使用 Sympy 集成到 Python 中 [英] Integrating in Python using Sympy

问题描述

我目前正在使用 Sympy 来帮助我进行数学计算.现在，我正在尝试执行数值积分，但每次运行脚本时都会出现错误.这是脚本:

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)

我确信实际的物理/数学可能有问题，但现在我只想整合它.这是我运行脚本时得到的输出:

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 <module>
    integrate(ig*x,x)
  File "C:\Python27\lib\site-packages\sympy\utilities\decorator.py", line 24, in threaded_func
    return func(expr, *args, **kwargs)
  File "C:\Python27\lib\site-packages\sympy\integrals\integrals.py", line 847, in integrate
    return integral.doit(deep = False)
  File "C:\Python27\lib\site-packages\sympy\integrals\integrals.py", line 364, in doit
    antideriv = self._eval_integral(function, xab[0])
  File "C:\Python27\lib\site-packages\sympy\integrals\integrals.py", line 577, in _eval_integral
    parts.append(coeff * ratint(g, x))
  File "C:\Python27\lib\site-packages\sympy\integrals\rationaltools.py", line 42, in ratint
    g, h = ratint_ratpart(p, q, x)
  File "C:\Python27\lib\site-packages\sympy\integrals\rationaltools.py", line 124, in ratint_ratpart
    H = f - A.diff()*v + A*(u.diff()*v).quo(u) - B*u
  File "C:\Python27\lib\site-packages\sympy\core\decorators.py", line 75, in __sympifyit_wrapper
    return func(a, sympify(b, strict=True))
  File "C:\Python27\lib\site-packages\sympy\polys\polytools.py", line 3360, in __mul__
    return f.mul(g)
  File "C:\Python27\lib\site-packages\sympy\polys\polytools.py", line 1295, in mul
    _, per, F, G = f._unify(g)
  File "C:\Python27\lib\site-packages\sympy\polys\polytools.py", line 377, in _unify
    F = f.rep.convert(dom)
  File "C:\Python27\lib\site-packages\sympy\polys\polyclasses.py", line 277, in convert
    return DMP(dmp_convert(f.rep, f.lev, f.dom, dom), dom, f.lev)
  File "C:\Python27\lib\site-packages\sympy\polys\densebasic.py", line 530, in dmp_convert
    return dup_convert(f, K0, K1)
  File "C:\Python27\lib\site-packages\sympy\polys\densebasic.py", line 506, in dup_convert
    return dup_strip([ K1.convert(c, K0) for c in f ])
  File "C:\Python27\lib\site-packages\sympy\polys\domains\domain.py", line 85, in convert
    raise CoercionFailed("can't convert %s of type %s to %s" % (a, K0, K1))
sympy.polys.polyerrors.CoercionFailed: can't convert DMP([1, 0], ZZ) of type ZZ[_b1] to RR
[Finished in 0.3s with exit code 1]

好的，所以我取出程序使用的数字并将其放入 wolfram alpha 中.事实证明积分不收敛，因此错误.我想这只是一个数学错误.

Alright, so I pulled out the numbers that the program was using and put it in wolfram alpha. Turns out that the integral doesn't converge, hence the error. I guess it WAS just a math error.

推荐答案

将符号库用于数值计算是一个非常糟糕的主意.只需使用 scipy/numpy.话虽如此，对于这样一个简单的积分，您可以使用 sympy.但是，您实际上应该使用 sympy 表达式，而不是在不透明的函数中转储所有内容.

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.

首先了解python中的变量是如何工作的:

Firstly, learn how do variables in python work:

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

此操作后ig不再是Symbol，它只是flux的返回值.

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

定义所有符号，然后用它们表达.积分足够简单，sympy 可以处理它.

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

最后，像 const*x/(x-const) 这样简单的积分应该手工完成，而不是浪费在软件上.

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

:我已经干净利落地重写了它，但由于错误，sympy 仍然无法正确集成.您可以在邮件列表或问题跟踪器上报告它，他们会尝试更正.话虽这么说，表达式很简单，可以手工整合.

: 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.

:

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

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

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