is DIFF(SIN(X) COS(X), X) The result is 2 2 COS (X) - SIN (X) ..Which was correct /* ********************** Problem 23. *************** */ %Input is DIFF(SIN(X) COS(X), X, 2) The result is - 4 COS(X) SIN(X) ..Which was correct /* ********************** Problem 24. *************** */ %Input is DERIVABBREV : TRUE The result is TRUE ..Which was correct /* ********************** Problem 25. *************** */ %Input is DIFF(EXP(F(X)), X, 2) The result is F(X) F(X) 2 %E F(X) + %E (F(X) ) X X X ..Which was correct /* ********************** Problem 26. *************** */ %Input is H(X) / [ I F(X, Y) dY ] / G(X) The result is H(X) / [ I F(X, Y) dY ] / G(X) ..Which was correct /* ********************** Problem 27. *************** */ %Input is DIFF(%, X) The result is H(X) / [ I F(X, Y) dY + F(X, H(X)) H(X) - F(X, G(X)) G(X) ] X X X / G(X) ..Which was correct /* ********************** Problem 28. *************** */ %Input is KILL(A, X, F, Y, T) The result is DONE ..Which was correct /* ********************** Problem 29. *************** */ %Input is DEPENDS(A, X) The result is [A(X)] ..Which was correct /* ********************** Problem 30. *************** */ %Input is DIFF(A . A, X) The result is A . A + A . A X X ..Which was correct /* ********************** Problem 31. *************** */ %Input is DEPENDS(F, [X, Y], [X, Y], T) The result is [F(X, Y), X(T), Y(T)] ..Which was correct /* ********************** Problem 32. *************** */ %Input is DIFF(F, T) The result is F Y + F X Y T X T ..Which was correct /* ********************** Problem 33. *************** */ %Input is DEPENDS(Y, X) The result is [Y(X)] ..Which was correct /* ********************** Problem 34. *************** */ %Input is KILL(F, G, J) The result is DONE ..Which was correct /* ********************** Problem 35. *************** */ %Input is 2 GRADEF(F(X, Y), X , G(X, Y)) The result is F(X, Y) ..Which was correct /* ********************** Problem 36. *************** */ %Input is DIFF(F(X, Y), X) The result is 2 G(X, Y) Y + X X ..Which was correct /* ********************** Problem 37. *************** */ %Input is N J(N, Z) GRADEF(J(N, Z), J(N, Z) , J(N - 1, Z) - ---------) N Z The result is J(N, Z) ..Which was correct /* ********************** Problem 38. *************** */ %Input is RATSIMP(DIFF(J(2, X), X, 2)) The result is 2 J(0, X) X - 3 J(1, X) X + 6 J(2, X) ------------------------------------ 2 X ..Which was correct /* ********************** Problem 39. *************** */ %Input is TEST(F) := BLOCK([U], U : INTEGRATE(F, X), RATSIMP(F - DIFF(U, X))) The result is TEST(F) := BLOCK([U], U : INTEGRATE(F, X), RATSIMP(F - DIFF(U, X))) ..Which was correct /* ********************** Problem 40. *************** */ %Input is TEST(SIN(X)) The result is 0 ..Which was correct /* ********************** Problem 41. *************** */ %Input is 1 TEST(-----) X + 1 The result is 0 ..Which was correct /* ********************** Problem 42. *************** */ %Input is 1 TEST(------) 2 X + 1 The result is 0 ..Which was correct /* ********************** Problem 43. *************** */ %Input is 3 INTEGRATE(SIN (X), X) The result is 3 COS (X) ------- - COS(X) 3 ..Which was correct /* ********************** Problem 44. *************** */ %Input is KILL(Q) The result is DONE ..Which was correct /* ********************** Problem 45. *************** */ %Input is X %E INTEGRATE(-------, X) X 2 + %E The result is X LOG(%E + 2) ..Which was correct /* ********************** Problem 46. *************** */ %Input is 1 INTEGRATE(--------, X) X LOG(X) The result is LOG(LOG(X)) ..Which was correct /* ********************** Problem 47. *************** */ %Input is INTEGRATE(SIN(3 + 2 X), X) The result is COS(2 X + 3) - ------------ 2 ..Which was correct /* ********************** Problem 48. *************** */ %Input is X INTEGRATE(%E ERF(X), X) The result is X 1/4 1 %E ERF(X) - %E ERF(X - -) 2 ..Which was correct /* ********************** Problem 49. *************** */ %Input is X INTEGRATE(------, X) 3 1 + X The result is 2 X - 1 2 ATAN(-------) LOG(X - X + 1) SQRT(3) LOG(X + 1) --------------- + ------------- - ---------- 6 SQRT(3) 3 ..Which was correct /* ********************** Problem 50. *************** */ %Input is DIFF(%, X) The result is 2 2 X - 1 1 ------------------ + -------------- - --------- 2 2 3 (X + 1) (2 X - 1) 6 (X - X + 1) 3 (---------- + 1) 3 ..Which was correct /* ********************** Problem 51. *************** */ %Input is RATSIMP(%) The result is X ------ 3 X + 1 ..Which was correct Congratulations: No differences! Testing rtest6.mac /* ********************** Problem 1. *************** */ %Input is 5/4 X INTEGRATE(----------, X, 0, INF) 5/2 (1 + X) The result is 9 1 BETA(-, -) 4 4 ..Which was correct /* ********************** Problem 2. *************** */ %Input is 2 GRADEF(Q(X), SIN(X )) The result is Q(X) ..Which was correct /* ********************** Problem 3. *************** */ %Input is DIFF(LOG(Q(R(X))), X) The result is 2 R(X) SIN(R (X)) X ---------------- Q(R(X)) ..Which was correct /* ********************** Problem 4. *************** */ %Input is INTEGRATE(%, X) The result is LOG(Q(R(X))) ..Which was correct Congratulations: No differences! Testing rtest6a.mac /* ********************** Problem 1. *************** */ %Input is KILL(ALL) The result is DONE ..Which was correct /* ********************** Problem 2. *************** */ %Input is 2 RISCH(X ERF(X), X) The result is 2 3 2 - X %PI X ERF(X) + (SQRT(%PI) X + SQRT(%PI)) %E ------------------------------------------------- 3 %PI ..Which was correct /* ********************** Problem 3. *************** */ %Input is EV(DIFF(%, X), RATSIMP) The result is 2 X ERF(X) ..Which was correct /* ********************** Problem 4. *************** */ %Input is ASSUME(A > 0) The result is [A > 0] ..Which was correct /* ********************** Problem 5. *************** */ %Input is 4 / [ SQRT(A) SQRT(Y) I %E dY ] / 0 The result is 4 / [ SQRT(A) SQRT(Y) I %E dY ] / 0 ..Which was correct /* ********************** Problem 6. *************** */ %Input is 2 Z CHANGEVAR(%, Y - --, Z, Y) A The result is 0 / ABS(Z) [ 2 Z %E - I ------------ dZ ] A / - 2 SQRT(A) ..Which was correct /* ********************** Problem 7. *************** */ %Input is ASSUME(P > 0) The result is [P > 0] ..Which was correct /* ********************** Problem 8. *************** */ %Input is A T - --- 1/2 4 - P T T %E %E The result is A T - P T - --- 4 SQRT(T) %E ..Which was correct /* ********************** Problem 9. *************** */ %Input is 1/2 1/2 1/2 - P T T %J (2 A T ) %E 1 The result is - P T %J (2 SQRT(A) SQRT(T)) SQRT(T) %E 1 ..Which was correct /* ********************** Problem 10. *************** */ %Input is FORGET(P > 0, A > 0) The result is [P > 0, A > 0] ..Which was correct /* ********************** Problem 11. *************** */ %Input is Y -- + X 2 Z The result is Y -- + X 2 Z ..Which was correct /* ********************** Problem 12. *************** */ %Input is PART(%, 1, 2, 2) The result is 2 ..Which was correct /* ********************** Problem 13. *************** */ %Input is REMVALUE(X) The result is [FALSE] ..Which was correct /* ********************** Problem 14. *************** */ %Input is B / [ X + I F(X) dX ] / A The result is B / [ I F(X) dX + X ] / A ..Which was correct /* ********************** Problem 15. *************** */ %Input is PART(%, 1, 1) The result is F(X) ..Which was correct /* ********************** Problem 16. *************** */ %Input is 2 2 2 X + X = Y The result is 2 2 X + 2 X = Y ..Which was correct /* ********************** Problem 17. *************** */ %Input is EXP : 1 + % The result is 2 2 X + 2 X + 1 = Y + 1 ..Which was correct /* ********************** Problem 18. *************** */ %Input is LHS(%) The result is 2 X + 2 X + 1 ..Which was correct /* ********************** Problem 19. *************** */ %Input is PART(EXP, 2) The result is 2 Y + 1 ..Which was correct /* ********************** Problem 20. *************** */ %Input is PART(%, 1) The result is 2 Y ..Which was correct /* ********************** Problem 21. *************** */ %Input is 3 2 2 3 1 + X + 8 X + Y + 36 X Y + 54 X Y + 27 Y The result is 3 2 2 3 27 Y + 54 X Y + 36 X Y + Y + 8 X + X + 1 ..Which was correct /* ********************** Problem 22. *************** */ %Input is PART(%, 2, [1, 3]) The result is 2 54 Y ..Which was correct /* ********************** Problem 23. *************** */ %Input is PIECE SQRT(-----) 54 The result is ABS(Y) ..Which was correct /* ********************** Problem 24. *************** */ %Input is W Z + Y + X The result is W Z + Y + X ..Which was correct /* ********************** Problem 25. *************** */ %Input is INPART(%, 3, 2) The result is Z ..Which was correct /* ********************** Problem 26. *************** */ %Input is G(1 + X) limit F(X) X -> 0- The result is G(X + 1) limit F(X) X -> 0- ..Which was correct /* ********************** Problem 27. *************** */ %Input is INPART(%, 1, 2) The result is G(X + 1) ..Which was correct /* ********************** Problem 28. *************** */ %Input is G(1 + X) limit F(X) X -> 0- The result is G(X + 1) limit F(X) X -> 0- ..Which was correct /* ********************** Problem 29. *************** */ %Input is IS(INPART(%, 0) = NOUNIFY(LIMIT)) The result is TRUE ..Which was correct /* ********************** Problem 30. *************** */ %Input is Y DPART(-- + X, 1, 2, 1) 2 Z The result is Y ---- + X 2 """ "Z" """ ..Which was correct /* ********************** Problem 31. *************** */ %Input is 4 EXP : EXPAND((A + B) ) The result is 4 3 2 2 3 4 B + 4 A B + 6 A B + 4 A B + A ..Which was correct /* ********************** Problem 32. *************** */ %Input is 2 2 (A + B) (X + Y) The result is 2 2 (B + A) (Y + X) ..Which was correct /* ********************** Problem 33. *************** */ %Input is EXPAND(%) The result is 2 2 2 2 2 2 2 2 2 2 B Y + 2 A B Y + A Y + 2 B X Y + 4 A B X Y + 2 A X Y + B X + 2 A B X 2 2 + A X ..Which was correct /* ********************** Problem 34. *************** */ %Input is EXP EXP : --- % The result is 4 3 2 2 3 4 2 2 2 2 2 2 (B + 4 A B + 6 A B + 4 A B + A )/(B Y + 2 A B Y + A Y + 2 B X Y 2 2 2 2 2 2 + 4 A B X Y + 2 A X Y + B X + 2 A B X + A X ) ..Which was correct /* ********************** Problem 35. *************** */ %Input is FACTOR(%) The result is 2 (B + A) -------- 2 (Y + X) ..Which was correct /* ********************** Problem 36. *************** */ %Input is DPART(EXP, 2, 4) The result is """""""""" 4 3 2 2 3 4 2 2 2 2 2 " 2 " (B + 4 A B + 6 A B + 4 A B + A )/(B Y + 2 A B Y + A Y + "2 B X Y" """""""""" 2 2 2 2 2 2 + 4 A B X Y + 2 A X Y + B X + 2 A B X + A X ) ..Which was correct /* ********************** Problem 37. *************** */ %Input is PART(EXP, 2, 4) The result is 2 2 B X Y ..Which was correct /* ********************** Problem 38. *************** */ %Input is 2 SUBST(A, Y + X, Y + (Y + X) + X) The result is 2 Y + X + A ..Which was correct /* ********************** Problem 39. *************** */ %Input is SUBST(- %I, %I, B %I + A) The result is A - %I B ..Which was correct /* ********************** Problem 40. *************** */ %Input is SUBST(X, Y, Y + X) The result is 2 X ..Which was correct /* ********************** Problem 41. *************** */ %Input is SUBST(X = 0, DIFF(SIN(X), X)) The result is 1 ..Which was correct /* ********************** Problem 42. *************** */ %Input is ERRCATCH(EV(DIFF(SIN(X), X), X = 0)) Non-variable 2nd argument to DIFF: 0 The result is [] ..Which was correct /* ********************** Problem 43. *************** */ %Input is ASSUME(NOT EQUAL(I, - 1)) The result is [NOT EQUAL(I, - 1)] Using ratsimp ..Which was correct /* ********************** Problem 44. *************** */ %Input is I EV(INTEGRATE(X , X), I = - 1) The result is LOG(X) ..Which was correct /* ********************** Problem 45. *************** */ %Input is I ERRCATCH(SUBST(- 1, I, INTEGRATE(X , X))) Division by 0 The result