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5.1.55 homog

Syntax:
homog ( ideal_expression )
homog ( module_expression )
Type:
int
Purpose:
tests for homogeneity: returns 1 for homogeneous input, 0 otherwise.
Note:
If the current ring has a weighted monomial ordering, homog tests for weighted homogeneity w.r.t. the given weights.
Syntax:

homog ( polynomial_expression, ring_variable )
homog ( vector_expression, ring_variable )
homog ( ideal_expression, ring_variable )
homog ( module_expression, ring_variable )
Type:
same as first argument
Purpose:
homogenizes polynomials, vectors, ideals, or modules by multiplying each monomial with a suitable power of the given ring variable.
Note:
If the current ring has a weighted monomial ordering, homog computes the weighted homogenization w.r.t. the given weights.
The homogenizing variable must have weight 1.
Example:
 
  ring r=32003,(x,y,z),ds;
  poly s1=x3y2+x5y+3y9;
  poly s2=x2y2z2+3z8;
  poly s3=5x4y2+4xy5+2x2y2z3+y7+11x10;
  ideal i=s1,s2,s3;
  homog(s2,z);
==> x2y2z4+3z8
  homog(i,z);
==> _[1]=3y9+x5yz3+x3y2z4
==> _[2]=x2y2z4+3z8
==> _[3]=11x10+y7z3+5x4y2z4+4xy5z4+2x2y2z6
  homog(i);
==> 0
  homog(homog(i,z));
==> 1
See ideal; module; poly; vector.