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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[xyz];
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