End -- module of endomorphisms

Synopsis

Usage:

End M
Inputs:
- M, a ring, an ideal, a module, or a chain complex,
Optional inputs:
- DegreeLimit => an integer or a list, default value null, see Hom(...,DegreeLimit=>...)
- MinimalGenerators => a Boolean value, default value true, see Hom(...,MinimalGenerators=>...)
- Strategy => a thing, default value null, see Hom(...,Strategy=>...)

Description

Constructs the module of endomorphisms of $M$.

i1 : R = QQ[a,b,c];

i2 : M = coker koszul_2 vars R

o2 = cokernel {1} | -b -c 0  |
              {1} | a  0  -c |
              {1} | 0  a  b  |

                            3
o2 : R-module, quotient of R

i3 : End M

o3 = subquotient (| 1 |, | -b 0  -c 0  0  0  0  0  0  |)
                  | 0 |  | a  -c 0  0  0  0  0  0  0  |
                  | 0 |  | 0  b  a  0  0  0  0  0  0  |
                  | 0 |  | 0  0  0  -b 0  -c 0  0  0  |
                  | 1 |  | 0  0  0  a  -c 0  0  0  0  |
                  | 0 |  | 0  0  0  0  b  a  0  0  0  |
                  | 0 |  | 0  0  0  0  0  0  -b 0  -c |
                  | 0 |  | 0  0  0  0  0  0  a  -c 0  |
                  | 1 |  | 0  0  0  0  0  0  0  b  a  |

                               9
o3 : R-module, subquotient of R

Code

../../../../../Macaulay2/m2/option.m2:15:14-18:8: --source code:
  (opts,f) -> args -> (
       -- Common code for functions created with >> to process options and arguments.
       uncurry(f, override (opts,args))
       )
| symbol  class            value                                                    location of symbol
| ------  -----            -----                                                    ------------------                             
| f       FunctionClosure  FunctionClosure[../../../../../Macaulay2/m2/Hom.m2:15:.  ../../../../../Macaulay2/m2/option.m2:15:8-15:9
| opts    OptionTable      OptionTable{DegreeLimit => null      }                   ../../../../../Macaulay2/m2/option.m2:15:3-15:7
|                                      MinimalGenerators => true                    
|                                      Strategy => null                             
| -- function f:
| ../../../../../Macaulay2/m2/Hom.m2:15:21-15:43: --source code:
| End = options Hom >> o -> M -> Hom(M, M, o)
| -- option table opts:
| OptionTable{DegreeLimit => null      }
|             MinimalGenerators => true
|             Strategy => null

For the programmer

The object End is a function closure.