Integrating in Python using Sympy

Question

I am currently using `Sympy` to help me perform mathematical calculations. Right now, I am trying to perform a numerical integration, but keep getting an error any time I run the script. Here is the script: ``` from sympy import * cst = { 'qe':1.60217646*10**-19, 'm0':N(1.25663706*10**-6) } d = 3.6*10**-2 l = 20.3*10**-2 n = 217.0 I = 10.2 # Circum of loops circ = l/n; # Radius r = N( circ/(2*pi) ) # Flux through a ring a distance R from the ceter def flux(rad, I, loopRad): distFromWire = loopRad - rad bPoint = cst['m0']*I/(2*pi*distFromWire) return ( bPoint*2*pi*rad ) # Integrate from r=0 to r=wireRad x = Symbol('x') ig = Symbol('ig') ig = flux(x, I, r) print(ig) integrate(ig*x,x) ``` I am sure there is probably something wrong with the actual physics/math, but right now I just want it to integrate. Here is the output I get when I run the script: ``` 8.05359718208634e-5*x/(-6.28318530717959*x + 0.000935483870967742) Traceback (most recent call last): File "script.py", line 34, in <mo…

Accepted Answer

It is a very bad idea to use a symbolic library for numerical work. Just use scipy/numpy. That being said, for such a simple integral you could have used sympy. However you should actually use sympy expressions, not dump everything in opaque functions.

Firstly, learn how do variables in python work:

```
ig = Symbol('ig')
ig = flux(x, I, r)
```

After this operation `ig` is not a Symbol any more, it is just the return value of `flux`.

Define all your symbols and then make an expression out of them. The integral is sufficiently simple for sympy to handle it.

Finally, integral as simple as `const*x/(x-const)` as in your case should be done by hand, not wasted on software.

[EDIT]: I have rewritten it cleanly, and still sympy does not integrate correctly because of a bug. You could report it on the mailing list or issue tracker and they will try to correct it. That being said, the expression is so simple that it can be integrated by hand.

[EDIT2]:

```
In [5]: integrate(a*x/(b*x+c), x)
Out[5]:

⎛         ⎛ 2        ⎞⎞
  ⎜x   c⋅log⎝b ⋅x + b⋅c⎠⎟
a⋅⎜─ - ─────────────────⎟
  ⎜b            2       ⎟
  ⎝            b        ⎠
```

Integrating in Python using Sympy

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