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IsHomog

test whether given polynomials are homogeneous

Syntax
IsHomog(F:POLY or VECTOR):BOOL
IsHomog(L:LIST):BOOL
IsHomog(I:IDEAL or MODULE):BOOL

Description
The first form of this function returns True if F is homogeneous. The second form returns True if every element of L is homogeneous. Otherwise, they return False. The third form returns True if the ideal/module can be generated by homogeneous elements, and False if not. Homogeneity is with respect to the first row of the weights matrix.

Example
/**/  Use R ::= QQ[x,y];
/**/  IsHomog(x^2-x*y);
true

/**/  IsHomog(x-y^2);
false

/**/  IsHomog([x^2-x*y, x-y^2]);
false

/**/  R := NewPolyRing(QQ, ["x","y"], Mat([[2,3],[1,2]]), 1);
/**/  Use R;
/**/  IsHomog(***x^3y^2+y^4***);
true

/**/  R := NewPolyRing(QQ, ["x","y"], Mat([[2,3],[1,2]]), 2);
/**/  Use R;
/**/  IsHomog(***x^3y^2+y^4***);
false

/**/  Use R ::= QQ[x,y];
/**/  IsHomog(Ideal(x^2+y,y));
true

See Also