sympy-intro.sagews

Sympy

Cells are evaluated in Sage, hence there are a few differences.

• Raw Python integer numbers are entered by appending an r, like 42r.
• The ^ symbol automatically expands to **.

%auto
from __future__ import division
import sympy as sy
from sympy import symbols, log, pi, oo, pprint, Function, limit
x, y, z, t = symbols('x y z t')
k, m, n = symbols('k m n', integer=True)
f, g, h = symbols('f g h', cls=Function)

ex = x * log(2*x) / log(x)
simplify(ex)

x + x*log(2)/log(x)

ex.subs({x : 2*pi})

2*pi*log(4*pi)/log(2*pi)

limit((x-3*x^2)/(1-x-2 * x^2), x, oo)

3/2

expr = (x^2 - 1)/(x - 1)
print expr
print expr.cancel()

(x**2 - 1)/(x - 1) x + 1

expr2 = log(expr).integrate(x)
pprint(expr2, use_unicode=True)

⎛ 2 ⎞ ⎛ 2 ⎞ ⎜ x 1 ⎟ ⎜ x 1 ⎟ x⋅log⎜───── - ─────⎟ - x + log⎜───── - ─────⎟ ⎝x - 1 x - 1⎠ ⎝x - 1 x - 1⎠

@interact
def diffit(i = slider(range(7), default = 3)):
    expr = sin(i * x) ^ (i * x)
    pprint(expr, use_unicode=True)
    print
    dexpr = expr.diff(x, i)
    pprint(dexpr, use_unicode=True)

Interact: please open in CoCalc