CASA Function: homogeneousForm

Collects the terms of a polynomial of a certain degree.

Calling Sequence:

• f := homogeneousForm(poly,vars,degree)

Parameters:

poly : polynom(anything,vars)

• A polynomial in the variables vars over some coefficient domain.

vars : list(name)

• A list of variable names.

degree : integer

• The degree of the terms that should be collected from the polynomial

Result:

p : homogeneousPolynom(vars)

• A homogeneous polynom over the same coefficient domain as poly in the variables vars of degree degree.

Description:

• homogeneousForm(poly,vars,degree) collects the terms of degree degree and returns the form (a homogeneous polynomial) that is built from that terms
• The sum over all homogeneous forms from degree 0 to the degree of poly in vars, should give poly.

Examples:

> f := x^2+3*x*y+y;

> f2:=homogeneousForm(f,[x,y],2);

> f1:=homogeneousForm(f,[x,y],1);

> f0:=homogeneousForm(f,[x,y],0);

> evalb(f = f2+f1+f0);

See Also: