Re: My start at creating a CAS system and Synthetic math Message #2 Posted by hugh steers on 3 Feb 2004, 6:56 a.m., in response to message #1 by Ben Salinas
hello ben,
i like your enthusiasm with this project. keep up the good work.
in parallel, you might also be interested in some stuff i am working on.
i have been searching for a while for the best (in a sense) way of working
with numbers for calculators, and for calculation in general.
the idea is that, historically, calculators had strictly limited cpu and capacity,
but those constraints are not as strict for a would-be modern calculator. this
is, i think, why you are interested in CAS and indeed we are seeing CAS availability
on real machines.to this end, i have been experimenting with a variation of the theory of constructive
reals for my concrete number representation. basically, constructive reals are a
form of approximating a real number in such a way as to track accuracy as well. when
accuracy falls below target, the numbers expand (ie increase precision) on demand.
there are many pitfalls of vanilla floating point as used by calculators, and this
is meant to redress that as best possible.
here is a link to an experimental command line calculator for your amusement.
http://www.voidware.com/tmp/crcalc.exe
put in -10 for (10 digits) and try these on crcalc and also on your real
calculator sand compare results.
examples:
tan(355/226)
crcalc: -7497258.18533~
hp48g: -7497089.06508 (only 4 correct digits)
10*((1+0.1/n)^n-1)/10 where n = 60*60*24*365 see: http://www.voidware.com/tvm.htm
hp15c: 312,925.02 (one 1 digit correct)
crcalc: 331667.006691~
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