ApCoCoA-1:Weyl.WRedGB
From ApCoCoAWiki
| This article is about a function from ApCoCoA-1. |
Weyl.WRedGB
Computes reduced Groebner basis of a D-ideal in Weyl algebra A_n.
Syntax
Weyl.WRedGB(GB:LIST):LIST
Description
This function converts Groebner basis GB computed by ApCoCoAServer into the reduced Groebner Basis. If GB is not a Groebner basis then the output will not be the reduced Groebner basis. In fact, this function reduces a list GB of Weyl polynomials using Weyl.WNR into a new list L such that Ideal(L) = Ideal(GB).
Note: This function is faster than Weyl.WRGB for a list GB of large size.
@param GB Groebner Basis of an ideal in the Weyl algebra.
@result The reduced Groebner Basis of the given ideal.
Example
A1::=QQ[x,d]; --Define appropriate ring Use A1; L:=[x,d,1]; Weyl.WRedGB(L); [1] ------------------------------- -- Done. -------------------------------
Example
A2::=ZZ/(7)[x[1..2],y[1..2]]; -- define appropriate ring Use A2; I:=Ideal(2x[1]^14y[1]^7,x[1]^2y[1]^3+x[1]^2-1,y[2]^7-1,x[2]^3y[2]^2-x[2]y[2]-3x[2]-1); GbI:=Weyl.WGB(I,0);Len(GbI); ------------------------------- -- CoCoAServer: computing Cpu Time = 0.485 ------------------------------- 42 -- size of complete GB of the ideal I ------------------------------- Time GbI:=Weyl.WRedGB(GbI); Cpu time = 10.89, User time = 11 ------------------------------- 11 -- GbI is now reduced Groebner Basis of the ideal I. ------------------------------- -- Done. -------------------------------
See also
Introduction to Groebner Basis in CoCoA
