up previous next
multiplicity

the multiplicity (degree) of a ring or quotient object

Syntax
multiplicity(R:RING or TAGGED("Quotient")):INT

Description
This function computes the multiplicity (or degree) of M, i.e., the leading coefficient of the Hilbert polynomial multiplied by the factorial of the degree of the Hilbert polynomial. The weights of the indeterminates of the polynomial ring of M must all be 1. M can be a module or a quotient.

Example
/**/  Use R ::= QQ[t,x,y,z];
/**/  multiplicity(R/ideal(x,y,z)^5);
35

See Also