How to solve a math equation in a programming language?

Question

I need help to solve this formula ((n * 2) + 10) / (n + 1) = 3, preferably in PHP. (The numbers 2, 10 and 3 should be variables that can be changed.)

I'm able to solve this equation on paper quite easily. However, when I try to implement this in PHP, I'm not sure where to start. I've done several Google queries and searches on here and nothing seems to help. I'm missing the proper approach to deal with this problem.

Any tips and pointers would be great, and if you provide the exact code, please explain how you got to this result.

Do you need to implement only this one, or all equation of the same kind ? — Benjamin Crouzier, Aug 31 '11 at 08:00
There are specialized languages for formula transformation/equation solving. PHP does not lend itself to it, as scientific uses are not its primary domain. You might find something in Python or Perl however (and then invoke those via exec). — mario, Aug 31 '11 at 08:02
@pinouchon only this one, however the numbers will be dynamic — xidew, Aug 31 '11 at 08:03
@pinouchon 2, 10 and 3. I edited the question to specify that those numbers can be dynamic. — xidew, Aug 31 '11 at 08:08
@mario I see, I had a hunch that would be the case... how would you solve it in Python then for example? If I can understand the process, I can probably give it a shot to solve it in PHP. — xidew, Aug 31 '11 at 08:11
@xidew check my answer, now i take into account your new requirements — Benjamin Crouzier, Aug 31 '11 at 08:36

score 15 · Answer 1 · 2011-08-31T08:58:41.977

15

You're wanting to solve an equation, not implement it. There's a difference. Implementing the equation would be as simple as typing it in. You'd probably want to make it an equality operator (==) though.

Equation solvers are complicated, complicated things. I wouldn't try to make one when there are such good ones ( http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems ) lying around.

edited Aug 31 '11 at 08:58

answered Aug 31 '11 at 08:01

"You're wanting to solve an equation, not implement it." Oh, how I wish I could up-vote this more than once... – Aug 31 '11 at 08:04
Thanks for pointing to the correct term. I will edit the question :) – xidew Aug 31 '11 at 08:04
phpCAS does not mean what you think it means. – mario Aug 31 '11 at 08:38

score 9 · Answer 2 · answered Aug 31 '11 at 08:13

9

You can use http://pear.php.net/package/PHP_ParserGenerator/redirected to parse the math expressions into a syntax tree, then do the maths.

((n * 2) + 10) / (n + 1) = 3 would look like:

enter image description here

The idea is to bring on the right subtree (here ...) all the numbers, and on the left all the unknownws, just as you'd do on paper.

In the end you'll have:

  +
 / \
n  -7

which is 0. And there you have your solution, for any math expression (with one unknown variable).

I'll leave the algorithm to you.

answered Aug 31 '11 at 08:13

Flavius

13,566
13
80
126

Very interesting, I will have a look :) – xidew Aug 31 '11 at 08:23
And how do you move all the numbers to the right side? Could you give us an example please? Thanks! – Carlos Jul 01 '22 at 14:27

score 4 · Accepted Answer · answered Aug 31 '11 at 08:13

4

<?php

// ((x * n) + y)/(n + 1) = z)
// => n=(y-z)/(z-x)
function eq ($x=0,$y=0,$z=0)
{
    if ($z!=$x)
    {
        $n=($y-$z)/($z-$x);
    } else
    {
        $n='NAN';
    }
    return $n;
}

?>

(My algebra is old and flakey but I think this is right)

answered Aug 31 '11 at 08:13

DaveyBoy

2,928
2
17
27

Your function works! Would you mind explaning what was your thought process when you were writing/thinking about it? – xidew Aug 31 '11 at 08:20
Your function is mathematically incorect. You're missing the case $y == $x && $z == $x. In such a case, the esemble `R - { 1 }` is solution of the equation. – Benjamin Crouzier Aug 31 '11 at 08:49
Also, if i call `eq(0, 0, 1);`, your function yields `-1`, yet `((x * n) + y)/(n + 1) = z)` gives `((0 * -1) + 0)/(-1 + 1) = 1)` which is impossible – Benjamin Crouzier Aug 31 '11 at 08:58
My get out clause is that my algebra is old and flakey and not something I use everyday. The main thing was to check for division by 0 (hence the check for Z<>X). My thinking behind the solution was to get the equation into the form of `x*n=c` (even if x is a fraction). Once it's in that form, the solution was a simple re-write of the equation into PHP – DaveyBoy Aug 31 '11 at 09:13
@pinouchon - obviously, more checks can be added for special cases. However, I'm a programmer and not a mathematician so my caveat is still valid - my algebra is old and flakey but I **think** this is right – DaveyBoy Aug 31 '11 at 09:21
@DaveWilsonLAMP check my answer where all special cases are handled. The drawbacks of not handling special cases is that in some cases, you answer is just **wrong**, eg `eq(0,0,0)`, `eq(1,1,1)`, `eq(0,0,1)`, `eq(1,1,2)`... – Benjamin Crouzier Aug 31 '11 at 09:29
@pinchoun - As I said **I am not a mathematician, I am a programmer**. As such, I drew on my algebra classes from 25 years ago to rearrange the original equation into something which will allow variables to be plugged in and an answer produced. The main thing that stood out was the "divide by 0" problem so I checked for that. Special cases did not occur to me as I did not run a whole load of numbers through the function to check for special cases - I don't have time to do that. My original answer included "I **think** this is right" so I was open to correction – DaveyBoy Aug 31 '11 at 10:02
I decided to give DaveWilsonLAMP the correct answer because he was the first who wrote the function even though it wasn't as complete as pinouchon, still was correct. @pinouchon have also a correct answer however, now I wish I could accept both of them... – xidew Aug 31 '11 at 10:32
@Flavius I actually voted up your answer. I didn't pick it because it was hard to understand at first but I understand what you were going for. What I learned from Dave and pinouchon answers is that the answer I was looking for was a simplified version of my equation. I learned a lot from all the answers here and I'm really grateful, unfortunately I can only pick one good answer... :-| – xidew Sep 09 '11 at 12:33

score 3 · Answer 4 · answered Aug 31 '11 at 08:19

how about using brute-force??!?! might be slow and not exact:

$step = 0.00001;
$err = 0.1; //error margin
$start = 0;
$response = 3;

for($i = $start;$i <= 3;$i += $step){
   if((($i * 2) + 10) / ($i + 1) >= $response - $err){
       echo "the answer is $i";
   }
}

You could improove this answer.. on every loop you could calculate the distance between the current answer and the desired answer, and adjust the parameters acording to that..

This reminds me my old A.I. class =)

Good Luck

That's a solution, but I'm looking for the proper way to solve it. Thanks for your answer though! — xidew, Aug 31 '11 at 08:22

score 0 · Answer 5 · answered Oct 27 '15 at 03:36

Here's how to solve that equation in C# with the Symbolism computer algebra library:

var n = new Symbol("n");

(((n * 2) + 10) / (n + 1) == 3)
    .IsolateVariable(n)
    .Disp();

The following is displayed on the console when that code is executed:

n == 7

How to solve a math equation in a programming language?

5 Answers5