Para una mejor visualizacin de ecuaciones

>>> from sympy import init_printing >>> init_printing(use_unicode=False, wrap_line=False, no_global=True)

Importar simbolos

>>> from sympy import Symbol

>>> x = Symbol(x) >>> y = Symbol(y)

>>> a, b, c = symbols(a,b,c)

Expandir

>>> ((x+y)**2).expand() x**2 + 2*x*y + y**2

Sustituir

>>> ((x+y)**2).subs(x, y) 4*y**2

>>> ((x+y)**2).subs(x, 1-y) 1

Apartar

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

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

>>> apart(1/( (x+2)*(x+1) ), x) 1 1 - ----- + ----- x + 2 x + 1

>>> (x+1)/(x-1) x + 1 -----

x - 1 >>> apart((x+1)/(x-1), x) 2

1 + ----- x 1

Juntar

>>> from sympy import together >>> together(1/x + 1/y + 1/z)

x*y + x*z + y*z --------------- x*y*z >>> together(apart((x+1)/(x-1), x), x)

x + 1 ----- x - 1

>>> together(apart(1/( (x+2)*(x+1) ), x), x) 1 ---------------

Resolver sistemas de ecuaciones

>>> from sympy.solvers import solve

>>> from sympy import Symbol

>>> x = Symbol('x')

>>> solve(x**2 - 1, x)

[-1, 1]

>>> from sympy import solve, symbols >>> x, y = symbols(x,y)

>>> solve(x**4 - 1, x) [-1, 1, -I, I] >>> solve([x + 5*y - 2, -3*x + 6*y - 15], [x, y])

{x: -3, y: 1}

>>> from sympy.solvers import solve

>>> from sympy import Symbol

>>> x = Symbol(x)

>>> solve(x**2 - 1, x)

[-1, 1]

Resolver sistemas lineales con matriz LU

>>> A = matrix([[1, 2], [3, 4]])

>>> b = matrix([-10, 10]) >>> x = lu_solve(A, b) >>> x

matrix( [[30.0], [-20.0]])

>>> from sympy import Matrix, solve_linear_system

>>> from sympy.abc import x, y

Solve the following system: x + 4 y == 2

-2 x + y == 14

>>> system = Matrix(( (1, 4, 2), (-2, 1, 14)))

>>> solve_linear_system(system, x, y)

{x: -6, y: 2}

sympy.solvers.solvers.

>>> from sympy import Matrix

>>> from sympy.abc import x, y, z

>>> from sympy.solvers.solvers import solve_linear_system_LU

>>> solve_linear_system_LU(Matrix([

... [1, 2, 0, 1],

... [3, 2, 2, 1],

... [2, 0, 0, 1]]), [x, y, z])

{x: 1/2, y: 1/4, z: -1/2}

Resolver sistemas de ecuaciones no lienales

>>> from sympy import roots, solve_poly_system

>>> solve(x**3 + 2*x + 3, x) ____ ____ 1 \/ 11 *I 1 \/ 11 *I

[-1, - - --------, - + --------] 2 2 2 2 >>> p = Symbol(p) >>> q = Symbol(q)

>>> sorted(solve(x**2 + p*x + q, x)) __________ __________ / 2 / 2

p \/ p - 4*q p \/ p - 4*q [- - + -------------, - - - -------------] 2 2 2 2

>>> solve_poly_system([y - x, x - 5], x, y) [(5, 5)] >>> solve_poly_system([y**2 - x**3 + 1, y*x], x, y)

___ ___ 1 \/ 3 *I 1 \/ 3 *I [(0, I), (0, -I), (1, 0), (- - + -------, 0), (- - - -------, 0)]

2 2 2 2

Derivadas

>>> from sympy import diff, Symbol, sin, tan

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

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

2 tan (x) + 1

Integrales

>>> from sympy import integrate, erf, exp, sin, log, oo, pi, sinh, symbols >>> x, y = symbols(x,y)

You can integrate elementary functions: >>> integrate(6*x**5, x) 6 x >>> integrate(sin(x), x)

-cos(x) >>> integrate(log(x), x) x*log(x) - x

>>> integrate(2*x + sinh(x), x) 2 x + cosh(x)

Also special functions are handled easily: >>> integrate(exp(-x**2)*erf(x), x) ____ 2

\/ pi *erf (x) -------------- 4