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Merge pull request #44 from pie-framework/beta
feat: linear-equation-equivalence
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,171 @@ | ||
| import { AstToMathJs } from "../conversion/ast-to-mathjs"; | ||
| import { LatexToAst } from "../conversion/latex-to-ast"; | ||
| import { | ||
| getUnknowns, | ||
| getCoefficients, | ||
| setXToOne, | ||
| solveLinearEquation, | ||
| } from "../symbolic/compare-equations"; | ||
|
|
||
| const lta = new LatexToAst(); | ||
| const atm = new AstToMathJs(); | ||
|
|
||
| describe("getUnknowns", () => { | ||
| it.each` | ||
| expression | unknowns | ||
| ${"x"} | ${["x"]} | ||
| ${"x +1"} | ${["x"]} | ||
| ${"((x^2 + x) / x) - 1"} | ${["x"]} | ||
| ${"1+2"} | ${[]} | ||
| ${"a +1+c"} | ${["a", "c"]} | ||
| ${"((y^2 + z) / x) - 1"} | ${["x", "y", "z"]} | ||
| ${"109h"} | ${["h"]} | ||
| ${"m+n+10"} | ${["m", "n"]} | ||
| `("$expression => $unknowns", ({ expression, unknowns }) => { | ||
| const equation = atm.convert(lta.convert(expression)); | ||
| const unknownsName = getUnknowns(equation); | ||
|
|
||
| expect(unknownsName).toEqual(unknowns); | ||
| }); | ||
| }); | ||
|
|
||
| describe("getCoefficients", () => { | ||
| it.each` | ||
| expression | coefficients | ||
| ${"x+0"} | ${[0, 1]} | ||
| ${"x +1"} | ${[1, 1]} | ||
| ${"((x^2 + x) / x) - 1"} | ${[0, 0, 1]} | ||
| ${"1+2"} | ${[1, 0]} | ||
| ${"a +1+c"} | ${[1, 0]} | ||
| ${"y^2+5y - 1"} | ${[-1, 5, 1]} | ||
| ${"2y^2+4y"} | ${[0, 4, 2]} | ||
| ${"109h"} | ${[0, 109]} | ||
| ${"m+n+10"} | ${[1, 0]} | ||
| ${"x-x"} | ${[0, 0]} | ||
| ${"x + 5 - 3 + x - 6 - x + 2"} | ${[-2, 1]} | ||
| ${"2x-x"} | ${[0, 1]} | ||
| ${"x - x - 2"} | ${[1, 0]} | ||
| `("$expression => $coefficients", ({ expression, coefficients }) => { | ||
| const equation = atm.convert(lta.convert(expression)); | ||
| const coefficientsList = getCoefficients(equation); | ||
|
|
||
| expect(coefficientsList).toEqual(coefficients); | ||
| }); | ||
| }); | ||
|
|
||
| describe("getCoefficients", () => { | ||
| it('equation: "x = x" - has coefficients [0, 0]', () => { | ||
| const equation = atm.convert(lta.convert("x-x")); | ||
| const coefficientsList = getCoefficients(equation); | ||
|
|
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| expect(coefficientsList).toEqual([0, 0]); | ||
| }); | ||
|
|
||
| it('equation: "1 = -2" - if equation has no coefficient for x it will return coefficients [1, 0]', () => { | ||
| const equation = atm.convert(lta.convert("1+2")); | ||
| const coefficientsList = getCoefficients(equation); | ||
|
|
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| expect(coefficientsList).toEqual([1, 0]); | ||
| }); | ||
|
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||
| it('equation: "m + n = - 2" - if equation has more than one variable, will return coefficients [1, 0]', () => { | ||
| const equation = atm.convert(lta.convert("m+n = - 2")); | ||
| const coefficientsList = getCoefficients(equation); | ||
|
|
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| expect(coefficientsList).toEqual([1, 0]); | ||
| }); | ||
| }); | ||
|
|
||
| describe("setXToOne", () => { | ||
| it.each` | ||
| expression | expressionNoX | ||
| ${"x+0"} | ${"1+0"} | ||
| ${"x +1"} | ${"1+1"} | ||
| ${"((x^2 + x) / x) - 1"} | ${"((1^2 + 1) / 1) - 1"} | ||
| ${"1+2"} | ${"1+2"} | ||
| ${"a +1+c"} | ${"a+1+c"} | ||
| ${"y^2+5x - 1"} | ${"y^2+5*1 - 1"} | ||
| ${"109h"} | ${"109h"} | ||
| ${"m+n+10"} | ${"m+n+10"} | ||