is [] ..Which was correct /* ********************** Problem 46. *************** */ %Input is MATRIX([A, B], [C, D]) The result is [ A B ] [ ] [ C D ] ..Which was correct /* ********************** Problem 47. *************** */ %Input is SUBST([, MATRIX, %) The result is [[A, B], [C, D]] ..Which was correct /* ********************** Problem 48. *************** */ %Input is 2 4 3 4 8 RATSUBST(A, X Y , X Y + X Y ) The result is 3 4 A X Y + A ..Which was correct /* ********************** Problem 49. *************** */ %Input is 4 3 2 COS (X) + COS (X) + COS (X) + COS(X) + 1 The result is 4 3 2 COS (X) + COS (X) + COS (X) + COS(X) + 1 ..Which was correct /* ********************** Problem 50. *************** */ %Input is 2 2 RATSUBST(1 - SIN (X), COS (X), %) The result is 4 2 2 SIN (X) - 3 SIN (X) + COS(X) (2 - SIN (X)) + 3 ..Which was correct /* ********************** Problem 51. *************** */ %Input is 2 2 4 RATSUBST(1 - COS (X), SIN (X), SIN (X)) The result is 4 2 COS (X) - 2 COS (X) + 1 ..Which was correct Congratulations: No differences! Testing rtest6b.mac /* ********************** Problem 1. *************** */ %Input is 1 ------ 2 2 + X The result is 1 ------ 2 X + 2 ..Which was correct /* ********************** Problem 2. *************** */ %Input is 3 SUBSTPART(-, %, 2, 1, 2) 2 The result is 1 -------- 3/2 X + 2 ..Which was correct /* ********************** Problem 3. *************** */ %Input is 3 2 2 3 1 + X + 8 X + Y + 36 X Y + 54 X Y + 27 Y The result is 3 2 2 3 27 Y + 54 X Y + 36 X Y + Y + 8 X + X + 1 ..Which was correct /* ********************** Problem 4. *************** */ %Input is SUBSTPART(FACTOR(PIECE), %, [1, 2, 3, 5]) The result is 3 (3 Y + 2 X) + Y + X + 1 ..Which was correct /* ********************** Problem 5. *************** */ %Input is - 1 Y 1 --- + - + - Z X X The result is 1 Y 1 - - + - + - Z X X ..Which was correct /* ********************** Problem 6. *************** */ %Input is SUBSTPART(XTHRU(PIECE), %, [2, 3]) The result is Y + 1 1 ----- - - X Z ..Which was correct /* ********************** Problem 7. *************** */ %Input is SUBSTPART(+, %, 1, 0) The result is 1 - - + Y + X + 1 Z ..Which was correct /* ********************** Problem 8. *************** */ %Input is 2 2 (K X - 1) (EPS + COS(X)) -------------------------- N + 3 K 1 RATSIMP(--------------------------) 5 K - N 2 The result is 2 2 2 2 (K X - 1) COS(X) + EPS K X - EPS ------------------------------------ 2 15 K + (5 N - 3 N ) K - N N 1 2 1 2 ..Which was correct /* ********************** Problem 9. *************** */ %Input is FACTOR(%) The result is (K X - 1) (K X + 1) (COS(X) + EPS) ---------------------------------- (3 K + N ) (5 K - N ) 1 2 ..Which was correct /* ********************** Problem 10. *************** */ %Input is SUBSTPART(RATSIMP(PIECE), %, 1, [1, 2]) The result is 2 2 (K X - 1) (COS(X) + EPS) -------------------------- (3 K + N ) (5 K - N ) 1 2 ..Which was correct /* ********************** Problem 11. *************** */ %Input is - SUBSTPART(- PIECE, %, 1, 1) The result is 2 2 (1 - K X ) (COS(X) + EPS) - -------------------------- (3 K + N ) (5 K - N ) 1 2 Using ratsimp ..Which was correct /* ********************** Problem 12. *************** */ %Input is B --------------------- + A 1 + X ((B + A) X + Y) The result is B --------------------- + A X (Y + (B + A) X) + 1 ..Which was correct /* ********************** Problem 13. *************** */ %Input is SUBSTPART(MULTTHRU(PIECE), %, 1, 2, 1) The result is B -------------------- + A 2 X Y + (B + A) X + 1 ..Which was correct /* ********************** Problem 14. *************** */ %Input is X . F(X) X X The result is X . F(X) X X ..Which was correct /* ********************** Problem 15. *************** */ %Input is 2 SUBSTINPART(D , %, 2) The result is 2 X . D ..Which was correct /* ********************** Problem 16. *************** */ %Input is SUBSTINPART(F1, F (1 + X), 0) 1 The result is F1(X + 1) ..Which was correct Congratulations: No differences! Testing rtest7.mac /* ********************** Problem 1. *************** */ %Input is KILL(ALL) The result is DONE ..Which was correct /* ********************** Problem 2. *************** */ %Input is 2 ATVALUE(F(X, Y), [X = 0, Y = 1], A ) The result is 2 A ..Which was correct /* ********************** Problem 3. *************** */ %Input is ATVALUE(F(X, Y) , X = 0, 1 + Y) X The result is @2 + 1 ..Which was correct /* ********************** Problem 4. *************** */ %Input is PRINTPROPS(ALL, ATVALUE) ! F(@1, @2) ! = @2 + 1 @1! !@1 = 0 2 F(0, 1) = A The result is DONE ..Which was correct /* ********************** Problem 5. *************** */ %Input is 2 2 DIFF(4 F (X, Y) - U (X, Y), X) The result is 8 F(X, Y) F(X, Y) - 2 U(X, Y) U(X, Y) X X ..Which was correct /* ********************** Problem 6. *************** */ %Input is AT(%, [X = 0, Y = 1]) The result is 2 ! 16 A - 2 U(0, 1) (U(X, Y) ! ) X! !X = 0, Y = 1 ..Which was correct /* ********************** Problem 7. *************** */ %Input is 2 ATVALUE(F(X, Y), [X = 0, Y = 1], A ) The result is 2 A ..Which was correct /* ********************** Problem 8. *************** */ %Input is ATVALUE(F(X, Y) , X = 0, 1 + Y) X The result is @2 + 1 ..Which was correct /* ********************** Problem 9. *************** */ %Input is PRINTPROPS(ALL, ATVALUE) ! F(@1, @2) ! = @2 + 1 @1! !@1 = 0 2 F(0, 1) = A The result is DONE ..Which was correct /* ********************** Problem 10. *************** */ %Input is 2 2 DIFF(4 F (X, Y) - U (X, Y), X) The result is 8 F(X, Y) F(X, Y) - 2 U(X, Y) U(X, Y) X X ..Which was correct /* ********************** Problem 11. *************** */ %Input is AT(%, [X = 0, Y = 1]) The result is 2 ! 16 A - 2 U(0, 1) (U(X, Y) ! ) X! !X = 0, Y = 1 ..Which was correct /* ********************** Problem 12. *************** */ %Input is F(Y + X ) 1 LISTOFVARS(---------) A + 2 G The result is [G, A, X , Y] 1 ..Which was correct /* ********************** Problem 13. *************** */ %Input is COEFF(B + TAN(X) + 2 A TAN(X) = 3 + 5 TAN(X), TAN(X)) The result is 2 A + 1 = 5 ..Which was correct /* ********************** Problem 14. *************** */ %Input is X COEFF(1 + X %E + Y, X, 0) The result is Y + 1 ..Which was correct /* ********************** Problem 15. *************** */ %Input is 5 + B X + A X The result is B X + A X + 5 ..Which was correct /* ********************** Problem 16. *************** */ %Input is RATCOEF(%, B + A) The result is X ..Which was correct /* ********************** Problem 17. *************** */ %Input is ISLINEAR(EXP, VAR) := BLOCK([C], C : BOTHCOEF(RAT(EXP, VAR), VAR), IS(FREEOF(VAR, C) AND C # 0)) 1 The result is ISLINEAR(EXP, VAR) := BLOCK([C], C : BOTHCOEF(RAT(EXP, VAR), VAR), IS(FREEOF(VAR, C) AND C # 0)) 1 ..Which was correct /* ********************** Problem 18. *************** */ %Input is 2 2 R - (X - R) ISLINEAR(-------------, X) X The result is TRUE ..Which was correct /* ********************** Problem 19. *************** */ %Input is 4 2 (B + A) (X ((D + C) + 2 X) + 1) The result is 4 2 (B + A) (X (2 X + (D + C) ) + 1) ..Which was correct /* ********************** Problem 20. *************** */ %Input is (LINENUM : 0, ISOLATE(%, X)) 2 (E1) (D + C) 4 (E2) (B + A) The result is E2 (X (2 X + E1) + 1) Using ratsimp Using ratsimp ..Which was correct /* ********************** Problem 21. *************** */ %Input is RATEXPAND(%) The result is 2 2 E2 X + E1 E2 X + E2 Using ratsimp Using ratsimp ..Which was correct /* ********************** Problem 22. *************** */ %Input is EV(%) The result is 4 2 4 2 4 2 (B + A) X + (B + A) (D + C) X + (B + A) ..Which was correct /* ********************** Problem 23. *************** */ %Input is 2 2 B + A X + X (B + A) (B + A + X) %E The result is 2 2 X + A X + B (B + A) (X + B + A) %E ..Which was correct /* ********************** Problem 24. *************** */ %Input is BLOCK([LINENUM : 2], EV(ISOLATE(%, X), EXPTISOLATE : TRUE)) (E3) B + A B (E4) %E The result is 2 2 X + A X E3 E4 (X + E3) %E Using ratsimp Using ratsimp ..Which was correct /* ********************** Problem 25. *************** */ %Input is 1 exp1 : INTEGRATE(------, X) 3 2 + X The result is 1/3 2 X - 2 ATAN(------------) 2 1/3 2/3 1/3 1/3 LOG(X - 2 X + 2 ) 2 SQRT(3) LOG(X + 2 ) - ----------------------- + ------------------ + ------------- 2/3 2/3 2/3 6 2 2 SQRT(3) 3 2 ..Which was correct /* ********************** Problem 26. *************** */ %Input is RADCAN(DIFF(%, X)) The result is 1 ------ 3 X + 2 ..Which was correct /* ********************** Problem 27. *************** */ %Input is BLOCK([LINENUM : 4], PICKAPART(exp1, 1)) 2 1/3 2/3 LOG(X - 2 X + 2 ) (E5) - ----------------------- 2/3 6 2 1/3 2 X - 2 ATAN(------------) 1/3 2 SQRT(3) (E6) ------------------ 2/3 2 SQRT(3) 1/3 LOG(X + 2 ) (E7) ------------- 2/3 3 2 The result is E7 + E6 + E5 Using ratsimp Using ratsimp ..Which was correct /* ********************** Problem 28. *************** */ %Input is 7 GAMMA(-) 2 The result is 15 SQRT(%PI) ------------ 8 ..Which was correct /* ********************** Problem 29. *************** */ %Input is NUMFACTOR(%) The result is 15 -- 8 ..Which was correct /* ********************** Problem 30. *************** */ %Input is 2 Y X + Y 2 + Y X Z Z Z X X The result is 2 2 Y + Y + X Y Z Z Z X X X ..Which was correct /* ********************** Problem 31. *************** */ %Input is DERIVDEGREE(%, Y, X) The result is 2 ..Which was correct /* ********************** Problem 32. *************** */ %Input is %I ALPHA U + %I V %E + -------- %I E + F The result is %I V + U %I ALPHA -------- + %E F + %I E ..Which was correct /* ********************** Problem 33. *************** */ %Input is REALPART(%) The result is E V + F U --------- + COS(ALPHA) 2 2 F + E ..Which was correct /* ********************** Problem 34. *************** */ %Input is RECTFORM(SIN(X + 2 %I)) The result is COSH(2) SIN(X) + %I SINH(2) COS(X) ..Which was correct /* ********************** Problem 35. *************** */ %Input is POLARFORM(%) The result is 2 2 2 2 SQRT(COSH (2) SIN (X) + SINH (2) COS (X)) %I ATAN2(SINH(2) COS(X), COSH(2) SIN(X)) %E ..Which was correct /* ********************** Problem 36. *************** */ %Input is RECTFORM(LOG(4 %I + 3)) The result is 4 LOG(5) + %I ATAN(-) 3 ..Which was correct /* ********************** Problem 37. *************** */ %Input is POLARFORM(%) The result is ATAN(4/3) %I ATAN(---------) 2 2 4 LOG(5) SQRT(LOG (5) + ATAN (-)) %E 3 ..Which was correct /* ********************** Problem 38. *************** */ %Input is 0.25 EV(RECTFORM((3.5 %I + 2) ), NUMER) The result is 0.3682587918166914 %I + 1.368266274774369 ..Which was correct /* ********************** Problem 39. *************** */ %Input is POLARFORM(%) The result is 0.2629125531370934 %I 1.416956998795383 %E ..Which was correct /* ********************** Problem 40. *************** */ %Input is DELETE(SIN(X), Y + SIN(X) + X) The result is Y + X ..Which was correct Congratulations: No differences! Testing rtest8.mac /* ********************** Problem 1. *************** */ %Input is BLOCK([], KILL(ALL), %RNUM : 0) The result is 0 ..Which was correct /* ********************** Problem 2. *************** */ %Input is 1 4 10 - - 2 X + X 2 The result is 10 4 1 X - 2 X + - 2 ..Which was correct /* ********************** Problem 3. *************** */ %Input is NROOTS(%, - 6, 9.1) The result is 4 ..Which was correct /* ********************** Problem 4. *************** */ %Input is 5 REALROOTS(- 1 - X + X , 5.0E-6) The result is 612003 [X = ------] 524288 ..Which was correct /* ********************** Problem 5. *************** */ %Input is EV(% , FLOAT) 1 The result is X = 1.167303085327148 Using ratsimp RAT replaced 1.16730309 by 4891//4190 = 1.167303102625298 RAT replaced 1.167303085327148 by 4891//4190 = 1.167303102625298 ..Which was correct /* ********************** Problem 6. *************** */ %Input is 5 EV(- 1 - X + X , %) The result is - 7.396496210176906E-6 ..Which was correct /* ********************** Problem 7. *************** */ %Input is 3 5 (1 + 2 X) = 13.5 (1 + X ) The result is 3 5 (2 X + 1) = 13.5 (X + 1) ..Which was correct /* ********************** Problem 8. *************** */ %Input is SORT(ALLROOTS(%)) The result is [X = - 1.015755543828121, X = 0.8296749902129362, X = 0.9999999999999999, X = - 0.9659625152196369 %I - 0.4069597231924075, X = 0.9659625152196369 %I - 0.4069597231924075] ..Which was correct /* ********************** Problem 9. *************** */ %Input is EXP1 : Z + X = Y The result is Z + X = Y ..Which was correct /* ********************** Problem 10. *************** */ %Input is 2 EXP : 2 A X - Y = 2 A The result is 2 2 A X - Y = 2 A ..Which was correct /* ********************** Problem 11. *************** */ %Input is Y - 2 Z = 2 The result is Y - 2 Z = 2 ..Which was correct /* ********************** Problem 12. *************** */ %Input is EV(LINSOLVE([EXP, EXP1, %], [X, Y, Z]), GLOBALSOLVE) The result is [X = A + 1, Y = 2 A, Z = A - 1] ..Which was correct /* ********************** Problem 13. *************** */ %Input is F1 : 2 X (1 - L1) - 2 (X - 1) L2 The result is 2 (1 - L1) X - 2 L2 (X - 1) ..Which was correct /* ********************** Problem 14. *************** */ %Input is F2 : L2 - L1 The result is L2 - L1 ..Which was correct /* ********************** Problem 15. *************** */ %Input is 2 F3 : L1 (- Y - X + 1) The result is 2 L1 (- Y - X + 1) ..Which was correct /* ********************** Problem 16. *************** */ %Input is 2 F4 : L2 (Y - (X - 1) ) The result is 2 L2 (Y - (X - 1) ) ..Which was correct /* ********************** Problem 17. *************** */ %Input is ALGSYS([F1, F2, F3, F4], [X, Y, L1, L2]) The result is [[X = 0, Y = %R1, L1 = 0, L2 = 0], [X = 1, Y = 0, L1 = 1, L2 = 1]] ..Which was correct /* ********************** Problem 18. *************** */ %Input is 2 2 F1 : X - Y The result is 2 2 X - Y ..Which was correct /* ********************** Problem 19. *************** */ %Input is 2 2 F2 : - 1 - Y + 2 Y - X + X The result is 2 2 2 Y - Y + X - X - 1 ..Which was correct /* ********************** Problem 20. *************** */ %Input is ALGSYS([F1, F2], [X, Y]) The result is 1 1 1 1 [[X = - -------, Y = -------], [X = -------, Y = - -------], SQRT(3) SQRT(3) SQRT(3) SQRT(3) 1 1 [X = - -, Y = - -], [X = 1, Y = 1]] 3 3 ..Which was correct /* ********************** Problem 21. *************** */ %Input is SOLVE(ASIN(COS(3 X)) (F(X) - 1), X) SOLVE is using arc-trig functions to get a solution. Some solutions will be lost. The result is %PI [X = ---, F(X) = 1] 6 ..Which was correct /* ********************** Problem 22. *************** */ %Input is F(X) EV(SOLVE(5 = 125, F(X)), SOLVERADCAN) The result is LOG(125) [F(X) = --------] LOG(5) ..Which was correct /* ********************** Problem 23. *************** */ %Input is 2 2 [4 X - Y = 12, X Y - X = 2] The result is 2 2 [4 X - Y = 12, X Y - X = 2] ..Which was correct /* ********************** Problem 24. *************** */ %Input is SOLVE(%, [X, Y]) The result is [[X = 2, Y = 2], [X = 0.5202594388652008 %I - 0.1331240357358706, Y = 0.07678378523787777 - 3.608003221870287 %I], [X = - 0.5202594388652008 %I - 0.1331240357358706, Y = 3.608003221870287 %I + 0.07678378523787777], [X = - 1.733751846381093, Y = - 0.1535675710019696]] ..Which was correct /* ********************** Problem 25. *************** */ %Input is 3 SOLVE(1 + A X + X , X) The result is SQRT(3) %I 1 3 (---------- - -) A SQRT(3) %I 1 SQRT(4 A + 27) 1 1/3 2 2 [X = (- ---------- - -) (--------------- - -) - --------------------------, 2 2 6 SQRT(3) 2 3 SQRT(4 A + 27) 1 1/3 3 (--------------- - -) 6 SQRT(3) 2 SQRT(3) %I 1 3 (- ---------- - -) A SQRT(3) %I 1 SQRT(4 A + 27) 1 1/3 2 2 X = (---------- - -) (--------------- - -) - --------------------------, 2 2 6 SQRT(3) 2 3 SQRT(4 A + 27) 1 1/3 3 (--------------- - -) 6 SQRT(3) 2 3 SQRT(4 A + 27) 1 1/3 A X = (--------------- - -) - --------------------------] 6 SQRT(3) 2 3 SQRT(4 A + 27) 1 1/3 3 (--------------- - -) 6 SQRT(3) 2 ..Which was correct /* ********************** Problem 26. *************** */ %Input is 3 SOLVE(X - 1) The result is SQRT(3) %I - 1 SQRT(3) %I + 1 [X = --------------, X = - --------------, X = 1] 2 2 Using ratsimp ..Which was correct /* ********************** Problem 27. *************** */ %Input is 6 SOLVE(X - 1) The result is SQRT(3) %I + 1 SQRT(3) %I - 1 SQRT(3) %I + 1 [X = --------------, X = --------------, X = - 1, X = - --------------, 2 2 2 SQRT(3) %I - 1 X = - --------------, X = 1] 2 Using ratsimp ..Which was correct /* ********************** Problem 28. *************** */ %Input is 6 EV(X - 1, % ) 1 The result is 6 (SQRT(3) %I + 1) ----------------- - 1 64 ..Which was correct /* ********************** Problem 29. *************** */ %Input is EXPAND(%) The result is 0 ..Which was correct /* ********************** Problem 30. *************** */ %Input is 2 EXP : X - 1 The result is 2 X - 1 ..Which was correct /* ********************** Problem 31. *************** */ %Input is SOLVE(%, X) The result is [X = - 1, X = 1] ..Which was correct /* ********************** Problem 32. *************** */ %Input is EV(EXP, % ) 1 The result is 0 ..Which was correct /* ********************** Problem 33. *************** */ %Input is 1 H := ----------- I, J - 1 + J + I The result is 1 H := ----------- I, J - 1 + J + I ..Which was correct /* ********************** Problem 34. *************** */ %Input is GENMATRIX(H, 3, 3) The result is [ 1 1 ] [ 1 - - ] [ 2 3 ] [ ] [ 1 1 1 ] [ - - - ] [ 2 3 4 ] [ ] [ 1 1 1 ] [ - - - ] [ 3 4 5 ] ..Which was correct /* ********************** Problem 35. *************** */ %Input is [2 X - (A - 1) Y = 5 B, C + B Y + A X = 0] The result is [2 X - (A - 1) Y = 5 B, B Y + A X + C = 0] ..Which was correct /* ********************** Problem 36. *************** */ %Input is AUGCOEFMATRIX(%, [X, Y]) The result is [ 2 1 - A - 5 B ] [ ] [ A B C ] ..Which was correct /* ********************** Problem 37. *************** */ %Input is MATRIX([2, 1 - A, - 5 B], [A, B, C]) The result is [ 2 1 - A - 5 B ] [ ] [ A B C ] ..Which was correct /* ********************** Problem 38. *************** */ %Input is ECHELON(%) The result is [ A - 1 5 B ] [ 1 - ----- - --- ] [ 2 2 ] [ ] [ 2 C + 5 A B ] [ 0 1 ------------ ] [ 2 ] [ 2 B + A - A ] Using ratsimp ..Which was correct /* ********************** Problem 39. *************** */ %Input is MATRIX([2, 1 - A, - 5 B], [A, B, C]) The result is [ 2 1 - A - 5 B ] [ ] [ A B C ] ..Which was correct /* ********************** Problem 40. *************** */ %Input is TRIANGULARIZE(%) The result is [ 2 1 - A - 5 B ] [ ] [ 2 ] [ 0 2 B + A - A 2 C + 5 A B ] ..Which was correct /* ********************** Problem 41. *************** */ %Input is MATRIX([2, 1 - A, - 5 B], [A, B, C]) The result is [ 2 1 - A - 5 B ] [ ] [ A B C ] ..Which was correct /* ********************** Problem 42. *************** */ %Input is RANK(%) The result is 2 ..Which was correct /* ********************** Problem 43. *************** */ %Input is A : MATRIX([3, 1], [2, 4]) The result is [ 3 1 ] [ ] [ 2 4 ] ..Which was correct /* ********************** Problem 44. *************** */ %Input is EXPAND(CHARPOLY(A, LAMBDA)) The result is 2 LAMBDA - 7 LAMBDA + 10 ..Which was correct /* ********************** Problem 45. *************** */ %Input is EXP : (PROGRAMMODE : TRUE, SOLVE(%)) The result is [LAMBDA = 5, LAMBDA = 2] ..Which was correct /* ********************** Problem 46. *************** */ %Input is MATRIX([X1], [X2]) The result is [ X1 ] [ ] [ X2 ] ..Which was correct /* ********************** Problem 47. *************** */ %Input is EV(A . % - LAMBDA %, EXP ) 1 The result is [ X2 - 2 X1 ] [ ] [ 2 X1 - X2 ] ..Which was correct /* ********************** Problem 48. *************** */ %Input is EXP : % = 0 1, 1 The result is X2 - 2 X1 = 0 ..Which was correct /* ********************** Problem 49. *************** */ %Input is 2 2 X2 + X1 = 1 The result is 2 2 X2 + X1 = 1 ..Which was correct /* ********************** Problem 50. *************** */ %Input is SOLVE([EXP, %], [X1, X2]) The result is 1 2 1 2 [[X1 = - -------, X2 = - -------], [X1 = -------, X2 = -------]] SQRT(5) SQRT(5) SQRT(5) SQRT(5) ..Which was correct Congratulations: No differences! Testing rtest9.mac /* ********************** Problem 1. *************** */ %Input is (KILL(ALL), DECLARE(L, SCALAR, [M1, M2, M3], NONSCALAR)) The result is DONE ..Which was correct /* ********************** Problem 2. *************** */ %Input is EXPAND((1 - L M1) . ((1 - L M2) . (1 - L M3))) The result is - L M3 + L M2 . L M3 - L M2 + L M1 . L M3 - L M1 . L M2 . L M3 + L M1 . L M2 - L M1 + 1 ..Which was correct /* ********************** Problem 3. *************** */ %Input is EV(%, DOTSCRULES) The result is 2 2 3 2 - L M3 + L (M2 . M3) - L M2 + L (M1 . M3) - L (M1 . M2 . M3) + L (M1 . M2) - L M1 + 1 ..Which was correct /* ********************** Problem 4. *************** */ %Input is RAT(%, L) The result is 3 2 - (M1 . M2 . M3) L + (M2 . M3 + M1 . M3 + M1 . M2) L + (- M3 - M2 - M1) L + 1 ..Which was correct /* ********************** Problem 5. *************** */ %Input is 2 RAT(X ) The result is 2 X ..Which was correct /* ********************** Problem 6. *************** */ %Input is DIFF(F(%), X) The result is 2 F(X ) X ..Which was correct /* ********************** Problem 7. *************** */ %Input is 4 (X - 2 Y) (1 + ------------) (A + Y) (X + 2 Y) 2 2 2 (X - 4 Y ) ------------------------------------ 2 2 X + 4 Y The result is 4 (X - 2 Y) (Y + A) (2 Y + X) (------------ + 1) 2 2 2 (X - 4 Y ) ------------------------------------ 2 2 4 Y + X ..Which was correct /* ********************** Problem 8. *************** */ %Input is RAT(%, Y, A, X) The result is 2 A + 2 Y --------- X + 2 Y ..Which was correct /* ********************** Problem 9. *************** */ %Input is 20 (3 + X) The result is 20 (X + 3) ..Which was correct /* ********************** Problem 10. *************** */ %Input is RAT(%) The result is 20 19 18 17 16 15 14 X + 60 X + 1710 X + 30780 X + 392445 X + 3767472 X + 28256040 X 13 12 11 10 + 169536240 X + 826489170 X + 3305956680 X + 10909657044 X 9 8 7 6 + 29753610120 X + 66945622770 X + 123591918960 X + 185387878440 X 5 4 3 2 + 222465454128 X + 208561363245 X + 147219785820 X + 73609892910 X + 23245229340 X + 3486784401 ..Which was correct /* ********************** Problem 11. *************** */ %Input is DIFF(%, X) The result is 19 18 17 16 15 14 20 X + 1140 X + 30780 X + 523260 X + 6279120 X + 56512080 X 13 12 11 10 + 395584560 X + 2203971120 X + 9917870040 X + 36365523480 X 9 8 7 6 + 109096570440 X + 267782491080 X + 535564982160 X + 865143432720 X 5 4 3 2 + 1112327270640 X + 1112327270640 X + 834245452980 X + 441659357460 X + 147219785820 X + 23245229340 ..Which was correct /* ********************** Problem 12. *************** */ %Input is FACTOR(%) The result is 19 20 (X + 3) ..Which was correct /* ********************** Problem 13. *************** */ %Input is RATWEIGHT(A, 1, B, 1) The result is [A, 1, B, 1] ..Which was correct /* ********************** Problem 14. *************** */ %Input is EXP : RAT(1 + B + A) The result is B + A + 1 ..Which was correct /* ********************** Problem 15. *************** */ %Input is 2 % The result is 2 2 B + (2 A + 2) B + A + 2 A + 1 ..Which was correct /* ********************** Problem 16. *************** */ %Input is 2 EV(EXP , RATWTLVL : 1) The result is 2 B + 2 A + 1 ..Which was correct /* ********************** Problem 17. *************** */ %Input is 2 POLY : 5.2E+20 - 5.5 X + 1.0E-20 X The result is 2 1.0E-20 X - 5.5 X + 5.2E+20 ..Which was correct /* ********************** Problem 18. *************** */ %Input is ERRCATCH(EV(%, X = 1.0E+20)) The result is [7.0E+19] ..Which was correct /* ********************** Problem 19. *************** */ %Input is EV(HORNER(POLY, X), KEEPFLOAT) The result is (1.0E-20 X - 5.5) X + 5.2E+20 ..Which was correct /* ********************** Problem 