up previous next
NR

normal reduction
Syntax

NR(X:POLY,L:LIST of POLY):POLY
NR(X:VECTOR,L:LIST of VECTOR):VECTOR


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).

Example
Use R ::= Q[x,y,z];
F := x^2y+xy^2+y^2;
NR(F,[xy-1,y^2-1]);
x + y + 1
-------------------------------
V := Vector(x^2+y^2+z^2,xyz);
NR(V,[Vector(x,y),Vector(y,z),Vector(z,x)]);
Vector(z^2, z^3 - yz - z^2)
-------------------------------


See Also