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degree(Module)

Synopsis

Description

We assume that M is a graded module over a singly graded polynomal ring or a quotient of a polynomial ring, over a field k.

If M is finite dimensional over k, the degree of M is its dimension over k. Otherwise, the degree of M is the integer d such that the hilbert polynomial of M has the form z |--> d z^e/e! + lower terms in z.

i1 : R = ZZ/101[x,y,z];
i2 : degree cokernel symmetricPower ( 2, vars R )

o2 = 4

Caveat

The degree in multigraded rings is not defined. If the base ring is ZZ, it is likely that the answer is not what you would expect. Similarly, if the degrees of the variables are not all one, the answer is harder to interpret.

See also