JetBundleXExpression JBΒΆ
jet.spad line 2820 [edit on github]
JetBundleXExpression implements arbitrary functions in a jet bundle which depend only on the independent variables x
. Otherwise it is identical with JetBundleExpression. Such a domain is needed for JetLinearFunction.
- 0: %
from AbelianMonoid
- 1: %
from MagmaWithUnit
- *: (%, %) -> %
from LeftModule %
- *: (%, 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
- /: (SparseMultivariatePolynomial(Integer, Kernel %), SparseMultivariatePolynomial(Integer, Kernel %)) -> %
from FunctionSpace Integer
- ^: (%, %) -> %
- ^: (%, Fraction Integer) -> %
from RadicalCategory
- ^: (%, Integer) -> %
from DivisionRing
- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- abs: % -> %
- acos: % -> %
- acosh: % -> %
- acot: % -> %
- acoth: % -> %
- acsc: % -> %
- acsch: % -> %
- airyAi: % -> %
- airyAiPrime: % -> %
- airyBi: % -> %
- airyBiPrime: % -> %
- algtower: % -> List Kernel %
from FunctionSpace Integer
- algtower: List % -> List Kernel %
from FunctionSpace Integer
- angerJ: (%, %) -> %
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- applyQuote: (Symbol, %) -> %
from FunctionSpace Integer
- applyQuote: (Symbol, %, %) -> %
from FunctionSpace Integer
- applyQuote: (Symbol, %, %, %) -> %
from FunctionSpace Integer
- applyQuote: (Symbol, %, %, %, %) -> %
from FunctionSpace Integer
- applyQuote: (Symbol, List %) -> %
from FunctionSpace Integer
- asec: % -> %
- asech: % -> %
- asin: % -> %
- asinh: % -> %
- associates?: (%, %) -> Boolean
from EntireRing
- associator: (%, %, %) -> %
from NonAssociativeRng
- atan: % -> %
- atanh: % -> %
- autoReduce: List % -> List %
from JetBundleFunctionCategory JB
- belong?: BasicOperator -> Boolean
from ExpressionSpace
- besselI: (%, %) -> %
- besselJ: (%, %) -> %
- besselK: (%, %) -> %
- besselY: (%, %) -> %
- binomial: (%, %) -> %
- box: % -> %
from ExpressionSpace
- ceiling: % -> %
- characteristic: () -> NonNegativeInteger
from NonAssociativeRing
- charlierC: (%, %, %) -> %
- charthRoot: % -> Union(%, failed) if Integer has CharacteristicNonZero
- Chi: % -> %
- Ci: % -> %
- class: % -> NonNegativeInteger
from JetBundleFunctionCategory JB
coerce: % -> Expression Integer
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- coerce: AlgebraicNumber -> %
coerce: Expression Integer -> %
- coerce: Fraction Integer -> %
from FunctionSpace Integer
- coerce: Fraction Polynomial Fraction Integer -> %
from FunctionSpace Integer
- coerce: Fraction Polynomial Integer -> %
- coerce: Integer -> %
from NonAssociativeRing
- coerce: JB -> %
from JetBundleFunctionCategory JB
- coerce: Kernel % -> %
from CoercibleFrom Kernel %
- coerce: Polynomial Fraction Integer -> %
from FunctionSpace Integer
- coerce: Polynomial Integer -> %
- coerce: SparseMultivariatePolynomial(Integer, Kernel %) -> %
from FunctionSpace Integer
- coerce: Symbol -> %
from CoercibleFrom Symbol
- commutator: (%, %) -> %
from NonAssociativeRng
- const?: % -> Boolean
from JetBundleFunctionCategory JB
- convert: % -> InputForm
from ConvertibleTo InputForm
- convert: % -> Pattern Float if Integer has ConvertibleTo Pattern Float
from ConvertibleTo Pattern Float
- convert: % -> Pattern Integer
from ConvertibleTo Pattern Integer
- convert: Factored % -> %
from FunctionSpace Integer
- cos: % -> %
- cosh: % -> %
- cot: % -> %
- coth: % -> %
- csc: % -> %
- csch: % -> %
- D: (%, List Symbol) -> %
