[Axiom-developer] [#119 solve returns wrong answers and multiple answers to same trig problem] Why Complex Float?

[wyscc]

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http://page.axiom-developer.org/zope/mathaction/119SolveReturnsWrongAnswersAndMultipleAnswersToSameTrigProblem/diff
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++added:

<pre>From: wyscc, Thur, 10 Mar 2005 08:16:00</pre>

Of course you don't, from a mathematical view point, and the problem is 
apparently the Interpreter needs help. If you put the argument into 
<code>Float</code> or the expression into <code>Expression Float</code>, Axiom 
will oblige.
\begin{axiom}
asin(1/2::Float)
asin(1/2)::Expression Float
\end{axiom}
But in fact, even coercion to <code>Complex Float</code> won't always work.
\begin{axiom}
asin(%i/2)
asin(%i/2)::Complex Float
\end{axiom}
There is no modemap from <code>Expression Integer</code> to <code>Complex 
Float</code> (Use hyperdoc <code>Browse, Selectable</code> to search, with wild 
character in the name field).  This is reasonable since it is not possible in 
general to evaluate numerically a symbolic expression. I believe the 
Interpreter actually tries this:
\begin{axiom}
asin(1/2)$Float
asin(1/2)$(Complex Float)
\end{axiom}
which succeed in both cases because <code>asin</code> has modemaps in those 
domains. Exactly why it was able to change a  non-existing coercion in one case 
but not the other is unclear, but this seems to be because the Interpreter code 
is not as categorical as the compiler code and these ``smart'' coercions may be 
done case by case. But even this reasoning has problem:

\begin{axiom}
asin(%i/2::Complex Float)  -- easiest
asin(%i/2)::Expression Complex Float::Complex Float -- harder
asin(%i/2)$(Complex Float)  -- doesn't work
\end{axiom}


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