- Abstract base class for modules
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- Finitely generated modules over a PID
- Elements of finitely generated modules over a PID
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- Finitely generated free graded left modules over connected graded algebras
- Elements of finitely generated free graded left modules
- Homomorphisms of finitely generated free graded left modules
- Homsets of finitely generated free graded left modules
- Finitely presented graded modules
- Elements of finitely presented graded modules
- Homomorphisms of finitely presented graded modules
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- Finitely presented graded modules over the Steenrod algebra
- Homomorphisms of finitely presented modules over the Steenrod algebra
- Discrete subgroups of\(\ZZ^n\)
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- Space of morphisms of vector spaces (linear transformations)
- Morphisms of vector spaces (linear transformations)
- Homspaces between free modules
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- Vectors with integer entries
- File: sage/modules/vector_integer_sparse.pyx (starting at line 1)
- Vectors with elements in\(\GF{2}\)
- Vectors with integer mod\(n\) entries, with small\(n\)
- File: sage/modules/vector_modn_sparse.pyx (starting at line 1)
- Vectors with rational entries
- File: sage/modules/vector_rational_sparse.pyx (starting at line 1)
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- Pickling for the old CDF vector class
- Pickling for the old RDF vector class
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Homsets of finitely generated free graded left modules¶
For an overview, see thefreegradedmodulesdocumentation.
EXAMPLES:
sage:fromsage.modules.fp_graded.free_moduleimportFreeGradedModulesage: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:homsetSet 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()
>>>fromsage.allimport*>>>fromsage.modules.fp_graded.free_moduleimportFreeGradedModule>>>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)>>>homsetSet 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 theoriginal software to Sage version 8.9.
Sverre Lunoee–Nielsen (2020-07-01): Refactored the code and addednew documentation and tests.
- classsage.modules.fp_graded.free_homspace.FreeGradedModuleHomspace(X,Y,category=None,base=None,check=True)[source]¶
Bases:
FPModuleHomspaceHomspace between two free graded modules.
- Element[source]¶
alias of
FreeGradedModuleMorphism