ConvertRationalConstraintsToTarski - Maple Help
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QuantifierElimination[QuantifierTools]

 ConvertRationalConstraintsToTarski
 convert a formula featuring rational constraints to a formula with only polynomial constraints

 Calling Sequence ConvertRationalConstraintsToTarski( expr )

Parameters

 expr - any boolean formula of rational constraints

Returns

 • An equivalent formula to expr as a Tarski formula, that is, with rational constraints converted to equivalent Tarski formulae (only polynomial constraints allowed).

Description

 • Converts a formula that may contain rational constraints (that is, constraints featuring rational functions - fractions of polynomials) to a Tarski formula, that is, a boolean formula of polynomial constraints.
 • As part of this conversion, the assumption is made that all denominators occurring are nonzero.
 • This may result in individual atoms changing, such as $0<\frac{x}{y}$ becoming the equivalent polynomial constraint $0. On the other hand, they may expand, such as $\frac{x}{y}=0$ becoming $x=0\wedge y\ne 0$.

Examples

 > $\mathrm{with}\left(\mathrm{QuantifierElimination}\right):$$\mathrm{with}\left(\mathrm{QuantifierTools}\right):$
 > $\mathrm{ConvertRationalConstraintsToTarski}\left(\frac{x}{y}\ne 0\right)$
 ${x}{\ne }{0}{\wedge }{y}{\ne }{0}$ (1)
 > $\mathrm{ConvertRationalConstraintsToTarski}\left(\frac{x}{y}\le 0\right)$
 ${x}{}{y}{\le }{0}{\wedge }{y}{\ne }{0}$ (2)
 > $\mathrm{ConvertRationalConstraintsToTarski}\left(\frac{x}{y}=0\right)$
 ${x}{=}{0}{\wedge }{y}{\ne }{0}$ (3)
 > $\mathrm{ConvertRationalConstraintsToTarski}\left(\frac{x}{y}<0\right)$
 ${0}{<}{-}{x}{}{y}$ (4)
 > $\mathrm{ConvertRationalConstraintsToTarski}\left(\mathrm{Or}\left(z=0,\frac{x}{y}<0\right)\right)$
 ${z}{=}{0}{\vee }{0}{<}{-}{x}{}{y}$ (5)

Compatibility

 • The QuantifierElimination:-QuantifierTools:-ConvertRationalConstraintsToTarski command was introduced in Maple 2023.
 • For more information on Maple 2023 changes, see Updates in Maple 2023.