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## [Axiom-developer] [#23 using exp as a symbol in ** ] (new)

**From**: |
anonymous |

**Subject**: |
[Axiom-developer] [#23 using exp as a symbol in ** ] (new) |

**Date**: |
Mon, 17 Jan 2005 22:39:02 -0600 |

trigcat.spad
WS> ElementaryFunctionCategory(): Category == with
WS> log : $ -> $ ++ log(x) returns the natural logarithm of x.
WS> exp : $ -> $ ++ exp(x) returns %e to the power x.
WS> "**": ($, $) -> $ ++ x**y returns x to the power y.
WS> add
WS> if $ has Monoid then
WS> x ** y == exp(y * log x)
etc
The more such stuff I see, the better is my live experience,
the more efficient is bug identification progress.
Much thanks!
Vladimir
Sunday, January 16, 2005, 7:08:49 PM, you write:
WS> The error apparently comes from EXPR where the implementation is
WS> x**y == exp(y * log(x))
WS> so exp^log(x) is computed as
WS> exp(log(x) * log(exp))
WS> which should be ok, but then the system handles log exp and tries to
simplify it
WS> to the identity map, and not finding the argument.
WS> William
WS> ---
>*> *
>*> Simpler:*
>*> *
>*> (1) -> exp^3*
>*> *
>*> 3*
>*> (1) exp*
>*> Type: Polynomial Integer*
>*> (2) -> a^log(x)*
>*> *
>*> log(x)*
>*> (2) a*
>*> Type: Expression Integer*
>*> (3) -> exp^log(x)*
>*> *
>*> >> System error:*
>*> Cannot take first of an empty list*
>*> *
>*> protected-symbol-warn called with (NIL)*
>*>*
--
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**[Axiom-developer] [#23 using exp as a symbol in ** ] (new)**,
*anonymous* **<=**