up previous next
normal reduction
NR(X: RINGELEM, L: LIST of RINGELEM): RINGELEM
NR(X: MODULEELEM, L: LIST of MODULEELEM): MODULEELEM 
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.
/**/ use R ::= QQ[x,y,z];
/**/ F := x^2*y +x*y^2 +y^2;
/**/ NR(F, [x*y1, y^21]);
x +y +1
// NOT YET IMPLEMENTED for MODULEELEM
