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

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

If X is not in I, then 'GenRepr' returns the empty list, [].

Example

Use R ::= Q[xy];
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
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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]
-------------------------------
See also: