| How about:
"Solve X^n + Y^n = Z^n for positive integers X,Y,Z,n; n>2" I have a wonderful prrof of this...
What exactly do you mean by "algebra problems"?
How about multiplying two long irreducible polynomials together,
and asking it to factor them?
How about some Diophantine equations -- easy to create, easy to
check, hard to solve. Sometimes impossible, as in X�+X = 4Y+1.
John
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| The idea is to be able to give it some problems which a really good
system would significantly aid the operator in solving within a
reasonable amount of time (within the time reasonably alloted to
a demo, say 10 minutes or so).
In theory, algebra includes everything through calculus and
differential equations. Anything is fair game within that broad
domain, including sensitive numerical problems. However, no
"package" may exist for solving particular classes of problems.
For example, Diophantine equations (the possible to solve ones)
would be excellent, except as of the date of the actual writing
of the published manual, there is no package for solving Diophantine
equations. The only mention (according to the index) is that
the function ExtendedGCD (which gives the GCD and the two multipliers
which produce the two arguments as result in one step) is documented
as being "important in finding integer solutions to linear
(Diophantine) equations." So that is a good suggestion, but, as
it happens one which I probably can't use, except where the steps
needed to solve it are likely to be obvious to a good demonstrator.
(Maple, I might add, does have a routine for solving Diophantine
equations of the proper, fairly general, form).
The polynomial factoring problem is a good one which should be usable.
Thanks.
Topher
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