Re: Computer Algebra Algorithms
- From: JohnCreighton_@xxxxxxxxxxx
- Date: 7 Apr 2005 22:55:19 -0700
mehran gupta wrote:
>Hi,
>
>
>Can anyone please point me to a good basic textbok or reference on
>computer algebra algorithms. I am mainly interested in writing C >code
>for simple algebraic simplication.
>
>
>Thank You,
>
>
>M. G.
I've been trying to follow this thread somewhat but there is many
more posts here then I want to toughly dissect. I don't really think
in the above posts enough motivation was given behind what you want to
do. If you want to learn CAS, learn lisp because that is what the open
source CAS are programmed in and a large part of the academic work in
AI uses lisp.
If you want to play around with a few simplification algorithms I see
no reason why you cannot use C. I agree with an above poster that C++
would be better if you wanted your C code to give a CAS the C code does
not have to look anything like the language the CAS uses. In your C++
code you could overload each operator for type mathEquation and then
these operators would construct expression trees based upon the rules
you define. This would suffer from the batch limitation as Richard
suggested. Each time you wanted to try some simplification you would
have to run the compiler and look at your results.
If you want to use C dynamically you are going to need some kind of
parser. The parser could be written in C or any other language. It
should return to you a tree structure representing the expression the
user typed at the command line. You could then perform some algebra on
it. In this case you may not care if you can overload the plus
operator. You could just call it as a C function pluss(a,b), since
everything would be done by your custom interpreter (would this really
be C?).
Java was mentioned as a language that wouldn't be a good choice
because it didn't support overloading of operators. Richard said
there is ways around this. I know in Java you can overload the
concatenation operator by creating a method called tostring, but I
don't think when I learned it you could do something equivalent for
times.
Richard mentioned a limitation of overload. It is well known that the
world is not made up of objects but objects are just a model we use at
an instance to dissect a problem. It is difficult to generalize
functions in object oriented programming because the functions must be
written for members of the same class or that implement the same
interface. Many programming languages such as Haskell have a much
better type checking system that allows better generalization and more
flexible polymorphism.
http://en.wikipedia.org/wiki/Polymorphism_%28computer_science%29
If you want to use C and you want to do something useful with CAS I
would suggest learning the external function interface of MAPLE. This
will allow you to Manipulate maple data structures in the Maple
workspace with C functions. I havn't got into it but perhaps you
could even use it to prevent the automatic simplification in Maple.
Apparently the best reference for this is the Maple advanced
programming guide. It is about 54 dollars.
.
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