from sympy import *

Símbolos e Expressões

a = symbols('tau10:15', integer=True) #,cls=sy.Function)
sum(a)

$\displaystyle \tau_{10} + \tau_{11} + \tau_{12} + \tau_{13} + \tau_{14}$

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x,y,z,pi = symbols('x y z pi')

expr = y*(x**2 + y * sin(x) + 3* exp(z) + pi*x)

expr = $\displaystyle y \left(\pi x + x^{2} + y \sin{\left(x \right)} + 3 e^{z}\right)$

expr * y = $\displaystyle y^{2} \left(\pi x + x^{2} + y \sin{\left(x \right)} + 3 e^{z}\right)$

expr - x² = $\displaystyle - x^{2} + y \left(\pi x + x^{2} + y \sin{\left(x \right)} + 3 e^{z}\right)$

expand(expr)

$\displaystyle \pi x y + x^{2} y + y^{2} \sin{\left(x \right)} + 3 y e^{z}$

factor(expr)

$\displaystyle y \left(\pi x + x^{2} + y \sin{\left(x \right)} + 3 e^{z}\right)$

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Substituição

expr.subs(x,2)

$\displaystyle y \left(2 \pi + y \sin{\left(2 \right)} + 3 e^{z} + 4\right)$

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Substituição de várias variáveis

expr.subs({x:2,z:20})

$\displaystyle y \left(2 \pi + y \sin{\left(2 \right)} + 4 + 3 e^{20}\right)$

expr.subs([(x,2),(z,20)])

$\displaystyle y \left(2 \pi + y \sin{\left(2 \right)} + 4 + 3 e^{20}\right)$

expr.evalf(subs={x:2,z:20,y:2,pi:3},)

$\displaystyle 2910991196.09593$

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Igualdade

Eq(expr,1024)

$\displaystyle y \left(\pi x + x^{2} + y \sin{\left(x \right)} + 3 e^{z}\right) = 1024$

Eq(2+2,4)

$\displaystyle \text{True}$

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Sympify

string = 'x/5 + e**y + z + 6**3 + 0.12 + mu' 
sympify(string)

$\displaystyle e^{y} + \mu + \frac{x}{5} + z + 216.12$

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Simplificação

expr = sin(x)**2 + cos(x)**2 + ln(y)

expr → $\displaystyle \log{\left(y \right)} + \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}$

simplify(expr) → $\displaystyle \log{\left(y \right)} + 1$

expr = ((x + 2) * (x + 3) )
factor(expr)

$\displaystyle \left(x + 2\right) \left(x + 3\right)$

expand(expr)

$\displaystyle x^{2} + 5 x + 6$

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Simplificação trigonométrica

expr = (tan(x)*sec(x)*Pow(cos(x),2) * Rational(5,3))
expr

$\displaystyle \frac{5 \cos^{2}{\left(x \right)} \tan{\left(x \right)} \sec{\left(x \right)}}{3}$

trigsimp(expr)

$\displaystyle \frac{5 \sin{\left(x \right)}}{3}$

sec(x).rewrite(cos)

$\displaystyle \frac{1}{\cos{\left(x \right)}}$

sec(x).rewrite(sin)

$\displaystyle \frac{1}{\sin{\left(x + \frac{\pi}{2} \right)}}$

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Simplificação potência

powsimp(x**z * x**y)

$\displaystyle x^{y + z}$

expand_power_exp(x**z * x**y)

$\displaystyle x^{y} x^{z}$

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Funções

binomial(10,x)

$\displaystyle {\binom{10}{x}}$

log(5,4)

$\displaystyle \frac{\log{\left(5 \right)}}{\log{\left(4 \right)}}$

factorial(y*x)

$\displaystyle \left(x y\right)!$

gamma(y)

$\displaystyle \Gamma\left(y\right)$

beta(x,10)

$\displaystyle \operatorname{B}\left(x, 10\right)$

hyper([2,8],[10],x)

$\displaystyle {{}_{2}F_{1}\left(\begin{matrix} 2, 8 \\ 10 \end{matrix}\middle| {x} \right)}$