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Case
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Algorithm
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General polynomial inequalities
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The Collins algorithm is used with McCallum's improved projection operator.
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Strict inequalities
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Strzebonski's method is used.
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Linear inequalities
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Methods based on either the simplex algorithm or the Loos-Weispfenning
linear quantifier elimination algorithm are used.
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Nonalgebraic functions
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A database of relations is used to determine the domains of function
values from the domains of their arguments. Polynomial-oriented
algorithms are used whenever the resulting domains correspond to
semialgebraic sets.
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Other algebra manipulations
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Polynomial expansion, polynomial factoring (performed by a variant of
the Cantor-Zassenhaus algorithm to factor modulo a prime with
Hensel lifting and recombination then used to build up factors over the
integers), common denominator fractions, and partial fractions
(calculated using either a version of the Padé technique or the
method of undetermined coefficients) are used.
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