sympy.ipynb
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SymPy: Open Source Symbolic Mathematics
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%load_ext sympyprinting
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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
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Rational(3,2)*pi + exp(I*x) / (x**2 + y)
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exp(I*x).subs(x,pi).evalf()
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e = x + 2*y
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srepr(e)
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exp(pi * sqrt(163)).evalf(50)
Algebra
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((x+y)**2 * (x+1)).expand()
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a = 1/x + (x*sin(x) - 1)/x
display(a)
simplify(a)
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solve(Eq(x**3 + 2*x**2 + 4*x + 8, 0), x)
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a, b = symbols('a b')
Sum(6*n**2 + 2**n, (n, a, b))
Calculus
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limit((sin(x)-x)/x**3, x, 0)
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(1/cos(x)).series(x, 0, 6)
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diff(cos(x**2)**2 / (1+x), x)
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integrate(x**2 * cos(x), (x, 0, pi/2))
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eqn = Eq(Derivative(f(x),x,x) + 9*f(x), 1)
display(eqn)
dsolve(eqn, f(x))
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%notebook save sympy.ipynb
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%notebook load basic_quantum.ipynb