5.1.15 degree

Syntax:

degree ( ideal_expression )
degree ( module_expression )

Type:

int

Purpose:

computes the (weighted) degree of the projective variety, respectively sheaf over the projective variety, defined by the ideal, respectively module, generated by the leading monomials of the input. This is equal to the (weighted) degree of the projective variety, respectively sheaf over the projective variety, defined by the ideal, respectively module, if the input is a standard basis with respect to a (weighted) degree ordering.

Example:

ring r3=32003,(x,y,z,h),dp; int a,b,c,t=11,10,3,1; poly f=x^a+y^b+z^(3*c)+x^(c+2)*y^(c-1)+x^(c-1)*y^(c-1)*z3 +x^(c-2)*y^c*(y2+t*x)^2; ideal i=jacob(f); i=homog(i,h); ideal i0=std(i); degree(i0); → 720

See dim; ideal; mult; std; vdim.