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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 ::= Q[x,y];
IsHomog(x^2-xy);
TRUE
-------------------------------
IsHomog(x-y^2);
FALSE
-------------------------------
IsHomog([x^2-xy,x-y^2]);
FALSE
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Use R ::= Q[x,y],Weights(Mat([[2,3],[1,2]]));
IsHomog(x^3y^2+y^4);
TRUE
-------------------------------
Use R ::= Q[x,y];
IsHomog(Ideal(x^2+y,y));
TRUE
------------------------------- 


See Also