[MATHEDCC] Computer Algebra Systems

Phil Mahler (mahlerp@admin.middlesex.cc.ma.us)
Sun, 22 Feb 1998 12:10:32 EST5EDT4,M4.1.0,M10.5.0

Responses to two different postings.
>
>The question of integrals has a similar answer. There are infinitely many
>integrals the TI-92 cannot do. There are a relative few that can be done
>with the tricks of calculus - substitution, parts, partical fractions. The
>fact that a few of these few can be done by symbolic methods but not by
>technology is surely not an argument against using technology.

Theoretically, if symbolic methods (tricks of calculus) will find an
antiderivative, so will a computer algebra system, such as Derive. The
algorithm exists, even it it's not wholly implemented in Derive. Just a
matter of time, I presume. In fact, theoretically, if an antiderivative
exists the CAS should be able to find it even if the calculus heuristics
won't.

>My TI-92 also handled this integral with ease. OTOH, I wwould be very
>interested in any problems which Derive (or Mathematica or Maple or ...)
>handles but which causes the TI-92 to stumble. I haven't found many
>which would be routine in the first two years of college math.

Maple will factor
x^8 - 3x^5 - 4x^4 - 5x^3 + x^2 + 2x + 2 completely, over the integers.
Neither the TI-92, nor Derive on a PC, will do this completely.

The writer may have been referring to antiderivatives, and this is certainly
not a routine problem in the first two years of college math, but it may be
of interest.

When I last taught calculus, Newton hadn't reached partial derivatives
yet, so I don't know of any examples of antiderivatives which the 92 won't
do, but I too would like to see an example of an antiderivative that is in
a calculus text that the 92 won't do. I saw none posted on this list.

Philip Mahler
Middlesex Community College
Bedford, MA

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