codim(QuotientRing) -- compute the codimension

Synopsis

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