Hi Paul,
This is a bug. I assume that the result is mathematically correct but
it is not a good transformation of the expression.
Can you open a GitHub issue for this and link back to this mailing
list thread (and send the link to the issue back here as well)?
The problem is with Pow.conjugate
In [1]: class CustomExpr(Expr): pass
In [2]: e = sqrt(1+2*CustomExpr(x))
In [3]: print(e)
sqrt(1 + 2*CustomExpr(x))
In [4]: print(e.conjugate())
-I*((2*re(CustomExpr(re(x) + I*im(x))) + 1)**2 + 4*im(CustomExpr(re(x)
+ I*im(x)))**2)**(1/4)*sin(atan2(2*im(CustomExpr(re(x) + I*im(x))),
2*re(CustomExpr(re(x) + I*im(x))) + 1)/2) + ((2*re(CustomExpr(re(x) +
I*im(x))) + 1)**2 + 4*im(CustomExpr(re(x) +
I*im(x)))**2)**(1/4)*cos(atan2(2*im(CustomExpr(re(x) + I*im(x))),
2*re(CustomExpr(re(x) + I*im(x))) + 1)/2)
This is because Pow.conjugate calls expand_complex which it should
not. Actually though the call to expand_complex is gated on the base
being not a positive number which exposes a bug here:
In [5]: (1 + 2*CustomExpr(x)).is_positive
Out[5]: False
That should return None rather than False so there is a bug in the
assumptions system.
The cause of this is that is_commutative is part of the assumptions
system (which it really shouldn't be) and CustomExpr has
is_commutative = None. A workaround is to define CustomExpr like this:
class CustomExpr(Expr):
is_commutative = True
--
Oscar
On Sun, 26 Jan 2025 at 14:11, Paul Royik <[email protected]> wrote:
>
> from sympy import Expr, log, Abs, sqrt
> from sympy.abc import x, u
>
> class CustomExpr(Expr):
> pass
>
> expr = log(Abs(sqrt(1+2/x)-1))
>
> print(expr.subs(x, u))
> print(expr.subs(x, CustomExpr(u)))
>
> The first one prints, as expected, log(|sqrt(1 + 2/u) - 1|)
>
> But the second prints something different:
> log(sqrt(i*sin(atan2(-2*im(CustomExpr(re(u) + i*im(u)))/(re(CustomExpr(re(u)
> + i*im(u)))**2 + im(CustomExpr(re(u) + i*im(u)))**2), 1 +
> 2*re(CustomExpr(re(u) + i*im(u)))/(re(CustomExpr(re(u) + i*im(u)))**2 +
> im(CustomExpr(re(u) + i*im(u)))**2))/2)*conjugate(((1 + 2*re(CustomExpr(re(u)
> + i*im(u)))/(re(CustomExpr(re(u) + i*im(u)))**2 + im(CustomExpr(re(u) +
> i*im(u)))**2))**2 + 4*im(CustomExpr(re(u) + i*im(u)))**2/(re(CustomExpr(re(u)
> + i*im(u)))**2 + im(CustomExpr(re(u) + i*im(u)))**2)**2)**(1/4)) -
> i*sin(atan2(-2*im(CustomExpr(re(u) + i*im(u)))/(re(CustomExpr(re(u) +
> i*im(u)))**2 + im(CustomExpr(re(u) + i*im(u)))**2), 1 + 2*re(CustomExpr(re(u)
> + i*im(u)))/(re(CustomExpr(re(u) + i*im(u)))**2 + im(CustomExpr(re(u) +
> i*im(u)))**2))/2)*conjugate(((1 + 2*re(CustomExpr(re(u) +
> i*im(u)))/(re(CustomExpr(re(u) + i*im(u)))**2 + im(CustomExpr(re(u) +
> i*im(u)))**2))**2 + 4*im(CustomExpr(re(u) + i*im(u)))**2/(re(CustomExpr(re(u)
> + i*im(u)))**2 + im(CustomExpr(re(u) + i*im(u)))**2)**2)**(1/4))*sqrt(1 +
> 2*CustomExpr(u)**(-1)) - cos(atan2(-2*im(CustomExpr(re(u) +
> i*im(u)))/(re(CustomExpr(re(u) + i*im(u)))**2 + im(CustomExpr(re(u) +
> i*im(u)))**2), 1 + 2*re(CustomExpr(re(u) + i*im(u)))/(re(CustomExpr(re(u) +
> i*im(u)))**2 + im(CustomExpr(re(u) + i*im(u)))**2))/2)*conjugate(((1 +
> 2*re(CustomExpr(re(u) + i*im(u)))/(re(CustomExpr(re(u) + i*im(u)))**2 +
> im(CustomExpr(re(u) + i*im(u)))**2))**2 + 4*im(CustomExpr(re(u) +
> i*im(u)))**2/(re(CustomExpr(re(u) + i*im(u)))**2 + im(CustomExpr(re(u) +
> i*im(u)))**2)**2)**(1/4)) + cos(atan2(-2*im(CustomExpr(re(u) +
> i*im(u)))/(re(CustomExpr(re(u) + i*im(u)))**2 + im(CustomExpr(re(u) +
> i*im(u)))**2), 1 + 2*re(CustomExpr(re(u) + i*im(u)))/(re(CustomExpr(re(u) +
> i*im(u)))**2 + im(CustomExpr(re(u) + i*im(u)))**2))/2)*conjugate(((1 +
> 2*re(CustomExpr(re(u) + i*im(u)))/(re(CustomExpr(re(u) + i*im(u)))**2 +
> im(CustomExpr(re(u) + i*im(u)))**2))**2 + 4*im(CustomExpr(re(u) +
> i*im(u)))**2/(re(CustomExpr(re(u) + i*im(u)))**2 + im(CustomExpr(re(u) +
> i*im(u)))**2)**2)**(1/4))*sqrt(1 + 2*CustomExpr(u)**(-1)) + 1 - sqrt(1 +
> 2*CustomExpr(u)**(-1))))
>
> Is this a bug or it works as expected?
>
> How to make print(expr.subs(x, CustomExpr(u))) output log(|sqrt(1 + 2/u) -
> 1|)?
>
> Thank you.
>
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