up previous next
interreduce, interreduced

interreduce a list of polynomials

interreduce(ref L: LIST of RINGELEM)
interreduced(L: LIST of RINGELEM): LIST of RINGELEM

These functions reduce each polynomial using the other polynomials as reduction rules. The process terminates when each is in normal form with respect to the others. The function interreduce takes a variable containing a list and overwrites that variable with the interreduced list. The second returns an interreduced list without affecting its arguments.

/**/  use QQ[x,y,z];

/**/  L := [x^3-x*y^2+y*z, x*y, z];
/**/  interreduce(ref L);
/**/  L;
[x*y, z, x^3]

/**/  SetVerbosityLevel(90);
/**/  interreduced([x^3-x*y^2+y*z, x^3+x*y, z]);
interreduced: round n.1
interreduced: round n.2
[z,  -x*y^2 -x*y,  x^3 +x*y]