CoCoA:Multiplicity

Multiplicity

the multiplicity (degree) of a ring or quotient object

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 ::= Q[t,x,y,z];
  Multiplicity(R/Ideal(x,y,z)^5);
35
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Syntax

Multiplicity(R:RING or TAGGED(<quotes>Quotient</quotes>)):INT

Hilbert

HilbertSeries

HVector

Poincare

   <type>groebner</type>
   <type>groebner-basic</type>
   <type>hilbert</type>
   <type>quotient</type>
   <type>ring</type>