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Macaulay2Doc :: presentation(Module)

presentation(Module) -- presentation of a module

Synopsis

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

See also