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Tutorial

Symbols

To make symbolic variables in SymPy you have to declare the variable explicitly:

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>>> pi**2
pi**2

>>> pi.evalf()
3.141592653589793238462643383

<<< E**2
exp(2)

>>> oo > 99999
True

>>> oo + 1
oo

Differentiation

You can differentiate any SymPy expression using diff(func, var). Higher derivatives can be solved using diff(func, var, n).

>>> from sympy import *
>>> x = Symbol('x')

>>> diff(sin(x), x)
cos(x)

>>> diff(sin(2*x), x, 1)
2*cos(2*x)

>>> diff(sin(2*x), x, 2)
-4*sin(2*x)

Integration

SymPy has support for both indefinite and definite integration:

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>>> integrate(exp(-x), (x, 0, oo))
1

>>> integrate(log(x), (x, 0, 1))
-1

Algebraic equations

SymPy is able to solve algebraic equations with one or several variables. solve(equation, variable) takes as first argument an equation that is supposed to be equaled to 0, and as second argument the unknown variable. In case of multiple equations and variables, solve returns a dictonary containing the results. Note that SymPy also handles complex numbers using the symbol I.

>>> from sympy import *
>>> solve(x**2 - 1, x)
[-1, 1]


>>> solve([x + 5*y - 2, -3*x + 6*y - 15], [x, y])
{x: -3, y: 1}


>>> solve(Eq(x**4, 1), x)
[-1, 1, -I, I]

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