GetAllPolynomials - Maple Help
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QuantifierElimination[QuantifierTools]

 GetAllPolynomials
 get all polynomials appearing in a Tarski formula

 Calling Sequence GetAllPolynomials(expr, output=t)

Parameters

 expr - any Tarski formula, can be quantified t - (optional) identical('set','list'); the type of output that will be returned (default: set)

Returns

 • A set or list of all polynomials appearing in expr.

Description

 • The polynomial corresponding to a relation is the difference of the left- and right-hand sides. Note that Maple represents relations of the form a>b or a>=b as b>a or b>=a, respectively, so if on input the right-hand side $b$ of such an inequality is $0$, the corresponding polynomial is $-a$ and not $a$.
 • Constant polynomials do appear in the output, i.e. if 1 < 0 is a constraint in expr then 1 will appear as a polynomial in the output.
 • Such a list or set produced by this function may be desirable to pass to CAD functions, as full CAD functions usually require a structure of flat polynomials to build a CAD from, and not a Tarski formula.
 • Even if t is a list, the output will not feature the same polynomial appearing more than once, i.e., duplicates are removed from the output regardless.

Examples

 > $\mathrm{with}\left(\mathrm{QuantifierElimination}\right):$$\mathrm{with}\left(\mathrm{QuantifierTools}\right):$
 > $\mathrm{GetAllPolynomials}\left(\mathrm{Implies}\left(0<{x}^{2}+5y,\mathrm{And}\left({x}^{5}z+y=0,x+z\le 1\right)\right)\right)$
 $\left\{{x}{+}{z}{-}{1}{,}{-}{{x}}^{{2}}{-}{5}{}{y}{,}{{x}}^{{5}}{}{z}{+}{y}\right\}$ (1)

Compatibility

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

 See Also