D.2.4.4 is_homog

Procedure from library poly.lib (see poly_lib).

Usage:

is_homog(id); id poly/ideal/vector/module/matrix

Return:

integer which is 1 if input is homogeneous (resp. weighted homogeneous if the monomial ordering consists of one block of type ws,Ws,wp or Wp, assuming that all weights are positive) and 0 otherwise

Note:

A vector is homogeneous, if the components are homogeneous of same degree, a module/matrix is homogeneous if all column vectors are homogeneous
//*** ergaenzen, wenn Matrizen-Spalten Gewichte haben

Example:

LIB "poly.lib";
ring r = 0,(x,y,z),wp(1,2,3);
is_homog(x5-yz+y3);
→ 0
ideal i = x6+y3+z2, x9-z3;
is_homog(i);
→ 1
ring s = 0,(a,b,c),ds;
vector v = [a2,0,ac+bc];
vector w = [a3,b3,c4];
is_homog(v);
→ 1
is_homog(w);
→ 0