20. *************** */ %Input is EV(%, X = 1.0E+20) The result is 7.0E+19 ..Which was correct /* ********************** Problem 21. *************** */ %Input is DIVIDE(Y + X, X - Y, X) The result is [1, 2 Y] ..Which was correct /* ********************** Problem 22. *************** */ %Input is DIVIDE(Y + X, X - Y) The result is [- 1, 2 X] ..Which was correct /* ********************** Problem 23. *************** */ %Input is 2 2 CONTENT(4 X Y + 2 X Y, Y) The result is 2 [2 X, 2 X Y + Y] ..Which was correct /* ********************** Problem 24. *************** */ %Input is 2 2 RESULTANT(1 + X + A Y, B + X Y + Y , X) The result is 4 3 2 2 Y + A Y + (2 B + 1) Y + B ..Which was correct /* ********************** Problem 25. *************** */ %Input is 2 2 BEZOUT(1 + X + A Y, B + X Y + Y , X) The result is [ 2 2 ] [ Y + B - A Y - Y ] [ ] [ 2 ] [ Y Y + B ] ..Which was correct /* ********************** Problem 26. *************** */ %Input is EXPAND(DETERMINANT(%)) The result is 4 3 2 2 2 Y + A Y + 2 B Y + Y + B ..Which was correct /* ********************** Problem 27. *************** */ %Input is 2 2 % - EXPAND(RESULTANT(1 + X + A Y, B + X Y + Y , X)) The result is 0 ..Which was correct /* ********************** Problem 28. *************** */ %Input is FACTOR(POLY_DISCRIMINANT((X - A) (X - B) (X - C), X)) The result is 2 2 2 (B - A) (C - A) (C - B) ..Which was correct /* ********************** Problem 29. *************** */ %Input is 3 - 11 + 10 X + 4 X EXP : ------------------ 5 5 + X The result is 3 4 X + 10 X - 11 ---------------- 5 X + 5 ..Which was correct /* ********************** Problem 30. *************** */ %Input is EV(MOD(%), MODULUS : 3) The result is 2 X + X - 1 -------------------- 4 3 2 X + X + X + X + 1 ..Which was correct /* ********************** Problem 31. *************** */ %Input is RATDIFF(EXP, X) The result is 7 5 4 2 8 X + 40 X - 55 X - 60 X - 50 - --------------------------------- 10 5 X + 10 X + 25 Using ratsimp ..Which was correct /* ********************** Problem 32. *************** */ %Input is 10 (%I + 1) ----------- 1/3 %I + 3 The result is 10 (%I + 1) ----------- 1/3 %I + 3 ..Which was correct /* ********************** Problem 33. *************** */ %Input is EV(RATDISREP(RAT(%)), ALGEBRAIC) The result is 2/3 1/3 2/3 1/3 (4 3 - 2 3 - 4) %I + 2 3 + 4 3 - 2 ..Which was correct /* ********************** Problem 34. *************** */ %Input is 2 TELLRAT(1 + A + A ) The result is 2 [A + A + 1] ..Which was correct /* ********************** Problem 35. *************** */ %Input is 1 A ------------- + ----------------- A SQRT(2) - 1 SQRT(3) + SQRT(2) The result is 1 A ------------- + ----------------- SQRT(2) A - 1 SQRT(3) + SQRT(2) ..Which was correct /* ********************** Problem 36. *************** */ %Input is EV(RATDISREP(RAT(%)), ALGEBRAIC) The result is (7 SQRT(3) - 10 SQRT(2) + 2) A - 2 SQRT(2) - 1 ---------------------------------------------- 7 ..Which was correct /* ********************** Problem 37. *************** */ %Input is 2 2 TELLRAT(Y = X ) The result is 2 2 2 [Y - X , A + A + 1] ..Which was correct /* ********************** Problem 38. *************** */ %Input is TAYLOR(X + 1, [X, 0, 3]) The result is 1 + X + . . . ..Which was correct /* ********************** Problem 39. *************** */ %Input is 1 - % The result is 2 3 1 - X + X - X + . . . ..Which was correct /* ********************** Problem 40. *************** */ %Input is TAYLOR(Z + Y + X + 1, [X, 0, 3], [Y, 1, 2], [Z, 2, 1]) The result is Z - 2 + 4 + . . . + (Y - 1) + . . . + X + . . . ..Which was correct /* ********************** Problem 41. *************** */ %Input is 1 - % The result is Z - 2 1 1 Z - 2 - ----- + - + . . . + (- -- + ----- + . . .) (Y - 1) 16 4 16 32 1 3 (Z - 2) 2 + (-- - --------- + . . .) (Y - 1) + . . . 64 256 1 Z - 2 1 3 (Z - 2) + (- -- + ----- + . . . + (-- - --------- + . . .) (Y - 1) 16 32 32 128 3 3 (Z - 2) 2 + (- --- + --------- + . . .) (Y - 1) + . . .) X 256 256 1 3 (Z - 2) 3 3 (Z - 2) + (-- - --------- + . . . + (- --- + --------- + . . .) (Y - 1) 64 256 256 256 3 15 (Z - 2) 2 2 + (--- - ---------- + . . .) (Y - 1) + . . .) X 512 2048 1 Z - 2 1 5 (Z - 2) + (- --- + ----- + . . . + (--- - --------- + . . .) (Y - 1) 256 256 256 1024 5 15 (Z - 2) 2 3 + (- ---- + ---------- + . . .) (Y - 1) + . . .) X + . . . 2048 4096 ..Which was correct /* ********************** Problem 42. *************** */ %Input is TAYLOR(Z + Y + X + 1, [X, 0, 3], [Y, 0, 3], [Z, 0, 3]) The result is Z + 1 + . . . + Y + . . . + X + . . . ..Which was correct /* ********************** Problem 43. *************** */ %Input is 1 - % The result is 3 2 2 3 - Z + Z - Z + 1 + . . . + (- 1 + 2 Z - 3 Z + 4 Z + . . .) Y 2 3 2 2 3 3 + (1 - 3 Z + 6 Z - 10 Z + . . .) Y + (- 1 + 4 Z - 10 Z + 20 Z + . . .) Y 2 3 + . . . + (- 1 + 2 Z - 3 Z + 4 Z + . . . 2 3 2 3 + (2 - 6 Z + 12 Z - 20 Z + . . .) Y + (- 3 + 12 Z - 30 Z + 60 Z + . . .) 2 2 3 3 Y + (4 - 20 Z + 60 Z - 140 Z + . . .) Y + . . .) X 2 3 2 3 + (1 - 3 Z + 6 Z - 10 Z + . . . + (- 3 + 12 Z - 30 Z + 60 Z + . . .) Y 2 3 2 + (6 - 30 Z + 90 Z - 210 Z + . . .) Y 2 3 3 2 + (- 10 + 60 Z - 210 Z + 560 Z + . . .) Y + . . .) X 2 3 2 3 + (- 1 + 4 Z - 10 Z + 20 Z + . . . + (4 - 20 Z + 60 Z - 140 Z + . . .) Y 2 3 2 + (- 10 + 60 Z - 210 Z + 560 Z + . . .) Y 2 3 3 3 + (20 - 140 Z + 560 Z - 1680 Z + . . .) Y + . . .) X + . . . ..Which was correct /* ********************** Problem 44. *************** */ %Input is I 2 EV(SUM(2 + I , I, 0, N), SIMPSUM) The result is 3 2 N + 1 2 N + 3 N + N 2 + --------------- - 1 6 ..Which was correct /* ********************** Problem 45. *************** */ %Input is 1 EV(SUM(--, I, 1, INF), SIMPSUM) I 3 The result is 1 - 2 ..Which was correct /* ********************** Problem 46. *************** */ %Input is 2 1 EV(SUM(I , I, 1, 4) SUM(--, I, 1, INF), SIMPSUM) 2 I The result is 2 5 %PI ..Which was correct /* ********************** Problem 47. *************** */ %Input is 2 SUM(I , I, 1, 5) The result is 55 ..Which was correct /* ********************** Problem 48. *************** */ %Input is I (1 + I) PRODUCT(--------- + X, I, 1, 4) 2 The result is (X + 1) (X + 3) (X + 6) (X + 10) ..Which was correct /* ********************** Problem 49. *************** */ %Input is LIMIT(X LOG(X), X, 0, PLUS) The result is 0 ..Which was correct /* ********************** Problem 50. *************** */ %Input is 1/X LIMIT((X + 1) , X, 0) The result is %E ..Which was correct /* ********************** Problem 51. *************** */ %Input is X %E LIMIT(---, X, INF) X The result is INF ..Which was correct /* ********************** Problem 52. *************** */ %Input is 1 LIMIT(SIN(-), X, 0) X The result is IND ..Which was correct /* ********************** Problem 53. *************** */ %Input is NUSUM(N N!, N, 0, N) Dependent equations eliminated: (1) The result is (N + 1)! - 1 ..Which was correct /* ********************** Problem 54. *************** */ %Input is 4 N N 4 NUSUM(----------------, N, 0, N) BINOMIAL(2 N, N) The result is 4 3 2 N 2 (N + 1) (63 N + 112 N + 18 N - 22 N + 3) 4 2 ------------------------------------------------ - ------ 693 BINOMIAL(2 N, N) 3 11 7 ..Which was correct /* ********************** Problem 55. *************** */ %Input is UNSUM(%, N) The result is 4 N N 4 ---------------- BINOMIAL(2 N, N) ..Which was correct /* ********************** Problem 56. *************** */ %Input is 2 UNSUM(PRODUCT(I , I, 1, N), N) The result is N - 1 /===\ ! ! 2 ( ! ! I ) (N - 1) (N + 1) ! ! I = 1 ..Which was correct /* ********************** Problem 57. *************** */ %Input is NUSUM(%, N, 1, N) Dependent equations eliminated: (2 3) The result is N /===\ ! ! 2 ! ! I - 1 ! ! I = 1 ..Which was correct /* ********************** Problem 58. *************** */ %Input is (3 + N) F(1 + N) N - 1 FUNCSOLVE((1 + N) F(N) - ---------------- = -----, F(N)) 1 + N 2 + N Dependent equations eliminated: (4 3) The result is N F(N) = --------------- (N + 1) (N + 2) ..Which was correct /* ********************** Problem 59. *************** */ %Input is (UNTELLRAT(A), 'DONE) The result is DONE ..Which was correct /* ********************** Problem 60. *************** */ %Input is S RESIDUE(-------, S, A %I) 2 2 A + S The result is 1 - 2 ..Which was correct /* ********************** Problem 61. *************** */ %Input is SIN(A X) RESIDUE(--------, X, 0) 4 X The result is 3 A - -- 6 ..Which was correct /* ********************** Problem 62. *************** */ %Input is TAYLOR(SQRT(SIN(X) + A X + 1), X, 0, 3) The result is 2 2 3 2 3 (A + 1) X (A + 2 A + 1) X (3 A + 9 A + 9 A - 1) X 1 + --------- - ----------------- + -------------------------- + . . . 2 8 48 Using ratsimp ..Which was correct /* ********************** Problem 63. *************** */ %Input is 2 % The result is 3 X 1 + (A + 1) X - -- + . . . 6 ..Which was correct /* ********************** Problem 64. *************** */ %Input is TAYLOR(SQRT(X + 1), X, 0, 5) The result is 2 3 4 5 X X X 5 X 7 X 1 + - - -- + -- - ---- + ---- + . . . 2 8 16 128 256 ..Which was correct /* ********************** Problem 65. *************** */ %Input is 2 % The result is 1 + X + . . . ..Which was correct /* ********************** Problem 66. *************** */ %Input is I 2.5 PRODUCT((1 + X ) , I, 1, INF) ------------------------------- 2 1 + X The result is INF /===\ ! ! I 2.5 ! ! (X + 1) ! ! I = 1 ----------------- 2 X + 1 ..Which was correct /* ********************** Problem 67. *************** */ %Input is EV(TAYLOR(%, X, 0, 3), KEEPFLOAT) The result is 2 3 1 + 2.5 X + 3.375 X + 6.5625 X + . . . ..Which was correct /* ********************** Problem 68. *************** */ %Input is 1 TAYLOR(----------, X, 0, 3) LOG(X + 1) The result is 2 3 1 1 X X 19 X - + - - -- + -- - ----- + . . . X 2 12 24 720 ..Which was correct /* ********************** Problem 69. *************** */ %Input is TAYLOR(COS(X) - SEC(X), X, 0, 5) The result is 4 2 X - X - -- + . . . 6 ..Which was correct /* ********************** Problem 70. *************** */ %Input is 3 TAYLOR((COS(X) - SEC(X)) , X, 0, 5) The result is 0 + . . . ..Which was correct /* ********************** Problem 71. *************** */ %Input is 1 TAYLOR(------------------, X, 0, 5) 3 (COS(X) - SEC(X)) The result is 2 4 1 1 11 347 6767 X 15377 X - -- + ---- + ------ - ----- - ------- - -------- + . . . 6 4 2 15120 604800 7983360 X 2 X 120 X ..Which was correct /* ********************** Problem 72. *************** */ %Input is 2 2 TAYLOR(SQRT(1 - K SIN (X)), X, 0, 6) The result is 2 2 4 2 4 6 4 2 6 K X (3 K - 4 K ) X (45 K - 60 K + 16 K ) X 1 - ----- - ---------------- - -------------------------- + . . . 2 24 720 Using ratsimp ..Which was correct /* ********************** Problem 73. *************** */ %Input is N TAYLOR((X + 1) , X, 0, 4) The result is 2 2 3 2 3 4 3 2 4 (N - N) X (N - 3 N + 2 N) X (N - 6 N + 11 N - 6 N) X 1 + N X + ----------- + -------------------- + ---------------------------- 2 6 24 + . . . ..Which was correct /* ********************** Problem 74. *************** */ %Input is TAYLOR(SIN(Y + X), X, 0, 3, Y, 0, 3) The result is 3 2 3 Y Y Y Y 2 Y - -- + . . . + (1 - -- + . . .) X + (- - + -- + . . .) X 6 2 2 12 2 1 Y 3 + (- - + -- + . . .) X + . . . 6 12 ..Which was correct /* ********************** Problem 75. *************** */ %Input is TAYLOR(SIN(Y + X), [X, Y], 0, 3) The result is 3 2 2 3 X + 3 Y X + 3 Y X + Y Y + X - ------------------------- + . . . 6 Using ratsimp ..Which was correct /* ********************** Problem 76. *************** */ %Input is 1 TAYLOR(----------, X, 0, 3, Y, 0, 3) SIN(Y + X) The result is 1 Y 1 1 1 2 1 3 - + - + . . . + (- -- + - + . . .) X + (-- + . . .) X + (- -- + . . .) X Y 6 2 6 3 4 Y Y Y + . . . ..Which was correct /* ********************** Problem 77. *************** */ %Input is END The result is END ..Which was correct Congratulations: No differences! Testing rtest9a.mac /* ********************** Problem 1. *************** */ %Input is KILL(ALL) The result is DONE ..Which was correct /* ********************** Problem 2. *************** */ %Input is I X 2 DEFTAYLOR(F(X), SUM(------, I, 4, INF) + X ) I 2 2 I! The result is [F] ..Which was correct /* ********************** Problem 3. *************** */ %Input is SQRT(F(X)) TAYLOR(%E , X, 0, 4) The result is 2 3 4 X 3073 X 12817 X 1 + X + -- + ------- + -------- + . . . 