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CarlaCosteaCarlaCostea
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Merge pull request #44 from pie-framework/beta
feat: linear-equation-equivalence
2 parents 73b69a3 + 6311ece commit 3e4350d

12 files changed

Lines changed: 516 additions & 64 deletions

‎.DS_Store‎

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‎package.json‎

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@@ -36,7 +36,6 @@
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"@semantic-release/github": "^7.2.3",
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"@semantic-release/npm": "^7.1.3",
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"@semantic-release/release-notes-generator": "^9.0.3",
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"prettier": "^2.3.2",
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"@types/fs-extra": "^9.0.1",
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"@types/glob": "^7.1.3",
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"@types/jest": "^26.0.14",
@@ -53,6 +52,7 @@
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"latex-utensils": "^2.0.3",
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"latex.js": "^0.12.4",
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"minimist": "^1.2.5",
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"prettier": "^2.3.2",
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"rollup": "^2.50.2",
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"rollup-plugin-cleanup": "^3.2.1",
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"semantic-release": "^17.4.7",

‎src/__tests__/compare-equations.spec.ts‎

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import { AstToMathJs } from "../conversion/ast-to-mathjs";
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import { LatexToAst } from "../conversion/latex-to-ast";
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import {
4+
getUnknowns,
5+
getCoefficients,
6+
setXToOne,
7+
solveLinearEquation,
8+
} from "../symbolic/compare-equations";
9+
10+
const lta = new LatexToAst();
11+
const atm = new AstToMathJs();
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13+
describe("getUnknowns", () => {
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it.each`
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expression | unknowns
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${"x"} | ${["x"]}
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${"x +1"} | ${["x"]}
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${"((x^2 + x) / x) - 1"} | ${["x"]}
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${"1+2"} | ${[]}
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${"a +1+c"} | ${["a", "c"]}
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${"((y^2 + z) / x) - 1"} | ${["x", "y", "z"]}
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${"109h"} | ${["h"]}
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${"m+n+10"} | ${["m", "n"]}
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`("$expression => $unknowns", ({ expression, unknowns }) => {
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const equation = atm.convert(lta.convert(expression));
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const unknownsName = getUnknowns(equation);
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expect(unknownsName).toEqual(unknowns);
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});
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});
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describe("getCoefficients", () => {
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it.each`
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expression | coefficients
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${"x+0"} | ${[0, 1]}
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${"x +1"} | ${[1, 1]}
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${"((x^2 + x) / x) - 1"} | ${[0, 0, 1]}
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${"1+2"} | ${[1, 0]}
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${"a +1+c"} | ${[1, 0]}
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${"y^2+5y - 1"} | ${[-1, 5, 1]}
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${"2y^2+4y"} | ${[0, 4, 2]}
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${"109h"} | ${[0, 109]}
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${"m+n+10"} | ${[1, 0]}
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${"x-x"} | ${[0, 0]}
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${"x + 5 - 3 + x - 6 - x + 2"} | ${[-2, 1]}
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${"2x-x"} | ${[0, 1]}
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${"x - x - 2"} | ${[1, 0]}
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`("$expression => $coefficients", ({ expression, coefficients }) => {
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const equation = atm.convert(lta.convert(expression));
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const coefficientsList = getCoefficients(equation);
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expect(coefficientsList).toEqual(coefficients);
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});
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});
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describe("getCoefficients", () => {
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it('equation: "x = x" - has coefficients [0, 0]', () => {
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const equation = atm.convert(lta.convert("x-x"));
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const coefficientsList = getCoefficients(equation);
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expect(coefficientsList).toEqual([0, 0]);
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});
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it('equation: "1 = -2" - if equation has no coefficient for x it will return coefficients [1, 0]', () => {
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const equation = atm.convert(lta.convert("1+2"));
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const coefficientsList = getCoefficients(equation);
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expect(coefficientsList).toEqual([1, 0]);
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});
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it('equation: "m + n = - 2" - if equation has more than one variable, will return coefficients [1, 0]', () => {
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const equation = atm.convert(lta.convert("m+n = - 2"));
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const coefficientsList = getCoefficients(equation);
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expect(coefficientsList).toEqual([1, 0]);
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});
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});
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describe("setXToOne", () => {
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it.each`
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expression | expressionNoX
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${"x+0"} | ${"1+0"}
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${"x +1"} | ${"1+1"}
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${"((x^2 + x) / x) - 1"} | ${"((1^2 + 1) / 1) - 1"}
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${"1+2"} | ${"1+2"}
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${"a +1+c"} | ${"a+1+c"}
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${"y^2+5x - 1"} | ${"y^2+5*1 - 1"}
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${"109h"} | ${"109h"}
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${"m+n+10"} | ${"m+n+10"}
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`("$expression => $expressionNoX", ({ expression, expressionNoX }) => {
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const equation = atm.convert(lta.convert(expression));
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const equationNoX = setXToOne(equation, "x");
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const result = atm.convert(lta.convert(expressionNoX));
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expect(equationNoX.toTex()).toEqual(result.toTex());
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});
97+
});
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describe("solveLinearEquation", () => {
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it.each`
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coefficients | xValue
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${[0, 1]} | ${0}
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${[1, 1]} | ${-1}
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${[0, 0, 1]} | ${0}
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${[]} | ${undefined}
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${[-1, 5, 1]} | ${undefined}
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${[0, 109]} | ${0}
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`("$coefficients => $xValue", ({ coefficients, xValue }) => {
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const result = solveLinearEquation(coefficients);
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expect(result).toEqual(xValue);
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});
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});
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describe("solveLinearEquation", () => {
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it('equation: "x = x" - has infinite solutions', () => {
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const coefficients = [0, 0];
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const result = solveLinearEquation(coefficients);
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expect(result).toEqual(Infinity);
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});
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it('equation: "x + 5 - 3 + x = 6 + x - 2" - solution should be 2', () => {
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const coefficients = [-2, 1];
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const result = solveLinearEquation(coefficients);
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expect(result).toEqual(2);
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});
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it('equation: "2x = x" - solution should be 0', () => {
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const coefficients = [0, 1];
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const result = solveLinearEquation(coefficients);
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expect(result).toEqual(0);
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});
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it('equation: "x = x + 2" - if equation has no solution it will return - Infinity', () => {
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const coefficients = [2, 0];
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const result = solveLinearEquation(coefficients);
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expect(result).toEqual(-Infinity);
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});
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it('equation: "3x - 2x = x + 7 + 9" - if equation has no solution it will return - Infinity', () => {
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const coefficients = [16, 0];
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const result = solveLinearEquation(coefficients);
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expect(result).toEqual(-Infinity);
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});
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it('equation: "2x^2 = 2x" - has no solution', () => {
152+
const coefficients = [0, 4, 2];
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const result = solveLinearEquation(coefficients);
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expect(result).toEqual(-2);
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});
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it('equation: "y^2+5y - 1" - if equation is quadratic, result is undefined', () => {
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const coefficients = [-1, 5, 1];
160+
const result = solveLinearEquation(coefficients);
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expect(result).toEqual(undefined);
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});
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it('equation: "y^2+5y + 1" - if equation is quadratic, result is undefined', () => {
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const coefficients = [1, 5, 1];
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const result = solveLinearEquation(coefficients);
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expect(result).toEqual(undefined);
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});
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});

