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Merge pull request #75 from cdwensley/actions
added operations for a module as an algebra
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,73 @@ | ||
| ############################################################################ | ||
| ## | ||
| #W module3.g XModAlg example files Chris Wensley | ||
| ## | ||
|
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||
| LoadPackage( "xmodalg" ); | ||
|
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| ## Chapter 2, Section 2.2.3 | ||
| m := [ [0,1,0], [0,0,1], [1,0,0] ]; | ||
| Print( "m = ", m, "\n" ); | ||
| A3 := Algebra( Rationals, [m] ); | ||
| SetName( A3, "A3" );; | ||
| V3 := Rationals^3;; | ||
| M3 := LeftAlgebraModule( A3, \*, V3 ); | ||
| SetName( M3, "M3" ); | ||
| famM3 := ElementsFamily( FamilyObj( M3 ) );; | ||
| v := [3,4,5];; | ||
| v2 := ObjByExtRep( famM3, v ); | ||
| Print( "v = ", v, ", v2 = ", v2, "\n" ); | ||
| Print( "m*v2 = ", m*v2, "\n" ); | ||
| genM3 := GeneratorsOfLeftModule( M3 );; | ||
| u2 := 6*genM3[1] + 7*genM3[2] + 8*genM3[3]; | ||
| u := ExtRepOfObj( u2 ); | ||
| Print( "u2 = ", u2, ", u = ", u, "\n" ); | ||
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| ## Chapter 2, Section 2.2.4 | ||
| D3 := LeftActingDomain( M3 );; | ||
| T3 := EmptySCTable( Dimension(M3), Zero(D3), "symmetric" );; | ||
| B3a := AlgebraByStructureConstants( D3, T3 ); | ||
| Print( "B3a = ", B3a, "\n" ); | ||
| Print( "B3a has generators: ", GeneratorsOfAlgebra( B3a ), "\n" ); | ||
| B3 := ModuleAsAlgebra( M3 ); | ||
| Print( "B3 has name: ", Name( B3 ), "\n" ); | ||
| Print( "B3 has generators: ", GeneratorsOfAlgebra( B3 ), "\n" ); | ||
|
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||
| ## Chapter 2, Section 2.2.5 | ||
| Print( "IsModuleAsAlgebra( B3 )? ", IsModuleAsAlgebra( B3 ), "\n" ); | ||
| Print( "IsModuleAsAlgebra( A3 )? ", IsModuleAsAlgebra( A3 ), "\n" ); | ||
|
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| ## Chapter 2, Section 2.2.6 | ||
| Print( "the known attributes of B3 are:\n" ); | ||
| Print( KnownAttributesOfObject( B3 ), "\n" ); | ||
| M2B3 := ModuleToAlgebraIsomorphism( B3 ); | ||
| Print( "M2B3 = ", M2B3, "\n" ); | ||
| Print( "Source( M2B3 ) = M3? ", Source( M2B3 ) = M3, "\n" ); | ||
| Print( "Source( M2B3 ) = V3? ", Source( M2B3 ) = V3, "\n" ); | ||
| B2M3 := AlgebraToModuleIsomorphism( B3 ); | ||
| Print( "B2M3 = ", B2M3, "\n" ); | ||
| Print( "Range( B2M3 ) = M3? ", Range( B2M3 ) = M3, "\n" ); | ||
| Print( "Range( B2M3 ) = V3? ", Range( B2M3 ) = V3, "\n" ); | ||
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| ## Chapter 2, Section 2.2.7 | ||
| act3 := AlgebraActionByModule( A3, M3 ); | ||
| Print( "the action act3 of A3 on B3 is:\n", act3, "\n" ); | ||
| a := 2*m + 3*m^2; | ||
| Print( "a = ", a, ":\n" ); | ||
| Print( "the image of a under act3 is:\n", Image( act3, a ), "\n" ); | ||
| Print( "the image of the action act3 is:\n", Image( act3 ), "\n" ); | ||
| Print( "\n" ); | ||
|
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| ## Chapter 4, Section 4.1.7 | ||
| X3 := XModAlgebraByModule( A3, M3 ); | ||
| Print( "Name( X3 ) = ", Name( X3 ), "\n" ); | ||
| Display( X3 ); | ||
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| ## Chapter 5, Section 5.1.1 | ||
| C3 := Cat1AlgebraOfXModAlgebra( X3 ); | ||
| Print( "Name( C3 ) = ", Name( C3 ), "\n" ); | ||
| Display( C3 ); | ||
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| ############################################################################ | ||
| ## | ||
| #E module3.g . . . . . . . . . . . . . . . . . . . . . . . . . . ends here |
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