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interreduce a list of polynomials
interreduced(L: LIST of RINGELEM): LIST of RINGELEM
This function returns an interreduced list
i.e. each polynomial in
is fully reduced with respect to the others,
generate the same ideal.
This is generally computed in several interreducing loops.
In each loop each polynomial in the list is fully reduced with respect
to the others, and this process terminates when a loop finds no
Verbosity shows how many loops are performed.
/**/ use QQ[x,y,z];
/**/ L := [x^3-x*y^2+y*z, x*y, z];
[z, x*y, x^3]
/**/ L; -- unmodified
[x^3 -x*y^2 +y*z, x*y, z]
/**/ L := [x^3*y^3 -y, x^3*y^2 +x, x^3*y +y^2];
interreduced: loop n.1
interreduced: loop n.2
interreduced: loop n.3
interreduced: loop n.4
interreduced: loop n.5