On Sat, Jul 22, 2023 at 04:34:11AM +0000, '68th' via FriCAS - computer algebra
system wrote:
>
> Looks like computer algebra systems are not the right tool to do elementary
> algebra. What kind of software is more suitable for transforming algebraic
> expressions? Or do human beings have to do it on paper despite all the hype
> how artificial "intelligence" and other fruits of digitalization make humans
> obsolete?
Well, actually FriCAS may be quite close to what want. As I wrote,
each FriCAS type has its own rules to perform calculation. So
you need appropriate FriCAS type. In the past I wrote a special
version of Expression that did no simplification on its own.
So internal form exactly represented input. All changes were
via application of transformation rules. I do not remember
what I did with printing, doing it naively would give ugly
result that exactly represented structure of the input. But
one can beautyfy it so that it looks like other expression.
One drawback is that when you input
x - x
you will get back x - x and need a rewrite rule to transform
it to 0. Another drawback is that even asking it x - x is
zero you will get no as an answer. Another question is
usefulness of this type.
To issustrate usfulness question consider even more elementary
math, namely we want to transform 42 into 25 + 17. One possibilty
would be to have very special "42" rule that transforms literal
42 into 25 + 17. Another way is more usual rewrite: rule
that transform any occurence of 42 in the input into 25 + 17.
This more general rule transforms cos(42) into cos(25 + 17).
But when writing general rules you may want rule that always gives
17 as second term (let me call it "17" rule), so transforms 43 into
26 + 17. But "17" rule must do some actual arithmetic, so the
question is how much artihmetic should be done? Should "17" rule
transform 25 + 18 into 26 + 17? Usual answer in rule systems
is that matching is mainly syntactic with possible
side condition. So normal "17" rule would do not artmetic
during matching, but a differnt rule could say math both literals
and sums. But rules get complicated quite quickly and instead
of giving commands you are really writing programs in a special
purpose programming language. Now, when you are writing programs
there is a lot of programming languages.
--
Waldek Hebisch
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