nerdamer/spec/solve.spec.js

javascript light-weight symbolic math expression evaluator

/* global expect */


'use strict';

var nerdamer = require('../nerdamer.core.js');
require('../Solve');

describe('Solve', function () {
    it('should solve correctly', function () {
        expect(nerdamer('solve(x=y/3416.3333333333344, y)').toString()).toEqual('[(1073228064103962/314146179365)*x]');
        expect(nerdamer('solve(x, x)').toString()).toEqual('[0]');
        expect(nerdamer('solve(5*y^x=8, x)').toString()).toEqual('[log(8/5)*log(y)^(-1)]');
        expect(nerdamer('solve(x^y+8=a*b, x)').toString()).toEqual('[(-8+a*b)^y^(-1)]');
        expect(nerdamer('solve(x^2, x)').toString()).toEqual('[0]');
        expect(nerdamer('solve(x^3, x)').toString()).toEqual('[0]');
        expect(nerdamer('solve(x+1, x)').toString()).toEqual('[-1]');
        expect(nerdamer('solve(x^2+1, x)').toString()).toEqual('[i,-i]');
        expect(nerdamer('solve(2*x^2+1, x)').toString()).toEqual('[(1/2)*i*sqrt(2),(-1/2)*i*sqrt(2)]');
        expect(nerdamer('solve(3*(x+5)*(x-4), x)').toString()).toEqual('[-5,4]');
        expect(nerdamer('solve(3*(x+a)*(x-b), x)').toString()).toEqual('[-a,b]');
        expect(nerdamer('solve(a*x^2+b, x)').toString()).toEqual('[a^(-1)*i*sqrt(a)*sqrt(b),-a^(-1)*i*sqrt(a)*sqrt(b)]');
        expect(nerdamer('solve(x^2+2*x+1, x)').toString()).toEqual('[-1]');
        expect(nerdamer('solve(-5 sqrt(14)x-14x^2 sqrt(83)-10=0,x)').toString()).toEqual('[(-1/28)*sqrt(-560*sqrt(83)+350)*sqrt(83)^(-1)+(-5/28)*sqrt(14)*sqrt(83)^(-1),(-5/28)*sqrt(14)*sqrt(83)^(-1)+(1/28)*sqrt(-560*sqrt(83)+350)*sqrt(83)^(-1)]');
        expect(nerdamer('solve(-5*sqrt(14)x-14x^2*sqrt(83)-10x=0,x)').toString()).toEqual('[(-5/14)*(2+sqrt(14))*sqrt(83)^(-1),0]');
        expect(nerdamer('solve(8*x^3-26x^2+3x+9,x)').toString()).toEqual('[3/4,-1/2,3]');
        expect(nerdamer('solve(a*x^2+b*x+c, x)').toString()).toEqual('[(1/2)*(-b+sqrt(-4*a*c+b^2))*a^(-1),(1/2)*(-b-sqrt(-4*a*c+b^2))*a^(-1)]');
        expect(nerdamer('solve(sqrt(x^3)+sqrt(x^2)-sqrt(x)=0,x)').toString()).toEqual('[0,78202389238903801/240831735646702201]');
        expect(nerdamer('solve(x^3-10x^2+31x-30,x)').toString()).toEqual('[3,5,2]');
        expect(nerdamer('solve(sqrt(x)+sqrt(2x+1)=5,x)').toString()).toEqual('[4]');
        expect(nerdamer('solve(x=2/(3-x),x)').toString()).toEqual('[1,2]');
        expect(nerdamer('solve(1/x=a,x)').toString()).toEqual('[a^(-1)]');
        expect(nerdamer('solve(sqrt(x^2-1),x)').toString()).toEqual('[1,-1]');
        expect(nerdamer('solve(m*x^9+n,x)').toString()).toEqual('[2*m^(-1/9)*n^(1/9),2*e^((2/9)*i*pi)*m^(-1/9)*n^(1/9),2*e^((4/9)*i*pi)*m^(-1/9)*n^(1/9),2*e^((2/3)*i*pi)*m^(-1/9)*n^(1/9),2*e^((8/9)*i*pi)*m^(-1/9)*n^(1/9),2*e^((10/9)*i*pi)*m^(-1/9)*n^(1/9),2*e^((4/3)*i*pi)*m^(-1/9)*n^(1/9),2*e^((14/9)*i*pi)*m^(-1/9)*n^(1/9),2*e^((16/9)*i*pi)*m^(-1/9)*n^(1/9)]');
