Package sagbi/SB.Interreduced

This article is about a function from ApCoCoA-2.

SB.Interreduced

This function is the same as the CoCoA function interreduced, just with Subalgebra reduction instead of Gröbner reduction.

Syntax

SB.Interreduced(L: LIST of POLY): LIST of POLY

Description

This function takes a list L and returns a list L' such that K[L] = K[L'], but L' is Subalgebra interreduced, i.e. no term appearing in the support of one of the polynomials in L is a product of terms appearing as leading terms of the other polynomials in L'.

• @param L A list of polynomials

• @return An interreduced list of polynomials

Example

Use QQ[x,y,z], DegRevLex;
L := [x^2*z^2 +x*y*z^2 +y^2*z^2,  x,  x*z,  y*z^2];
SB.Interreduced(L);
-- [x,  x*z,  y*z^2,  y^2*z^2]

Example

Use QQ[x,y,z], DegRevLex;
L := [x +y +z,  x*y +x*z +y*z,  x*y*z];
SB.Interreduced(L) = L;
-- true
-- Hence L is a SAGBI basis of QQ[L]

See also

Package sagbi/SB.SDA

Package sagbi/SB.ReductionStep