codim Module -- calculate the codimension

codim Module -- calculate the codimension

Synopsis:

Usage: c = codim M

Function: codim -- calculate the codimension

Input:

M, an instance of class Module: A module over a ring R.

Output:

c, an instance of class ZZ: The number dim R - dim M.

The returned value is the usual codimension if R is an integral domain, or all components have the same dimension.

i1 : R = ZZ/101[a..d];

i2 : M = coker matrix{{a,b},{c,d}}



o2 = cokernel | a b |

              | c d |



                            2

o2 : R-module, quotient of R

i3 : codim M



o3 = 1

Caveat:

If R is ZZ, then the computation effectively tensors first with the rational numbers, yielding the wrong answers in some cases.R must be a quotient of a commutative polynomial ring.