|This article is about a function from ApCoCoA-2.|
This function is the same as the CoCoA function interreduced, just with Subalgebra reduction instead of Gröbner reduction.
SB.Interreduced(L: LIST of POLY): LIST of POLY
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
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]
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]