big float arithmetic & mgrp, also Interval Arithmetic project

There is at least one way to do this, (display of complex) but it requires a 
lot of re-thinking.

Instead of treating 3+4*%i  as a sum of 3  and a product of 4 and %I,
treat it as a "complex number".  Then you can display complex numbers 
however you like.

That is, ((mcomplex)  3   4)

I'm not sure if you want to do   a+b*%i    as   ((mcomplex) $a $b).  It 
would depend
on whether a and b were necessarily "real",  forever.

Oh, by the way, it might also be good to use common lisp complex number 
objects,
but that would be restrictive.  CL does not have native bigfloats, or other 
things
we might want. e.g. interval.

which reminds me.  If anyone wants a project:  define an interval as 
interval(a,b).
all numbers between a and b on the real line.
using tellsimp (etc)  define all you need.

Problem:   interval(-1,1) -  interval(-1,1)      is NOT zero.  It is 
interval(-2,0).
Also there is a need to round "outward" on some float operations.

Is anyone keeping a list of projects?

RJF


----- Original Message ----- 
From: "Raymond Toy" <raymond.toy at ericsson.com>
To: "Barton Willis" <willisb at unk.edu>
Cc: <maxima at math.utexas.edu>
Sent: Tuesday, May 02, 2006 8:12 AM
Subject: Re: [Maxima] big float arithmetic & mgrp


>>>>>> "Barton" == Barton Willis <willisb at unk.edu> writes:
>
>    Barton> I guess all this sorting is to arrange the terms into the 
> canonical order.
>
> I wish the canonical order were to print the real part followed by the
> imaginary part like 1+2*%i instead of 2*%i+1.  I find that
> annoying. :-)
>
>    Barton>  Maybe
>    Barton> products and quotients of complex floats (doubles and big 
> floats) should
>    Barton> automatically
>    Barton> expand:
>
>    Barton> (3.4 + 5.6*%i) * (6.5 + %i*3.4) --> 47.9599...*%i + 3.0599..
>
> That seems ok to me.  A bit of work to implement, though.
>
> Ray
>
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