### 5.1.52 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.

User manual for Singular version 4-0-3, 2016, generated by texi2html.