        expect(nerdamer('solve(sqrt(97)x^2-sqrt(13)x+sqrt(14)x+sqrt(43)x^2+sqrt(3)*sqrt(101)=0,x)').toString()).toEqual('[(-1/2)*(sqrt(43)+sqrt(97))^(-1)*sqrt(14)+(1/2)*(sqrt(43)+sqrt(97))^(-1)*sqrt(-2*sqrt(13)*sqrt(14)-4*sqrt(101)*sqrt(3)*sqrt(43)-4*sqrt(101)*sqrt(3)*sqrt(97)+27)+(1/2)*(sqrt(43)+sqrt(97))^(-1)*sqrt(13),(-1/2)*(sqrt(43)+sqrt(97))^(-1)*sqrt(-2*sqrt(13)*sqrt(14)-4*sqrt(101)*sqrt(3)*sqrt(43)-4*sqrt(101)*sqrt(3)*sqrt(97)+27)+(-1/2)*(sqrt(43)+sqrt(97))^(-1)*sqrt(14)+(1/2)*(sqrt(43)+sqrt(97))^(-1)*sqrt(13)]');
        expect(nerdamer('solve(a*y^2*x^3-1, x)').toString()).toEqual('[((-1/2)*abs(a^(-1)*y^(-2))+(1/2)*a^(-1)*y^(-2))^(1/3)+((1/2)*a^(-1)*y^(-2)+(1/2)*abs(a^(-1)*y^(-2)))^(1/3),(((-1/2)*abs(a^(-1)*y^(-2))+(1/2)*a^(-1)*y^(-2))^(1/3)+((1/2)*a^(-1)*y^(-2)+(1/2)*abs(a^(-1)*y^(-2)))^(1/3))*((1/2)*i*sqrt(3)+1/2),(((-1/2)*abs(a^(-1)*y^(-2))+(1/2)*a^(-1)*y^(-2))^(1/3)+((1/2)*a^(-1)*y^(-2)+(1/2)*abs(a^(-1)*y^(-2)))^(1/3))*((1/2)*i*sqrt(3)+1/2)^2]');
        expect(nerdamer('solve((1/2)*sqrt(-4*x+4*y)-2+y, y)').toString()).toEqual('[(-1/2)*(-5+sqrt(-4*x+9)),(-1/2)*(-5-sqrt(-4*x+9))]');
        expect(nerdamer('solve(log(a*x-c)-b=21, x)').toString()).toEqual('[-(-c-e^(21+b))*a^(-1)]');
        expect(nerdamer('solve(x/(x-a)+4,x)').toString()).toEqual('[(4/5)*a]');
        expect(nerdamer('solve(3*sin(a^2*x-b)-4,x)').toString()).toEqual('[a^(-2)*asin(4/3)]');
        expect(nerdamer('solve(a*log(x^2-4)-4,x)').toString()).toEqual('[(1/2)*sqrt(16+4*e^(4*a^(-1))),(-1/2)*sqrt(16+4*e^(4*a^(-1)))]');
        expect(nerdamer('solve(x/(x^2+2*x+1)+4,x)').toString()).toEqual('[(1/8)*sqrt(17)-9/8,(-1/8)*sqrt(17)-9/8]');
        expect(nerdamer('solve((a*x^2+1),x)').toString()).toEqual('[a^(-1)*sqrt(-a),-a^(-1)*sqrt(-a)]');
        expect(nerdamer('solve(sqrt(x)-2x+x^2,x)').toString()).toEqual('[(-1/2)*sqrt(5)+3/2,0,1,832040/2178309]');
        expect(nerdamer('solve((2x+x^2)^2-x,x)').toString()).toEqual('[0,((-1/6)*sqrt(3)^(-1)*sqrt(59)+43/54)^(1/3)+((1/6)*sqrt(3)^(-1)*sqrt(59)+43/54)^(1/3)-4/3,(((-1/6)*sqrt(3)^(-1)*sqrt(59)+43/54)^(1/3)+((1/6)*sqrt(3)^(-1)*sqrt(59)+43/54)^(1/3)-4/3)*((1/2)*i*sqrt(3)+1/2),(((-1/6)*sqrt(3)^(-1)*sqrt(59)+43/54)^(1/3)+((1/6)*sqrt(3)^(-1)*sqrt(59)+43/54)^(1/3)-4/3)*((1/2)*i*sqrt(3)+1/2)^2]');
        expect(nerdamer('solve((5*x^4-2)/(x+1)/(x^2-1),x)').toString()).toEqual('[72425485/91070226,-72425485/91070226,(316684236/398209345)*i,(-316684236/398209345)*i]');
        expect(nerdamer('solve(0=(x^(2)-2)/(e^(x)-1), x)').toString()).toEqual('[sqrt(2),-sqrt(2)]');
        expect(nerdamer('solve(4/y^2=x^2+1,y)').toString()).toEqual('[(1/2)*(-1-x^2)^(-1)*sqrt(16+16*x^2),(-1/2)*(-1-x^2)^(-1)*sqrt(16+16*x^2)]');
        expect(nerdamer('solve(1/(x+x^2), x)').toString()).toEqual('[]');
