5.1.57 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 ( ideal_expression, intvec_expression )

Type:

int

Purpose:

tests for homogeneity wrt. the given weight vector: returns 1 for homogeneous input, 0 otherwise.

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