CODEWITHSUNDEEP
pythonexpressionsympyuser-defined
George Datseris
George Datseris

Reputation: 411

Exact user defined expressions in Sympy derivatives

I am using Sympy to calculate the derivative of a complicated potential. I have defined x, y, D0, e, C, k, d, b as Sympy Symbols. Then I go on to do the following definitions:

import sympy as sm
x, y, D0, e, C, k, d, b = sm.symbols("x, y, D0, e, C, k, d, b")
phi = sm.atan2(y,x)
D = D0 + e*D0*sm.sin(k*phi)
rho = sm.sqrt(x**2 + y**2)

U = (2**b)/((2*D-d)**b)*(D - rho)**b

The symbol "U" stands for the 2D potential.

Now when I differentiate this vs. x using:

sm.simplify(U.diff(x))

I get an extremely long answer: extremely long naswer

As you can see, in the answer there is explicitly the full expression for e.g. D : D0 + e*D0*sin(k*phi) . Also, instead of sin(phi) I get sin(atan2(x,y) and the same happens for all of my defined expressions.

Is there a way for the result to automatically show my definitions instead of the long versions, without having the need to use the subs method for every single user-defined variable?

E.g. instead of D0 + e*D0*sin(k*phi) Sympy automatically uses the symbol D?

Upvotes: 1

Views: 373

Answers (1)

asmeurer
asmeurer

Reputation: 91490

When you write phi = sm.atan2(y,x), this assigns a Python variable to the result of atan2(y, x). If you want phi to be a symbol, you have to define it that way

phi = symbols('phi')

and then substitute phi in as atan2(y, x) later.

U.subs(phi, atan2(y, x))

This is worth reading regarding this.

Upvotes: 1

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