type/realalgnum - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : type/realalgnum

type/realalgnum

check for an object of type realalgnum (real algebraic number)

 

Calling Sequence

Parameters

Description

Subtypes

Supertypes

Examples

Calling Sequence

type(x, realalgnum)

Parameters

x

-

any expression

Description

• 

The type realalgnum forms a representation of real algebraic numbers.

• 

The type( x, 'realalgnum' ) function returns true if one of the following holds:

– 

x is rational,

– 

x is of the form RootOf( p, c .. d ) where cd are rational numbers isolating a root of p, and p is a non-linear univariate polynomial in _Z with coefficients of type realalgnum, or

– 

x is a sum, product, or quotient of expressions of type realalgnum.

• 

The type realalgnum is defined and used in the RootFinding and QuantifierElimination packages.

Subtypes

• 

type/rational

Supertypes

• 

type/algnum

Examples

withRootFinding:

type12,'realalgnum'

true

(1)

typeRootOf_Z22,1..2,'realalgnum'

true

(2)

typeRootOf_Z25RootOf_Z39,2..3,3..4,'realalgnum'

true

(3)

typeRootOf_Z22,1..2RootOf_Z23,1..2,'realalgnum'

true

(4)

typeRootOf_Z22,1..2+RootOf_Z23,1..2RootOf_Z32,1..2,'realalgnum'

true

(5)

type1.34,'realalgnum'

false

(6)

type∞,'realalgnum'

false

(7)

type1+I,'realalgnum'

false

(8)

typex,'realalgnum'

false

(9)

The only RootOf selector accepted is a range of rational numbers:

typeRootOf_Z22,'realalgnum'

false

(10)

typeRootOf_Z2y,index=real1,'realalgnum'

false

(11)

typeRootOf_Z22,2,'realalgnum'

false

(12)

typeRootOf_Z22,index=1,'realalgnum'

false

(13)

typeRootOf_Z22,1.1..2.3,'realalgnum'

false

(14)

Non-rational (sub-)expressions are not accepted:

typeRootOf_Z232,1..2,'realalgnum'

false

(15)

typeRootOf_Z22,1..213,'realalgnum'

false

(16)

See Also

QuantifierElimination[PartialCylindricalAlgebraicDecompose]

QuantifierElimination[QuantifierEliminate]

RootFinding[EvaluateAtRoot]

RootFinding[RefineRoot]

RootOf