🚀 go-pugleaf

Checksum: 2978283719 (verify with brik -cv)
Submitted-by: Carlos Ferraro <carlos@fy.chalmers.se>
Posting-number: Volume 7, Issue 44
Archive-name: poly.cf


BEGIN_DOC poly.doc

(Unshure of which version you have? Hit REVIEW once you are 
in the LIBRARIES menu !)
Gbg. , November 92

Hello everybody!

This is a very little (1702 bytes) and very fast (full
sys-rpl !) xlib to deal with the fundamental polynom necessities:

ROOTS (all roots of poly), PDIV (poly div), PMULT (obvious), 
PADD (poly add), PEVAL (poly eval in a point), PDER (poly der).

IMPORTANT : Unlike other polynom utilities I use vectors 
instead of lists to represent polynoms.

## ROOTS takes all the roots (real or complex) of a real poly.
Up to 2nd degree polynoms can also have complex coefficients.
An aptent to round every element of the resulting polynoms,
as well as every root - taking the real and imaginary
parts of the complex numbers separatelly - is made. 
Sometimes it works fine, sometimes not, see :

Taking the roots of [ 4 33 68 15 ] :
the answer { -4.9999999998 -3 -.25000000005 } = { -5 -3 -.25 }
comes in 1,78 seconds !!!

Taking the roots of [ 5 16 18 18 13 2 ]  gives 
the answer { -1 (0,-1) (0,1) -2 -.2 } in 7,1 seconds !!

Taking the roots of [ (1,0) (9,0) (20,0) (12,0) ] gives
the answer { (-6,0) -2 -1 } after only 2 seconds !!
Observe that althought the coefficients look complex, they
are merely real numbers !

## PDIV  checks for 2 vectors at level 1 and 2 and if not found,
dispatches to the usual / (division). It will give the
(eventual) rest at level 2. If it's found to be close to
zero, it won't appear.

## PMULT checks for 2 vectors at level 1 and 2 and if not found,
dispatches to the usual * (multiplication)

## PADD is obvious.

## PEVAL takes a vector from level 2 and a number or a
symbol from level 1.

## PDER takes a vector from level 1.


In the next coming versions I may replace PDER by
a prog taking rational poly as well. Also PADD may desappear and
instead a partial fraction "solver" will come.


INSTRUCTIONS FOR DOWNLOADING:
First you must uudecode or ASC-> the corresponding versions.
In order to make it really ease for you, I include both
the code of the librarie and an auto-instalation program called INSTL in a 
directory called XLIBS which simply  will auto-purge itself once the lib is 
installed ! Simply go into XLIBS and press INSTL. The  calc will turn off, but 
don't worry, it's part of the instrucctions! When you turn it on, you'll find
a little surprize in your CST! Yes, I include 1 menu-label (GROB) called
POLY who will   auto-include in your CST...for your comfort!
Once the libs are installed, the values are :
Library POLY , LID 1224 , bytes 1702 , chksum #15FAh .

(Observe that this values are from taking "bytes" when the stack shows :
Library 1224 : POLY )

INSTRUCCIONS TO PURGE THE LIBRARIES:
Althought I can't imagine why anybody would like to purge this beauty, 
here it is:
:&:1224 DUP DETACH PURGE

Thanks ...
a lot to Detlef Mueller for his <-LIB-> and <-RPL-> !!

Any questions? Call me!

END_DOC


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END_UU
--
+--------------------------+----------------+
| carlos@fy.chalmers.se    | "The ultimate  |
| Carlos Angel Ferraro     |  truth was the |
| Mathematical physics     |  penultimate   |
| University of Gothemburg |  falsehood..." |
| SWEDEN                   |                |
+--------------------------+----------------+