Ordering of roots in solveset

[nickme68]

I am not sure is it bug or feature, but it is not convenient. While solving quadratic equation (for example) solveset gives root in some order, when I convert its output to the tuple (for extracting particular root) the order of roots is changed.

s = solveset(x**2-2, x)
print(s)
print(tuple(s))

Output:

{-sqrt(2), sqrt(2)}
(sqrt(2), -sqrt(2))

[nickme68]

If roots are integers, then orders are the same:

s = solveset(x**2-4, x)
print(s)
print(tuple(s))

Output:

{-2, 2}
(-2, 2)

[ThePauliPrinciple]

Sets are not supposed to be ordered.
You could use SymPy's ordered to always obtain the same ordering for SymPy objects:

from sympy import *
from sympy.abc import x
s = solveset(x**2-2, x)
tuple(ordered(s))

[nickme68]

"Sets are not supposed to be ordered" - I understand it! But why two serializations of the same set (for print or display and for converting to the tuple or list) use different orderings? Looks a little bit inconsistently!

[nickme68]

My use case:

sol = solveset(x**2 - 2, x) # solve given equation
display(sol) # -> {-sqrt(2), sqrt(2)}
# I want to extract positive one
my_root = tuple(sol)[1]
display(my_root) # -> -sqrt(2)

I can fix this problem using print(tuple(sol)) in the second line instead of display, but then I will miss Latex-style of output.

[ThePauliPrinciple]

I think it is better to simply check for solutions that are positive rather depend on any ordering:

from sympy import *
from sympy.abc import x
s = [a for a in solveset(x**2-2, x) if a.is_positive]
print(s)
s[0]

If you want to display a tuple in LaTeX, you can use SymPy's Tuple (note that it works different from tuple)

Tuple(*solveset(x**2-2, x))

or convert automatically with sympify

sympify(tuple(solveset(x**2-2, x)))

[nickme68]

OK, my equation has parameters, I want to look at roots and extract particular one (for example with plus sign in front of square root). Solutions you suggest are to complicated for me:

1. use display to look at solution (set);
2. if set is finite then use Tuple or tuple to look at ordered list of roots;
3. choose particular root using its index.

I would like to skip step 2 in this sequence! ;-) And I can't skip step 1 because set may be not finite, then tuple will fail.
Anyway, thank you! Tuple was new command for me.

[oscarbenjamin]

Although a set does not have an a priori defined order Python will iterate over the elements of a set in a particular order for a given set in a particular Python process. The fact that the printer displays the elements of the set in a different order is inconvenient. I have this problem regularly when trying to extract the symbols from an expression in an interactive session:

In [24]: t, x, y, z = expr.free_symbols

In [25]: expr.free_symbols
Out[25]: {t, x, y, z}

In [26]: t, x, y, z = expr.free_symbols

In [27]: [t, x, y, z]
Out[27]: [t, x, z, y]

It would be better if the printer didn't change the order of the elements of a Python set IMO.

[smichr]

RootOf will give you more control of which root you are selecting:

>>> p = Poly(x**2 -y, x)
>>> RootOf(p, 0)
-sqrt(y)
>>> RotooOf(p, 1)
sqrt(y)