        expect(nerdamer('solve(1/(x+x^2-1), x)').toString()).toEqual('[]');
        expect(nerdamer('solve(-1+11000*(-100*(10+x)^(-1)+20)^(-2)*(10+x)^(-2), x)').toString()).toEqual('[(-1/2)*sqrt(110)-5,(1/2)*sqrt(110)-5]');
        expect(nerdamer('solve(x^3+y^3=3, x)').toString()).toEqual('[((-1/2)*y^3+3/2+abs((-1/2)*y^3+3/2))^(1/3)+((-1/2)*y^3-abs((-1/2)*y^3+3/2)+3/2)^(1/3),(((-1/2)*y^3+3/2+abs((-1/2)*y^3+3/2))^(1/3)+((-1/2)*y^3-abs((-1/2)*y^3+3/2)+3/2)^(1/3))*((1/2)*i*sqrt(3)+1/2),(((-1/2)*y^3+3/2+abs((-1/2)*y^3+3/2))^(1/3)+((-1/2)*y^3-abs((-1/2)*y^3+3/2)+3/2)^(1/3))*((1/2)*i*sqrt(3)+1/2)^2]');
        expect(nerdamer('solve(sqrt(10x+186)=x+9,x)').toString()).toEqual('[7]');
        expect(nerdamer('solve(x^3+8=x^2+6,x)').toString()).toEqual('[-1,1+i,-i+1]');
        expect(nerdamer('solve(x^3-10x^2+31x-30,x)').toString()).toEqual('[3,5,2]');
        expect(nerdamer('solve(8x^3-26x^2+3x+9,x)').toString()).toEqual('[3/4,-1/2,3]');
        expect(nerdamer('solve(x^3-1/2x^2-13/2x-3,x)').toString()).toEqual('[-2,3,-1/2]');
        expect(nerdamer('solve(x^3+2x^2+3x-4=0,x)').evaluate().text()).toEqual('[0.776045435028538,0.388022717514269+0.6720750612256601*i,-0.388022717514269+0.6720750612256599*i]');
        expect(nerdamer('solve(x*log(x),x)').toString()).toEqual('[1]');
        expect(nerdamer('solve((9x+x^2)^3+10800x+40x^4+4440x^2+720x^3+20(9*x+x^2)^2+8000,x) ').toString()).toEqual('[-5,-4]');
        expect(nerdamer('solve((x^3-4)/(x^3+7x-11),x)').evaluate().text()).toEqual('[1.587401051968199,0.7937005259840910+1.3747296369986024*i,-0.793700525984099+1.374729636998602*i]');
        expect(nerdamer('solve((93222358/131836323)*(-2*y+549964829/38888386)=10, y)').toString()).toEqual('[1/3625267041734188]');
        expect(nerdamer('solve(sqrt(x)+sqrt(2x+1)=5,x) ').toString()).toEqual('[4]');
        expect(nerdamer('solve(sqrt(x)-1,x) ').toString()).toEqual('[1]');
        expect(nerdamer('solve(sqrt(x)+1,x)').toString()).toEqual('[]');
        expect(nerdamer('solve((x-1)*(x+1)*x=3x,x)').toString()).toEqual('[0,2,-2]');
        expect(nerdamer('solve(sqrt(x^2+1),x)').toString()).toEqual('[i,-i]');
        expect(nerdamer('solve(sqrt(x^2-1),x)').toString()).toEqual('[1,-1]');
        expect(nerdamer('solve(((x+1)*((x+1)+1))/2=n,x)').toString()).toEqual('[-3/2+sqrt(1/4+2*n),-3/2-sqrt(1/4+2*n)]');
        expect(nerdamer('solve(sqrt(10x+186)=x+9,x)').toString()).toEqual('[7]');
        expect(nerdamer('solve(x^3+8=x^2+6,x)').toString()).toEqual('[-1,1+i,-i+1]');
        expect(nerdamer('solve(x^2=x^-2,x)').toString()).toEqual('[1,-1,i,-i]');
        expect(nerdamer('solve((x+1)(x+1)x=3x,x)').toString()).toEqual('[0,-1+sqrt(3),-1-sqrt(3)]');
        expect(nerdamer('solve(log(y) = -t, y)').toString() ).toEqual('[e^(-t)]');
        expect(nerdamer('solve(y=exp(4x),x)').toString() ).toEqual('[(1/4)*log(y)]');

