CoCoA:NFsAreZero

NFsAreZero

test if normal forms are zero

Description

This function returns TRUE if each component of L

has normal form 0 with respect to M, i.e., if each component is an

element of M. Otherwise, it returns FALSE. The coefficient ring is assumed to be a field.

Example

  Use S ::= Q[t,x,y,z];
  I := Ideal(t^31-t^6-x, t^8-y, t^10-z);
  F := y^5-z^4;
  G := (t^8-y)(3F+t^10-z);
  NFsAreZero([F,G],I);   -- F and G are in I
TRUE
-------------------------------
  NFsAreZero([F,x,G],I); -- x is not in I
FALSE
-------------------------------

Syntax

NFsAreZero(L:LIST of POLY,M IDEAL):BOOL
NFsAreZero(L:LIST of VECTOR,M:MODULE):BOOL

IsIn

NF

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