- D: (%, List Symbol, List NonNegativeInteger) -> %
- D: (%, Symbol) -> %
- D: (%, Symbol, NonNegativeInteger) -> %
- definingPolynomial: % -> %
from ExpressionSpace
- denom: % -> SparseMultivariatePolynomial(Integer, Kernel %)
from FunctionSpace Integer
- denominator: % -> %
from JetBundleFunctionCategory JB
- differentiate: (%, JB) -> %
from JetBundleFunctionCategory JB
- differentiate: (%, List Symbol) -> %
- differentiate: (%, List Symbol, List NonNegativeInteger) -> %
- differentiate: (%, Symbol) -> %
- differentiate: (%, Symbol, NonNegativeInteger) -> %
- digamma: % -> %
- dilog: % -> %
- dimension: (List %, SparseEchelonMatrix(JB, %), NonNegativeInteger) -> NonNegativeInteger
from JetBundleFunctionCategory JB
- diracDelta: % -> %
- distribute: % -> %
from ExpressionSpace
- distribute: (%, %) -> %
from ExpressionSpace
- divide: (%, %) -> Record(quotient: %, remainder: %)
from EuclideanDomain
- dSubst: (%, JB, %) -> %
from JetBundleFunctionCategory JB
- Ei: % -> %
- ellipticF: (%, %) -> %
- ellipticK: % -> %
- ellipticPi: (%, %, %) -> %
- elt: (BasicOperator, %) -> %
from ExpressionSpace
- elt: (BasicOperator, %, %) -> %
from ExpressionSpace
- elt: (BasicOperator, %, %, %) -> %
from ExpressionSpace
- elt: (BasicOperator, %, %, %, %) -> %
from ExpressionSpace
- elt: (BasicOperator, %, %, %, %, %) -> %
from ExpressionSpace
- elt: (BasicOperator, %, %, %, %, %, %) -> %
from ExpressionSpace
- elt: (BasicOperator, %, %, %, %, %, %, %) -> %
from ExpressionSpace
- elt: (BasicOperator, %, %, %, %, %, %, %, %) -> %
from ExpressionSpace
- elt: (BasicOperator, %, %, %, %, %, %, %, %, %) -> %
from ExpressionSpace
- elt: (BasicOperator, List %) -> %
from ExpressionSpace
- erf: % -> %
- erfi: % -> %
- euclideanSize: % -> NonNegativeInteger
from EuclideanDomain
- eval: (%, %, %) -> %
from InnerEvalable(%, %)
- eval: (%, BasicOperator, % -> %) -> %
from ExpressionSpace
- eval: (%, BasicOperator, %, Symbol) -> %
from FunctionSpace Integer
- eval: (%, BasicOperator, List % -> %) -> %
from ExpressionSpace
- eval: (%, Equation %) -> %
from Evalable %
- eval: (%, Kernel %, %) -> %
from InnerEvalable(Kernel %, %)
- eval: (%, List %, List %) -> %
from InnerEvalable(%, %)
- eval: (%, List BasicOperator, List %, Symbol) -> %
from FunctionSpace Integer
- eval: (%, List BasicOperator, List(% -> %)) -> %
from ExpressionSpace
- eval: (%, List BasicOperator, List(List % -> %)) -> %
from ExpressionSpace
- eval: (%, List Equation %) -> %
from Evalable %
- eval: (%, List Kernel %, List %) -> %
from InnerEvalable(Kernel %, %)
- eval: (%, List Symbol, List NonNegativeInteger, List(% -> %)) -> %
from FunctionSpace Integer
- eval: (%, List Symbol, List NonNegativeInteger, List(List % -> %)) -> %
from FunctionSpace Integer
- eval: (%, List Symbol, List(% -> %)) -> %
from ExpressionSpace
- eval: (%, List Symbol, List(List % -> %)) -> %
from ExpressionSpace
- eval: (%, Symbol, % -> %) -> %
from ExpressionSpace
- eval: (%, Symbol, List % -> %) -> %
from ExpressionSpace
- eval: (%, Symbol, NonNegativeInteger, % -> %) -> %
from FunctionSpace Integer
- eval: (%, Symbol, NonNegativeInteger, List % -> %) -> %
from FunctionSpace Integer
- even?: % -> Boolean
from ExpressionSpace
- exp: % -> %
- 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
- extractSymbol: SparseEchelonMatrix(JB, %) -> SparseEchelonMatrix(JB, %)
from JetBundleFunctionCategory JB
- factorial: % -> %
- factorials: % -> %
