SB.IsSagbiOf |
Syntax |
SB.IsSagbiOf(Gens:LIST of POLY, Basis:LIST of POLY):BOOL |
Description |
Example |
Set Indentation; Use R::=QQ[x,y], DegLex; G:=[x^2-y^2,x^2y,x^2y^2-y^4,x^2y^4,y^6x^2y^6-y^8]; SBasis:=SB.Sagbi(G); SBasis; SB.IsSagbiOf(G,SBasis); ------------------------------------------------------- -- output: -- This SAGBI-basis generates the same subalgebra as the -- the polynomials of the set G [ x^2 - y^2, x^2y, x^2y^2 - y^4, x^2y^4, x^2y^12 - y^8, y^6, x^2y^6 - y^8, x^2y^16 + x^4y^8 - y^12, x^2y^10 - 3/8y^12, y^14 - y^8, y^14 - y^8] ------------------------------- TRUE ------------------------------- -- Done. ------------------------------- |
Example |
Set Indentation; Use R::=QQ[x,y], DegLex; G:=[x+y,xy]; SBasis:=SB.Sagbi(G); SBasis; SB.IsSagbiOf(G,SBasis); ------------------------------------------------------- -- output: -- This SAGBI-basis generates the same subalgebra as the -- the polynomials of the set G [ x + y, xy] ------------------------------- TRUE ------------------------------- -- Done. ------------------------------- |
Example |
Set Indentation; Use R::=QQ[x,y], DegLex; G:=[x+y,xy]; Basis:=[x^3+x^2y]; -- The polynomial y^3+x^2y is not a member of K[G]. -- Therefore it is impossible that the given Basis generates -- the same subalgebra. SB.IsSagbiOf(G,Basis); ------------------------------------------------------- -- output: FALSE ------------------------------- -- Done. ------------------------------- |
See Also |