FieldDerivativeStructure (Hipparchus 2.2 API)

java.lang.Object
- org.hipparchus.analysis.differentiation.FieldDerivativeStructure<T>

Type Parameters:

T - the type of the field elements

All Implemented Interfaces:

FieldDerivative<T,FieldDerivativeStructure<T>>, CalculusFieldElement<FieldDerivativeStructure<T>>, FieldElement<FieldDerivativeStructure<T>>
```
public class FieldDerivativeStructure<T extends CalculusFieldElement<T>>
extends Object
implements FieldDerivative<T,FieldDerivativeStructure<T>>
```
Class representing both the value and the differentials of a function.
This class is similar to DerivativeStructure except function parameters and value can be any CalculusFieldElement.

Instances of this class are guaranteed to be immutable.

See Also:

DerivativeStructure, FDSFactory, DSCompiler

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`FieldDerivativeStructure<T>`	`abs()` absolute value.
`FieldDerivativeStructure<T>`	`acos()` Arc cosine operation.
`FieldDerivativeStructure<T>`	`acosh()` Inverse hyperbolic cosine operation.
`FieldDerivativeStructure<T>`	`add(double a)` '+' operator.
`FieldDerivativeStructure<T>`	`add(FieldDerivativeStructure<T> a)` Compute this + a.
`FieldDerivativeStructure<T>`	`add(T a)` '+' operator.
`FieldDerivativeStructure<T>`	`asin()` Arc sine operation.
`FieldDerivativeStructure<T>`	`asinh()` Inverse hyperbolic sine operation.
`FieldDerivativeStructure<T>`	`atan()` Arc tangent operation.
`FieldDerivativeStructure<T>`	`atan2(FieldDerivativeStructure<T> x)` Two arguments arc tangent operation.
`static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T>`	`atan2(FieldDerivativeStructure<T> y, FieldDerivativeStructure<T> x)` Two arguments arc tangent operation.
`FieldDerivativeStructure<T>`	`atanh()` Inverse hyperbolic tangent operation.
`FieldDerivativeStructure<T>`	`cbrt()` Cubic root.
`FieldDerivativeStructure<T>`	`ceil()` Get the smallest whole number larger than instance.
`FieldDerivativeStructure<T>`	`compose(double... f)` Compute composition of the instance by a univariate function.
`FieldDerivativeStructure<T>`	`compose(T... f)` Compute composition of the instance by a univariate function.
`FieldDerivativeStructure<T>`	`copySign(double sign)` Returns the instance with the sign of the argument.
`FieldDerivativeStructure<T>`	`copySign(FieldDerivativeStructure<T> sign)` Returns the instance with the sign of the argument.
`FieldDerivativeStructure<T>`	`copySign(T sign)` Returns the instance with the sign of the argument.
`FieldDerivativeStructure<T>`	`cos()` Cosine operation.
`FieldDerivativeStructure<T>`	`cosh()` Hyperbolic cosine operation.
`FieldDerivativeStructure<T>`	`differentiate(int varIndex, int differentiationOrder)` Differentiate w.r.t.
`FieldDerivativeStructure<T>`	`divide(double a)` '÷' operator.
`FieldDerivativeStructure<T>`	`divide(FieldDerivativeStructure<T> a)` Compute this ÷ a.
`FieldDerivativeStructure<T>`	`divide(T a)` '÷' operator.
`FieldDerivativeStructure<T>`	`exp()` Exponential.
`FieldDerivativeStructure<T>`	`expm1()` Exponential minus 1.
`FieldDerivativeStructure<T>`	`floor()` Get the largest whole number smaller than instance.
`T[]`	`getAllDerivatives()` Get all partial derivatives.
`int`	`getExponent()` Return the exponent of the instance value, removing the bias.
`FDSFactory<T>`	`getFactory()` Get the factory that built the instance.
`Field<FieldDerivativeStructure<T>>`	`getField()` Get the `Field` to which the instance belongs.
`int`	`getFreeParameters()` Get the number of free parameters.
`int`	`getOrder()` Get the derivation order.
`T`	`getPartialDerivative(int... orders)` Get a partial derivative.
`FieldDerivativeStructure<T>`	`getPi()` Get the Archimedes constant π.
`double`	`getReal()` Get the real value of the number.
`T`	`getValue()` Get the value part of the derivative structure.