- factorials: (%, Symbol) -> %
- floor: % -> %
- formalDiff2: (%, PositiveInteger, SparseEchelonMatrix(JB, %)) -> Record(DPhi: %, JVars: List JB)
from JetBundleFunctionCategory JB
- formalDiff2: (List %, PositiveInteger, SparseEchelonMatrix(JB, %)) -> Record(DSys: List %, JVars: List List JB)
from JetBundleFunctionCategory JB
- formalDiff: (%, List NonNegativeInteger) -> %
from JetBundleFunctionCategory JB
- formalDiff: (%, PositiveInteger) -> %
from JetBundleFunctionCategory JB
- formalDiff: (List %, PositiveInteger) -> List %
from JetBundleFunctionCategory JB
- fractionPart: % -> %
- freeOf?: (%, %) -> Boolean
from ExpressionSpace
- freeOf?: (%, JB) -> Boolean
from JetBundleFunctionCategory JB
- freeOf?: (%, Symbol) -> Boolean
from ExpressionSpace
- fresnelC: % -> %
- fresnelS: % -> %
- gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
from GcdDomain
- getNotation: () -> Symbol
from JetBundleFunctionCategory JB
- ground?: % -> Boolean
from FunctionSpace Integer
- ground: % -> Integer
from FunctionSpace Integer
- hankelH1: (%, %) -> %
- hankelH2: (%, %) -> %
- height: % -> NonNegativeInteger
from ExpressionSpace
- hermiteH: (%, %) -> %
- hypergeometricF: (List %, List %, %) -> %
- integral: (%, SegmentBinding %) -> %
- integral: (%, Symbol) -> %
- inv: % -> %
from DivisionRing
- is?: (%, BasicOperator) -> Boolean
from ExpressionSpace
- is?: (%, Symbol) -> Boolean
from ExpressionSpace
- isExpt: % -> Union(Record(var: Kernel %, exponent: Integer), failed)
from FunctionSpace Integer
- isExpt: (%, BasicOperator) -> Union(Record(var: Kernel %, exponent: Integer), failed)
from FunctionSpace Integer
- isExpt: (%, Symbol) -> Union(Record(var: Kernel %, exponent: Integer), failed)
from FunctionSpace Integer
- isMult: % -> Union(Record(coef: Integer, var: Kernel %), failed)
from FunctionSpace Integer
- isPlus: % -> Union(List %, failed)
from FunctionSpace Integer
- isPower: % -> Union(Record(val: %, exponent: Integer), failed)
from FunctionSpace Integer
- isTimes: % -> Union(List %, failed)
from FunctionSpace Integer
- jacobiCn: (%, %) -> %
- jacobiDn: (%, %) -> %
- jacobiMatrix: (List %, List List JB) -> SparseEchelonMatrix(JB, %)
from JetBundleFunctionCategory JB
- jacobiMatrix: List % -> SparseEchelonMatrix(JB, %)
from JetBundleFunctionCategory JB
- jacobiP: (%, %, %, %) -> %
- jacobiSn: (%, %) -> %
- jacobiTheta: (%, %) -> %
- jacobiZeta: (%, %) -> %
- jetVariables: % -> List JB
from JetBundleFunctionCategory JB
- kelvinBei: (%, %) -> %
- kelvinBer: (%, %) -> %
- kelvinKei: (%, %) -> %
- kelvinKer: (%, %) -> %
- kernel: (BasicOperator, %) -> %
from ExpressionSpace
- kernel: (BasicOperator, List %) -> %
from ExpressionSpace
- kernels: % -> List Kernel %
from ExpressionSpace
- kernels: List % -> List Kernel %
from ExpressionSpace
- kummerM: (%, %, %) -> %
- kummerU: (%, %, %) -> %
- laguerreL: (%, %, %) -> %
- lambertW: % -> %
- latex: % -> String
from SetCategory
- lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %)
from LeftOreRing
- leadingDer: % -> JB
from JetBundleFunctionCategory JB
- leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- leftPower: (%, PositiveInteger) -> %
from Magma
- leftRecip: % -> Union(%, failed)
from MagmaWithUnit
- legendreP: (%, %, %) -> %
- legendreQ: (%, %, %) -> %
- lerchPhi: (%, %, %) -> %
- li: % -> %
- log: % -> %
- lommelS1: (%, %, %) -> %
- lommelS2: (%, %, %) -> %
- mainKernel: % -> Union(Kernel %, failed)
