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Multiplicity

Syntax

Multiplicity(R:RING or TAGGED("Quotient")):INT
    

Summary

the multiplicity (degree) of a ring or quotient object

Description

This function computes the multiplicity (or degree) of the ring R, 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 current ring must all be 1.

example

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