The TPSA type exposes the following members.
Constructors
| Name | Description | |
|---|---|---|
 | TPSA | Creates a new TPSA object. |
Methods
| Name | Description | |
|---|---|---|
| arcsin | Arc sine function. |
| arctan | Arc tangent function. |
| BesselJ | Bessel J function. |
| BesselJ0 | Bessel J0 function. |
 | binomial | Computes the binomial coefficient of the two arguments. |
| Clear(Double) | Clears the instance and sets the constant term to the value of the optional argument. |
| Clear(array<Int32>[]()[][]%) | Clears specific terms of the instance specified by an array of indices. |
| clone | Creates a new copy of the instance. |
| comp | Performs the function composition of the instance and an array of TPSA objects. |
| copy | Copy the argument to the instance. |
| cos | Cosine function. |
| cosh | Hyperbolic cosine function. |
| cotan | Cotangent function. |
| cotanh | Hyperbolic cotangent function. |
| csc | Cosecant function. |
| csch | Hyperbolic cosecant function. |
| Divide(Double) | Divides the instance by a double. |
| Divide(TPSA%) | Divides the instance by a TPSA object and returns itself. |
| Equals | Determines whether the specified Object is equal to the current Object. (Inherited from Object.) |
| Eval(array<Double>[]()[][]) | Evaluate the instance at numerical values of the variables. |
| Eval(array<array<Double>[]()[][]>[]()[][]) | Evalutes the instance at a set of numerical values of the variables. |
| exp | Exponential function. |
| factorial | The factorial of the integer argument. |
| Filter | Zeros coefficients of the instance corresponding to an array of indices. |
| FilterKeep | Returns the complement of Filter. |
 | Finalize | Allows an Object to attempt to free resources and perform other cleanup operations before the Object is reclaimed by garbage collection. (Inherited from Object.) |
| GetHashCode | 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.) |
| GetTerm | Returns the coefficient of the term with variables having the exponents of the argument. |
| GetTermIndex | Returns the index in tps of the term with variables
having the exponents of the argument. |
| GetType | Gets the Type of the current instance. (Inherited from Object.) |
| grad | Returns the gradient of the instance as an array of TPSA objects. |
| Init | Initializes the class for creating TPSA objects of the given number of variable and order. |
| Inverse | The multiplicative inverse of the instance. |
| log | Log function. |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) |
| Minus()()()() | Converts the instance to its arithmetic negative. |
| Minus(Double) | Subtracts a real value from the instance. Something like a -= operator. |
| Minus(TPSA) | Subtracts a TPSA object from the instance. |
| one | Returns the unit element or elements representing the variables depending on the argument. |
| Plus(Double) | Adds a real value to the instance. Something like a += operator. |
| Plus(array<TPSA>[]()[][]) | Adds a TPSA object to the instance. Something like a += operator. |
| Power | Raises the instance to a power and returns itself. |
| sec | Secant function. |
| sech | Hyperbolic secant function. |
| SetOrder | Clips terms of the instance whose order is either higher or lower than a given value,
and returns a new object. |
| sin | Sine function. |
| sinh | Hyperbolic sine function. |
| sort | Sorts jagged arrays of integers. |
| sqrt | The square root of the instance. |
| tan | Tangent function. |
| tanh | Hyperbolic tangent function. |
| Times(Double) | Multiplies the instance by a double. |
| Times(array<TPSA>[]()[][]) | Multiplies the instance by a TPSA object and returns itself. |
| ToString()()()() | Returns a String that represents the current Object. (Inherited from Object.) |
| ToString(Double, String) | Returns a string representation of the instance. |
Operators
| Name | Description | |
|---|---|---|
 | Addition(Double, TPSA) | Adds a double to a TPSA object. |
| Addition(TPSA, Double) | The addition operator that acts on two instances. |
| Addition(TPSA, TPSA) | Overloaded addition operator for two TPSA objects. |
| Division(Double, TPSA) | Divides a double by a TPSA object. |
| Division(TPSA, Double) | Divides a TPSA object by a double. |
| Division(TPSA, TPSA) | Divide two TPSA objects. |
| Exponent | Raises the instance to a power. |
| Multiply(Double, TPSA) | Multiplies a TPSA object by a double. |
| Multiply(TPSA, Double) | Overloade multiply a TPSA object by a double. |
| Multiply(TPSA, TPSA) | Multiply two TPSA objects. |
| Subtraction(Double, TPSA) | Overloaded subtraction operator with one argument being a double. |
| Subtraction(TPSA, Double) | The subtraction operator that acts on two instances. |
| Subtraction(TPSA, TPSA) | Overloaded subtraction operator for two TPSA objects. |
| UnaryNegation | The arithmetic negative of the instance. |
Fields
| Name | Description | |
|---|---|---|
 | exponents | A list of TPSATerms lists, each consisting of a list, corresponding to its term, of exponents of the variables. |
| order | A list of TPSATerms integers, each consisting of the order of the corresponding term. |
| tps | The coefficients of the object. |
| vars | 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. |
| zero | The zero element of the algebra. |
Properties
| Name | Description | |
|---|---|---|
 | TPSAOrder | Order of the TPSA. |
| TPSATerms | The number of terms in the TPSA. |
| TPSAVariables | The number of variables in the TPSA. |
