It is a homemade library for JavaScript. It can parse expressions, solve and simplify systems of linear equations, find eigenvalues and eigenvectors, or calculate real roots of polynomials with integer coefficients for a specified accuracy.
npm install @yaffle/expression
or
npm install Yaffle/Expression
example.mjs:
import {ExpressionParser, Polynomial, Expression} from './node_modules/@yaffle/expression/index.js';
// Exact polynomial roots can be found for some polynomials:
var p = Polynomial.toPolynomial(ExpressionParser.parse("10x^5−17x^4−505x^3+1775x^2−249x−630"), ExpressionParser.parse("x"));
console.log(p.getroots().toString()); // -1/2,5,21/5,(-73^0.5-7)/2,(73^0.5-7)/2
// Polynomial roots:
var p = Polynomial.toPolynomial(ExpressionParser.parse("x^5−2x^4−11x^3+26x^2−2x−13"), ExpressionParser.parse("x"));
console.log(p.getZeros().map(x => x.toString({rounding: {fractionDigits: 20}})).toString()); // -3.41190231035920486644,-0.60930943815581736137,1.07534597839596488553,1.92498144931467217779,3.02088432080438516449
// parse a matrix from a string:
var matrix = ExpressionParser.parse('{{1,2,3},{4,5,6},{7,8,9}}').matrix;
console.log('matrix: ' + matrix.toString()); // matrix: {{1,2,3},{4,5,6},{7,8,9}}
var eigenvalues = Expression.getEigenvalues(matrix);
console.log('eigenvalues: ' + eigenvalues.toString()); // eigenvalues: 0,(-3*33^0.5+15)/2,(3*33^0.5+15)/2
console.log('eigenvalues: ' + eigenvalues.map(x => x.toMathML({rounding: {fractionDigits: 10}}))); // eigenvalues: <mn>0</mn>,<mrow><mo>−</mo><mn>1.1168439698</mn></mrow>,<mn>16.1168439698</mn>
var eigenvectors = Expression.getEigenvectors(matrix, eigenvalues);
console.log('eigenvectors: ' + eigenvectors.toString()); // eigenvectors: {{1},{-2},{1}},{{(-3*33^0.5-11)/22},{(-3*33^0.5+11)/44},{1}},{{(3*33^0.5-11)/22},{(3*33^0.5+11)/44},{1}}
var y = Expression.diagonalize(matrix, eigenvalues, eigenvectors);
console.log('diagonalization: ' + matrix.toString() + ' = ' + y.T.toString() + " * " + y.L.toString() + " * " + y.T_INVERSED.toString()); // diagonalization: {{1,2,3},{4,5,6},{7,8,9}} = {{1,(-3*33^0.5-11)/22,(3*33^0.5-11)/22},{-2,(-3*33^0.5+11)/44,(3*33^0.5+11)/44},{1,1,1}} * {{0,0,0},{0,(-3*33^0.5+15)/2,0},{0,0,(3*33^0.5+15)/2}} * {{1/6,-1/3,1/6},{(-33^0.5-1)/12,(-33^0.5+3)/18,(-33^0.5+15)/36},{(33^0.5-1)/12,(33^0.5+3)/18,(33^0.5+15)/36}}
//var y = Expression.getFormaDeJordan(...);
// Compute the first 100 digits of the square root of 2:
console.log(ExpressionParser.parse('sqrt(2)').toMathML({rounding: {fractionDigits: 100}})); // <mn>1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727</mn>
// simplify an expression:
const simplify = ExpressionParser.parse;
console.log(simplify('x * y * -x / (x ^ 2)').toString()) // '-y'
// parsing with substitutions:
var result = ExpressionParser.parse('A*B', new ExpressionParser.Context(function (id) {
if (id === 'A') {
return ExpressionParser.parse('{{1,2},{3,4}}');
}
if (id === 'B') {
return ExpressionParser.parse('{{-4,2},{3,-1}}');
}
})).simplify();
console.log(result.toString());
// Square root of a matrix:
console.log(ExpressionParser.parse('{{33,24},{48,57}}**(1/2)').toString()); // {{5,2},{4,7}}
// Nth-root of a matrix:
console.log(ExpressionParser.parse('{{33,24},{48,57}}**(1/n)').toString()); // {{(3^(4/n)+2*3^(2/n))/3,(3^(4/n)-3^(2/n))/3},{(2*3^(4/n)-2*3^(2/n))/3,(2*3^(4/n)+3^(2/n))/3}}
// Nth-power of a matrix:
console.log(ExpressionParser.parse('{{33,24},{48,57}}**n').toString()); // {{(3^(4*n)+2*3^(2*n))/3,(3^(4*n)-3^(2*n))/3},{(2*3^(4*n)-2*3^(2*n))/3,(2*3^(4*n)+3^(2*n))/3}}
// Note: toLaTeX is deprecated
import './node_modules/@yaffle/expression/toLaTeX.js';
console.log(ExpressionParser.parse('{{1,2},{3,4}}').toLaTeX()); // \begin{pmatrix}1 & 2 \\ 3 & 4\end{pmatrix}to run from a webbrowser create example.mjs (see above), example.html, npm install http-server, npx http-server, and open it in a web browser:
<meta charset="utf-8" />
<script type="module" src="example.mjs"></script>See the console output.
npm install @yaffle/expression --save
node --experimental-modules example.mjs nthRoot(a, n)
primeFactor(a)
Matrix
.I(size)
.Zero(rows, cols)
rows()
cols()
e(row, column) - get element
isSquare()
map(mapFunction)
transpose()
scale(x)
multiply(b)
add(b)
subtract(b)
augment(b)
rowReduce(...)
swapRows(...)
toRowEchelon(...)
determinant()
rank()
inverse()
toString()
pow(n)
eql()
Polynomial
.ZERO
.of(a0, a1, ...)
.from(arrayLike)
.pseudoRemainder(p1, p2)
.polynomialGCD(p1, p2)
.resultant(p1, p2)
.toPolynomial(expression, variable)
#getDegree()
#getCoefficient(index)
#getLeadingCoefficient() - same as p.getCoefficient(p.getDegree())
#getContent()
#add(other)
#multiply(other)
#scale(coefficient)
#shift(n)
#divideAndRemainder(other)
#modularInverse(m)
#getroots()
#getZeros([precision, complex])
#numberOfRoots(interval)
#calcAt(point)
#_exponentiateRoots(n)
#_scaleRoots(s)
#_translateRoots(h)
#factorize() - find some factor of a polynomial with integer coefficients
ExpressionParser
parse(string, context)
Expression
.ZERO
.ONE
.TWO
.TEN
.PI
.E
.I
#add
#subtract
#multiply
#divide
#pow
#equals
#toString()
#toMathML()
#toLaTeX()
Expression.Integer
integer
Expression.Symbol
symbol
Expression.NthRoot
radicand
Expression.Matrix
matrix
Expression.Polynomial
polynomial
Expression.Sin
argument
Expression.Cos
argument
Expression.Complex
real
imaginary
Expression.ExpressionPolynomialRoot
root
- https://coffeequate.readthedocs.io/en/latest/usage/
- http://algebrite.org - this page contains the list of "JavaScript Computer Algebra Systems"
- https://github.com/sloisel/numeric
- https://nerdamer.com/