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codim(QuotientRing) -- compute the codimension

Synopsis

Function: codim
Usage:

codim R
Inputs:
- R, a quotient ring
Optional inputs:
- Generic => ..., default value false,
Outputs:
- an integer, the codimension of R

Description

Computes the codimension of the presentation ideal of R over its ambient polynomial ring.

i1 : R = QQ[x,y]/(ideal(x,y) * ideal(x-1))

o1 = R

o1 : QuotientRing

i2 : codim R

o2 = 1

However, the following may not be the expected result.

i3 : R = QQ[x,y]/(ideal(x,y) * ideal(x-1))

o3 = R

o3 : QuotientRing

i4 : codim R

o4 = 1

i5 : codim (R/x)

o5 = 2

See also

dim(QuotientRing) -- compute the Krull dimension

Ways to use this method:

codim(PolynomialRing)
codim(QuotientRing) -- compute the codimension