##// END OF EJS Templates
upstream » ipython
RSS

Clone from https://github.com/ipython/ipython.git

Removed the timer callback in favor of the idle one and re-use wx waiting time after an event is processed. This make things more reactive. Also, the created window is now made insivisible and is not supposed to be ever show or detroyed. Finally, fixed the bug in window closing for linux platform using the glutSetOption available on Freeglut.
Removed the timer callback in favor of the idle one and re-use wx waiting time after an event is processed. This make things more reactive. Also, the created window is now made insivisible and is not supposed to be ever show or detroyed. Finally, fixed the bug in window closing for linux platform using the glutSetOption available on Freeglut.
Brian E. Granger - - Load All Authors

File last commit:

r4637:d919e2ec
r4831:c6756143
Show More
sympy.ipynb
267 lines | 36.2 KiB | text/plain | TextLexer
/ docs / examples / notebooks / sympy.ipynb
History | Annotation | Raw |Copy content |Copy permalink

SymPy: Open Source Symbolic Mathematics

In [1]:
%load_ext sympyprinting
In [2]:
from __future__ import division
from sympy import *
x, y, z = symbols("x y z")
k, m, n = symbols("k m n", integer=True)
f, g, h = map(Function, 'fgh')

Elementary operations

In [3]:
Rational(3,2)*pi + exp(I*x) / (x**2 + y)
Out[3]:
$$\frac{3}{2} \pi + \frac{e^{\mathbf{\imath} x}}{x^{2} + y}$$
In [4]:
exp(I*x).subs(x,pi).evalf()
Out[4]:
$$-1.0$$
In [5]:
e = x + 2*y
In [6]:
srepr(e)
Out[6]:
Add(Symbol('x'), Mul(Integer(2), Symbol('y')))
In [7]:
exp(pi * sqrt(163)).evalf(50)
Out[7]:
$$262537412640768743.99999999999925007259719818568888$$

Algebra

In [8]:
((x+y)**2 * (x+1)).expand()
Out[8]:
$$x^{3} + 2 x^{2} y + x^{2} + x y^{2} + 2 x y + y^{2}$$
In [9]:
a = 1/x + (x*sin(x) - 1)/x
display(a)
simplify(a)
$$\frac{x \operatorname{sin}\left(x\right) -1}{x} + \frac{1}{x}$$
Out[9]:
$$\operatorname{sin}\left(x\right)$$
In [10]:
solve(Eq(x**3 + 2*x**2 + 4*x + 8, 0), x)
Out[10]:
[-2⋅ⅈ, 2⋅ⅈ, -2]
In [11]:
a, b = symbols('a b')
Sum(6*n**2 + 2**n, (n, a, b))
Out[11]:
$$\sum_{n=a}^{b} \left(2^{n} + 6 n^{2}\right)$$

Calculus

In [12]:
limit((sin(x)-x)/x**3, x, 0)
Out[12]:
$$- \frac{1}{6}$$
In [13]:
(1/cos(x)).series(x, 0, 6)
Out[13]:
$$1 + \frac{1}{2} x^{2} + \frac{5}{24} x^{4} + \operatorname{\mathcal{O}}\left(x^{6}\right)$$
In [14]:
diff(cos(x**2)**2 / (1+x), x)
Out[14]:
$$- 4 \frac{x \operatorname{sin}\left(x^{2}\right) \operatorname{cos}\left(x^{2}\right)}{x + 1} - \frac{\operatorname{cos}^{2}\left(x^{2}\right)}{\left(x + 1\right)^{2}}$$
In [15]:
integrate(x**2 * cos(x), (x, 0, pi/2))
Out[15]:
$$-2 + \frac{1}{4} \pi^{2}$$
In [16]:
eqn = Eq(Derivative(f(x),x,x) + 9*f(x), 1)
display(eqn)
dsolve(eqn, f(x))
$$9 \operatorname{f}\left(x\right) + \frac{\partial^{2}}{\partial^{2} x} \operatorname{f}\left(x\right) = 1$$
Out[16]:
$$\operatorname{f}\left(x\right) = C_{1} \operatorname{cos}\left(3 x\right) + C_{2} \operatorname{sin}\left(3 x\right) + \frac{1}{9}$$