‎src/fixtures/latex-equal/symbolic/equation-with-no-variables.ts‎

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@@ -5,7 +5,7 @@ export default {
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{
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target: "4=4",
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eq: ["4=4", "2+2=4"],
8-
// ne: ["1", "3=3", "9=8", "a=b", "0=0", "\\true=\\true"],
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ne: ["1", "3=3", "9=8", "a=b", "0=0", "\\true=\\true"],
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},
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{
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target: "4=4=2+2",

‎src/fixtures/latex-equal/symbolic/equiv-symbolic.ts‎

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@@ -9,7 +9,6 @@ export default {
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{
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// equation with variable
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target: "y= \\frac{1}{2}x +5",
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eq: [
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// flip sides of equation
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"\\frac{1}{2}x +5 = y",
@@ -21,19 +20,19 @@ export default {
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"y = 0.5x+5 ",
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// Use division sign rather than fraction form
2322
"y =x÷2 +5",
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// // Multiply both sides of the equation by a non-zero number
25-
// "-2y =-x -10",
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// Multiply both sides of the equation by a non-zero number
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"-2y =-x -10",
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// Add a number to both sides of the equation
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"y-5 =\\frac{x}{2}",
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"-5 =\\frac{1}{2}x-y",
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// Subtract one of the variables from both sides of the equation
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"0=x/2-y+5",
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// // Add a new variable to both sides of the equation
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// "z=x/2-y+5 +z",
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// // Divide both sides of the equation by y
34-
// "1=\\frac{x}{2y}+\\frac{5}{y}",
35-
// // Combine several of the above
36-
// "x-2y+z=z-10",
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// Add a new variable to both sides of the equation
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"z=x/2-y+5 +z",
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// Divide both sides of the equation by y TO DO- equation is transformed in a quadratic eequation
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"1=\\frac{x}{2y}+\\frac{5}{y}",
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// Combine several of the above
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"x-2y+z=z-10",
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],
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ne: [
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"\\frac{1}{2}x +5 = x",
@@ -61,17 +60,16 @@ export default {
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// target: "2x<4",
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// eq: ["4>2x", "x+x < 2*2", "x<2"],
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// },
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// {
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// // 3-way inequality with variable(s)
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// target: "1<2x ≤ 3",
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// eq: ["3 ≥ 2x>1", "x/x<x+x≤1.5*2", "1/2<x ≤1.5"], //
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// },
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// {
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// // inequality with no variable(s)
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// target: "1<2",
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// eq: ["0<1", "x+1>x"],
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// },
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// expression (no equal or inequality sign)
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{
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// 3-way inequality with variable(s)
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target: "1<2x ≤ 3",
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eq: [
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"3 ≥ 2x>1",
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"x/x<x+x≤1.5*2",
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// "1/2<x ≤1.5"
70+
],
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},
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// expressions (no equal or inequality sign)
7573
{
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target: "\\frac{1}{3}*(8c)-5",
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eq: [

