Java: solving symbolic algebraic equations

Question

I'm having trouble adding this functionality to my calculator app. Here's what I had in mind:

I want to solve: 2x = 5 + 4x.

To solve this is no problem if I would use an external token library to parse the equation, but since my entire program is built around a shunting yard parser (EXP4J), it complicates things. You might say that I could just use the token parser for specific cases, but when you consider that I have FUNCTIONS using EXP4J, it becomes really tangled.

So, while I could make it work for 2x = 5 + 4x by simply alternating to a token parser for this specific case, calculations that use EXP4J, like:

2x = 5*exp4jfunc(x + 5,x) + cos(x) are completely beyond me.

Does anyone have any idea on how to get around this? I don't even know how my CASIO tackles this, as it freezes on solve-for-x equations like x = 9^x...

Solving equations isnt as easy as you think. And it has nothing to do with your parser. Anything except polynomials is going to be VERY difficult to solve, just from a mathematical standpoint. At least if you go with a general approach. — Mario Dekena, Mar 20 '16 at 21:12
What you want in general is called a "computer algebra system"; see https://en.wikipedia.org/wiki/Computer_algebra_system. These are very different than tools that compute the value of a formula because they have to manipulate the equations symbolically. These are pretty hard to build, especially if you want to handle many different types of equations; you need different solver techniques per equation type. You can get a small idea of what it takes to implement one by looking at a very simple one for high school algebra: http://www.semdesigns.com/Products/DMS/SimpleDMSDomainExample.html — Ira Baxter, Mar 21 '16 at 03:26
PS: it is pretty easy to write a *parser*. See http://stackoverflow.com/questions/2245962/is-there-an-alternative-for-flex-bison-that-is-usable-on-8-bit-embedded-systems/2336769#2336769. It would not be hard to write a parser for your exp4j example. The solver part is hard, as I said above. — Ira Baxter, Mar 21 '16 at 03:33
@daedsidog: Did ever find solution for this? I am trying to solve the similiar problem. For example: `x*1/40+5=12` So here I already know the solution which is `12` but I want to solve for `x` like `x=(12-5)*40` which results in `x=280`. — Kishor Prakash, Nov 19 '18 at 09:45

axelclk · Answer 1 · 2018-04-14T17:43:59.370

With the symja library you can solve your problem like this:

package org.matheclipse.core.examples;

import org.matheclipse.core.eval.ExprEvaluator;
import org.matheclipse.core.interfaces.IExpr;
import org.matheclipse.parser.client.SyntaxError;
import org.matheclipse.parser.client.math.MathException;

public class Solve2Example {

    public static void main(String[] args) {
        try {
            ExprEvaluator util = new ExprEvaluator();
            IExpr result = util.evaluate("Solve(2*x==5 + 4*x,x)");
            // print: {{x->-5/2}}
            System.out.println(result.toString());

            result = util.evaluate("Roots(2*x==5+4*x, x)");
            // print: x==-5/2
            System.out.println(result.toString());
        } catch (SyntaxError e) {
            // catch Symja parser errors here
            System.out.println(e.getMessage());
        } catch (MathException me) {
            // catch Symja math errors here
            System.out.println(me.getMessage());
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
}

You can look into the implementation of the Roots() function how the parsed AST is transformed to solve the equation.

score 1 · Answer 2 · edited Jun 20 '20 at 09:12

I am not really familiar with exp4j... Given that the Expression class doesn't seem to provide much access to the parsed structure, a symbolic approach seems not really feasible with exp4j.

One thing you could try with exp4j instead:

Split the equation at = into left and right
Build a new equation that is the difference of both sides:

String diff = "(" + left + ") - (" + right + ")"
Parse diff with exp4j
Use a numerical method (e.g. the Secant method) with setVariable() and evaluate() to find the solution(s).

Shameless plug: If you are considering to use a different parser, take a look at this one

score -1 · Answer 3 · answered Mar 20 '16 at 21:17

First, define the domain of your equations. Are you talking about linear equations, polynomials, general non-linear equations, differential equations? Then define your dimension: Do you have one variable or many? Finally, select the appropriate solver (numerical, symbolical, Gauss, Newton etc.).

Once you have defined this, you need to transform the syntax tree of exp4j into the format required by the solver. However it seems that you won't be able to do this with exp4j, since it does not expose the structure of an expression as an API.

I would advice to use a proper AST. If you cannot do that, you can see in the implementation, that the internal structure is basically just a token list.

Java: solving symbolic algebraic equations

3 Answers3

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