Expression sequence with the following three elements:

exprout : Rational Tarski Formula, resulting from converting expr to prenex form and removing any constraints recognized as lifting constraints

liftingconstraints = cons, where cons is the set of the real lifting constraints removed from expr,

opencad = truefalse, value determining whether open CAD is suggested to use

Suggests arguments to pass to QuantifierElimination's CylindricalAlgebraicDecompose or PartialCylindricalAlgebraicDecompose command for expr, with the purpose of optimizing the computational efficiency of such a call. This will lead to a (partial) CAD with a smaller number of cells.

Usage of lifting constraints and/or open CAD for either command can speed up lifting considerably, so this function can separate out the real lifting constraints (see QuantifierElimination options for definition) from an existentially quantified $\mathrm{And}$, and possibly suggest to use open CAD for formulae that contain no equations or non-strict inequalities.

This generates a sequence of arguments amenable to pass to either routine, where that call will then be faster to process.

SuggestCADOptions preprocesses expr for a subsequent (partial) CAD. In particular, the input formula is converted to prenex form, and all denominators are removed (see ConvertRationalConstraintsToTarski).

$\mathrm{with}\left(\mathrm{QuantifierElimination}\right)\:$$\mathrm{with}\left(\mathrm{QuantifierTools}\right)$

$\left[\mathrm{AlphaConvert}\,\mathrm{ConvertRationalConstraintsToTarski}\,\mathrm{ConvertToPrenexForm}\,\mathrm{GetAllPolynomials}\,\mathrm{GetEquationalConstraints}\,\mathrm{GetUnquantifiedFormula}\,\mathrm{NegateFormula}\,\mathrm{SuggestCADOptions}\right]$

$\mathrm{f1}≔\mathrm{exists}\left(\left[y\&comma;x\right]\&comma;\mathrm{And}\left(x^2+y^2-1=0\&comma;b^2{\left(x-c\right)}^2+a^2{y}^2-a^2{b}^2=0\&comma;0<a\&comma;a<1\&comma;0<b\&comma;b<1\&comma;0\le c\&comma;c<1\right)\right)$

$\mathrm{f1}≔\exists \left(\left[y\&comma;x\right]\&comma;x^2+y^2-1=0\wedge b^2{\left(x-c\right)}^2+a^2{y}^2-a^2{b}^2=0\wedge 0<a\wedge a<1\wedge 0<b\wedge b<1\wedge 0\le c\wedge c<1\right)$

$\mathrm{SuggestCADOptions}\left(\mathrm{f1}\right)$

$\exists \left(\left[y\&comma;x\right]\&comma;x^2+y^2-1=0\wedge a^2{b}^2-a^2{y}^2-b^2{c}^2+2b^{2}cx-b^2{x}^2=0\right),\mathrm{liftingconstraints}=\left\{-c\le 0\&comma;a<1\&comma;b<1\&comma;c<1\&comma;-a<0\&comma;-b<0\right\},\mathrm{opencad}=\mathrm{false}$

$\mathrm{f2}≔\mathrm{forall}\left(x\&comma;0<4x^8-4\left(L-3\right)x^6-2\left(3L-6\right)x^4-2\left(L-3\right)x^2+1\right)$

$\mathrm{f2}≔\forall \left(x\&comma;0<4x^8-4\left(L-3\right)x^6-2\left(3L-6\right)x^4-2\left(L-3\right)x^2+1\right)$

$\mathrm{SuggestCADOptions}\left(\mathrm{f2}\right)$

$\forall \left(x\&comma;-4x^8+4x^{6}L-12x^6+6x^{4}L-12x^4+2x^{2}L-6x^2<1\right),\mathrm{liftingconstraints}=\varnothing ,\mathrm{opencad}=\mathrm{true}$

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

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