{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# StringApplet to SageMath converter\n", "\n", "This is a manual of [`converter.py`](https://github.com/haruhisa-enomoto/StringApplet-to-SageMath-converter).\n", "It converts the exported tex file produced by [String Applet](https://www.math.uni-bielefeld.de/~jgeuenich/string-applet/)\n", "into a data which we can use to construct the poset of torsion classes in [SageMath](https://www.sagemath.org/).\n", "We assume that you have installed SageMath.\n", "\n", "AUTHOR: [Haruhisa Enomoto](http://haruhisa-enomoto.github.io/)\n", "\n", "### Table of contents\n", "\n", "- [String Applet](#String-Applet): an explanation of String Applet.\n", "- [Usage](#Usage): how to use `converter.py`. In particular, you can use two functions:\n", " - [SAtoSage](#SAtoSage%28tex_path%29)\n", " - [export](#export%28tex_path,-output_path%29)\n", "- [See also](#See-also): Other materials which can be helpful." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## String Applet\n", "\n", "[String Applet](https://www.math.uni-bielefeld.de/~jgeuenich/string-applet/) is a web program developed by [Jan Geuenich](https://www.math.uni-bielefeld.de/~jgeuenich/), which is a **very** useful tool when we want to observe (and play with) concrete examples in the representation theory of algebras. Here are the description from the site.\n", "\n", "This web program can deal with special biserial algebras, string algebras, and gentle algebras, thus a large class of algebras (you don't have to know definitions to use it, since this program automatically checks whether your inputed algebra is OK). After inputing your algebra, it displays many combinatorial invariants of these algebras and their module categories.\n", "\n", "We can easily input our finite-dimensional algebras intuitively by a quiver and relations in the left bottom input form.\n", "For example, the following represents an algebra $\\Lambda:= k[1 \\xrightarrow{a}2 \\xrightarrow{b}3]/\\langle ab \\rangle$.\n", "\n", "\n", "\n", "Then, by clicking **Update**, lots of information on this algebra is shown in the right part." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In particular, String Applet computes the support $\\tau$-tilting quiver if a given algebra is representation-finite.\n", "This quiver is nothing but the Hasse quiver of the lattice of torsion classes $\\mathsf{tors}\\,\\Lambda$ like this:\n", "\n", "\n", "\n", "*The aim of this code is* **to make this poset available in SageMath.**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Usage\n", "\n", "First, please download [``converter.py``](https://github.com/haruhisa-enomoto/StringApplet-to-SageMath-converter/blob/main/converter.py) in your PC ([this](https://github.com/haruhisa-enomoto/StringApplet-to-SageMath-converter/raw/main/converter.py) is a direct link of this file). It is recommended that you download it in your working directory (where your Jupyter Notebook or Sage file belongs).\n", "\n", "### Step 1. Export the tex file from String Applet\n", "\n", "The first step is to export the tex file from String Applet **after showing the s$\\tau$-Tilting quiver**.\n", "\n", "1. Input your favorite algebra on String Applet by a quiver with relations, and click \"Update\" on the left part.\n", "2. Click \"$\\tau$-Tilting\" tab on the right part. Then there is a button \"Show\" in the s$\\tau$-Tilting quiver part.\n", "\n", "\n", "\n", "(If there is no \"Show\" button, make sure that your algebra is representation-finite, which is shown in the left part.)\n", "3. Click this \"Show\" button. Then the Hasse quiver will be shown.\n", "4. Place the cursor over \"Export\", then click \"As LaTeX\". Then save the latex file in the same directory as [``converter.py``](https://github.com/haruhisa-enomoto/StringApplet-to-SageMath-converter/blob/main/converter.py).\n", "\n", "\n", "\n", "For example, suppose the filename is ``SA.tex``." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step 2. Load `converter.py` and use it\n", "\n", "Then load `converter.py` in SageMath. There are several ways to do it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you are using SageMath on Jupyter Notebook or Interactive Shell, then just write" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": true }, "outputs": [], "source": [ "load(\"converter.py\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and excute it. In this case, make sure that `converter.py` is in your working directory. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you are writing your own SageMath file (like `foo.sage`), then write\n", "\n", "```\n", "import converter\n", "```\n", "\n", "in the beginning of your file (also in this case, make sure that `foo.sage` and `converter.py` belong to the same directory)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For simplicity, we assume the former case from now on. (For the latter case, you should write ``converter.SAtoSage`` instead of just `SAtoSage`, or write ``from converter import SAtoSage``.