CoCoA:GenRepr

GenRepr

representation in terms of generators

Description

This function returns a list giving a representation of X in terms of

generators for I. Let the generators for I be [G_1,...,G_t]. If X is

in I, then GenRepr will return a list [F_1,...,F_t] such that <verbatim>

            X = F_1*G_1 + ... + F_t*G_t.

</verbatim> If X is not in I, then GenRepr returns the empty list, [].

Example

  Use R ::= Q[x,y];
  I := Ideal(x+y^2,x^2-xy);
  GenRepr(x^3-x^2y-y^3-xy,I);
[-y, x]
-------------------------------
  -y I.Gens[1] + x I.Gens[2];
x^3 - x^2y - y^3 - xy
-------------------------------
  GenRepr(x+y,I);
[ ]
-------------------------------
  x+y IsIn I;  -- the empty list was returned above since x+y is not in I
FALSE
-------------------------------
  V1:= Vector(x,y,y^2); V2:= Vector(x-y,0,x^2);
  X := x^2 V1 - y^2 V2;
  M := Module(V1,V2);
  GenRepr(X,M);
[x^2, -y^2]
-------------------------------

Syntax

GenRepr(X:POLY,I:IDEAL):LIST of POLY
GenRepr(X:VECTOR,I:MODULE):LIST of POLY

DivAlg

IsIn

NF

   <type>ideal</type>
   <type>module</type>
   <type>polynomial</type>
   <type>vector</type>