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Algebra System in TypeScript","homepage":"https://github.com/geometryzen/symbolic-math#readme","keywords":["algebrite","algebra","blade","cas","computer","eigenmath","geometric","math","multivector","symbolic","system"],"repository":{"type":"git","url":"git+https://github.com/geometryzen/symbolic-math.git"},"author":{"name":"David Geo Holmes","email":"david.geo.holmes@gmail.com"},"bugs":{"url":"https://github.com/geometryzen/symbolic-math/issues"},"license":"MIT","readme":"[![npm version](https://badge.fury.io/js/symbolic-math.svg)](https://badge.fury.io/js/symbolic-math)\n\nsymbolic-math is a Javascript (Typescript) library for symbolic mathematics.\n\n## Example\n\n```typescript\nimport { assert } from \"chai\";\nimport {\n    Cons,\n    create_script_context,\n    create_sym, ExtensionEnv,\n    is_rat,\n    items_to_cons,\n    LambdaExpr,\n    Native,\n    native_sym,\n    one,\n    ScriptContext,\n    ScriptContextOptions,\n    SyntaxKind,\n    U\n} from \"symbolic-math\";\nimport { assert_one_value_execute } from \"./assert_one_value_execute\";\n\ndescribe(\"example\", function () {\n    it(\"Geometric Algebra\", function () {\n        const lines: string[] = [\n            `G30=algebra([1,1,1],[\"i\",\"j\",\"k\"])`,\n            `e1=G30[1]`,\n            `e2=G30[2]`,\n            `e3=G30[3]`,\n            `grad(s) = d(s,x) * e1 + d(s,y) * e2 + d(s,z) * e3`,\n            `div(v) = d(v|e1,x) + d(v|e2,y) + d(v|e3,z)`,\n            `curl(v) = (d(v|e3,y)-d(v|e2,z))*e1+(d(v|e1,z)-d(v|e3,x))*e2+(d(v|e2,x)-d(v|e1,y))*e3`,\n            `ddrv(v,a) = (a|e1)*d(v,x)+(a|e2)*d(v,y)+(a|e3)*d(v,z)`,\n            `A = Ax * e1 + Ay * e2 + Az * e3`,\n            `B = Bx * e1 + By * e2 + Bz * e3`,\n            `C = Cx * e1 + Cy * e2 + Cz * e3`,\n            `cross(A,B)`,\n            `A|B`,\n            `A^B`\n        ];\n        const sourcetText = lines.join('\\n');\n        const options: ScriptContextOptions = {\n            syntaxKind: SyntaxKind.Native,\n            useCaretForExponentiation: false,\n            useDefinitions: false\n        };\n        const context = create_script_context(options);\n        const { values } = context.executeScript(sourcetText);\n        assert.strictEqual(context.renderAsInfix(values[0]), \"Ay*Bz*i-Az*By*i-Ax*Bz*j+Az*Bx*j+Ax*By*k-Ay*Bx*k\");\n        assert.strictEqual(context.renderAsInfix(values[1]), \"Ax*Bx+Ay*By+Az*Bz\");\n        assert.strictEqual(context.renderAsInfix(values[2]), \"Ax*By*i^j-Ay*Bx*i^j+Ax*Bz*i^k-Az*Bx*i^k+Ay*Bz*j^k-Az*By*j^k\");\n        context.release();\n    });\n});\n\nconst VERSIN = create_sym('versin');\nconst negOne = one.neg();\n\n/**\n * Registers an implementation of the versin function with the environment.\n */\nexport function define_versin($: ScriptContext): ScriptContext {\n    // If we also want to control the name as it appears in the script\n    const match: U = items_to_cons(VERSIN);   // TODO \n    return $.defineFunction(match, versin_lambda);\n}\n\nconst versin_lambda: LambdaExpr = (argList: Cons, $: ExtensionEnv) => {\n    const x = argList.head;\n    // versin(n*pi) = 1 - (-1)**n\n    const pi = native_sym(Native.PI);\n    const n = $.evaluate(Native.divide, x, pi);\n    if (is_rat(n) && n.isInteger()) {\n        return $.subtract(one, $.power(negOne, n));\n    }\n    else {\n        // versin(x) = 1 - cos(x)\n        return $.subtract(one, $.evaluate(Native.cosine, x));\n    }\n    // If not expanding.\n    // return cons(VERSIN, argList);\n};\n\ndescribe(\"versin\", function () {\n    it(\"versin(x)\", function () {\n        const lines: string[] = [\n            `versin(x)`\n        ];\n        const rootContext = create_script_context({\n        });\n        const context = define_versin(rootContext);\n        const value = assert_one_value_execute(lines.join('\\n'), context);\n        assert.strictEqual(context.renderAsInfix(value), \"1-cos(x)\");\n        context.release();\n    });\n    it(\"versin(pi)\", function () {\n        const lines: string[] = [\n            `pi=tau(1)/2`,\n            `versin(pi)`\n        ];\n        const rootContext = create_script_context({\n        });\n        const context = define_versin(rootContext);\n        const value = assert_one_value_execute(lines.join('\\n'), context);\n        assert.strictEqual(context.renderAsInfix(value), \"2\");\n        context.release();\n    });\n    it(\"versin(2*pi)\", function () {\n        const lines: string[] = [\n            `pi=tau(1)/2`,\n            `versin(2*pi)`\n        ];\n        const rootContext = create_script_context({\n        });\n        const context = define_versin(rootContext);\n        const value = assert_one_value_execute(lines.join('\\n'), context);\n        assert.strictEqual(context.renderAsInfix(value), \"0\");\n        context.release();\n    });\n});\n```\n\n## Features\n\n* arbitrary-precision arithmetic\n* complex quantities\n* geometric algebra\n* trigonometric functions\n* special functions\n* simplification\n* expansion\n* substitution\n* factoring\n* symbolic and numeric roots\n* units of measure\n* hyperreal numbers\n* matrices\n* derivatives and gradients\n* tensors\n* booleans\n* integrals\n* multi-integrals\n* Native, Python, and Scheme syntax\n* open for extension\n\n## Getting Started\n\nPlease take a look at the [tutorial](https://github.com/geometryzen/symbolic-math/blob/master/TUTORIAL.md) file.\n\n## Contributing\n\nPlease take a look at the [contributing](https://github.com/geometryzen/symbolic-math/blob/master/CONTRIBUTING.md) file.\n\n## References\n\nsymbolic-math is a fork of [Algebrite by Davide Della Casa](https://github.com/davidedc/Algebrite).\nThe fork adds Geometric Algebra, S.I. Units of Measure, and changes the way that expressions are matched and transformed.  \n\nAlgebrite started as a port of [the EigenMath CAS by George Weigt](http://eigenmath.sourceforge.net/Eigenmath.pdf) to TypeScript.\nAnother fork of EigenMath: [SMIB by Philippe Billet](http://smib.sourceforge.net/).\n\nAnother CAS of similar nature is [SymPy](http://www.sympy.org/en/index.html) made in Python.\n\nThree other Javascript CAS are\n\n* [javascript-cas by Anthony Foster](https://github.com/aantthony/javascript-cas) supporting \"differentiation, complex numbers, sums, vectors (dot products, cross products, gradient/curl etc)\"\n* [Coffeequate by Matthew Alger](http://coffeequate.readthedocs.org/) supporting \"quadratic and linear equations, simplification of most algebraic expressions, uncertainties propagation, substitutions, variables, constants, and symbolic constants\".\n* [Algebra.js by Nicole White](http://algebra.js.org) which among other things can build and solve equations via a \"chainable\" API.\n","readmeFilename":"README.md"}