(Comp.sys.hp48)
Item: 396 by detlef@mwhh.hanse.de
Author: [Romain Desplats]
  Subj: Fraction library
  Date: Mon Dec 16 1991

Hi.

I post this article for a friend of mine who has no news access. Please
reply to him, not to me, if there are any questions/comments about the
software.

Bye,
          8-),Detlef
-----------------------------------------------------------------------------


FRACTION LIBRARY


-  This is a new "Frac" lib written originally in RPL then converted into ML
routines.

-  This version is quick and small (in terms of memory).

-  I am not going to describe the advantages of ML versus RPL anymore.  Let's
look at the contents of this library.

RX       : Takes any numbers, list, algebraic, array of
           numbers and the program you want to apply to that object.
        eg. :       2:[[.1 .2]]                
                    1:<<->Q>>                T:.25_ms
        output      {{1/10 1/5}}             T:'1/4'*1_ms

        Note that arrays would be converted into lists if you didn't
        have reals or complex anymore.

EC       : Works with list to fully expand and fully collect.
           (Never gets stuck with the fully expand)

PGCD  :  Called by Sã     12 : { 2 2 3 }

Sã     :  Gets you :
            a/b square root c/d
            as 1/3 square root 2/3
          from a number

         but also tries to get pi or 1/pi as a fraction.


        [ [1 .866 0]                 { {1  û3/2 0}
          [.866 1 0]                   {û3/2  1 0}
          [0   0  1] ]                 {0    1     0} }


        90degre:1.5707_rad 90degre:pi/2*1_rad


         Note : this works for numbers (xl<1/308) because of pi.

FR       :  Return one single fraction
            u+inv(A)/cosx/sinx/3 = ...
            works with lists

        try something like this: { { INV(x) }  A+A/B }

LX      :   Then there is the LX program which works about the same way
            with lists.  Apply a program to all arguments of a list :

        eg. : {x { x2 } cosx}
        << / 2 >>

RN         :  Tries to cancel machine rounding errors (it works as RX)
      IN  {-0. 99999 [1.23456 1.20001]}
      OUT  {-0.1 [1.23456 1.2]}


have fun and e-mail me for any comments at

dehon@platon.greco-prog.fr



Romain Desplats