‎src/fixtures/latex-equal/symbolic/linear-equations-in-one-variable.ts‎

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export default {
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mode: "symbolic",
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tests: [
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{
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target: "x=9",
6+
eq: ["30-2x=12", "10+10-3x+x+10=12", "\\frac{1}{x}=\\frac{1}{9}"],
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ne: ["31-2x=12"],
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},
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{
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target: "a=9",
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eq: ["30-2a=12"],
12+
ne: ["31-2x=12", "b=9"],
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},
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{
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// infinite solutions equations
16+
target: "a=a",
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eq: ["2a=2a"],
18+
ne: ["12=12", "a=0"],
19+
},
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{
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// infinite solutions equations
22+
target: "5c+5c=5c+5c",
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eq: ["10c=10c", "c=c"],
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ne: ["12=12"],
25+
},
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{
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// if equations have no solutions they will not be equivalent
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target: "x=x+2",
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ne: ["2x=2x+4"],
30+
},
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{
32+
target: "((x^2 + x) / x) - 1=0",
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eq: ["3x=0", "109x=0"],
34+
},
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{
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target: "q=9",
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eq: ["15-q-6=0"],
38+
ne: ["31-2q=12", "qa=9", "q=q"],
39+
},
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{
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target: "2x+3=8",
42+
eq: [
43+
"4x+6=16",
44+
"2x=5",
45+
"x=2.5",
46+
"x=\\frac{5}{2}",
47+
"2.500000=x",
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"2x+3-8=0",
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"2x+3-8-m=0-m",
50+
],
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ne: ["5x+6=16", "2x+4-8=0", "x+3=4"],
52+
},
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{
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target: "4x+2=6x-4",
55+
eq: ["-2x+6=0"],
56+
},
57+
{
58+
target: "y^2+5y - 1=0",
59+
ne: ["y^2+5y +1=0"],
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},
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],
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};

‎src/fixtures/latex-equal/symbolic/linear-equations-in-two-variables.ts‎

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export default {
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mode: "symbolic",
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tests: [
4+
{
5+
target: "y= \\frac{1}{2}x +5",
6+
eq: [
7+
// Multiply both sides of the equation by a non-zero number
8+
"-2y =-x -10",
9+
// Divide both sides of the equation by y
10+
"1=\\frac{x}{2y}+\\frac{5}{y}",
11+
// Combine several of the above
12+
"x-2y+z=z-10",
13+
// Multiply both sides of the equation by a variable
14+
"y^2=\\frac{xy}{2}+5y",
15+
],
16+
},
17+
{
18+
// linear equations with 2 unknowns that are not x or y
19+
target: "a=\\frac{1}{2}b +5",
20+
eq: [
21+
"-2a =-b -10",
22+
"1=\\frac{b}{2a}+\\frac{5}{a}",
23+
"b-2a+c=c-10",
24+
],
25+
},
26+
{
27+
// linear equations with 2 unknowns that are not x or y
28+
target: "a=\\frac{1}{2}b +5",
29+
eq: [
30+
"-2a =-b -10",
31+
"1=\\frac{b}{2a}+\\frac{5}{a}",
32+
"b-2a+c=c-10",
33+
],
34+
},
35+
{
36+
// Multiply both sides of the equation by a variable
37+
target: "x+2y=7",
38+
eq: ["x*x+2yx-7x=0"],
39+
},
40+
{
41+
// Multiply both sides of the equation by a variable
42+
target: "x+2y=7",
43+
eq: ["x^2+2yx-7x=0"],
44+
},
45+
{
46+
// Divide both sides of the equation by a variable
47+
target: "x+2y=7",
48+
eq: ["\\frac{x}{y}+2-7/y=0", "\\frac{x}{x}+\\frac{2y}{x}=\\frac{7}{x}"],
49+
},
50+
],
51+
};

‎src/fixtures/latex-equal/symbolic/quadratic-equations.ts‎

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export default {
2+
mode: "symbolic",
3+
4+
tests: [
5+
{
6+
// // quadratic equation
7+
//only: true,
8+
// target: "x^2-7x+10=0",
9+
// eq: ["2x^2-14x+20=0"],
10+
},
11+
],
12+
};

‎src/latex-equal.ts‎

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@@ -40,6 +40,6 @@ export const latexEqual = (a: Latex, b: Latex, opts: Opts) => {
4040
if (opts.mode === "literal") {
4141
return isLiteralEqual(amo, bmo, opts.literal);
4242
} else {
43-
return isSymbolicEqual(amo, bmo, opts.symbolic);
43+
return isSymbolicEqual(amo, bmo);
4444
}
4545
};

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