from ExpressionSpace
- map: (% -> %, Kernel %) -> %
from ExpressionSpace
- meixnerM: (%, %, %, %) -> %
- minPoly: Kernel % -> SparseUnivariatePolynomial %
from ExpressionSpace
- multiEuclidean: (List %, %) -> Union(List %, failed)
from EuclideanDomain
- nthRoot: (%, Integer) -> %
from RadicalCategory
- numDepVar: () -> PositiveInteger
from JetBundleFunctionCategory JB
- numer: % -> SparseMultivariatePolynomial(Integer, Kernel %)
from FunctionSpace Integer
- numerator: % -> %
from JetBundleFunctionCategory JB
- numIndVar: () -> PositiveInteger
from JetBundleFunctionCategory JB
- odd?: % -> Boolean
from ExpressionSpace
- one?: % -> Boolean
from MagmaWithUnit
- operators: % -> List BasicOperator
from ExpressionSpace
- opposite?: (%, %) -> Boolean
from AbelianMonoid
- order: % -> NonNegativeInteger
from JetBundleFunctionCategory JB
- orderDim: (List %, SparseEchelonMatrix(JB, %), NonNegativeInteger) -> NonNegativeInteger
from JetBundleFunctionCategory JB
- P: (PositiveInteger, List NonNegativeInteger) -> %
from JetBundleFunctionCategory JB
- P: (PositiveInteger, NonNegativeInteger) -> %
from JetBundleFunctionCategory JB
- P: List NonNegativeInteger -> %
from JetBundleFunctionCategory JB
- P: NonNegativeInteger -> %
from JetBundleFunctionCategory JB
- paren: % -> %
from ExpressionSpace
- patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if Integer has PatternMatchable Float
from PatternMatchable Float
- patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %)
from PatternMatchable Integer
- permutation: (%, %) -> %
- pi: () -> %
- plenaryPower: (%, PositiveInteger) -> %
from NonAssociativeAlgebra %
- polygamma: (%, %) -> %
- polylog: (%, %) -> %
- principalIdeal: List % -> Record(coef: List %, generator: %)
from PrincipalIdealDomain
- product: (%, SegmentBinding %) -> %
- product: (%, Symbol) -> %
- quo: (%, %) -> %
from EuclideanDomain
- recip: % -> Union(%, failed)
from MagmaWithUnit
- reduce: % -> %
reduce(x)
reduces the algebraics inx
.
- reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer)
- reducedSystem: Matrix % -> Matrix Integer
- reduceMod: (List %, List %) -> List %
from JetBundleFunctionCategory JB
- rem: (%, %) -> %
from EuclideanDomain
- retract: % -> AlgebraicNumber
- retract: % -> Fraction Integer
from RetractableTo Fraction Integer
- retract: % -> Fraction Polynomial Integer
- retract: % -> Integer
from RetractableTo Integer
- retract: % -> JB
from RetractableTo JB
- retract: % -> Kernel %
from RetractableTo Kernel %
- retract: % -> Polynomial Integer
- retract: % -> Symbol
from RetractableTo Symbol
- retract: JetBundleExpression JB -> %
retract(p)
is likeretractIfCan(p)
put yields a hard error, ifp
contains further jet variables.
- retractIfCan: % -> Union(AlgebraicNumber, failed)
- retractIfCan: % -> Union(Fraction Integer, failed)
from RetractableTo Fraction Integer
- retractIfCan: % -> Union(Fraction Polynomial Integer, failed)
- retractIfCan: % -> Union(Integer, failed)
from RetractableTo Integer
- retractIfCan: % -> Union(JB, failed)
from RetractableTo JB
- retractIfCan: % -> Union(Kernel %, failed)
from RetractableTo Kernel %
- retractIfCan: % -> Union(Polynomial Integer, failed)
- retractIfCan: % -> Union(Symbol, failed)
from RetractableTo Symbol
- retractIfCan: JetBundleExpression JB -> Union(%, failed)
retractIfCan(p)
checks whetherp
depends only on the independent variables. If yes, it is coerced.
