GetAllPolynomials - Maple Help
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QuantifierElimination[QuantifierTools]

  

GetAllPolynomials

  

get all polynomials appearing in a Tarski formula

 

Calling Sequence

Parameters

Returns

Description

Examples

Compatibility

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

withQuantifierElimination&colon;withQuantifierTools&colon;

GetAllPolynomialsImplies0<x2&plus;5y&comma;Andx5z&plus;y&equals;0&comma;x&plus;z1

x+z1&comma;x25y&comma;x5z+y

(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

QuantifierElimination

QuantifierTools