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

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 $0<xy$. On the other hand, they may expand, such as $\frac{x}{y}=0$ becoming $x=0\wedge y\ne 0$.

$\mathrm{with}\left(\mathrm{QuantifierElimination}\right)\&colon;$$\mathrm{with}\left(\mathrm{QuantifierTools}\right)\&colon;$

$\mathrm{ConvertRationalConstraintsToTarski}\left(\frac{x}{y}\ne 0\right)$

$x\ne 0\wedge y\ne 0$

$\mathrm{ConvertRationalConstraintsToTarski}\left(\frac{x}{y}\le 0\right)$

$xy\le 0\wedge y\ne 0$

$\mathrm{ConvertRationalConstraintsToTarski}\left(\frac{x}{y}=0\right)$

$x=0\wedge y\ne 0$

$\mathrm{ConvertRationalConstraintsToTarski}\left(\frac{x}{y}<0\right)$

$0<-xy$

$\mathrm{ConvertRationalConstraintsToTarski}\left(\mathrm{Or}\left(z=0\&comma;\frac{x}{y}<0\right)\right)$

$z=0\vee 0<-xy$

The QuantifierElimination:-QuantifierTools:-ConvertRationalConstraintsToTarski command was introduced in Maple 2023.

For more information on Maple 2023 changes, see Updates in Maple 2023.