#16439: Allow inverse trig functions to all take complex input
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Reporter: kcrisman | Owner:
Type: defect | Status: new
Priority: minor | Milestone: sage-6.3
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by kcrisman):
> Why don't complex numbers have these attributes? This should be possible
- for example wolfram alpha
[http://www.wolframalpha.com/input/?i=acos%281%2F%28-0.9+%2B+i%29%29 gives
a value] for `acos(-0.9+i)`.
Complex number ''do'' have these attributes, just not the minimalist
`complex` Python data type.
{{{
sage: a = complex(1,1)
sage: a.[tab]
a.conjugate a.imag a.real
sage: a._[tab]
a.__abs__ a.__hash__ a.__rdivmod__
a.__add__ a.__init__ a.__reduce__
a.__class__ a.__int__ a.__reduce_ex__
a.__coerce__ a.__le__ a.__repr__
a.__delattr__ a.__long__ a.__rfloordiv__
a.__div__ a.__lt__ a.__rmod__
a.__divmod__ a.__mod__ a.__rmul__
a.__doc__ a.__mul__ a.__rpow__
a.__eq__ a.__ne__ a.__rsub__
a.__float__ a.__neg__ a.__rtruediv__
a.__floordiv__ a.__new__ a.__setattr__
a.__format__ a.__nonzero__ a.__sizeof__
a.__ge__ a.__pos__ a.__str__
a.__getattribute__ a.__pow__ a.__sub__
a.__getnewargs__ a.__radd__ a.__subclasshook__
a.__gt__ a.__rdiv__ a.__truediv__
}}}
And the built-in `math` module doesn't do `arcsec`
{{{
sage: math.a[tab]
math.acos math.asin math.atan math.atanh
math.acosh math.asinh math.atan2
}}}
and even then only takes ones with real output
{{{
sage: math.acos(1)
0.0
sage: math.acos(2)
ValueError: math domain error
sage: math.acos(a)
TypeError: can't convert complex to float
}}}
> I think the computations should be performed using `CDF` and then
coerced back to `complex`. Complex output from these functions should be
handled by the plot function separately.
Maybe. Is `CDF` basically the same as `complex`? Is there precedent for
this?
--
Ticket URL: <http://trac.sagemath.org/ticket/16439#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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