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General algebraic expressions simplification

RSIM and FCTR leave any non-rational (sub)expressions unchanged and treat i (the complex unit) like any other variable. To simplify non-rational algebraic expressions (like square- and yth-root, exponentials, logarithmic, trigonometric and hyperbolic functions) and expressions that involve complex arguments ALG48 provides the command ASIM.

Unlike the simplification of rational expressions, the simplification of general algebraic expressions is somewhat subjective and heuristic in nature. No algorithm will do it optimally in all cases. ASIM does the following:

In addition, ASIM simplifies the quadratic algebraic extensions (i and the square roots of irreducible integers) and moves them to the numerator of the expressions. E.g.,

If the calculator is in Radian mode, ASIM also substitutes the exact value of the trigonometric functions for arguments that are integer multiples of p, p/2 and p/4. A table of the rules that ASIM uses to simplify non-rational expressions is given in appendix.

ASIM takes the principal solution approach to simplification, that is, it performs simplification that hold in the most common or ``natural'' case, but that are not necessarily true in all cases. For instance, ASIM simplifies tex2html_wrap_inline1674 into x, even though, strictly speaking, this is valid only when x is positive, and it simplifies acos(cos(x)) into x which is only true for 0 £ x< p (the ``principal'' case).


Claude-Nicolas Fiechter (fiechter@cs.pitt.edu), 12 May 1998