2 18432 307200 ..Which was correct /* ********************** Problem 4. *************** */ %Input is SIN(X) POWERSERIES(LOG(------), X, 0) X The result is INF ==== I1 2 I1 2 I1 \(- 1) 2 BERN(2 I1) X >------------------------------ / I1 (2 I1)! ==== I1 = 1 ------------------------------------- 2 ..Which was correct /* ********************** Problem 5. *************** */ %Input is SIN(3 X) EV(-------- + X, TRIGEXPAND, EXPAND) SIN(X) The result is 2 2 - SIN (X) + 3 COS (X) + X ..Which was correct /* ********************** Problem 6. *************** */ %Input is TRIGEXPAND(SIN(Y + 10 X)) The result is COS(10 X) SIN(Y) + SIN(10 X) COS(Y) ..Which was correct /* ********************** Problem 7. *************** */ %Input is 2 2 X + 3 COS (X) - SIN (X) The result is 2 2 - SIN (X) + 3 COS (X) + X ..Which was correct /* ********************** Problem 8. *************** */ %Input is EXPAND(TRIGREDUCE(%)) The result is 2 COS(2 X) + X + 1 ..Which was correct /* ********************** Problem 9. *************** */ %Input is DECLARE(J, INTEGER, E, EVEN, O, ODD) The result is DONE ..Which was correct /* ********************** Problem 10. *************** */ %Input is 1 SIN((- + E) %PI + X) 2 The result is COS(X) ..Which was correct /* ********************** Problem 11. *************** */ %Input is 1 SIN((- + O) %PI + X) 2 The result is - COS(X) ..Which was correct /* ********************** Problem 12. *************** */ %Input is 2 EXP(Y + X ) (LINEL : 500, DIFF(-----------, X, 2)) Y + X The result is 2 2 2 2 2 Y + X Y + X Y + X Y + X 4 X %E 2 %E 4 X %E 2 %E ------------- + ---------- - ------------ + ---------- Y + X Y + X 2 3 (Y + X) (Y + X) ..Which was correct /* ********************** Problem 13. *************** */ %Input is SCONCAT(OPTIMIZE(%)) The result is BLOCK([%1,%2,%3,%4],%1:Y+X,%2:X^2,%3:%E^(Y+%2),%4:1/%1,4*%2*%4*%3+2*%4*%3-4*X*%3/%1^2+2*%3/%1^3) ..Which was correct /* ********************** Problem 14. *************** */ %Input is LINEL : 79 The result is 79 ..Which was correct /* ********************** Problem 15. *************** */ %Input is A + 2 T LAPLACE(%E SIN(T) T, T, S) The result is A %E (2 S - 4) --------------- 2 2 (S - 4 S + 5) ..Which was correct /* ********************** Problem 16. *************** */ %Input is T / [ 2 B F(T) + I SINH(A X) F(T - X) dX = T ] / 0 The result is T / [ 2 I F(T - X) SINH(A X) dX + B F(T) = T ] / 0 ..Which was correct /* ********************** Problem 17. *************** */ %Input is LAPLACE(%, T, S) The result is A LAPLACE(F(T), T, S) 2 B LAPLACE(F(T), T, S) + --------------------- = -- 2 2 3 S - A S Using ratsimp ..Which was correct /* ********************** Problem 18. *************** */ %Input is LINSOLVE([%], [LAPLACE(F(T), T, S)]) The result is 2 2 2 S - 2 A [LAPLACE(F(T), T, S) = --------------------] 5 2 3 B S + (A - A B) S ..Which was correct Congratulations: No differences! Testing rtest10.mac /* ********************** Problem 1. *************** */ %Input is KILL(ALL) The result is DONE ..Which was correct /* ********************** Problem 2. *************** */ %Input is N! -------- (1 + N)! The result is N! -------- (N + 1)! ..Which was correct /* ********************** Problem 3. *************** */ %Input is MINFACTORIAL(%) The result is 1 ----- N + 1 ..Which was correct /* ********************** Problem 4. *************** */ %Input is 2 2 (1 + N) N! The result is 2 2 (N + 1) N! ..Which was correct /* ********************** Problem 5. *************** */ %Input is FACTCOMB(%) The result is 2 (N + 1)! ..Which was correct /* ********************** Problem 6. *************** */ %Input is QUNIT(17) The result is SQRT(17) + 4 ..Which was correct /* ********************** Problem 7. *************** */ %Input is EXPAND(% (SQRT(17) - 4)) The result is 1 ..Which was correct /* ********************** Problem 8. *************** */ %Input is CF([1, - 2, 1] + [1, 2, - 3]) The result is [1, 1, 1, 2] ..Which was correct /* ********************** Problem 9. *************** */ %Input is CFDISREP(%) The result is 1 1 + --------- 1 1 + ----- 1 1 + - 2 Using ratsimp ..Which was correct /* ********************** Problem 10. *************** */ %Input is CFLENGTH : 4 The result is 4 ..Which was correct /* ********************** Problem 11. *************** */ %Input is CF(SQRT(3)) The result is [1, 1, 2, 1, 2, 1, 2, 1, 2] ..Which was correct /* ********************** Problem 12. *************** */ %Input is CFEXPAND(%) The result is [ 265 97 ] [ ] [ 153 56 ] ..Which was correct /* ********************** Problem 13. *************** */ %Input is % 1, 2 EV(-----, NUMER) % 2, 2 The result is 1.732142857142857 Using ratsimp RAT replaced 1.73214285 by 97//56 = 1.732142857142857 RAT replaced 1.732142857142857 by 97//56 = 1.732142857142857 ..Which was correct /* ********************** Problem 14. *************** */ %Input is CF([1, - 2, 1] + [1, 2, - 3]) The result is [1, 1, 1, 2] ..Which was correct /* ********************** Problem 15. *************** */ %Input is CFDISREP(%) The result is 1 1 + --------- 1 1 + ----- 1 1 + - 2 Using ratsimp ..Which was correct /* ********************** Problem 16. *************** */ %Input is CFLENGTH : 4 The result is 4 ..Which was correct /* ********************** Problem 17. *************** */ %Input is CF(SQRT(3)) The result is [1, 1, 2, 1, 2, 1, 2, 1, 2] ..Which was correct /* ********************** Problem 18. *************** */ %Input is CFEXPAND(%) The result is [ 265 97 ] [ ] [ 153 56 ] ..Which was correct /* ********************** Problem 19. *************** */ %Input is % 1, 2 EV(-----, NUMER) % 2, 2 The result is 1.732142857142857 Using ratsimp RAT replaced 1.73214285 by 97//56 = 1.732142857142857 RAT replaced 1.732142857142857 by 97//56 = 1.732142857142857 ..Which was correct /* ********************** Problem 20. *************** */ %Input is DECLARE(J, EVEN) The result is DONE ..Which was correct /* ********************** Problem 21. *************** */ %Input is FEATUREP(J, INTEGER) The result is TRUE ..Which was correct /* ********************** Problem 22. *************** */ %Input is MAP(F, B Z + A Y + X) The result is F(B Z) + F(A Y) + F(X) ..Which was correct /* ********************** Problem 23. *************** */ %Input is 1 MAP(LAMBDA([U], PARTFRAC(U, X)), ------------------- + X) 2 3 2 + 5 X + 4 X + X The result is 1 1 1 ----- - ----- + -------- + X X + 2 X + 1 2 (X + 1) ..Which was correct /* ********************** Problem 24. *************** */ %Input is 2 Y + Y X MAP(RATSIMP, ------ + ------) Y 2 X + X The result is 1 Y + ----- + 1 X + 1 ..Which was correct /* ********************** Problem 25. *************** */ %Input is MAP(=, [A, B], [- 0.5, 3]) The result is [A = - 0.5, B = 3] ..Which was correct /* ********************** Problem 26. *************** */ %Input is FULLMAP(G, B C + A) The result is G(B) G(C) + G(A) ..Which was correct /* ********************** Problem 27. *************** */ %Input is MAP(G, B C + A) The result is G(B C) + G(A) ..Which was correct /* ********************** Problem 28. *************** */ %Input is FULLMAPL(+, [3, [4, 5]], [[A, 1], [0, - 1.5]]) The result is [[A + 3, 4], [4, 3.5]] ..Which was correct /* ********************** Problem 29. *************** */ %Input is 2 2 EXP1 : X + (1 + 2 A + A ) Y The result is 2 2 (A + 2 A + 1) Y + X ..Which was correct /* ********************** Problem 30. *************** */ %Input is SCANMAP(FACTOR, %) The result is 2 2 (A + 1) Y + X ..Which was correct /* ********************** Problem 31. *************** */ %Input is B + A X C + U V The result is A X + B U V + C ..Which was correct /* ********************** Problem 32. *************** */ %Input is SCANMAP('F, %) The result is F(F(F(A) F(X)) + F(B)) F(F(F(U) F(F(V) )) + F(C)) ..Which was correct /* ********************** Problem 33. *************** */ %Input is APPEND([X + Y, 0, - 3.2], [2.5E+20, X]) The result is [Y + X, 0, - 3.2, 2.5E+20, X] ..Which was correct /* ********************** Problem 34. *************** */ %Input is UNION(X, Y) := IF X = [] THEN Y ELSE (IF MEMBER(T : FIRST(X), Y) THEN UNION(REST(X), Y) ELSE CONS(T, UNION(REST(X), Y))) The result is UNION(X, Y) := IF X = [] THEN Y ELSE (IF MEMBER(T : FIRST(X), Y) THEN UNION(REST(X), Y) ELSE CONS(T, UNION(REST(X), Y))) ..Which was correct /* ********************** Problem 35. *************** */ %Input is 1 2 2 1 UNION([A, B, 1, -, X ], [- X , A, Y, -]) 2 2 The result is 2 2 1 [B, 1, X , - X , A, Y, -] 2 ..Which was correct /* ********************** Problem 36. *************** */ %Input is BERNPOLY(X, 5) The result is 4 3 5 5 X 5 X X X - ---- + ---- - - 2 3 6 ..Which was correct /* ********************** Problem 37. *************** */ %Input is MAPLIST(NUMFACTOR, %) The result is 5 5 1 [1, - -, -, - -] 2 3 6 ..Which was correct /* ********************** Problem 38. *************** */ %Input is APPLY(MIN, %) The result is 5 - - 2 ..Which was correct Congratulations: No differences! Testing rtest11.mac /* ********************** Problem 1. *************** */ %Input is KILL(ALL) The result is DONE ..Which was correct /* ********************** Problem 2. *************** */ %Input is DISPLAY(B ) 1, 2 B = B 1, 2 1, 2 The result is DONE ..Which was correct /* ********************** Problem 3. *************** */ %Input is 1 EXP1 : INTEGRATE(------, X) 3 2 + X The result is 1/3 2 X - 2 ATAN(------------) 2 1/3 2/3 1/3 1/3 LOG(X - 2 X + 2 ) 2 SQRT(3) LOG(X + 2 ) - ----------------------- + ------------------ + ------------- 2/3 2/3 2/3 6 2 2 SQRT(3) 3 2 ..Which was correct /* ********************** Problem 4. *************** */ %Input is EXP2 : DIFF(EXP1, X) The result is 1/3 1 2 X - 2 1 --------------------- - --------------------------- + ----------------- 1/3 2 2/3 2 1/3 2/3 2/3 1/3 (2 X - 2 ) 6 2 (X - 2 X + 2 ) 3 2 (X + 2 ) 3 (------------- + 1) 2/3 3 2 ..Which was correct /* ********************** Problem 5. *************** */ %Input is RADCAN(EXP2) The result is 1 ------ 3 X + 2 ..Which was correct /* ********************** Problem 6. *************** */ %Input is 1/3 2 X - 2 ATAN(------------) 1/3 1/3 2/3 1/3 2 LOG(2 + X) 2 SQRT(3) - LOG(2 - 2 X + X ) REVEAL(EXP1 : ------------- + ------------------ + -------------------------, 2/3 2/3 2/3 3 2 2 SQRT(3) 6 2 2) The result is Negterm + Quotient + Quotient Using ratsimp ..Which was correct /* ********************** Problem 7. *************** */ %Input is G(L) := CATCH(MAP(LAMBDA([X], IF X < 0 THEN THROW(X) ELSE F(X)), L)) The result is G(L) := CATCH(MAP(LAMBDA([X], IF X < 0 THEN THROW(X) ELSE F(X)), L)) ..Which was correct /* ********************** Problem 8. *************** */ %Input is G([1, 2, 3, 7]) The result is [F(1), F(2), F(3), F(7)] ..Which was correct /* ********************** Problem 9. *************** */ %Input is G([1, 2, - 3, 7]) The result is - 3 ..Which was correct /* ********************** Problem 10. *************** */ %Input is 2 EXP1 : B X + Y The result is 2 Y + B X ..Which was correct /* ********************** Problem 11. *************** */ %Input is ORDERLESS(Y) The result is DONE ..Which was correct /* ********************** Problem 12. *************** */ %Input is 2 B X + Y The result is 2 B X + Y ..Which was correct /* ********************** Problem 13. *************** */ %Input is % - EXP1 The result is 2 2 Y - Y Using ratsimp ..Which was correct /* ********************** Problem 14. *************** */ %Input is UNORDER() The result is [Y] ..Which was correct /* ********************** Problem 15. *************** */ %Input is 2 EXP : B X + A The result is 2 B X + A ..Which was correct /* ********************** Problem 16. *************** */ %Input is ORDERGREAT(A) The result is DONE ..Which was correct /* ********************** Problem 17. *************** */ %Input is 2 B X + A The result is 2 A + B X ..Which was correct /* ********************** Problem 18. *************** */ %Input is % - EXP The result is 2 2 A - A Using ratsimp ..Which was correct /* ********************** Problem 19. *************** */ %Input is UNORDER() The result is [A] ..Which was correct /* ********************** Problem 20. *************** */ %Input is 2 EXP : B X + A The result is 2 B X + A ..Which was correct /* ********************** Problem 21. *************** */ %Input is ORDERGREAT(A) The result is DONE ..Which was correct /* ********************** Problem 22. *************** */ %Input is 2 B X + A The result is 2 A + B X ..Which was correct /* ********************** Problem 23. *************** */ %Input is % - EXP The result is 2 2 A - A Using ratsimp ..Which was correct /* ********************** Problem 24. *************** */ %Input is UNORDER() The result is [A] ..Which was correct /* ********************** Problem 25. *************** */ %Input is DECLARE(F, LINEAR) The result is DONE ..Which was correct /* ********************** Problem 26. *************** */ %Input is F(3 B + 2 A) The result is 3 F(B) + 2 F(A) ..Which was correct /* ********************** Problem 27. *************** */ %Input is F(Y + 2 X, X) The result is F(1, X) Y + 2 F(X, X) ..Which was correct /* ********************** Problem 28. *************** */ %Input is DECLARE(F, ADDITIVE) The result is DONE ..Which was correct /* ********************** Problem 29. *************** */ %Input is F(3 B + 2 A) The result is 3 F(B) + 2 F(A) ..Which was correct /* ********************** Problem 30. *************** */ %Input is DECLARE(F, OUTATIVE) The result is DONE ..Which was correct /* ********************** Problem 31. *************** */ %Input is F(2 A) The result is 2 F(A) ..Which was correct /* ********************** Problem 32. *************** */ %Input is DECLARE(F, MULTIPLICATIVE) The result is DONE ..Which was correct /* ********************** Problem 33. *************** */ %Input is F(2 A B) The result is 2 F(A) F(B) ..Which was correct /* ********************** Problem 34. *************** */ %Input is (KILL(FUNCTIONS), DECLARE(G, LASSOCIATIVE)) The result is DONE ..Which was correct /* ********************** Problem 35. *************** */ %Input is G(G(A, B), G(C, D)) The result is G(G(G(A, B), C), D) ..Which was correct /* ********************** Problem 36. *************** */ %Input is G(G(A, B), G(C, D)) - G(A, G(B, G(C, D))) The result is 0 ..Which was correct /* ********************** Problem 37. *************** */ %Input is DECLARE(G, RASSOCIATIVE) The result is DONE ..Which was correct /* ********************** Problem 38. *************** */ %Input is G(G(A, B), G(C, D)) The result is G(G(G(A, B), C), D) ..Which was correct /* ********************** Problem 39. *************** */ %Input is G(G(A, B), G(C, D)) - G(A, G(B, G(C, D))) The result is 0 ..Which was correct /* ********************** Problem 40. *************** */ %Input is (KILL(H), DECLARE(H, COMMUTATIVE)) The result is DONE ..Which was correct /* ********************** Problem 41. *************** */ %Input is H(X, Z, Y) The result is H(X, Y, Z) ..Which was correct /* ********************** Problem 42. *************** */ %Input is (KILL(H), DECLARE(H, SYMMETRIC)) The result is DONE ..Which was correct /* ********************** Problem 43. *************** */ %Input is H(X, Z, Y) The result is H(X, Y, Z) ..Which was correct /* ********************** Problem 44. *************** */ %Input is (KILL(H), DECLARE(H, ANTISYMMETRIC)) The result is DONE ..Which was correct /* ********************** Problem 45. *************** */ %Input is H(X, Z, Y) The result is - H(X, Y, Z) ..Which was correct /* ********************** Problem 46. *************** */ %Input is (KILL(ALL), DECLARE(J, NARY)) The result is DONE ..Which was correct /* ********************** Problem 47. *************** */ %Input is J(J(A, B), J(C, D)) The result is J(A, B, C, D) ..Which was correct /* ********************** Problem 48. *************** */ %Input is DECLARE(F, ODDFUN) The result is DONE ..Which was correct /* ********************** Problem 49. *************** */ %Input is F(- X) The result is - F(X) ..Which was correct /* ********************** Problem 50. *************** */ %Input is DECLARE(G, EVENFUN) The result is DONE ..Which was correct /* ********************** Problem 51. *************** */ %Input is G(- X) The result is G(X) ..Which was correct /* ********************** Problem 52. *************** */ %Input is (KILL(ALL), DECLARE(F, POSFUN)) The result is DONE ..Which was correct /* ********************** Problem 53. *************** */ %Input is IS(F(X) > 0) The result is TRUE ..Which was correct /* ********************** Problem 54. *************** */ %Input is (KILL(ALL), B : 1) 1, X The result is 1 ..Which was correct /* ********************** Problem 55. *************** */ %Input is ARRAY(F, 2, 3) The result is #2A((NIL NIL NIL NIL) (NIL NIL NIL NIL) (NIL NIL NIL NIL)) ..Which was correct /* ********************** Problem 56. *************** */ %Input is ARRAYINFO(B) The result is [HASH_TABLE, TRUE, [1, X]] ..Which was correct /* ********************** Problem 57. *************** */ %Input is ARRAYINFO(F) The result is [DECLARED, 2, [2, 3]] ..Which was correct /* ********************** Problem 58. *************** */ %Input is BLOCK([USE_FAST_ARRAYS : FALSE], KILL(bb), bb : 7, ARRAYINFO(bb)) 1, x The result is [HASHED, 2, [1, x]] ..Which was correct /* ********************** Problem 59. *************** */ %Input is BLOCK([USE_FAST_ARRAYS : TRUE], KILL(bb), bb : 7, ARRAYINFO(bb)) 1, x The result is [HASH_TABLE, TRUE, [1, x]] ..Which was correct /* ********************** Problem 60. *************** */ %Input is PROPERTIES(CONS) The result is [System Function] ..Which was correct /* ********************** Problem 61. *************** */ %Input is ASSUME(VAR1 > 0) The result is [VAR1 > 0] ..Which was correct /* ********************** Problem 62. *************** */ %Input is PROPERTIES(VAR1) The result is [Database Info, VAR1 > 0] ..Which was correct /* ********************** Problem 63. *************** */ %Input is VAR2 : 2 The result is 2 ..Which was correct /* ********************** Problem 64. *************** */ %Input is PROPERTIES(VAR2) The result is [VALUE] ..Which was correct /* ********************** Problem 65. *************** */ %Input is X GRADEF(R, X, -) R The result is R ..Which was correct /* ********************** Problem 66. *************** */ %Input is Y GRADEF(R, Y, -) R The result is R ..Which was correct /* ********************** Problem 67. *************** */ %Input is PRINTPROPS(R, ATOMGRAD) Y R = - Y R X R = - X R The result is DONE ..Which was correct /* ********************** Problem 68. *************** */ %Input is PROPVARS(ATOMGRAD) The result is [R] ..Which was correct /* ********************** Problem 69. *************** */ %Input is X GRADEF(R, X, -) R The result is R ..Which was correct /* ********************** Problem 70. *************** */ %Input is Y GRADEF(R, Y, -) R The result is R ..Which was correct /* ********************** Problem 71. *************** */ %Input is PRINTPROPS(R, ATOMGRAD) Y R = - Y R X R = - X R Y R = - Y R X R = - X R The result is DONE ..Which was correct /* ********************** Problem 72. *************** */ %Input is PROPVARS(ATOMGRAD) The result is [R] ..Which was correct /* ********************** Problem 73. *************** */ %Input is PUT(%E, TRANSCENDENTAL, TYPE) The result is TRANSCENDENTAL ..Which was correct /* ********************** Problem 74. *************** */ %Input is PUT(%PI, TRANSCENDENTAL, TYPE) The result is TRANSCENDENTAL ..Which was correct /* ********************** Problem 75. *************** */ %Input is BLOCK([ALGEBRAIC : FALSE], PUT(%I, ALGEBRAIC, TYPE)) The result is FALSE ..Which was correct /* ********************** Problem 76. *************** */ %Input is TYPEOF(X) := BLOCK([Q], IF NUMBERP(X) THEN RETURN(ALGEBRAIC), IF NOT ATOM(X) THEN RETURN(MAPLIST(TYPEOF, X)), Q : GET(X, TYPE), IF Q = FALSE THEN ERROR("NOT NUMERIC") ELSE Q) The result is TYPEOF(X) := BLOCK([Q], IF NUMBERP(X) THEN RETURN(ALGEBRAIC), IF NOT ATOM(X) THEN RETURN(MAPLIST(TYPEOF, X)), Q : GET(X, TYPE), IF Q = FALSE THEN ERROR("NOT NUMERIC") ELSE Q) ..Which was correct /* ********************** Problem 77. *************** */ %Input is BLOCK([ALGEBRAIC : FALSE], ERRCATCH(TYPEOF(X %PI + 2 %E))) NOT NUMERIC The result is [] ..Which was correct /* ********************** Problem 78. *************** */ %Input is BLOCK([ALGEBRAIC : FALSE], TYPEOF(%PI + 2 %E)) The result is [TRANSCENDENTAL, [FALSE, TRANSCENDENTAL]] ..Which was correct /* ********************** Problem 79. *************** */ %Input is 2 IS(X >= 2 X - 1) The result is TRUE ..Which was correct /* ********************** Problem 80. *************** */ %Input is ASSUME(A > 1) The result is [A > 1] ..Which was correct /* ********************** Problem 81. *************** */ %Input is 2 IS(LOG(1 + LOG(1 + A)) > 0 AND 1 + A > 2 A) The result is TRUE ..Which was correct /* ********************** Problem 82. *************** */ %Input is FREEOF(Y, SIN(2 Y + X)) The result is FALSE ..Which was correct /* ********************** Problem 83. *************** */ %Input is FREEOF(COS(Y), *, COS(X) + SIN(Y)) The result is TRUE ..Which was correct Congratulations: No differences! Testing rtest12.mac /* ********************** Problem 1. *************** */ %Input is (KILL(ALL), CLEAR_RULES(), MATCHDECLARE(A, TRUE)) The result is DONE ..Which was correct /* ********************** Problem 2. *************** */ %Input is 2 2 TELLSIMP(SIN (A), 1 - COS (A)) The result is [^RULE1, SIMPEXPT] ..Which was correct /* ********************** Problem 3. *************** */ %Input is 2 SIN (Y) The result is 2 1 - COS (Y) ..Which was correct /* ********************** Problem 4. *************** */ %Input is KILL(RULES) The result is DONE ..Which was correct /* ********************** Problem 5. *************** */ %Input is NONZEROANDFREEOF(X, E) := IS(E # 0 AND FREEOF(X, E)) The result is NONZEROANDFREEOF(X, E) := IS(E # 0 AND FREEOF(X, E)) ..Which was correct /* ********************** Problem 6. *************** */ %Input is MATCHDECLARE(A, NONZEROANDFREEOF(X), B, FREEOF(X)) The result is DONE ..Which was correct /* ********************** Problem 7. *************** */ %Input is DEFMATCH(LINEAR, B + A X, X) The result is LINEAR ..Which was correct /* ********************** Problem 8. *************** */ %Input is 2 LINEAR(Y + (1 + Y) Z + 3 Z, Z) The result is 2 [B = Y , A = Y + 4, X = Z] Using ratsimp Using ratsimp ..Which was correct /* ********************** Problem 9. *************** */ %Input is MATCHDECLARE([A, F], TRUE) The result is DONE ..Which was correct /* ********************** Problem 10. *************** */ %Input is CONSTINTERVAL(L, H) := CONSTANTP(H - L) The result is CONSTINTERVAL(L, H) := CONSTANTP(H - L) ..Which was correct /* ********************** Problem 11. *************** */ %Input is MATCHDECLARE(B, CONSTINTERVAL(A)) The result is DONE ..Which was correct /* ********************** Problem 12. *************** */ %Input is MATCHDECLARE(X, ATOM) The result is DONE ..Which was correct /* ********************** Problem 13. *************** */ %Input is B / [ BLOCK(REMOVE(INTEGRATE, OUTATIVE), DEFMATCH(CHECKLIMITS, I F dX), ] / A DECLARE(INTEGRATE, OUTATIVE)) The result is DONE ..Which was correct /* ********************** Problem 14. *************** */ %Input is 2 %PI + X / [ I SIN(T) dT ] / %PI + X The result is X + 2 %PI / [ I SIN(T) dT ] / X + %PI ..Which was correct /* ********************** Problem 15. *************** */ %Input is CHECKLIMITS(%) The result is [B = X + 2 %PI, A = X + %PI, X = T, F = SIN(T)] Using ratsimp Using ratsimp ..Which was correct /* ********************** Problem 16. *************** */ %Input is X / [ I SIN(T) dT ] / 0 The result is T / [ I SIN(T) dT ] / 0 ..Which was correct /* ********************** Problem 17. *************** */ %Input is CHECKLIMITS(%) The result is FALSE ..Which was correct /* ********************** Problem 18. *************** */ %Input is (KILL(ALL), MATCHDECLARE(X, FREEOF(%I))) The result is DONE ..Which was correct /* ********************** Problem 19. *************** */ %Input is %IARGS : FALSE The result is FALSE ..Which was correct /* ********************** Problem 20. *************** */ %Input is TELLSIMP(SIN(%I X), %I SINH(X)) The result is [SINRULE1, SIMP-%SIN] ..Which was correct /* ********************** Problem 21. *************** */ %Input is TRIGEXPAND(SIN(%I Y + X)) The result is SIN(X) COS(%I Y) + %I COS(X) SINH(Y) ..Which was correct /* ********************** Problem 22. *************** */ %Input is %IARGS : TRUE The result is TRUE ..Which was correct /* ********************** Problem 23. *************** */ %Input is 0 ERRCATCH(0 ) 0 0 has been generated The result is [] ..Which was correct /* ********************** Problem 24. *************** */ %Input is 0 EV(TELLSIMP(0 , 1), SIMP : FALSE) The result is [^RULE2, SIMPEXPT] ..Which was correct /* ********************** Problem 25. *************** */ %Input is 0 0 The result is 1 ..Which was correct /* ********************** Problem 26. *************** */ %Input is REMRULE(^, ^RULE2) The result is ^ ..Which was correct /* ********************** Problem 27. *************** */ %Input is 2 2 TELLSIMP(SIN (X), 1 - COS (X)) The result is [^RULE3, SIMPEXPT] ..Which was correct /* ********************** Problem 28. *************** */ %Input is 2 (1 + SIN(X)) The result is 2 (SIN(X) + 1) ..Which was correct /* ********************** Problem 29. *************** */ %Input is EXPAND(%) The result is 2 2 SIN(X) - COS (X) + 2 ..Which was correct /* ********************** Problem 30. *************** */ %Input is 2 SIN (X) The result is 2 1 - COS (X) ..Which was correct /* ********************** Problem 31. *************** */ %Input is KILL(RULES) The result is DONE ..Which was correct /* ********************** Problem 32. *************** */ %Input is MATCHDECLARE(A, TRUE) The result is DONE ..Which was correct /* ********************** Problem 33. *************** */ %Input is 2 2 TELLSIMP(SIN (A), 1 - COS (A)) The result is [^RULE4, SIMPEXPT] ..Which was correct /* ********************** Problem 34. *************** */ %Input is 2 SIN (Y) The result is 2 1 - COS (Y) ..Which was correct /* ********************** Problem 35. *************** */ %Input is KILL(RULES) The result is DONE ..Which was correct /* ********************** Problem 36. *************** */ %Input is (KILL(ALL), NONZEROANDFREEOF(X, E) := IS(E # 0 AND FREEOF(X, E))) The result is NONZEROANDFREEOF(X, E) := IS(E # 0 AND FREEOF(X, E)) ..Which was correct /* ********************** Problem 37. *************** */ %Input is MATCHDECLARE(A, NONZEROANDFREEOF(X), B, FREEOF(X)) The result is DONE ..Which was correct /* ********************** Problem 38. *************** */ %Input is DEFMATCH(LINEAR, B + A X, X) The result is LINEAR ..Which was correct /* ********************** Problem 39. *************** */ %Input is 2 LINEAR(Y + (1 + Y) Z + 3 Z, Z) The result is 2 [B = Y , A = Y + 4, X = Z] Using ratsimp Using ratsimp ..Which was correct /* ********************** Problem 40. *************** */ %Input is MATCHDECLARE([A, F], TRUE) The result is DONE ..Which was correct /* ********************** Problem 41. *************** */ %Input is CONSTINTERVAL(L, H) := CONSTANTP(H - L) The result is CONSTINTERVAL(L, H) := CONSTANTP(H - L) ..Which was correct /* ********************** Problem 42. *************** */ %Input is MATCHDECLARE(B, CONSTINTERVAL(A)) The result is DONE ..Which was correct /* ********************** Problem 43. *************** */ %Input is MATCHDECLARE(X, ATOM) The result is DONE ..Which was correct /* ********************** Problem 44. *************** */ %Input is B / [ BLOCK(REMOVE(INTEGRATE, OUTATIVE), DEFMATCH(CHECKLIMITS, I F dX), ] / A DECLARE(INTEGRATE, OUTATIVE)) The result is DONE ..Which was correct /* ********************** Problem 45. *************** */ %Input is 2 %PI + X / [ I SIN(T) dT ] / %PI + X The result is X + 2 %PI / [ I SIN(T) dT ] / X + %PI ..Which was correct /* ********************** Problem 46. *************** */ %Input is CHECKLIMITS(%) The result is [B = X + 2 %PI, A = X + %PI, X = T, F = SIN(T)] Using ratsimp Using ratsimp ..Which was correct /* ********************** Problem 47. *************** */ %Input is X / [ I SIN(T) dT ] / 0 The result is T / [ I SIN(T) dT ] / 0 ..Which was correct /* ********************** Problem 48. *************** */ %Input is CHECKLIMITS(%) The result is FALSE ..Which was correct /* ********************** Problem 49. *************** */ %Input is REMVALUE(A, B, F, X) The result is [A, B, F, X] ..Which was correct /* ********************** Problem 50. *************** */ %Input is (KILL(ALL), MATCHDECLARE([A, A1, A2], TRUE)) The result is DONE ..Which was correct /* ********************** Problem 51. *************** */ %Input is ONELESS(X, Y) := IS(X = Y - 1) The result is ONELESS(X, Y) := IS(X = Y - 1) ..Which was correct /* ********************** Problem 52. *************** */ %Input is LET(A1 A2!, A1!, ONELESS, A2, A1) The result is A1 A2! --> A1! WHERE ONELESS(A2, A1) ..Which was correct /* ********************** Problem 53. *************** */ %Input is A1! EV(LET(---, (A1 - 1)!), LETRAT) A1 The result is A1! --- --> (A1 - 1)! A1 ..Which was correct /* ********************** Problem 54. *************** */ %Input is N M! (N - 1)! EV(LETSIMP(-------------), LETRAT) M The result is (M - 1)! N! ..Which was correct /* ********************** Problem 55. *************** */ %Input is 2 2 LET(SIN (A), 1 - COS (A)) The result is 2 2 SIN (A) --> 1 - COS (A) ..Which was correct /* ********************** Problem 56. *************** */ %Input is 4 SIN (X) The result is 4 SIN (X) ..Which was correct /* ********************** Problem 57. *************** */ %Input is LETSIMP(%) The result is 4 2 COS (X) - 2 COS (X) + 1 ..Which was correct /* ********************** Problem 58. *************** */ %Input is MATCHDECLARE([A, A1, A2], TRUE) The result is DONE ..Which was correct /* ********************** Problem 59. *************** */ %Input is ONELESS(X, Y) := IS(X = Y - 1) The result is ONELESS(X, Y) := IS(X = Y - 1) ..Which was correct /* ********************** Problem 60. *************** */ %Input is LET(A1 A2!, A1!, ONELESS, A2, A1) The result is A1 A2! --> A1! WHERE ONELESS(A2, A1) ..Which was correct /* ********************** Problem 61. *************** */ %Input is A1! EV(LET(---, (A1 - 1)!), LETRAT) A1 The result is A1! --- --> (A1 - 1)! A1 ..Which was correct /* ********************** Problem 62. *************** */ %Input is N M! (N - 1)! EV(LETSIMP(-------------), LETRAT) M The result is (M - 1)! N! ..Which was correct /* ********************** Problem 63. *************** */ %Input is 2 2 LET(SIN (A), 1 - COS (A)) The result is 2 2 SIN (A) --> 1 - COS (A) ..Which was correct /* ********************** Problem 64. *************** */ %Input is 4 SIN (X) The result is 4 SIN (X) ..Which was correct /* ********************** Problem 65. *************** */ %Input is LETSIMP(%) The result is 4 2 COS (X) - 2 COS (X) + 1 ..Which was correct /* ********************** Problem 66. *************** */ %Input is PFEFORMAT : TRUE The result is TRUE ..Which was correct /* ********************** Problem 67. *************** */ %Input is 2 POISSIMP(SIN (X)) The result is 1/2 - 1/2 COS(2 X) ..Which was correct /* ********************** Problem 68. *************** */ %Input is 2 (2 A - B) COS(2 Y + X) - (5 + A B) SIN(U - 4 X) The result is 2 (2 A - B) COS(2 Y + X) + (A B + 5) SIN(4 X - U) ..Which was correct /* ********************** Problem 69. *************** */ %Input is EXP1 : OUTOFPOIS(POISEXPT(%, 2)) The result is 2 2 2 1/2 (2 A - B) COS(4 Y + 2 X) - (2 A - B) (- A B - 5) SIN(2 Y + 5 X - U) 2 2 + (2 A - B) (- A B - 5) SIN(2 Y - 3 X + U) - 1/2 (- A B - 5) COS(8 X - 2 U) 2 2 2 + 1/2 (- A B - 5) + 1/2 (2 A - B) ..Which was correct /* ********************** Problem 70. *************** */ %Input is PRINTPOIS(%) 2 - (B - 2 A ) (- A B - 5) SIN(- 2 Y - 5 X + U) 2 (2 A - B) (- A B - 5) SIN(2 Y - 3 X + U) 2 - 1/2 (- A B - 5) COS(2 U - 8 X) 2 2 2 1/2 (- A B - 5) + 1/2 (2 A - B) 2 2 1/2 (2 A - B) COS(4 Y + 2 X) The result is DONE ..Which was correct /* ********************** Problem 71. *************** */ %Input is OUTOFPOIS(POISINT(EXP1, Y)) The result is 2 2 2 1/8 (2 A - B) SIN(4 Y + 2 X) - 1/2 (B - 2 A ) (- A B - 5) COS(2 Y + 5 X - U) 2 - 1/2 (2 A - B) (- A B - 5) COS(2 Y - 3 X + U) Using ratsimp ..Which was correct /* ********************** Problem 72. *************** */ %Input is OUTOFPOIS(POISSIMP(%)) The result is 2 2 2 1/8 (2 A - B) SIN(4 Y + 2 X) - 1/2 (B - 2 A ) (- A B - 5) COS(2 Y + 5 X - U) 2 - 1/2 (2 A - B) (- A B - 5) COS(2 Y - 3 X + U) Using ratsimp ..Which was correct /* ********************** Problem 73. *************** */ %Input is 5 5 POISSIMP(COS (X) + SIN (X)) The result is 1/16 SIN(5 X) + 1/16 COS(5 X) - 5/16 SIN(3 X) + 5/16 COS(3 X) + 5/8 SIN(X) + 5/8 COS(X) ..Which was correct /* ********************** Problem 74. *************** */ %Input is PFEFORMAT : FALSE The result is FALSE ..Which was correct Congratulations: No differences! Testing rtest13.mac /* ********************** Problem 1. *************** */ %Input is 2 SIN(X) 3 X Y + X Y = ------ X X The result is 2 SIN(X) X Y + 3 X Y = ------ X X ..Which was correct /* ********************** Problem 2. *************** */ %Input is SOLN1 : ODE2(%, Y, X) The result is %C - COS(X) Y = ----------- 3 X ..Which was correct /* ********************** Problem 3. *************** */ %Input is IC1(SOLN1, X = %PI, Y = 0) The result is COS(X) + 1 Y = - ---------- 3 X Using ratsimp ..Which was correct /* ********************** Problem 4. *************** */ %Input is 3 Y (Y ) + Y = 0 X X X The result is 3 Y + Y (Y ) = 0 X X X ..Which was correct /* ********************** Problem 5. *************** */ %Input is SOLN2 : ODE2(%, Y, X) The result is 3 Y + 6 %K1 Y ------------ = X + %K2 6 ..Which was correct /* ********************** Problem 6. *************** */ %Input is RATSIMP(IC2(SOLN2, X = 0, Y = 0, Y = 2)) X The result is 3 2 Y - 3 Y - ---------- = X 6 Using ratsimp ..Which was correct /* ********************** Problem 7. *************** */ %Input is BC2(SOLN2, X = 0, Y = 1, X = 1, Y = 3) The result is 3 Y - 10 Y 3 --------- = X - - 6 2 ..Which was correct /* ********************** Problem 8. *************** */ %Input is 2 2 2 2 2 2 2 2 2 2 2 2 EXP : - K L M N - K L N + K M N + K N The result is 2 2 2 2 2 2 2 2 2 2 2 2 - K L M N + K M N - K L N + K N ..Which was correct /* ********************** Problem 9. *************** */ %Input is 2 2 EQ1 : L + K = 1 The result is 2 2 L + K = 1 ..Which was correct /* ********************** Problem 10. *************** */ %Input is 2 2 EQ2 : N - M = 1 The result is 2 2 N - M = 1 ..Which was correct /* ********************** Problem 11. *************** */ %Input is SCSIMP(EXP, EQ1, EQ2) The result is 4 4 K N ..Which was correct /* ********************** Problem 12. *************** */ %Input is - K2 K3 - K1 K2 + K1 K4 EXQ : ----------------------- 2 K3 The result is K1 K4 - K2 K3 - K1 K2 --------------------- 2 K3 ..Which was correct /* ********************** Problem 13. *************** */ %Input is EQ3 : K1 K4 - K2 K3 = 0 The result is K1 K4 - K2 K3 = 0 ..Which was correct /* ********************** Problem 14. *************** */ %Input is EQ4 : K3 K4 + K1 K2 = 0 The result is K3 K4 + K1 K2 = 0 ..Which was correct /* ********************** Problem 15. *************** */ %Input is SCSIMP(EXQ, EQ3, EQ4) The result is K4 -- K3 ..Which was correct /* ********************** Problem 16. *************** */ %Input is 2 EXP1 : Z + Y X + 2 X The result is 2 Z + X Y + 2 X ..Which was correct /* ********************** Problem 17. *************** */ %Input is EXP2 : - 1 - Z + 