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My start at creating a CAS system and Synthetic math
Message #1 Posted by Ben Salinas on 2 Feb 2004, 11:42 p.m.

Just wanted to let ya'll (yes, I'm from Texas) what I'm doing with this synthetic math.

I got an independent study class approved using this textbook, which basically means I will get a credit for this at school and it will be on my transcript. In the mean time, I have typed up 2 chapters of summaries available at http://geocities.com/piguy31415926/indep_study.html I have also implemented some of what I have learned so far into a java program (or 4 actually). Right now I basicially have the basic operations for polynomials with coefficients as fractions as will as basic operations for fractions. Take a look.

I'm off to work on Chapter 4

-Ben Salinas

      
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~

            
Re: My start at creating a CAS system and Synthetic math
Message #3 Posted by Bill Wiese on 3 Feb 2004, 2:11 p.m.,
in response to message #2 by hugh steers

Hi guys,

I would encourage you folks to look at something like the(Waterloo) Maple symbolic math engine. I believe it exists as a freestanding product and a subset accompanies Mathematica (and maybe MathCAD).

I'm not terribly familiar with it as I'm more of a Matlab person (or was, awhile back...)

Without a GUI front end symbolic entry appears to be a bit burdensome.

But something like this on a PDA with some kinda GUI would be great.

In fact, that'd be a great math engine: a PDA on one side w/Maple, and flip it over to the other side for a nice calc keyboard + 2line LCD display.

Bill
San Jose


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