Single variable derivative of expression(symbolic)

Question

I have written an HTML code using JavaScript to differentiate a single variable function. My code is here. I have used Mathjax to print the output. But the output produced is not simplified. For example, the derivative of sin(x)/cos(x) is produced as

((((cos(x))*(cos(x)))-((sin(x))*(-(sin(x)))))/((cos(x))^2))

which can be simplified to

(sin(x)^2+cos(x)^2)/cos(x)^2

I have constructed expression tree with the application of Dijkstra's shunting yard algorithm. And then constructed the expression tree of derivative recursively. But I have problem with the simplification.

Can anyone please help with the simplification of the output produced? My knowledge is not beyond elementary data structures.

Please be more specific in the question. At least examples what you are getting and what is desirable output. The question should work even if the link is dead. — IvanH, Nov 17 '13 at 16:08
@SumitKumarJha - What IvanH was asking for is code sample. Do you have a specific coding/algorithmic problem - either with correctness or performance of your code? — Chandranshu, Nov 17 '13 at 16:52
@Chandranshu- I wanted to know, if there exists an algorithm for simplification of algebraic expression.(Like simplification of radicals etc.) — Sumit Kumar Jha, Nov 17 '13 at 16:54
I think you want at least three things: removal of unneeded parentheses, collection of a^n * a ==> a^(n+1), and collection of sign terms. — ellisbben, Nov 19 '13 at 18:13
SICP discusses symbolic differentiation and how to achieve a few simplifications by adding rules to the differentiation: http://mitpress.mit.edu/sicp/full-text/sicp/book/node39.html — ellisbben, Nov 19 '13 at 18:17
You could always look into an existing library? https://github.com/jiggzson/nerdamer — ArchHaskeller, Sep 29 '15 at 22:51

score 1 · Answer 1 · answered Jan 15 '14 at 10:08

Well i can think only of implementation of algebraic rules.

extremlly hard to code
even harder to debug

1.create a list of simplification equations

like:
```
cos^2(x)+sin^2(x)=1
...
```
this is easy
but be careful not to add cyclic equations here (so it would loop without end)
or rules that not simplify the output

2.create list of substitution methods

3.go through equation

test all the simplification rules
if it is applyable then apply it (hard to code)
if none found then try substitutions (extremlly hard to code it right)
if still none found then stop

4.do the point 3 for all representations of equation

equation can be writen in more ways
multiplicative
exponentiol
fractional,etc ...
you need to test all the variations

Single variable derivative of expression(symbolic)

1 Answers1