Homsets of finitely generated free graded left modules - Modules

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# Homsets of finitely generated free graded left modules

For an overview, see the `free graded modules documentation`.

EXAMPLES:

Sage

    sage: from sage.modules.fp_graded.free_module import FreeGradedModule
    sage: A = SteenrodAlgebra(2)
    sage: F1 = FreeGradedModule(A, (1,3), names='g')
    sage: F2 = FreeGradedModule(A, (2,3), names='h')
    sage: homset = Hom(F1, F2)
    sage: homset
    Set of Morphisms from Free graded left module on 2 generators ...
    sage: homset([F2((Sq(1), 1)), F2((0, Sq(2)))])
    Module morphism:
      From: Free graded left module on 2 generators over mod 2 Steenrod algebra, milnor basis
      To:   Free graded left module on 2 generators over mod 2 Steenrod algebra, milnor basis
      Defn: g[1] |--> Sq(1)*h[2] + h[3]
            g[3] |--> Sq(2)*h[3]
    sage: TestSuite(homset).run()

Python

    >>> from sage.all import *
    >>> from sage.modules.fp_graded.free_module import FreeGradedModule
    >>> A = SteenrodAlgebra(Integer(2))
    >>> F1 = FreeGradedModule(A, (Integer(1),Integer(3)), names='g')
    >>> F2 = FreeGradedModule(A, (Integer(2),Integer(3)), names='h')
    >>> homset = Hom(F1, F2)
    >>> homset
    Set of Morphisms from Free graded left module on 2 generators ...
    >>> homset([F2((Sq(Integer(1)), Integer(1))), F2((Integer(0), Sq(Integer(2))))])
    Module morphism:
      From: Free graded left module on 2 generators over mod 2 Steenrod algebra, milnor basis
      To:   Free graded left module on 2 generators over mod 2 Steenrod algebra, milnor basis
      Defn: g[1] |--> Sq(1)*h[2] + h[3]
            g[3] |--> Sq(2)*h[3]
    >>> TestSuite(homset).run()

AUTHORS:

- Robert R. Bruner, Michael J. Catanzaro (2012): Initial version.

- Sverre Lunoee–Nielsen and Koen van Woerden (2019-11-29): Updated the original software to Sage version 8.9.

- Sverre Lunoee–Nielsen (2020-07-01): Refactored the code and added new documentation and tests.

class sage.modules.fp_graded.free_homspace.FreeGradedModuleHomspace(X, Y, category=None, base=None, check=True)

  Bases: `FPModuleHomspace`

  Homspace between two free graded modules.

  Element

    alias of `FreeGradedModuleMorphism`