Sinopsis

>>> from  sympy  import  pprint ,  init_printing ,  Símbolo ,  sin ,  cos ,  exp ,  sqrt ,  serie ,  Integral ,  Función 
>>> 
>>> x  =  Símbolo ( "x" ) 
>>> y  =  Símbolo ( "y" ) 
>>> f  =  Función ( "f" ) 
>>> # pprint usará Unicode de manera predeterminada si está disponible 
>>> pprint ( x  **  exp ( x )) 
⎛ x⎞ 
⎝ℯ ⎠ 
x    
>>> # Una salida sin Unicode 
>>> pprint ( Integral ( f ( x ),  x ),  use_unicode = False ) 
  /        
|         
| f(x) dx 
|         
/         
>>> # Comparar con la misma expresión pero esta vez Unicode está habilitado 
>>> pprint ( Integral ( f ( x ),  x ),  use_unicode = True ) 
⌠         
⎮ f(x) dx 
⌡      
>>> # Alternativamente, puede llamar a init_printing() una vez y realizar una impresión bonita sin la función pprint. 
>>> init_printing () 
>>> sqrt ( sqrt ( exp ( x ))) 
   ____ 
4 ╱ x 
╲╱ ℯ   
>>> ( 1 / cos ( x )) . serie ( x ,  0 ,  10 ) 
     2 4 6 8          
    x 5⋅x 61⋅x 277⋅x ⎛ 10⎞ 
1 + ── + ──── + ───── + ────── + O⎝x ⎠ 
    2 24 720 8064

>>> from  sympy  import  init_printing ,  Símbolo ,  expandir 
>>> init_printing () 
>>> 
>>> a  =  Símbolo ( "a" ) 
>>> b  =  Símbolo ( "b" ) 
>>> e  =  ( a  +  b )  **  3 
>>> e 
(a + b)³ 
>>> e . expand () 
a³ + 3⋅a²⋅b + 3⋅a⋅b² + b³

>>> de  sympy  importar  Racional ,  pprint 
>>> e  =  2 ** 50  /  Racional ( 10 )  **  50 
>>> pprint ( e ) 
1/88817841970012523233890533447265625

>>> from  sympy  import  init_printing ,  símbolos ,  ln ,  diff 
>>> init_printing () 
>>> x ,  y  =  símbolos ( "x y" ) 
>>> f  =  x ** 2  /  y  +  2  *  x  -  ln ( y ) 
>>> diff ( f ,  x ) 
2⋅x     
─── + 2 
  y 
>>> diff ( f ,  y ) 
    2     
   x 1 
- ── - ─ 
    2 y 
   y 
>>> diff ( diff ( f ,  x ),  y ) 
-2⋅x 
──── 
   2 
  y

>>> de  sympy  importar  símbolos ,  cos 
>>> de  sympy.plotting  importar  plot3d 
>>> x ,  y  =  símbolos ( "x y" ) 
>>> plot3d ( cos ( x  *  3 )  *  cos ( y  *  5 )  -  y ,  ( x ,  - 1 ,  1 ),  ( y ,  - 1 ,  1 )) 
<sympy.plotting.plot.Plot objeto en 0x3b6d0d0>

>>> from  sympy  import  init_printing ,  Símbolo ,  límite ,  raíz cuadrada ,  oo 
>>> init_printing () 
>>> 
>>> x  =  Símbolo ( "x" ) 
>>> límite ( raíz cuadrada ( x ** 2  -  5  *  x  +  6 )  -  x ,  x ,  oo ) 
-5/2 
>>> límite ( x  *  ( raíz cuadrada ( x ** 2  +  1 )  -  x ),  x ,  oo ) 
1/2 
>>> límite ( 1  /  x ** 2 ,  x ,  0 ) 
∞ 
>>> límite ((( x  -  1 )  /  ( x  +  1 ))  **  x ,  x ,  oo ) 
-2 
ℯ

