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Simplifying Simps with Square Root

I have an expression that I think could be simplified somewhat, and for some reason sympy is not doing what I think is a simple simplification. My example code looks like this:

# coding: utf-8

# In[1]:

from __future__ import division
from sympy import *
init_printing()

# In[3]:

d, R, c = symbols('d R c', Positive = True, Real = True)
Δt = symbols('\Delta_t', Real = True)

# In[4]:

Δt = (1/c**2)*(-R*c+sqrt(c**2*(R+d)**2))
Δt

# In[5]:

simplify(Δt)

I've posted the code above for the fun of cut and paste ... The graphical output from iPython looks like this:

enter image description here

I expected the end result to be as follows:

enter image description here

I thought that based on how I defined the variables, simplifications would occur, at least sqrt ((R + d) ** 2) ... What am I doing wrong?

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2 answers


Try real = True

and positive = True

(lower case):

import sympy as sp

d, R, c = sp.symbols('d R c', positive = True, real = True)
dt = sp.symbols('\Delta_t', real = True)

dt = (1/c**2)*(-R*c+sp.sqrt(c**2*(R+d)**2))

print sp.simplify(dt)


Output:

d/c
+4


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To expand on @ user5402's answer, SymPy only makes simplifications that are valid for common complex numbers by default. In particular, it sqrt(x**2) = x

is generally not true. This is true if x

positive. Installing x

both Symbol('x', positive=True)

reports SymPy, that this is so.



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