CoCoA:NR

NR

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 <ttref>DivAlg</ttref>. 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 <ttref>GenRepr</ttref> or <ttref>NF</ttref> 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)
-------------------------------

Syntax

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

DivAlg

GenRepr

NF

   <type>polynomial</type>
   <type>vector</type>