Sympy_Resumen
-
Upload
guillermo-diaz-toro -
Category
Documents
-
view
213 -
download
0
description
Transcript of Sympy_Resumen
-
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