Eno Tonisson* (Estonia), eno@math.ut.ee 

Preliminary Phases Of The Conversion Step And Computer Algebra Systems

The students have to learn different algorithms for solving algebra problems in
school mathematics.  It is possible to distinguish between various phases in
every algorithm step.  Example: Phase A. Assessment: Is it necessary to make
the step?; Phase B. Assigning concrete roles to the elements of an equation,
expression, etc. (assigning concrete values to the variables of the rule
mentioned in Phase C); Phase C. Application of the rule (property).

The first two phases have not found in-depth treatment in school textbooks.  In
reality, a number of mistakes are made in these very phases.  How do computer
algebra systems handle these phases? This paper is focused on the means to
execute the first two phases in different computer algebra systems (DERIVE,
Maple, Mathematica, MuPAD).  The issues covered include the handling of
conditions, the decomposition of the expression, etc.