Cotangent producing incorrect real/imaginary parts. #29400
Description
While doing some complex analysis, I encountered a bug when evaluating the cotangent function of a complex number when multiplied by a complex number. When p and q are complex, real(pcot(q)) or imag(pcot(q)) produces a wrong result, while real(p/tan(q)) or imag(p/tan(q)) produces the correct result.
For example:
sage: a=(1+2*i)/tan(3+4*i)
sage: b=(1+2*i)*cot(3+4*i)
sage: a.real().n()
2.00110119720514
sage: b.real().n()
-2.00147637268110
sage: a.imag().n()
-1.00101956794753
sage: b.imag().n()
1.00026921699559
Additionally, when trying to numerically evaluate b with cotangent, it simply returns an error. The numerical evaluation of a with tangent is returned without error.
sage: a.n()
2.00110119720513 - 1.00101956794753*I
sage: b.n()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-97-d3276c847f4d> in <module>
----> 1 b.n()
/usr/lib/python3.8/site-packages/sage/structure/element.pyx in sage.structure.element.Element.n (build/cythonized/sage/structure/element.c:8033)()
857 0.666666666666667
858 """
--> 859 return self.numerical_approx(prec, digits, algorithm)
860
861 def _mpmath_(self, prec=53, rounding=None):
/usr/lib/python3.8/site-packages/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression.numerical_approx (build/cythonized/sage/symbolic/expression.cpp:34713)()
5998 res = x.pyobject()
5999 else:
-> 6000 raise TypeError("cannot evaluate symbolic expression numerically")
6001
6002 # Important -- the we get might not be a valid output for numerical_approx in
TypeError: cannot evaluate symbolic expression numerically
I conducted this same test using both tangent and cotangent in Maxima. They are both correct, and agree with the results involving tangent in Sage. But for whatever reason in Sage, cotangent does not seem to work correctly when evaluating numerically or getting the real/imaginary part.
Upstream: Fixed upstream, in a later stable release.
Component: symbolics
Keywords: defect cotangent sympy
Author: Dave Morris
Branch/Commit: 275f5b9
Reviewer: Matthias Koeppe
Issue created by migration from https://trac.sagemath.org/ticket/29400