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5.1.18 degree
Syntax:
degree ( ideal_expression )
degree ( module_expression )
Type:
- string
Purpose:
- computes the (Krull) dimension and the multiplicity of the
ideal, resp. module, generated by the leading monomials of the input
and prints it. This is equal to the dimension and
multiplicity of the ideal, resp. module, if the input is a standard
basis with respect to a degree ordering.
Example:
| | ring r3=32003,(x,y,z),ds;
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);
ideal i0=std(i);
degree(i0);
==> // dimension (local) = 0
==> // multiplicity = 314
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See
dim;
ideal;
mult;
std;
vdim.
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