| `("$expression => $expressionNoX", ({ expression, expressionNoX }) => { | ||
| const equation = atm.convert(lta.convert(expression)); | ||
| const equationNoX = setXToOne(equation, "x"); | ||
| const result = atm.convert(lta.convert(expressionNoX)); | ||
|
|
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| expect(equationNoX.toTex()).toEqual(result.toTex()); | ||
| }); | ||
| }); | ||
|
|
||
| describe("solveLinearEquation", () => { | ||
| it.each` | ||
| coefficients | xValue | ||
| ${[0, 1]} | ${0} | ||
| ${[1, 1]} | ${-1} | ||
| ${[0, 0, 1]} | ${0} | ||
| ${[]} | ${undefined} | ||
| ${[-1, 5, 1]} | ${undefined} | ||
| ${[0, 109]} | ${0} | ||
| `("$coefficients => $xValue", ({ coefficients, xValue }) => { | ||
| const result = solveLinearEquation(coefficients); | ||
|
|
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| expect(result).toEqual(xValue); | ||
| }); | ||
| }); | ||
|
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| describe("solveLinearEquation", () => { | ||
| it('equation: "x = x" - has infinite solutions', () => { | ||
| const coefficients = [0, 0]; | ||
| const result = solveLinearEquation(coefficients); | ||
|
|
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| expect(result).toEqual(Infinity); | ||
| }); | ||
|
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| it('equation: "x + 5 - 3 + x = 6 + x - 2" - solution should be 2', () => { | ||
| const coefficients = [-2, 1]; | ||
| const result = solveLinearEquation(coefficients); | ||
|
|
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| expect(result).toEqual(2); | ||
| }); | ||
|
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| it('equation: "2x = x" - solution should be 0', () => { | ||
| const coefficients = [0, 1]; | ||
| const result = solveLinearEquation(coefficients); | ||
|
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| expect(result).toEqual(0); | ||
| }); | ||
|
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| it('equation: "x = x + 2" - if equation has no solution it will return - Infinity', () => { | ||
| const coefficients = [2, 0]; | ||
| const result = solveLinearEquation(coefficients); | ||
|
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| expect(result).toEqual(-Infinity); | ||
| }); | ||
|
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| it('equation: "3x - 2x = x + 7 + 9" - if equation has no solution it will return - Infinity', () => { | ||
| const coefficients = [16, 0]; | ||
| const result = solveLinearEquation(coefficients); | ||
|
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| expect(result).toEqual(-Infinity); | ||
| }); | ||
|
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| it('equation: "2x^2 = 2x" - has no solution', () => { | ||
| const coefficients = [0, 4, 2]; | ||
| const result = solveLinearEquation(coefficients); | ||
|
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| expect(result).toEqual(-2); | ||
| }); | ||
|
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| it('equation: "y^2+5y - 1" - if equation is quadratic, result is undefined', () => { | ||
| const coefficients = [-1, 5, 1]; | ||
| const result = solveLinearEquation(coefficients); | ||
|
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| expect(result).toEqual(undefined); | ||
| }); | ||
|
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| it('equation: "y^2+5y + 1" - if equation is quadratic, result is undefined', () => { | ||
| const coefficients = [1, 5, 1]; | ||
| const result = solveLinearEquation(coefficients); | ||
|