>>> from  sympy  import  init_printing ,  Símbolo ,  Función ,  Eq ,  dsolve ,  sin ,  diff 
>>> init_printing () 
>>> 
>>> x  =  Símbolo ( "x" ) 
>>> f  =  Función ( "f" ) 
>>> 
>>> eq  =  Eq ( f ( x ) . diff ( x ),  f ( x )) 
>>> eq 
d               
──(f(x)) = f(x) 
dx          
>>>    
>>> dsolve ( eq ,  f ( x )) 
           x 
f(x) = C₁⋅ℯ

>>> 
>>> eq  =  Eq ( x ** 2  *  f ( x ) . diff ( x ),  - 3  *  x  *  f ( x )  +  sen ( x )  /  x ) 
>>> eq 
2 d sen(x) 
x ⋅──(f(x)) = -3⋅x⋅f(x) + ────── 
   dx x    
>>> 
>>> dsolve ( eq ,  f ( x )) 
       C₁ - cos(x) 
f(x) = ───────────    
            x³

>>> from  sympy  import  init_printing ,  integrate ,  Symbol ,  exp ,  cos ,  erf 
>>> init_printing () 
>>> x  =  Symbol ( "x" ) 
>>> # Función polinómica 
>>> f  =  x ** 2  +  x  +  1 
>>> f 
2         
x + x + 1 
>>> integrate ( f ,  x ) 
3 2     
xx      
── + ── + x 
3 2      
>>> # Función racional 
>>> f  =  x  /  ( x ** 2  +  2  *  x  +  1 ) 
>>> f 
     x       
──────────── 
2           
x + 2⋅x + 1

>>> integrar ( f ,  x ) 
               1   
log(x + 1) + ───── 
             x + 1 
>>> # Funciones polinomiales exponenciales 
>>> f  =  x ** 2  *  exp ( x )  *  cos ( x ) 
>>> f 
2 x        
x ⋅ℯ ⋅cos(x) 
>>> integrar ( f ,  x ) 
2 x 2 xxx        
x ⋅ℯ ⋅sin(x) x ⋅ℯ ⋅cos(x) x ℯ ⋅sin(x) ℯ ⋅cos(x) 
──────────── + ──────────── - x⋅ℯ ⋅sin(x) + ───────── - ───────── 
     2 2 2 2     
>>> # Una integral no elemental 
>>> f  =  exp ( - ( x ** 2 ))  *  erf ( x ) 
>>> f 
   2        
-x         
ℯ ⋅erf(x) 
>>> integrate ( f ,  x )

  ___ 2    
╲╱ π ⋅erf (x) 
───────────── 
      4

>>> de  sympy  import  Símbolo ,  cos ,  sin ,  pprint 
>>> x  =  Símbolo ( "x" ) 
>>> e  =  1  /  cos ( x ) 
>>> pprint ( e ) 
  1    
────── 
cos (x) 
>>> pprint ( e . serie ( x ,  0 ,  10 )) 
     2 4 6 8          
    x 5⋅x 61⋅x 277⋅x ⎛ 10⎞ 
1 + ── + ──── + ──── ─ + ────── + O⎝x ⎠ 
    2 24 720 8064           
>>> e  =  1 / sin ( x ) 
>>> pprint ( e ) 
  1    
────── 
sin(x) 
>>> pprint ( e . serie ( x ,  0 ,  4 )) 
           3         
1 x 7⋅x ⎛ 4⎞ 
─ + ─ + ──── + O⎝x ⎠ 
x6 360

>>> from  sympy  import  * 
>>> x  =  Símbolo ( "x" ) 
>>> y  =  Símbolo ( "y" ) 
>>> hechos  =  Q . positivo ( x ),  Q . positivo ( y ) 
>>> con  suponiendo ( * hechos ): 
...     print ( ask ( Q . positivo ( 2  *  x  +  y ))) 
Verdadero

>>> from  sympy  import  * 
>>> x  =  Symbol ( "x" ) 
>>> # Suposición sobre x 
>>> fact  =  [ Q . prime ( x )] 
>>> con  suposición ( * fact ): 
...     print ( ask ( Q . reasonal ( 1  /  x ))) 
Verdadero