# presentation(Module) -- presentation of a module

## Synopsis

• Function: presentation
• Usage:
presentation M
• Inputs:
• M,
• Outputs:
• , a presentation matrix of M

## Description

A presentation of M is a map p so that coker p is isomorphic to M. The presentation obtained is expressed in terms of the given generators, i.e., the modules cover M and target p are identical. The isomorphism can be obtained as map(M,coker p,1).

Since a module M may be described as a submodule or a subquotient module of a free module, some computation may be required to produce a presentation. See also trim, or minimalPresentation, which do a bit more work to try to eliminate redundant generators.

 i1 : R = QQ[a,b,c]; i2 : I = ideal"a2-b2,abc" 2 2 o2 = ideal (a - b , a*b*c) o2 : Ideal of R i3 : M = I/(I^2+a*I) o3 = subquotient (| a2-b2 abc |, | a4-2a2b2+b4 a3bc-ab3c a2b2c2 a3-ab2 a2bc |) 1 o3 : R-module, subquotient of R i4 : presentation M o4 = {2} | a b2 0 0 | {3} | 0 0 a b2 | 2 4 o4 : Matrix R <--- R