Calculate symbolic square root of expression (with parameters) in python?

Question

Is it possible to calculate a square root of an expression in python ? For example , the square root of: (a^4 - 8a^2 -16a + 16)?

Of course the result will be with a, not a numeric value. I read about math.sqrt() and tried doing this , but pycharm insisted that i would assign a value into a .

import math
a = 16
b = math.sqrt(a**4 - 8*(a**2) -16*a +16 )
print b

this code works , but I do not want to assign into a , I want an expression as a result .

Yes, it is possible. Have you tried doing this yourself yet? — Martijn Pieters, Mar 21 '15 at 09:33
@matsjoyce: so why does the user need to try sympy to execute a mathematical expression? Python can do this directly without any help. — Martijn Pieters, Mar 21 '15 at 09:34
@MartijnPieters He wants it with `a` as a variable in the answer, not a numerical value. — matsjoyce, Mar 21 '15 at 09:34
@MartijnPieters I read about math.sqrt and tried doing this , but pycharm insisted that i would assign a value into a . — Noam, Mar 21 '15 at 09:35
@Noam: why not elaborate on that then in your question? What larger problem are you trying to solve here? What do you need this for? — Martijn Pieters, Mar 21 '15 at 09:36
@matsjoyce: my point is more that this question is *too vague* and open to multiple interpretations, widely differing. — Martijn Pieters, Mar 21 '15 at 09:36
I think your question might be better phrased "Is it possible to simplify an algebraic expression with Python?" since that sounds like what you want to do. — Weeble, Mar 21 '15 at 09:37
Might help if you provide an example of what you *expect the output to be*. — Hamish, Mar 21 '15 at 09:37
ok I should have wrote that . sorry . well I need this because I like programming and hate doing my math homework .... lol — Noam, Mar 21 '15 at 09:38
@MartijnPieters He seems to want symbolic manipulation, e.g. `sqrt(a^2+8a+4) = a + 2`. I agree about being broad, though. — matsjoyce, Mar 21 '15 at 09:39
@matsjoyce: again, that's open to interpretation. A good question is clearer than this. — Martijn Pieters, Mar 21 '15 at 09:39
@MartijnPieters sorry . I edited this question , I hope it is better now — Noam, Mar 21 '15 at 09:45
@Noam See http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-5-Sympy.ipynb#Sympy---Symbolic-algebra-in-Python, although your quaternary doesn't seem to simplify easily. — matsjoyce, Mar 21 '15 at 09:59

score 3 · Answer 1 · answered Mar 21 '15 at 10:01

Okay, I'm assuming that what you want is to take an algebraic expression, and simplify it by factoring parts of it. Is that right?

You could use sympy for this general class of question, but I note that (to the best of my knowledge) your example doesn't have a simpler answer! Here's an example where it can work:

>>> from sympy import Symbol, factor
>>> a = Symbol("a")
>>> factor(a**4 - 8*a**3 + 20*a**2 - 16*a + 4)
(a**2 - 4*a + 2)**2

However, I don't think your example has any factors. Is it actually an instance of a problem you need to solve, or just a general example of the shape of the problem?

score 0 · Answer 2 · answered Mar 21 '15 at 18:17

Python has a lot of batteries inside, however its huge standard library does not contain any symbolic algebraic module. Thus, if you want to do symbolic calculations, you have to use external modules, such as SymPy (as already suggested), or mathematical systems, such as SageMath.

What you can do in "standard" Python is to define a function which takes a as a parameter and that returns the corresponding value of your expression:

def f(a):
    import math
    return math.sqrt(a**4 - 8*(a**2) -16*a +16)

Depending on your application, this could be enough.

Calculate symbolic square root of expression (with parameters) in python?

2 Answers2