- riemannZeta: % -> %
- rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- rightPower: (%, PositiveInteger) -> %
from Magma
- rightRecip: % -> Union(%, failed)
from MagmaWithUnit
- rootOf: % -> %
- rootOf: (%, Symbol) -> %
- rootOf: (SparseUnivariatePolynomial %, Symbol) -> %
- rootOf: Polynomial % -> %
- rootOf: SparseUnivariatePolynomial % -> %
- rootsOf: % -> List %
- rootsOf: (%, Symbol) -> List %
- rootsOf: (SparseUnivariatePolynomial %, Symbol) -> List %
- rootsOf: Polynomial % -> List %
- rootsOf: SparseUnivariatePolynomial % -> List %
- rootSum: (%, SparseUnivariatePolynomial %, Symbol) -> %
- sample: %
from AbelianMonoid
- sec: % -> %
- sech: % -> %
- setNotation: Symbol -> Void
from JetBundleFunctionCategory JB
- Shi: % -> %
- Si: % -> %
- sign: % -> %
- simplify: (List %, SparseEchelonMatrix(JB, %)) -> Record(Sys: List %, JM: SparseEchelonMatrix(JB, %), Depend: Union(failed, List List NonNegativeInteger))
from JetBundleFunctionCategory JB
- simpMod: (List %, List %) -> List %
from JetBundleFunctionCategory JB
- simpMod: (List %, SparseEchelonMatrix(JB, %), List %) -> Record(Sys: List %, JM: SparseEchelonMatrix(JB, %), Depend: Union(failed, List List NonNegativeInteger))
from JetBundleFunctionCategory JB
- simpOne: % -> %
from JetBundleFunctionCategory JB
- sin: % -> %
- sinh: % -> %
- sizeLess?: (%, %) -> Boolean
from EuclideanDomain
- smaller?: (%, %) -> Boolean
from Comparable
- solveFor: (%, JB) -> Union(%, failed)
from JetBundleFunctionCategory JB
- sortLD: List % -> List %
from JetBundleFunctionCategory JB
- sqrt: % -> %
from RadicalCategory
- squareFree: % -> Factored %
- squareFreePart: % -> %
- struveH: (%, %) -> %
- struveL: (%, %) -> %
- subst: (%, Equation %) -> %
from ExpressionSpace
- subst: (%, JB, %) -> %
from JetBundleFunctionCategory JB
- subst: (%, List Equation %) -> %
from ExpressionSpace
- subst: (%, List Kernel %, List %) -> %
from ExpressionSpace
- subtractIfCan: (%, %) -> Union(%, failed)
- summation: (%, SegmentBinding %) -> %
- summation: (%, Symbol) -> %
- symbol: List % -> SparseEchelonMatrix(JB, %)
from JetBundleFunctionCategory JB
- tan: % -> %
- tanh: % -> %
- tower: % -> List Kernel %
from ExpressionSpace
- tower: List % -> List Kernel %
from ExpressionSpace
- U: () -> %
from JetBundleFunctionCategory JB
- U: PositiveInteger -> %
from JetBundleFunctionCategory JB
- unit?: % -> Boolean
from EntireRing
- unitCanonical: % -> %
from EntireRing
- unitNormal: % -> Record(unit: %, canonical: %, associate: %)
from EntireRing
- unitStep: % -> %
- univariate: (%, Kernel %) -> Fraction SparseUnivariatePolynomial %
from FunctionSpace Integer
- variables: % -> List Symbol
from FunctionSpace Integer
- variables: List % -> List Symbol
from FunctionSpace Integer
- weberE: (%, %) -> %
- weierstrassP: (%, %, %) -> %
- weierstrassPInverse: (%, %, %) -> %
- weierstrassPPrime: (%, %, %) -> %
- weierstrassSigma: (%, %, %) -> %
- weierstrassZeta: (%, %, %) -> %
- whittakerM: (%, %, %) -> %
- whittakerW: (%, %, %) -> %
- X: () -> %
from JetBundleFunctionCategory JB
- X: PositiveInteger -> %
from JetBundleFunctionCategory JB
- zero?: % -> Boolean
from AbelianMonoid
- zeroOf: % -> %
- zeroOf: (%, Symbol) -> %
- zeroOf: (SparseUnivariatePolynomial %, Symbol) -> %
- zeroOf: Polynomial % -> %
- zeroOf: SparseUnivariatePolynomial % -> %
- zerosOf: % -> List %
- zerosOf: (%, Symbol) -> List %
- zerosOf: (SparseUnivariatePolynomial %, Symbol) -> List %
- zerosOf: Polynomial % -> List %
- zerosOf: SparseUnivariatePolynomial % -> List %
Algebra %
AlgebraicallyClosedFunctionSpace Integer
ArcTrigonometricFunctionCategory
BiModule(%, %)
BiModule(Fraction Integer, Fraction Integer)
CharacteristicNonZero if Integer has CharacteristicNonZero
CoercibleFrom Fraction Integer
CoercibleFrom Fraction Polynomial Integer
CoercibleFrom Polynomial Integer
ConvertibleTo Pattern Float if Integer has ConvertibleTo Pattern Float
Evalable %
FullyLinearlyExplicitOver Integer
InnerEvalable(%, %)
InnerEvalable(Kernel %, %)
JetBundleBaseFunctionCategory JB
Module %
NonAssociativeAlgebra Fraction Integer
PartialDifferentialRing Symbol
PatternMatchable Float if Integer has PatternMatchable Float
RetractableTo Fraction Integer
RetractableTo Fraction Polynomial Integer
RetractableTo Polynomial Integer