next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
Macaulay2Doc :: dim(Ring)

dim(Ring) -- compute the Krull dimension

Synopsis

Description

Computes the Krull dimension of the given ring.

The singular locus of a cuspidal plane curve

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing
i2 : I =ideal(y^2*z-x^3)

              3    2
o2 = ideal(- x  + y z)

o2 : Ideal of R
i3 : sing = singularLocus(R/I)

o3 = sing

o3 : QuotientRing
i4 : dim sing

o4 = 1
The exterior algebra is artinian:
i5 : R = ZZ/101[a,b,SkewCommutative => true]

o5 = R

o5 : PolynomialRing, 2 skew commutative variables
i6 : dim R

o6 = 0
The Weyl algebra in 2 variables:
i7 : R = ZZ/101[x,dx,y,dy,WeylAlgebra => {x=>dx, y=>dy}];
i8 : dim R

o8 = 4

See also