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After loading `converter.py`, you can use two functions:\n", "\n", "- [SAtoSage](#SAtoSage%28tex_path%29)\n", "- [export](#export%28tex_path,-output_path%29)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### SAtoSage(`tex_path`)\n", "\n", "Return the data which can be used to construct the poset of torsion classes in SageMath from the tex file exported by StringApplet.\n", "\n", "INPUT:\n", "\n", "- `tex_path` -- a path of the exported tex file.\n", "\n", "OUTPUT:\n", "\n", "a data from which we can construct poset or lattice in SageMath.\n", "\n", "EXAMPLE:\n", "Assume that you has `SA.tex` in the working directory. Then for example, we have" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11],\n", " [(1, 0),\n", " (2, 0),\n", " (3, 0),\n", " (4, 1),\n", " (5, 1),\n", " (6, 3),\n", " (7, 3),\n", " (4, 2),\n", " (8, 2),\n", " (9, 4),\n", " (6, 5),\n", " (9, 5),\n", " (10, 6),\n", " (8, 7),\n", " (10, 7),\n", " (11, 8),\n", " (11, 9),\n", " (11, 10)])" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data = SAtoSage(\"SA.tex\")\n", "data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This data consists of a tuple `(tors, rels)`, where\n", "- `tors` is a list of torsion classes, indexed by integers.\n", "- `rels` is a list of covering relations (U,T) of torsion classes. (U,T) is a covering relation if there is a Hasse arrow $U \\leftarrow T$.\n", "\n", "To construct a poset from this data, you just do the following in SageMath." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Finite poset containing 12 elements" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tors_poset = Poset(data)\n", "tors_poset" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that **the orientation of Hasse quiver in SageMath is opposite to the representation theorist's convention**, so `0` is the largest torsion class $\\mathsf{mod}\\, \\Lambda$ and `11` is the smallest torsion class $0$.\n", "\n", "In case you want to consider this poset as a lattice, use ``LatticePoset`` instead of ``Poset``." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Finite lattice containing 12 elements" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tors_lattice = LatticePoset(data)\n", "tors_lattice" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Maybe *it's recommended to use `LatticePoset` because we can use more functions including join, meets and so on*. For example, the following count the number of join-irreducible torsion classes." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The number of join-irreducible torsion class is\n", "5\n" ] } ], "source": [ "print(\"The number of join-irreducible torsion class is\")\n", "print(len(tors_lattice.join_irreducibles()))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since join-irreducibles are in bijection with bricks, from this, we can conclude that our algebra $\\Lambda$ has $5$ bricks!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### export(`tex_path`, `output_path`)\n", "\n", "If you want to export the data of this poset to another file, then use this function. This will be useful if you want to use the poset data later.\n", "\n", "INPUT:\n", "\n", "- ``tex_path`` -- a path of the exported tex file\n", "\n", "- ``output_path`` -- a path of the output file\n", " (error will be raised if the file already exists)\n", "\n", "EXAMPLE:\n", "\n", "By executing this function, we make another file of the name `output_path`.\n", "For example, if you want to export the poset data to a new file `output.sage`, do the following." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "export(\"SA.tex\", \"output.sage\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The content of `output.sage` is as follows:\n", "\n", "```\n", "data = ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [(1, 0), (2, 0), (3, 0), (4, 1), (5, 1), (6, 3), (7, 3), (4, 2), (8, 2), (9, 4), (6, 5), (9, 5), (10, 6), (8, 7), (10, 7), (11, 8), (11, 9), (11, 10)])\n", "```\n", "\n", "Namely, the data created by `SAtoSage` function is saved in the variable `data`.\n", "Therefore, you can use this data as follows." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "load(\"output.sage\")" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Finite lattice containing 12 elements" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tors_lattice = LatticePoset(data)\n", "tors_lattice" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## See also\n", "\n", "- [Manual of Lattices in SageMath](https://doc.sagemath.org/html/en/reference/combinat/sage/combinat/posets/lattices.html). You can see various operations which you can apply to our lattice of torsion classes.\n", "- [The lattice of torsion classes in SageMath](https://github.com/haruhisa-enomoto/tors-lattice), which is another SageMath program I've developed. This computes various objects from the poset of torsion classes." ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.1", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }