Equality with absolute value

Asked Jun 27 '22 at 14:55

Active Jun 27 '22 at 20:12

Viewed 98 times

Solving the equality with absolute value I use sympy with nonlinsolve function.

For example, I solve |a + b| = a + b as follows

from sympy import nonlinsolve, symbols, Abs

a,b = symbols('a, b', real = True)
eqn = [Abs(a + b) - (a + b)]
nonlinsolve(eqn, [a, b])

Output is OK:

{(Interval(-b, oo), b)}

However when I try to solve |a - b| = -(a + b) as below:

from sympy import nonlinsolve, symbols, Abs
a,b = symbols('a, b', real = True)
eqn = [Abs(a - b) + (a + b)]
res = nonlinsolve(eqn, [a, b])

Output is:

False

However clearly there exists at least one solution like a = b = 0.

Update

It seems that the different behaviour in different version. In Python 2.7 the result is

But in Python 3 it is False.

Could you advise the reason of such a behaviour and possible countermeasures, since I'd prefer to use Python 3?

edited Jun 27 '22 at 20:12

asked Jun 27 '22 at 14:55

Artem

Where does `Abs()` come from ? – EvgenyKolyakov Jun 27 '22 at 15:19
It is sympy.functions.elementary.complexes.Abs. Added to import. Thx. – Artem Jun 27 '22 at 19:09
The second snippet produces `FiniteSet((FiniteSet(Interval(b, oo)), Complement(FiniteSet(b), FiniteSet(0))))` for me using Sympy 1.5.1, but `EmptySet` when using Sympy 1.10.1. – Brian61354270 Jun 27 '22 at 19:14
@Brian, Thanks, I used Python in R through reticulate + Rmarkdown. Seems some interferience. Got the same result in Python IDE as you. Checking. – Artem Jun 27 '22 at 19:20
Seems different behaviours in Python 2 and Python 3. (correct behaviour in Python 2). – Artem Jun 27 '22 at 19:38