dp_gr_main, dp_gr_mod_main

dp_gr_main(plist,vlist,homo,modular,order)

dp_gr_mod_main(plist,vlist,homo,modular,order)

:: Groebner basis computation (built-in functions)

return

list

plist, vlist

list

order

number, list or matrix

homo

flag

modular

flag or prime

• These functions are fundamental built-in functions for Groebner basis computation and gr(),hgr() and gr_mod() are all interfaces to these functions.
• If homo is not equal to 0, homogenization is applied before entering Buchberger algorithm
• For dp_gr_mod_main(), modular means a computation over GF(modular). For dp_gr_main(), modular has the following mean.
  1. If modular is 1 , trace lifting is used. Primes for trace lifting are generated by lprime(), starting from lprime(0), until the computation succeeds.
  2. If modular is an integer greater than 1, the integer is regarded as a prime and trace lifting is executed by using the prime. If the computation fails then 0 is returned.
  3. If modular is negative, the above rule is applied for -modular but the Groebner basis check and ideal-membership check are omitted in the last stage of trace lifting.
• gr(P,V,O), hgr(P,V,O) and gr_mod(P,V,O,M) execute dp_gr_main(P,V,0,1,O), dp_gr_main(P,V,1,1,O) and dp_gr_mod_main(P,V,0,M,O) respectively.
• Actual computation is controlled by various parameters set by dp_gr_flags(), other then by homo and modular.

References

section dp_ord, section dp_gr_flags, dp_gr_print, section gr, hgr, gr_mod, dgr, section Controlling Groebner basis computations

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