/Groebner_Nim

An implementation of Groebner Nim in Kotlin/JS.

Primary LanguageKotlin

Gröbner Nim

An implementation of Gröbner Nim in Kotlin/JS.

Description

Gröbner Nim is a game that involves the production of sticks. It is named for Gröbner bases, and by sheer coincidence simulates the computation of a Gröbner basis over the modulo-2 field. A full description appears in a paper I wrote with Haley Dozier. You can find the game in action here, along with a summary of how to play, along with a couple of variants.

Purpose

The game is pedagogical in nature, and I wrote it for a summer program with high school students. However, I have had some fun trying to beat the computer.

Status

This is a work-in-progress and is provided free-of-charge, so while it is in current use, it isn't guaranteed to be suitable for any needs except my own, and even then I encounter bugs on occasion.

Usage

  • First build it in Idea, obtaining the files Groebner_Nim.js, Groebner_Nim.js.map in the build/distributions folder.

  • Copy these files to the folder where your HTML source code resides.

  • In the HTML file, create a canvas element. The example linked above uses dimensions of 600×600.

    • For now, it is essential to give the ID game_canvas to the canvas element; that is, <canvas id="game_canvas" ...>.

  • At the beginning of the HTML file, preferably in the header, add the following line:

    <script type="text/javascript" src="path/to/kotlin.js"></script> <script type="text/javascript" src="path/to/Groebner_Nim.js"></script>

    path/to/ is the path to wherever you've placed Groebner_Nim.js. If Groebner_Nim.js is in the same folder as the HTML file, you can simply write src=Groebner_Nim.js and ignore the path. You can probably place this line anywhere in the file, just so long as it appears before the line stated below.

    After that, you should be able to access the following functions from JavaScript: Groebner_Nim.random_game(), Groebner_Nim.level_zero_game(), Groebner_Nim.level_one_game(), Groebner_Nim.replay(). The example page above invokes these when the user clicks a button; for instance,

        <input type="button" value="Random" onclick="Groebner_Nim.random_game()">

    ...but there are other ways to do it.

Structure

The source code is in Kotlin and compiles to JavaScript. Once Kotlin compiles to WebAssembly, I intend to bypass JavaScript entirely.

  • simple.kt handles the game control. The unfortunate name is due to Idea's defaults, and I plan to change it once I get around to figuring out how.
  • Games.kt defines a game of Groebner_Solitaire, along with a JS_Game data class, a front-end for JavaScript.
  • Grids.kt defines the abstract Grid class and the JS_Grid data class, a front-end for JavaScript.
  • Orderings.kt defines several ways to evaluate the head of a stick.
    • An abstract Ordering class.
    • Three objects that implement and instantiate it: GrevLex_Ordering, Lex_Ordering, and Weighted_GrevLex.
  • Points.kt defines a Point data class.
  • Sticks.kt defines both a Stick data class and several functions related to determining when the game finishes.

There is also an example HTML page, index.html.

Examples of this package in "real-world" use

Already linked, but here it is again.

License

Gröbner Nim by John Perry is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

CC-BY-SA