RealClosedFieldΒΆ

reclos.spad line 258

RealClosedField provides common access functions for all real closed fields.

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (%, Fraction Integer) -> %
from RightModule Fraction Integer
*: (%, Integer) -> %
from RightModule Integer
*: (Fraction Integer, %) -> %
from LeftModule Fraction Integer
*: (Integer, %) -> %
from AbelianGroup
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
from AbelianGroup
-: (%, %) -> %
from AbelianGroup
/: (%, %) -> %
from Field
<: (%, %) -> Boolean
from PartialOrder
<=: (%, %) -> Boolean
from PartialOrder
=: (%, %) -> Boolean
from BasicType
>: (%, %) -> Boolean
from PartialOrder
>=: (%, %) -> Boolean
from PartialOrder
^: (%, Fraction Integer) -> %
from RadicalCategory
^: (%, Integer) -> %
from DivisionRing
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
abs: % -> %
from OrderedRing
allRootsOf: Polynomial % -> List %
allRootsOf(pol) creates all the roots of pol naming each uniquely
allRootsOf: Polynomial Fraction Integer -> List %
allRootsOf(pol) creates all the roots of pol naming each uniquely
allRootsOf: Polynomial Integer -> List %
allRootsOf(pol) creates all the roots of pol naming each uniquely
allRootsOf: SparseUnivariatePolynomial % -> List %
allRootsOf(pol) creates all the roots of pol naming each uniquely
allRootsOf: SparseUnivariatePolynomial Fraction Integer -> List %
allRootsOf(pol) creates all the roots of pol naming each uniquely
allRootsOf: SparseUnivariatePolynomial Integer -> List %
allRootsOf(pol) creates all the roots of pol naming each uniquely
annihilate?: (%, %) -> Boolean
from Rng
antiCommutator: (%, %) -> %
from NonAssociativeSemiRng
approximate: (%, %) -> Fraction Integer
approximate(n, p) gives an approximation of n that has precision p
associates?: (%, %) -> Boolean
from EntireRing
associator: (%, %, %) -> %
from NonAssociativeRng
characteristic: () -> NonNegativeInteger
from NonAssociativeRing
coerce: % -> %
from Algebra %
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: Fraction Integer -> %
from Algebra Fraction Integer
coerce: Integer -> %
from NonAssociativeRing
commutator: (%, %) -> %
from NonAssociativeRng
divide: (%, %) -> Record(quotient: %, remainder: %)
from EuclideanDomain
euclideanSize: % -> NonNegativeInteger
from EuclideanDomain
expressIdealMember: (List %, %) -> Union(List %, failed)
from PrincipalIdealDomain
exquo: (%, %) -> Union(%, failed)
from EntireRing
extendedEuclidean: (%, %) -> Record(coef1: %, coef2: %, generator: %)
from EuclideanDomain
extendedEuclidean: (%, %, %) -> Union(Record(coef1: %, coef2: %), failed)
from EuclideanDomain
factor: % -> Factored %
from UniqueFactorizationDomain
gcd: (%, %) -> %
from GcdDomain
gcd: List % -> %
from GcdDomain
gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
from GcdDomain
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
inv: % -> %
from DivisionRing
latex: % -> String
from SetCategory
lcm: (%, %) -> %
from GcdDomain
lcm: List % -> %
from GcdDomain
lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %)
from LeftOreRing
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
mainDefiningPolynomial: % -> Union(SparseUnivariatePolynomial %, failed)
mainDefiningPolynomial(x) is the defining polynomial for the main algebraic quantity of x
mainForm: % -> Union(OutputForm, failed)
mainForm(x) is the main algebraic quantity name of x
mainValue: % -> Union(SparseUnivariatePolynomial %, failed)
mainValue(x) is the expression of x in terms of SparseUnivariatePolynomial(\%)
max: (%, %) -> %
from OrderedSet
min: (%, %) -> %
from OrderedSet
multiEuclidean: (List %, %) -> Union(List %, failed)
from EuclideanDomain
negative?: % -> Boolean
from OrderedRing
nthRoot: (%, Integer) -> %
from RadicalCategory
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
positive?: % -> Boolean
from OrderedRing
prime?: % -> Boolean
from UniqueFactorizationDomain
principalIdeal: List % -> Record(coef: List %, generator: %)
from PrincipalIdealDomain
quo: (%, %) -> %
from EuclideanDomain
recip: % -> Union(%, failed)
from MagmaWithUnit
rem: (%, %) -> %
from EuclideanDomain
rename!: (%, OutputForm) -> %
rename!(x, name) changes the way x is printed
rename: (%, OutputForm) -> %
rename(x, name) gives a new number that prints as name
retract: % -> Fraction Integer
from RetractableTo Fraction Integer
retract: % -> Integer
from RetractableTo Integer
retractIfCan: % -> Union(Fraction Integer, failed)
from RetractableTo Fraction Integer
retractIfCan: % -> Union(Integer, failed)
from RetractableTo Integer
rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
from MagmaWithUnit
rootOf: (SparseUnivariatePolynomial %, PositiveInteger) -> Union(%, failed)
rootOf(pol, n) creates the nth root for the order of pol and gives it unique name
rootOf: (SparseUnivariatePolynomial %, PositiveInteger, OutputForm) -> Union(%, failed)
rootOf(pol, n, name) creates the nth root for the order of pol and names it name
sample: %
from AbelianMonoid
sign: % -> Integer
from OrderedRing
sizeLess?: (%, %) -> Boolean
from EuclideanDomain
smaller?: (%, %) -> Boolean
from Comparable
sqrt: % -> %
sqrt(x) is x ^ (1/2)
sqrt: (%, PositiveInteger) -> %
sqrt(x, n) is x ^ (1/n)
sqrt: Fraction Integer -> %
sqrt(x) is x ^ (1/2)
sqrt: Integer -> %
sqrt(x) is x ^ (1/2)
squareFree: % -> Factored %
from UniqueFactorizationDomain
squareFreePart: % -> %
from UniqueFactorizationDomain
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
unit?: % -> Boolean
from EntireRing
unitCanonical: % -> %
from EntireRing
unitNormal: % -> Record(unit: %, canonical: %, associate: %)
from EntireRing
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer

Algebra Integer

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

BiModule(Integer, Integer)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicZero

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

DivisionRing

EntireRing

EuclideanDomain

Field

FullyRetractableTo Fraction Integer

GcdDomain

IntegralDomain

LeftModule %

LeftModule Fraction Integer

LeftModule Integer

LeftOreRing

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Module Integer

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OrderedAbelianGroup

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedRing

OrderedSet

PartialOrder

PrincipalIdealDomain

RadicalCategory

RetractableTo Fraction Integer

RetractableTo Integer

RightModule %

RightModule Fraction Integer

RightModule Integer

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

UniqueFactorizationDomain

unitsKnown