up
previous
next
NR
Syntax
NR(X:POLY,L:LIST of POLY):POLY
NR(X:VECTOR,L:LIST of VECTOR):VECTOR
Summary
normal reduction
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