|
||
| expect(result).toEqual(undefined); | ||
| }); | ||
| }); |
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62 changes: 62 additions & 0 deletions
62
src/fixtures/latex-equal/symbolic/linear-equations-in-one-variable.ts
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,62 @@ | ||
| export default { | ||
| mode: "symbolic", | ||
| tests: [ | ||
| { | ||
| target: "x=9", | ||
| eq: ["30-2x=12", "10+10-3x+x+10=12", "\\frac{1}{x}=\\frac{1}{9}"], | ||
| ne: ["31-2x=12"], | ||
| }, | ||
| { | ||
| target: "a=9", | ||
| eq: ["30-2a=12"], | ||
| ne: ["31-2x=12", "b=9"], | ||
| }, | ||
| { | ||
| // infinite solutions equations | ||
| target: "a=a", | ||
| eq: ["2a=2a"], | ||
| ne: ["12=12", "a=0"], | ||
| }, | ||
| { | ||
| // infinite solutions equations | ||
| target: "5c+5c=5c+5c", | ||
| eq: ["10c=10c", "c=c"], | ||
| ne: ["12=12"], | ||
| }, | ||
| { | ||
| // if equations have no solutions they will not be equivalent | ||
| target: "x=x+2", | ||
| ne: ["2x=2x+4"], | ||
| }, | ||
| { | ||
| target: "((x^2 + x) / x) - 1=0", | ||
| eq: ["3x=0", "109x=0"], | ||
| }, | ||
| { | ||
| target: "q=9", | ||
| eq: ["15-q-6=0"], | ||
| ne: ["31-2q=12", "qa=9", "q=q"], | ||
| }, | ||
| { | ||
| target: "2x+3=8", | ||
| eq: [ | ||
| "4x+6=16", | ||
| "2x=5", | ||
| "x=2.5", | ||
| "x=\\frac{5}{2}", | ||
| "2.500000=x", | ||
| "2x+3-8=0", | ||
| "2x+3-8-m=0-m", | ||
| ], | ||
| ne: ["5x+6=16", "2x+4-8=0", "x+3=4"], | ||
| }, | ||
| { | ||
| target: "4x+2=6x-4", | ||
| eq: ["-2x+6=0"], | ||
| }, | ||
| { | ||
| target: "y^2+5y - 1=0", | ||
| ne: ["y^2+5y +1=0"], | ||
| }, | ||
| ], | ||
| }; |
51 changes: 51 additions & 0 deletions
51
src/fixtures/latex-equal/symbolic/linear-equations-in-two-variables.ts
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,51 @@ | ||
| export default { | ||
| mode: "symbolic", | ||
| tests: [ | ||
| { | ||
| target: "y= \\frac{1}{2}x +5", | ||
| eq: [ | ||
| // Multiply both sides of the equation by a non-zero number | ||
| "-2y =-x -10", | ||
| // Divide both sides of the equation by y | ||
| "1=\\frac{x}{2y}+\\frac{5}{y}", | ||
| // Combine several of the above | ||
| "x-2y+z=z-10", | ||
| // Multiply both sides of the equation by a variable | ||
| "y^2=\\frac{xy}{2}+5y", | ||
| ], | ||
| }, | ||
| { | ||
| // linear equations with 2 unknowns that are not x or y | ||
| target: "a=\\frac{1}{2}b +5", | ||
| eq: [ | ||
| "-2a =-b -10", | ||
| "1=\\frac{b}{2a}+\\frac{5}{a}", | ||
| "b-2a+c=c-10", | ||
| ], | ||
| }, | ||
| { | ||
| // linear equations with 2 unknowns that are not x or y | ||
| target: "a=\\frac{1}{2}b +5", | ||
| eq: [ | ||
| "-2a =-b -10", | ||
| "1=\\frac{b}{2a}+\\frac{5}{a}", | ||
| "b-2a+c=c-10", | ||
| ], | ||
| }, | ||
| { | ||
| // Multiply both sides of the equation by a variable | ||
| target: "x+2y=7", | ||
| eq: ["x*x+2yx-7x=0"], | ||
| }, | ||
| { | ||
| // Multiply both sides of the equation by a variable | ||
| target: "x+2y=7", | ||
| eq: ["x^2+2yx-7x=0"], | ||
| }, | ||
| { | ||
| // Divide both sides of the equation by a variable | ||
| target: "x+2y=7", | ||
| eq: ["\\frac{x}{y}+2-7/y=0", "\\frac{x}{x}+\\frac{2y}{x}=\\frac{7}{x}"], | ||
| }, | ||
| ], | ||
| }; |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,12 @@ | ||
| export default { | ||
| mode: "symbolic", | ||
|
|
||
| tests: [ | ||
| { | ||
| // // quadratic equation | ||
| //only: true, | ||
| // target: "x^2-7x+10=0", | ||
| // eq: ["2x^2-14x+20=0"], | ||
| }, | ||
| ], | ||
| }; |
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