How to simplify sqrt expressions in sympy

Question

I'm using sympy v1.0 in a Jupyter Notebook. I'm having trouble getting expression to simplify how I'd like. Here's a toy example; it does the same thing my more complicated expressions do...

import sympy
sympy.init_printing(use_latex='mathjax')
x, y = sympy.symbols("x, y", real=True, positive=True)
sympy.simplify(sqrt(2*x/y))

gives me...

But I would prefer...

How can I get sympy to group things in this way? Ive tried some of the other simplify functions, but they all give me the same result. Or am I missing something else?

If you don't set x and y as real and positive, SymPy won't split them apart (because it's invalid to do so). — asmeurer, Apr 23 '16 at 16:53
@asmeurer Thank you this does indeed help. It still pulls the 2 out, but that's easier to deal with. I found I can also improvise by squaring everything to check how it gathers everything. — Matt Hall, Apr 25 '16 at 23:40

score 1 · Accepted Answer · answered Jul 07 '19 at 18:41

1

Use "symbol trickery" for numbers that you want to behave like symbols and "vanilla symbols" when you don't want simplifications (as @asmeurer pointed out):

>>> _2,x,y = list(map(Symbol,'2xy'))
>>> sqrt(_2*x/y)
sqrt(2*x/y)

answered Jul 07 '19 at 18:41

smichr

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Thanks! This feels like a workaround too, but a bit more workable than the other answer, so I'll accept it. Cheers. – Matt Hall Jul 08 '19 at 16:04
Thank you. And yes, it's just one of several ways to work around this issue. – smichr Jul 08 '19 at 17:13
For me, the assumption `positive=True` on the symbols still breaks out the terms of the `sqrt` Any solution for this? – BallpointBen Jan 14 '21 at 21:27

Matt Messersmith · Answer 2 · 2016-04-22T19:03:21.517

sympy really wants to simplify by pulling terms out of sqrt, which makes sense. I think you have to do what you want manually, i.e., get the simplification you want without the sqrt call, and then fudge it using Symbol with a LaTex \sqrt wrap. For example:

from sympy import *
init_printing(use_latex='mathjax')

# Wanted to show this will work for slightly more complex expressions,
# but at the end it should still simplify to 2x/y
x, y = symbols("x, y", real=True, positive=True)
z = simplify((2*2*3*x)/(1*2*3*y))

Symbol("\sqrt{" + latex(z) + "}", real=True, positive=True) # Wrap the simplified fraction in \sqrt{}

This really isn't ideal, but I looked through the docs for about an hour, and just couldn't find support for what you want directly. The sympy library is more about actual symbolic manipulation, less about printing, so I can hardly blame them.

I appreciate your insight, but this feels too complicated. The suggestion of not specifying real, positive symbols helped me. Thank you anyway. — Matt Hall, Apr 25 '16 at 23:38

How to simplify sqrt expressions in sympy

2 Answers2