Sympy session

~/tmp ❯❯❯ conda activate torch1
(torch1) ~/tmp ❯❯❯ python

>>> from sympy import *
>>> x = Symbol('x')
>>> y = Symbol('y')
>>> (x + y)**2
(x + y)**2
>>> ((x + y)**2).expand()
x**2 + 2*x*y + y**2
>>>
>>> from sympy.interactive import printing
>>> printing.init_printing(use_latex=True)
>>>
>>>
>>> ((x + y)**2).expand()
 2            2
x  + 2⋅x⋅y + y
>>> init_printing()
>>>
>>>
>>> ((x + y)**2).expand()
 2            2
x  + 2⋅x⋅y + y
>>> a = Integral(cos(x)*exp(x), x)
>>> Eq(a, a.doit())
⌠                 x           x
⎮  x             ℯ ⋅sin(x)   ℯ ⋅cos(x)
⎮ ℯ ⋅cos(x) dx = ───────── + ─────────
⌡                    2           2
>>>
>>>
>>> (sqrt(2-x) + sqrt(2+x)).factor()
  ________     _______
╲╱ -x + 2  + ╲╱ x + 2
>>> (-x) + sqrt(2+x)).factor()
KeyboardInterrupt
>>> (4 + 2*sqrt(2-x)*sqrt(2+x)).factor()
  ⎛  ________   _______    ⎞
2⋅⎝╲╱ -x + 2 ⋅╲╱ x + 2  + 2⎠
>>> (4 - x + x + 2*sqrt(2-x)*sqrt(2+x)).factor()
  ⎛  ________   _______    ⎞
2⋅⎝╲╱ -x + 2 ⋅╲╱ x + 2  + 2⎠
>>> (x**2 + 2*x + 1).factor()
       2
(x + 1)
>>> (x**3 - sqrt(2-x)**3).factor()
 3       ________       ________
x  + x⋅╲╱ -x + 2  - 2⋅╲╱ -x + 2
>>> (x**3 - sqrt(2-x)**3).expand
<bound method Expr.expand of x**3 - (-x + 2)**(3/2)>
>>> (x**3 - sqrt(2-x)**3).expand()
 3       ________       ________
x  + x⋅╲╱ -x + 2  - 2⋅╲╱ -x + 2
>>> factor(sqrt(2-x) + sqrt(2+x))
  ________     _______
╲╱ -x + 2  + ╲╱ x + 2
>>>
>>>
>>> (x**3 - 8*y**6).factor()
⎛       2⎞ ⎛ 2        2      4⎞
⎝x - 2⋅y ⎠⋅⎝x  + 2⋅x⋅y  + 4⋅y ⎠
>>>
>>>
>>> (x^4 - 1).factor()
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
AttributeError: 'Not' object has no attribute 'factor'
>>> (x**4 - 1).factor()
                ⎛ 2    ⎞
(x - 1)⋅(x + 1)⋅⎝x  + 1⎠
>>> (2*x**3 + x**2*y-6*x*y-3*y**2)
   3    2                2
2⋅x  + x ⋅y - 6⋅x⋅y - 3⋅y
>>> (2*x**3 + x**2*y-6*x*y-3*y**2).factor()
          ⎛ 2      ⎞
(2⋅x + y)⋅⎝x  - 3⋅y⎠
>>>
>>>
>>> x2 = x**2
>>> (x2 + 6*x - 7).factor()
(x - 1)⋅(x + 7)
>>>