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RE: [Axiom-developer] Math Chat
From: |
Page, Bill |
Subject: |
RE: [Axiom-developer] Math Chat |
Date: |
Wed, 15 Dec 2004 21:39:26 -0500 |
On Wednesday, December 15, 2004 7:52 PM Bob McElrath
>
> Well I sat down to try to find something to allocate my
> bounty for, andI keep running into walls. This time
> it was Bill's observation that %pi::Float works but
> %e::Float doesn't...so I dug into the code...
I think it was Martin. But no matter...
> I keep wanting to ask dumb questions so I created an
> IRC channel for axiom: #axiom-developer on irc.freenode.net.
> This is for rapid communication, and is a good way to give
> support. I hope others will join me.
Sorry, I would but I can't IRC from were I'am at right now.
Briefly %pi is a macro for pi()
%e is a macro for exp(1)
See
)display op pi
)display op exp
Examining the differences between %pi and %e in Axiom
takes you quite quickly down into the details of types
and conversions... worth the trip, I think!
It is important to remember these distinctions:
:: is a conversion from one type to another
@ specifies a desired target type
$ specifies exactly what package to call
In Axiom the type of pi() is Pi. This might seem strange
at first until you think of the importance of %pi in many
areas of mathematics. It is convenient to have it's special
properties encoded in a special type. Try
)show Pi
to see all of the operations defined in this domain.
Notice that expressions like
%pi+1
are also of type Pi.
%e on the other hand is of type Expression Integer.
We can convert %pi to the same type as %e
pI:Expression Integer:=%pi
But then objects of type Expression Integer cannot
be converted to Float (in general)
pI::Float
You would think that we could still do
address@hidden
to request the target type Float by Axiom says
no.
In fact I think that it is strange that Axiom
allows
pi()::Float
but it turns out that Float does have a function called
by pi()$Float since
Float has TRANFUN
etc. etc.
Exercise: what is this?
pi$Float
Have fun!
Regards,
Bill Page.