    });
    it('should solve system of equations correctly', function () {
        expect(nerdamer.solveEquations(['x+y=1', '2*x=6', '4*z+y=6']).toString()).toEqual('x,3,y,-2,z,2');
        expect(nerdamer.solveEquations(['x+y=a', 'x-y=b', 'z+y=c'], ['x', 'y', 'z']).toString()).toEqual('x,0.5*a+0.5*b,y,-0.5*b+0.5*a,z,-0.5*a+0.5*b+c');
        expect(nerdamer.solveEquations(['x-2*y=-3', 'x+y-z+2*d=8', '5*d-1=19', 'z+d=7']).toString()).toEqual('d,4,x,1,y,2,z,3');
        expect(nerdamer.solveEquations('x^2+4=x-y').toString()).toEqual('(1/2)*(1+sqrt(-15-4*y)),(1/2)*(-sqrt(-15-4*y)+1)');
        expect(nerdamer.solveEquations(['x+y=3', 'y^3-x=7']).toString()).toEqual('x,1,y,2');
        expect(nerdamer.solveEquations(['x^2+y=3', 'x+y+z=6', 'z^2-y=7']).toString()).toEqual('x,1,y,2,z,3');
        expect(nerdamer.solveEquations(['x*y-cos(z)=-3', '3*z^3-y^2+1=12', '3*sin(x)*cos(y)-x^3=-4']).toString()).toEqual('x,1.10523895006979,y,-2.98980336936266,z,1.88015428627437');
        expect(nerdamer.solveEquations(['x=i','x+y=3']).toString()).toEqual('x,i,y,-i+3');
        expect(nerdamer.solveEquations(["x/(45909438.9 + 0 + x)=0", "45909438.9+0+x=45909438.9"]).toString()).toEqual('x,0');
        expect(nerdamer.solveEquations(["a=1"]).toString()).toEqual('a,1');
        expect(nerdamer.solveEquations(["x=5", "0.6=1-(x/(10+y))"]).toString()).toEqual('x,5,y,2.5');
    });
    /** #55: nerdamer.solveEquation quits working */
    it('should handle text("fractions") without later impact', function () {
        expect(nerdamer.solveEquations("x+1=2", "x").toString()).toEqual('1');
        expect(nerdamer('x=1').text("fractions")).toEqual('x=1');
        expect(nerdamer.solveEquations("x+1=2", "x").toString()).toEqual('1');
    });
    it('should parse equations correctly', function () {
        expect(nerdamer("-(a+1)=(a+3)^2").toString()).toEqual('-1-a=(3+a)^2');
    });
    //NOTE: contains duplicates
    it('should solve functions with factorials', function () {
        expect(nerdamer('solve(x!-x^2,x)').text('decimals', 20)).toEqual('[-2.200391782610595,-4.010232827899529,-2.938361683501947,1,1.000000000000001,3.562382285390900,3.562382285390896,0.9999999999999910,1.000000000000000]');
    });
    it('should solve for variables other than x', function () {
        expect(nerdamer('solve(2*a^(2)+4*a*6=128, a)').toString()).toEqual('[4,-16]');
    });
    it('should solve nonlinear system of equations with multiple parameter functions', function () {
        var ans = nerdamer.solveEquations([
            `y=x * 2`,
            `z=y + max (y * 0.1, 23)`,
            `j=y + max (y * 0.1, 23)`,
            `6694.895373 = j + z + (max(j * 0.280587, z * 0.280587, 176))`
        ]);
        expect(ans.toString()).toEqual('j,2935.601831019821,x,1334.3644686453729,y,2668.7289372907458,z,2935.601831019821');
    });

    it('should solve factors', function () {
        expect(nerdamer('solve((x-1)*(-a*c-a*x+c*x+x^2),x)').text()).toEqual('[1,-c,a]');
    });
    
    it('should solve circle equations', function() {
        var eq1 ="x^2+y^2=1";
        var eq2 ="x+y=1";
        var sol = nerdamer.solveEquations([eq1, eq2]);
        expect(sol.toString()).toEqual('x,1,0,y,0,1');
    });
});