CoCoA:IsHomog

IsHomog

test whether given polynomials are homogeneous

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
------------------------------
  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
-------------------------------

Syntax

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

Deg

MDeg

Weights Modifier

   <type>boolean</type>
   <type>polynomial</type>