CoCoA:NF

NF

normal form

Description

The first function returns the normal form of F with respect to I.

It also computes a Groebner basis of I if that basis has not been

computed previously.

The second function returns the normal form of V with respect to M. It

also computes a Groebner basis of M if that basis has not been

computed previously.

The coefficient ring is assumed to be a field. Note that the

definition of normal form depends on the current value of the option

FullRed of the panel GROEBNER. If FullRed is FALSE it means that a polynomial is in normal form when its leading term with respect to the the current term ordering cannot be reduced. If FullRed is TRUE it means that a polynomial is in NF if and only if each monomial cannot be reduced.

Example

  Use R ::= Q[x,y,z];
  Set FullRed;
  I := Ideal(z);
  NF(x^2+xy+xz+y^2+yz+z^2,I);
x^2 + xy + y^2
-------------------------------
  UnSet FullRed;
  NF(x^2+xy+xz+y^2+yz+z^2,I);
x^2 + xy + y^2 + xz + yz + z^2
-------------------------------

Syntax

NF(F:POLY,I:IDEAL):POLY
NF(V:VECTOR,M:MODULE):VECTOR

DivAlg

FullRed

GenRepr

IsIn

NFsAreZero

NR

   <type>groebner</type>
   <type>groebner-basic</type>
   <type>ideal</type>
   <type>module</type>
   <type>polynomial</type>
   <type>vector</type>