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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
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See
ideal;
module;
poly;
vector.
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