diff --git a/CHANGES.md b/CHANGES.md index 1d05321..038fdc7 100644 --- a/CHANGES.md +++ b/CHANGES.md @@ -1,5 +1,9 @@ # CHANGES to the 'XModAlg' package +## 1.32 -> 1.33 (27/08/25) + * (27/08/25) added installation instructions to the manual introduction + replaced \mathcal by \mathbb which suits MathJax better + ## 1.27 -> 1.32 (11/04/25) * (31/01/25) added Nizar Shammu's thesis to the list of references; removed all operations involving direct sums of crossed modules diff --git a/README.md b/README.md index 44c1fec..0e7a9ef 100644 --- a/README.md +++ b/README.md @@ -9,14 +9,12 @@ This package allows for computation with crossed modules of commutative algebras ## Distribution - * The 'XModAlg' package is distributed with the deposited GAP packages, see: - - * It will, in due course, be available from the GitHub repository at: +The 'XModAlg' package may be obtained from the GitHub repository at: ## Copyright -The 'XModAlg' package is Copyright © Zekeriya Arvasi and Alper Odabas et al, 2014--2025. +The 'XModAlg' package is Copyright Zekeriya Arvasi and Alper Odabas et al, 2014--2025. 'XModAlg' is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by @@ -34,6 +32,7 @@ For details, see . true ``` * The file `manual.pdf` is in the `doc` subdirectory. + * To run the test file read `testall.g` from the `tst` subdirectory. ## Contact diff --git a/doc/cat1.xml b/doc/cat1.xml index 92b213c..dbb0e38 100644 --- a/doc/cat1.xml +++ b/doc/cat1.xml @@ -58,7 +58,7 @@ If the conditions, \mathbf{Cat1Alg2:} \quad (\ker t)(\ker h) = \{0_{A}\} are satisfied, then the algebraic system -\mathcal{C} := (e;t,h : A \rightarrow R) +\mathbb{C} := (e;t,h : A \rightarrow R) is called a cat^{1}-algebra. A system which satisfies the condition \mathbf{Cat1Alg1} is called a precat^{1}-algebra. @@ -292,7 +292,7 @@ Cat1-algebra [GF(2^2)_c6=>..] :- -Let \mathcal{C} = (e;t,h:A\rightarrow R) +Let \mathbb{C} = (e;t,h:A\rightarrow R) be a cat^{1}-algebra, and let A^{\prime}, R^{\prime} be subalgebras of A and R respectively. If the restriction morphisms @@ -305,14 +305,14 @@ e^{\prime} = e|_{R^{\prime}} : R^{\prime}\rightarrow A^{\prime} satisfy the \mathbf{Cat1Alg1} and \mathbf{Cat1Alg2} conditions, then the system -\mathcal{C}^{\prime } = (e^{\prime};t^{\prime},h^{\prime} +\mathbb{C}^{\prime } = (e^{\prime};t^{\prime},h^{\prime} : A^{\prime} \rightarrow R^{\prime}) is called a subcat^{1}-algebra of -\mathcal{C} = (e;t,h:A\rightarrow R). +\mathbb{C} = (e;t,h:A\rightarrow R).

If the morphisms satisfy only the \mathbf{Cat1Alg1} condition -then \mathcal{C}^{\prime } is called a -sub-precat^{1}-algebra of \mathcal{C}. +then \mathbb{C}^{\prime } is called a +sub-precat^{1}-algebra of \mathbb{C}.

The operations in this subsection are used for constructing subcat^{1}-algebras of a given cat^{1}-algebra. @@ -370,8 +370,8 @@ true Cat^{1}-algebra morphisms -Let \mathcal{C} = (e;t,h:A\rightarrow R), -\mathcal{C}^{\prime } = (e^{\prime}; t^{\prime }, h^{\prime } +Let \mathbb{C} = (e;t,h:A\rightarrow R), +\mathbb{C}^{\prime } = (e^{\prime}; t^{\prime }, h^{\prime } : A^{\prime} \rightarrow R^{\prime}) be cat^{1}-algebras, and let \phi : A\rightarrow A^{\prime} diff --git a/doc/intro.xml b/doc/intro.xml index 2b6df3a..d553e22 100644 --- a/doc/intro.xml +++ b/doc/intro.xml @@ -2,7 +2,7 @@ - + @@ -53,5 +53,46 @@ and described in detail in the paper .

There are aspects of commutative algebras for which no ⪆ functions yet exist, for example semidirect products. We have included here functions for all homomorphisms of algebras. +

+The package is loaded with the command + + LoadPackage( "xmodalg" ); +]]> + +

+ +The package may be obtained as a compressed .tar file +XModAlg-version.tar.gz from the GitHub release site: +https://github.com/gap-packages/xmodalg/releases/tag/version. +GitHub repository +The package also has a GitHub repository at: +https://github.com/gap-packages/xmodalg. +

+ +Once the package is loaded, the manual doc/manual.pdf +can be found in the documentation folder. +The html versions, with or without MathJax, +may be rebuilt as follows: +

+ + ReadPackage( "xmodalg", "makedoc.g" ); +]]> + +

+ +It is possible to check that the package has been installed correctly +by running the test files (this terminates the ⪆ session): +

