The TPSA type exposes the following members.

Constructors

  NameDescription
Public methodTPSA
Creates a new TPSA object.

Methods

  NameDescription
Public methodarcsin
Arc sine function.
Public methodarctan
Arc tangent function.
Public methodBesselJ
Bessel J function.
Public methodBesselJ0
Bessel J0 function.
Public methodStatic memberbinomial
Computes the binomial coefficient of the two arguments.
Public methodClear(Double)
Clears the instance and sets the constant term to the value of the optional argument.
Public methodClear(array<Int32>[]()[][]%)
Clears specific terms of the instance specified by an array of indices.
Public methodclone
Creates a new copy of the instance.
Public methodcomp
Performs the function composition of the instance and an array of TPSA objects.
Public methodcopy
Copy the argument to the instance.
Public methodcos
Cosine function.
Public methodcosh
Hyperbolic cosine function.
Public methodcotan
Cotangent function.
Public methodcotanh
Hyperbolic cotangent function.
Public methodcsc
Cosecant function.
Public methodcsch
Hyperbolic cosecant function.
Public methodDivide(Double)
Divides the instance by a double.
Public methodDivide(TPSA%)
Divides the instance by a TPSA object and returns itself.
Public methodEquals
Determines whether the specified Object is equal to the current Object.
(Inherited from Object.)
Public methodEval(array<Double>[]()[][])
Evaluate the instance at numerical values of the variables.
Public methodEval(array<array<Double>[]()[][]>[]()[][])
Evalutes the instance at a set of numerical values of the variables.
Public methodexp
Exponential function.
Public methodStatic memberfactorial
The factorial of the integer argument.
Public methodFilter
Zeros coefficients of the instance corresponding to an array of indices.
Public methodFilterKeep
Returns the complement of Filter.
Protected methodFinalize
Allows an Object to attempt to free resources and perform other cleanup operations before the Object is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetHashCode
Serves as a hash function for a particular type. GetHashCode()()()() is suitable for use in hashing algorithms and data structures like a hash table.
(Inherited from Object.)
Public methodGetTerm
Returns the coefficient of the term with variables having the exponents of the argument.
Public methodStatic memberGetTermIndex
Returns the index in tps of the term with variables having the exponents of the argument.
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodgrad
Returns the gradient of the instance as an array of TPSA objects.
Public methodStatic memberInit
Initializes the class for creating TPSA objects of the given number of variable and order.
Public methodInverse
The multiplicative inverse of the instance.
Public methodlog
Log function.
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodMinus()()()()
Converts the instance to its arithmetic negative.
Public methodMinus(Double)
Subtracts a real value from the instance. Something like a -= operator.
Public methodMinus(TPSA)
Subtracts a TPSA object from the instance.
Public methodStatic memberone
Returns the unit element or elements representing the variables depending on the argument.
Public methodPlus(Double)
Adds a real value to the instance. Something like a += operator.
Public methodPlus(array<TPSA>[]()[][])
Adds a TPSA object to the instance. Something like a += operator.
Public methodPower
Raises the instance to a power and returns itself.
Public methodsec
Secant function.
Public methodsech
Hyperbolic secant function.
Public methodSetOrder
Clips terms of the instance whose order is either higher or lower than a given value, and returns a new object.
Public methodsin
Sine function.
Public methodsinh
Hyperbolic sine function.
Public methodStatic membersort
Sorts jagged arrays of integers.
Public methodsqrt
The square root of the instance.
Public methodtan
Tangent function.
Public methodtanh
Hyperbolic tangent function.
Public methodTimes(Double)
Multiplies the instance by a double.
Public methodTimes(array<TPSA>[]()[][])
Multiplies the instance by a TPSA object and returns itself.
Public methodToString()()()()
Returns a String that represents the current Object.
(Inherited from Object.)
Public methodToString(Double, String)
Returns a string representation of the instance.

Operators

  NameDescription
Public operatorStatic memberAddition(Double, TPSA)
Adds a double to a TPSA object.
Public operatorStatic memberAddition(TPSA, Double)
The addition operator that acts on two instances.
Public operatorStatic memberAddition(TPSA, TPSA)
Overloaded addition operator for two TPSA objects.
Public operatorStatic memberDivision(Double, TPSA)
Divides a double by a TPSA object.
Public operatorStatic memberDivision(TPSA, Double)
Divides a TPSA object by a double.
Public operatorStatic memberDivision(TPSA, TPSA)
Divide two TPSA objects.
Public operatorStatic memberExponent
Raises the instance to a power.
Public operatorStatic memberMultiply(Double, TPSA)
Multiplies a TPSA object by a double.
Public operatorStatic memberMultiply(TPSA, Double)
Overloade multiply a TPSA object by a double.
Public operatorStatic memberMultiply(TPSA, TPSA)
Multiply two TPSA objects.
Public operatorStatic memberSubtraction(Double, TPSA)
Overloaded subtraction operator with one argument being a double.
Public operatorStatic memberSubtraction(TPSA, Double)
The subtraction operator that acts on two instances.
Public operatorStatic memberSubtraction(TPSA, TPSA)
Overloaded subtraction operator for two TPSA objects.
Public operatorStatic memberUnaryNegation
The arithmetic negative of the instance.

Fields

  NameDescription
Public fieldStatic memberexponents
A list of TPSATerms lists, each consisting of a list, corresponding to its term, of exponents of the variables.
Public fieldStatic memberorder
A list of TPSATerms integers, each consisting of the order of the corresponding term.
Public fieldtps
The coefficients of the object.
Public fieldStatic membervars
A list of TPSA objects representing the variables of the algebra, i.e., each is a polynomial whose only nonzero coefficient is the one corresponding the linear term of its variable and having value unity.
Public fieldStatic memberzero
The zero element of the algebra.

Properties

  NameDescription
Public propertyStatic memberTPSAOrder
Order of the TPSA.
Public propertyStatic memberTPSATerms
The number of terms in the TPSA.
Public propertyStatic memberTPSAVariables
The number of variables in the TPSA.

See Also