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NR

normal reduction

Syntax
NR(X: RINGELEM, L: LIST of RINGELEM): RINGELEM
NR(X: MODULEELEM, L: LIST of MODULEELEM): MODULEELEM

Description
This function returns the normal remainder of X with respect to L, i.e., it returns the remainder from the division algorithm. To get both the quotients and the remainder, use DivAlg .

Note that if the list does not form a Groebner basis, the remainder may not be zero even if X is in the ideal or module generated by L (use GenRepr or NF instead).

Currently (v 5.0.3) the internal code for computing NF(F, I) and NR(F, GBasis(I)) is identical, but the second is slower just for the overhead in interpreting a possibly long list of polynomials.

Example
/**/  Use R ::= QQ[x,y,z];
/**/  F := x^2*y +x*y^2 +y^2;
/**/  NR(F, [x*y-1, y^2-1]);
x +y +1

// NOT YET IMPLEMENTED for MODULEELEM

See Also