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formation -- recover the methods used to make a module

Synopsis

Description

If the module was created as a direct sum, tensor product, of Hom-module, then the expression will reflect that. In each case, the result is a function application, and the sequence of arguments is easily obtained.

i1 : M = ZZ^2 ++ ZZ^3

       5
o1 = ZZ

o1 : ZZ-module, free
 
i2 : t = formation M

                  2    3
o2 = directSum (ZZ , ZZ )

o2 : Expression of class FunctionApplication
 
i3 : peek t

                                       2    3
o3 = FunctionApplication{directSum, (ZZ , ZZ )}
 
i4 : t#1

        2    3
o4 = (ZZ , ZZ )

o4 : Sequence
 
i5 : value t

       5
o5 = ZZ

o5 : ZZ-module, free
 
i6 : M = directSum(ZZ^2, ZZ^3, ZZ^4)

       9
o6 = ZZ

o6 : ZZ-module, free
 
i7 : t = formation M

                  2    3    4
o7 = directSum (ZZ , ZZ , ZZ )

o7 : Expression of class FunctionApplication
 
i8 : t#1

        2    3    4
o8 = (ZZ , ZZ , ZZ )

o8 : Sequence
 
i9 : M = ZZ^2 ** ZZ^3

       6
o9 = ZZ

o9 : ZZ-module, free
 
i10 : t = formation M

                2    3
o10 = tensor (ZZ , ZZ )

o10 : Expression of class FunctionApplication
 
i11 : t#1

         2    3
o11 = (ZZ , ZZ )

o11 : Sequence

If the module was not obtained that way, then null is returned.

i12 : formation ZZ^6

The same remarks apply to certain other types of objects, such as chain complexes.

i13 : R = QQ[x,y];
 
i14 : C = res coker vars R;
 
i15 : D = C ++ C

       2      4      2
o15 = R  <-- R  <-- R  <-- 0
                            
      0      1      2      3

o15 : ChainComplex
 
i16 : formation D

                  1      2      1         1      2      1
o16 = directSum (R  <-- R  <-- R  <-- 0, R  <-- R  <-- R  <-- 0)
                                                               
                 0      1      2      3  0      1      2      3

o16 : Expression of class FunctionApplication

See also

Ways to use formation :

For the programmer

The object formation is a method function.