5 Y + 3 X The result is - Z + 5 Y + 3 X - 1 ..Which was correct /* ********************** Problem 18. *************** */ %Input is 2 2 EXP3 : 5 - Y + X + Z The result is 2 2 Z - Y + X + 5 ..Which was correct /* ********************** Problem 19. *************** */ %Input is ELIMINATE([EXP3, EXP2, EXP1], [Y, Z]) The result is 8 7 6 5 4 3 2 [7425 X - 1170 X + 1299 X + 12076 X + 22887 X - 5154 X - 1291 X + 7688 X + 15376] ..Which was correct /* ********************** Problem 20. *************** */ %Input is EQN1 : F(X) = SIN(X) + G(X) X X The result is F(X) = G(X) + SIN(X) X X ..Which was correct /* ********************** Problem 21. *************** */ %Input is EQN2 : G(X) = F(X) - COS(X) X X X The result is G(X) = F(X) - COS(X) X X X ..Which was correct /* ********************** Problem 22. *************** */ %Input is ATVALUE(G(X) , X = 0, A) X The result is A ..Which was correct /* ********************** Problem 23. *************** */ %Input is ATVALUE(F(X), X = 0, 1) The result is 1 ..Which was correct Congratulations: No differences! Testing rtest13s.mac /* ********************** Problem 1. *************** */ %Input is MATCHFIX({, }) The result is "{" ..Which was correct /* ********************** Problem 2. *************** */ %Input is INFIX(|) The result is "|" ..Which was correct /* ********************** Problem 3. *************** */ %Input is EXP1 : {X | X > 0} The result is {X | X > 0} ..Which was correct /* ********************** Problem 4. *************** */ %Input is EXP2 : {X | X < 2} The result is {X | X < 2} ..Which was correct /* ********************** Problem 5. *************** */ %Input is INFIX(OU) The result is "OU" ..Which was correct /* ********************** Problem 6. *************** */ %Input is INFIX(OI) The result is "OI" ..Which was correct /* ********************** Problem 7. *************** */ %Input is EXP1 OU EXP2 The result is {X | X > 0} OU {X | X < 2} ..Which was correct /* ********************** Problem 8. *************** */ %Input is EXP1 OU EXP2 The result is {X | X > 0} OU {X | X < 2} ..Which was correct /* ********************** Problem 9. *************** */ %Input is EXP1 : {1, 2, 3} The result is {1, 2, 3} ..Which was correct /* ********************** Problem 10. *************** */ %Input is {3, 4, 5} The result is {3, 4, 5} ..Which was correct /* ********************** Problem 11. *************** */ %Input is EXP1 OU EXP1 OU % The result is {1, 2, 3} OU {1, 2, 3} OU {3, 4, 5} ..Which was correct /* ********************** Problem 12. *************** */ %Input is INFIX(ou, 100, 100) The result is "OU" ..Which was correct /* ********************** Problem 13. *************** */ %Input is EXP2 : INFIX(OI, 120, 120) The result is "OI" ..Which was correct /* ********************** Problem 14. *************** */ %Input is EXP1 OU EXP1 OU {7} The result is {1, 2, 3} OU {1, 2, 3} OU {7} ..Which was correct /* ********************** Problem 15. *************** */ %Input is KILL(OU) The result is DONE ..Which was correct /* ********************** Problem 16. *************** */ %Input is foo(OU) The result is foo(OU) ..Which was correct Congratulations: No differences! Testing rtest14.mac /* ********************** Problem 1. *************** */ %Input is JN(3, 4) The result is 0.1320342093678868 ..Which was correct /* ********************** Problem 2. *************** */ %Input is J0(1) The result is 0.7651977429270346 ..Which was correct /* ********************** Problem 3. *************** */ %Input is BESSEL(2, 3) The result is 0.1289432631185581 - 5.717744443938835E-8 %I Using ratsimp RAT replaced 0.1289432631185581 by 1075//8337 = 0.1289432649634161 RAT replaced -5.717744444379852E-8 by -1//17489414 = -5.717744459591385E-8 RAT replaced 0.1289432631185581 by 1075//8337 = 0.1289432649634161 RAT replaced -5.717744443938835E-8 by -1//17489414 = -5.717744459591385E-8 ..Which was correct /* ********************** Problem 4. *************** */ %Input is (ASSUME(p > 0), TRUE) The result is TRUE ..Which was correct /* ********************** Problem 5. *************** */ %Input is (ASSUME(A + 4 p > 0), TRUE) The result is TRUE ..Which was correct /* ********************** Problem 6. *************** */ %Input is - A T ----- 1/2 4 - p T SPECINT(T %E %E , T) The result is SQRT(%PI) ------------ A 3/2 2 (p + -) 4 ..Which was correct /* ********************** Problem 7. *************** */ %Input is 2 - T ---- 2 ---- 3/4 B - p T SPECINT(T %E %E , T) The result is 2 2 B p B p ---- 8 SQRT(%PI) %M (----) 3 7/8 4 - 5/8, - 1/4 2 3 GAMMA(-) B %E (-------------------------------- 4 5/8 3 1/4 3 2 GAMMA(-) B SQRT(p) 8 2 3/8 B p 2 SQRT(%PI) %M (----) - 5/8, 1/4 2 - ---------------------------------)/4 7 1/4 GAMMA(-) B SQRT(p) 8 ..Which was correct /* ********************** Problem 8. *************** */ %Input is - 1 --- 1/2 1/2 2 - 2 A T - p T SPECINT(T %E %E , T) The result is A A --- A --- SQRT(A) 2 p --- 2 p SQRT(2) SQRT(%PI) ERF(-------) %E 2 p SQRT(%PI) %E SQRT(p) SQRT(2) %E (--------------- - ------------------------------------) SQRT(2) 2 ---------------------------------------------------------------------- SQRT(p) ..Which was correct /* ********************** Problem 9. *************** */ %Input is 2 - p T RADCAN(SPECINT(SIN(A T) COSH(B T ) %E , T)) The result is 2 2 2 p + 2 %I A p + A 2 %I A p + A - ------------------ ------------- 4 B 2 B %I p + A - SQRT(%PI) %E (%E ERF(---------) 2 SQRT(B) 2 2 A p + 2 %I A p --- ------------- 2 B %I p - A 2 B p + %I A - %E ERF(---------) + %I %E ERF(---------) 2 SQRT(B) 2 SQRT(B) 2 2 2 p %I A p p 2 %I A p + A --- ------ --- ------------- 2 B p - %I A B 2 B 2 B - %I %E ERF(---------) + (%I - %I %E ) %E - %E 2 SQRT(B) 2 A --- 2 B + %E )/(8 SQRT(B)) Using ratsimp ..Which was correct /* ********************** Problem 10. *************** */ %Input is 1/2 1/2 1/2 - p T SPECINT(T %J (2 A T ) %E , T) 1 The result is - A/p SQRT(A) %E --------------- 2 p ..Which was correct /* ********************** Problem 11. *************** */ %Input is 2 - p T SPECINT(T %J (A T) %E , T) 1 The result is 3 A -------------- 2 A 5/2 4 (-- + 1) p 2 p ..Which was correct /* ********************** Problem 12. *************** */ %Input is - p T SPECINT(T HSTRUVE (T) %E , T) 1 The result is 2 2 16 (2 p SQRT(p + 1) + 2 p ) ----------------------------------------- 3/2 4 2 2 9 %PI p (2 p SQRT(p + 1) + 2 p + 1) ..Which was correct /* ********************** Problem 13. *************** */ %Input is 3/2 1/2 - p T RADCAN(SPECINT(T HSTRUVE (T ) %E , T)) 1 The result is 1 1 - --- --- 4 p 4 p %E (SQRT(p) (140 p + 10) %E + SQRT(%PI) %I 2 %I %I (140 %I ERF(---------) p + 20 %I ERF(---------) p + 5 %I ERF(---------))) 2 SQRT(p) 2 SQRT(p) 2 SQRT(p) 4 /(8 %PI p ) Using ratsimp ..Which was correct /* ********************** Problem 14. *************** */ %Input is A T A T - p T SPECINT(T %IBES (---) %IBES (---) %E , T) 0 2 1 2 The result is A T A T %IBES (---) %IBES (---) 0 2 1 2 ----------------------- 2 p ..Which was correct /* ********************** Problem 15. *************** */ %Input is 3/4 - p T SPECINT(T %J (T) %J (T) %E , T) 1/2 1/4 The result is 1 1 2 %I (------------- - -------------) 2 %I 3/4 2 %I 3/4 (---- + 1) (1 - ----) p p ------------------------------------ 3/4 1 3/2 2 GAMMA(-) p 4 ..Which was correct /* ********************** Problem 16. *************** */ %Input is 5/2 2 1/2 - p T SPECINT(T %Y (T ) %E , T) 1/2 The result is %I 5/2 - 1/p 3 SQRT(%PI) %I ERF(-------) p %E SQRT(p) - 12 ((- ---------------------------------------- 8 %I 3/2 - 1/p SQRT(%PI) %I ERF(-------) p %E SQRT(p) - -------------------------------------- 2 %I - 1/p SQRT(%PI) %I ERF(-------) SQRT(p) %E 2 SQRT(p) 3 p p 2 - ----------------------------------------- - ---- - -)/p 2 4 2 %I 3/2 - 1/p SQRT(%PI) %I ERF(-------) p %E SQRT(p) + 2 (-------------------------------------- 4 %I - 1/p SQRT(%PI) %I ERF(-------) SQRT(p) %E SQRT(p) p + ----------------------------------------- + -)/p 2 2 %I - 1/p SQRT(%PI) %I ERF(-------) SQRT(p) %E SQRT(p) 4 - -----------------------------------------)/(%PI p ) 2 ..Which was correct /* ********************** Problem 17. *************** */ %Input is 1/2 2 1/2 - p T SPECINT(T %J (T ) %E , T) 1/2 The result is %I - 1/p %I ERF(-------) %E SQRT(p) - ----------------------- 3/2 SQRT(%PI) p ..Which was correct /* ********************** Problem 18. *************** */ %Input is 1/2 - p T SPECINT(T %IBES (T) %E , T) 1 The result is SQRT(%PI) %IBES (T) 1 ------------------- 3/2 2 p ..Which was correct /* ********************** Problem 19. *************** */ %Input is 1/2 - p T SPECINT(T %H (T ) %E , T) 2/3, 1 The result is 1 - --- 1 1 8 p 4 %I GAMMA(-) %M (- ---) %E 3 - 3/2, 1/3 4 p - ----------------------------------------- 5/6 2 3/2 3 (- 1) SQRT(3) GAMMA(-) p 3 1 - --- 1 1 8 p 4 GAMMA(-) %M (- ---) %E 3 - 3/2, 1/3 4 p + -------------------------------------- 5/6 2 3/2 3 (- 1) GAMMA(-) p 3 1 - --- 2 1 8 p 8 %I GAMMA(-) %M (- ---) %E 3 - 3/2, - 1/3 4 p - ------------------------------------------- 1/6 1 3/2 3 (- 1) SQRT(3) GAMMA(-) p 3 ..Which was correct /* ********************** Problem 20. *************** */ %Input is 1/2 - p T SPECINT(T %H (T) %E , T) 3/4, 2 The result is 1 1 1 3/8 9/4 5 %I GAMMA(-) %P (------------) (-- - 1) p 4 - 3/2, - 3/4 1 4 SQRT(-- + 1) p 2 p ----------------------------------------------------------- 1/4 2 3 18 (- 1) SQRT(2) GAMMA (-) 4 1 1 1 3/8 9/4 5 GAMMA(-) %P (------------) (-- - 1) p 4 - 3/2, - 3/4 1 4 SQRT(-- + 1) p 2 p + -------------------------------------------------------- 1/4 2 3 18 (- 1) SQRT(2) GAMMA (-) 4 3 1 3/4 4 %I GAMMA(-) %P (------------) p 4 - 3/2, 3/4 1 SQRT(-- + 1) 2 p + --------------------------------------------- 3/4 2 1 1 3/8 (- 1) GAMMA (-) (-- - 1) 4 4 p ..Which was correct /* ********************** Problem 21. *************** */ %Input is 3/2 - p T SPECINT(T %H (T) %E , T) 1/2, 1 The result is 1 1 SQRT(2) %I (------ - ------------) 1 1 2 2 -- + 1 (-- + 1) p 2 2 4 p p ------------------------------ - ---------------------------------- 1 2 3 2 SQRT(2) SQRT(%PI) (-- + 1) p SQRT(%PI) p 2 p ..Which was correct /* ********************** Problem 22. *************** */ %Input is 3/2 - T SPECINT(T %Y (A T) %E , T) 1 The result is 1 3/4 1 1 15 %I (------ - 1) (--------------------- + ---------------------) 2 2 3/2 2 3/2 A + 1 (SQRT(A + 1) + 1) (1 - SQRT(A + 1)) --------------------------------------------------------------------- 2 16 SQRT(A + 1) ..Which was correct /* ********************** Problem 23. *************** */ %Input is 2 - p T SPECINT(T %J (A T) %E , T) 1 The result is 3 A -------------- 2 A 5/2 4 (-- + 1) p 2 p ..Which was correct /* ********************** Problem 24. *************** */ %Input is 1/2 1/2 1/2 - p T SPECINT(T %J (2 A T ) %E , T) 1 The result is - A/p SQRT(A) %E --------------- 2 p ..Which was correct /* ********************** Problem 25. *************** */ %Input is 3/2 - p T SPECINT(T %M (T) %E , T) 1/2, 1 The result is 1 1 6 (--------- + --------------------) 1 1 1 2 1 - ----- (p + -) (1 - -----) 1 2 1 p + - p + - 2 2 ------------------------------------ 1 4 (p + -) 2 ..Which was correct /* ********************** Problem 26. *************** */ %Input is (ASSUME(p > A), TRUE) The result is TRUE ..Which was correct /* ********************** Problem 27. *************** */ %Input is A T 2 1/2 - p T SPECINT(%E T ERF(T ) %E , T) The result is 1 1 3 15 (--------------- - ---------------------- + -------------------------) 1 1 3/2 2 1 5/2 SQRT(----- + 1) (p - A) (----- + 1) 4 (p - A) (----- + 1) p - A p - A p - A ------------------------------------------------------------------------- 7/2 4 (p - A) ..Which was correct Congratulations: No differences! Error Summary: [BROKE, (QUOTE, rtest3), BROKE, (QUOTE, rtest4)] real time : 10.920 secs run time : 8.400 secs Maxima 5.5 Sun May 6 01:05:36 CDT 2001 (with enhancements by W. Schelter). Licensed under the GNU Public License (see file COPYING) (C1) date Sun May 6 01:10:33 CDT 2001 make[1]: Leaving directory `/home/wfs/cvs/maxima'