+ + TestPackage( "xmodalg" ); +Architecture: . . . . . +testing: . . . . . +. . . +#I No errors detected while testing +]]> + diff --git a/doc/xmod.xml b/doc/xmod.xml index 8b05081..75d8fd9 100644 --- a/doc/xmod.xml +++ b/doc/xmod.xml @@ -24,7 +24,7 @@ algebras and their implementation in this package. 2d-algebra A crossed module is a k-algebra morphism -\mathcal{X}:=(\partial:S\rightarrow R) +\mathbb{X}:=(\partial:S\rightarrow R) with a left action of R on S satisfying {\bf XModAlg\ 1} ~:~ \partial(r \cdot s) @@ -34,7 +34,7 @@ with a left action of R on S satisfying for all s,s^{\prime }\in S, \ r\in R. The morphism \partial is called the boundary map -of \mathcal{X} +of \mathbb{X}

Note that, although in this definition we have used a left action, in the category of commutative algebras left and right actions coincide. @@ -67,10 +67,10 @@ structures. Arg="A I" /> Let A be an algebra and I an ideal of A. -Then \mathcal{X} = (inc:I\rightarrow A) is a +Then \mathbb{X} = (inc:I\rightarrow A) is a crossed module whose action is left multiplication of A on I. Conversely, given a crossed module -\mathcal{X} = (\partial : S \rightarrow R), +\mathbb{X} = (\partial : S \rightarrow R), it is the case that {\partial(S)} is an ideal of R.

@@ -150,14 +150,14 @@ gap> Size2d( XIAk4 ); Arg="X0" /> These four attributes are used in the construction of a crossed module -\mathcal{X} where: +\mathbb{X} where: Source(X) and Range(X) are the source and the range of the boundary map respectively; -Boundary(X) is the boundary map of the crossed module \mathcal{X}; +Boundary(X) is the boundary map of the crossed module \mathbb{X}; XModAlgebraAction(X) is the action used in the crossed module. @@ -169,19 +169,19 @@ endomorphisms of Source(X). The following standard ⪆ operations have special &XModAlg; implementations: -Display(X) is used to list the components of \mathcal{X}; +Display(X) is used to list the components of \mathbb{X}; -Size2d(X) for a crossed module \mathcal{X} +Size2d(X) for a crossed module \mathbb{X} returns a 2-element list, the sizes of the source and range, -Dimension(X) for a crossed module \mathcal{X} +Dimension(X) for a crossed module \mathbb{X} returns a 2-element list, the dimensions of the source and range, Name(X) is used for giving a name to the crossed module -\mathcal{X} by associating the names of source and range algebras. +\mathbb{X} by associating the names of source and range algebras. @@ -236,7 +236,7 @@ whose kernel lies in the annihilator of S. Define the action of R on S by r\cdot s = \widetilde{r}s where \widetilde{r} \in \partial^{-1}(r), as described in section . -Then \mathcal{X}=(\partial : S\rightarrow R) +Then \mathbb{X}=(\partial : S\rightarrow R) is a crossed module with the defined action.

Continuing with the example in that section, @@ -269,10 +269,10 @@ Crossed module [A2->Q2] :- -A crossed module \mathcal{X}^{\prime } +A crossed module \mathbb{X}^{\prime } = (\partial ^{\prime }:S^{\prime}\rightarrow R^{\prime }) is a subcrossed module of the crossed module -\mathcal{X} = (\partial :S\rightarrow R) if +\mathbb{X} = (\partial :S\rightarrow R) if S^{\prime }\leq S, R^{\prime}\leq R, \partial^{\prime } = \partial|_{S^{\prime }}, and the action of S^{\prime } on R^{\prime } @@ -312,8 +312,8 @@ Crossed module [ -> ..] :-

(Pre-)Crossed Module Morphisms -Let \mathcal{X} = (\partial:S\rightarrow R) and -\mathcal{X}^{\prime} = +Let \mathbb{X} = (\partial:S\rightarrow R) and +\mathbb{X}^{\prime} = (\partial^{\prime }:S^{\prime }\rightarrow R^{\prime }) be (pre)crossed modules and let \theta :S\rightarrow S^{\prime }, \varphi : R\rightarrow R^{\prime } be algebra homomorphisms. @@ -325,7 +325,7 @@ Then if for all r\in R, s\in S, the pair (\theta ,\varphi ) is called a morphism between -\mathcal{X} and \mathcal{X}^{\prime } +\mathbb{X} and \mathbb{X}^{\prime }

The conditions can be thought as the commutativity of the following diagrams: @@ -433,8 +433,8 @@ true -Let (\theta,\varphi) : \mathcal{X} = (\partial : S \rightarrow R) - \rightarrow \mathcal{X}^{\prime} = (\partial^{\prime} +Let (\theta,\varphi) : \mathbb{X} = (\partial : S \rightarrow R) + \rightarrow \mathbb{X}^{\prime} = (\partial^{\prime} : S^{\prime} \rightarrow R^{\prime}) be a crossed module homomorphism. Then the crossed module @@ -442,7 +442,7 @@ Then the crossed module \ker(\theta,\varphi) = (\partial| : \ker\theta \rightarrow \ker\varphi ) is called the kernel of (\theta,\varphi). -Also, \ker(\theta ,\varphi ) is an ideal of \mathcal{X}. +Also, \ker(\theta ,\varphi ) is an ideal of \mathbb{X}. An example is given below. @@ -464,8 +464,8 @@ true -Let (\theta,\varphi) : \mathcal{X} = (\partial : S \rightarrow R) - \rightarrow \mathcal{X}^{\prime} = (\partial^{\prime} : S^{\prime} +Let (\theta,\varphi) : \mathbb{X} = (\partial : S \rightarrow R) + \rightarrow \mathbb{X}^{\prime} = (\partial^{\prime} : S^{\prime} \rightarrow R^{\prime}) be a crossed module homomorphism. Then the crossed module