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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
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