`FieldDerivativeStructure<T>`	`hypot(FieldDerivativeStructure<T> y)` Returns the hypotenuse of a triangle with sides `this` and `y` - sqrt(this² +y²) avoiding intermediate overflow or underflow.
`static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T>`	`hypot(FieldDerivativeStructure<T> x, FieldDerivativeStructure<T> y)` Returns the hypotenuse of a triangle with sides `x` and `y` - sqrt(x² +y²) avoiding intermediate overflow or underflow.
`FieldDerivativeStructure<T>`	`integrate(int varIndex, int integrationOrder)` Integrate w.r.t.
`FieldDerivativeStructure<T>`	`linearCombination(double[] a, FieldDerivativeStructure<T>[] b)` Compute a linear combination.
`FieldDerivativeStructure<T>`	`linearCombination(double a1, FieldDerivativeStructure<T> b1, double a2, FieldDerivativeStructure<T> b2)` Compute a linear combination.
`FieldDerivativeStructure<T>`	`linearCombination(double a1, FieldDerivativeStructure<T> b1, double a2, FieldDerivativeStructure<T> b2, double a3, FieldDerivativeStructure<T> b3)` Compute a linear combination.
`FieldDerivativeStructure<T>`	`linearCombination(double a1, FieldDerivativeStructure<T> b1, double a2, FieldDerivativeStructure<T> b2, double a3, FieldDerivativeStructure<T> b3, double a4, FieldDerivativeStructure<T> b4)` Compute a linear combination.
`FieldDerivativeStructure<T>`	`linearCombination(FieldDerivativeStructure<T>[] a, FieldDerivativeStructure<T>[] b)` Compute a linear combination.
`FieldDerivativeStructure<T>`	`linearCombination(FieldDerivativeStructure<T> a1, FieldDerivativeStructure<T> b1, FieldDerivativeStructure<T> a2, FieldDerivativeStructure<T> b2)` Compute a linear combination.
`FieldDerivativeStructure<T>`	`linearCombination(FieldDerivativeStructure<T> a1, FieldDerivativeStructure<T> b1, FieldDerivativeStructure<T> a2, FieldDerivativeStructure<T> b2, FieldDerivativeStructure<T> a3, FieldDerivativeStructure<T> b3)` Compute a linear combination.
`FieldDerivativeStructure<T>`	`linearCombination(FieldDerivativeStructure<T> a1, FieldDerivativeStructure<T> b1, FieldDerivativeStructure<T> a2, FieldDerivativeStructure<T> b2, FieldDerivativeStructure<T> a3, FieldDerivativeStructure<T> b3, FieldDerivativeStructure<T> a4, FieldDerivativeStructure<T> b4)` Compute a linear combination.
`FieldDerivativeStructure<T>`	`linearCombination(T[] a, FieldDerivativeStructure<T>[] b)` Compute a linear combination.
`FieldDerivativeStructure<T>`	`linearCombination(T a1, FieldDerivativeStructure<T> b1, T a2, FieldDerivativeStructure<T> b2)` Compute a linear combination.
`FieldDerivativeStructure<T>`	`linearCombination(T a1, FieldDerivativeStructure<T> b1, T a2, FieldDerivativeStructure<T> b2, T a3, FieldDerivativeStructure<T> b3)` Compute a linear combination.
`FieldDerivativeStructure<T>`	`linearCombination(T a1, FieldDerivativeStructure<T> b1, T a2, FieldDerivativeStructure<T> b2, T a3, FieldDerivativeStructure<T> b3, T a4, FieldDerivativeStructure<T> b4)` Compute a linear combination.
`FieldDerivativeStructure<T>`	`log()` Natural logarithm.
`FieldDerivativeStructure<T>`	`log10()` Base 10 logarithm.
`FieldDerivativeStructure<T>`	`log1p()` Shifted natural logarithm.
`FieldDerivativeStructure<T>`	`multiply(double a)` '×' operator.
`FieldDerivativeStructure<T>`	`multiply(FieldDerivativeStructure<T> a)` Compute this × a.
`FieldDerivativeStructure<T>`	`multiply(int n)` Compute n × this.
`FieldDerivativeStructure<T>`	`multiply(T a)` '×' operator.
`FieldDerivativeStructure<T>`	`negate()` Returns the additive inverse of `this` element.
`FieldDerivativeStructure<T>`	`newInstance(double value)` Create an instance corresponding to a constant real value.
`FieldDerivativeStructure<T>`	`pow(double p)` Power operation.
`static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T>`	`pow(double a, FieldDerivativeStructure<T> x)` Compute a^x where a is a double and x a `FieldDerivativeStructure`
`FieldDerivativeStructure<T>`	`pow(FieldDerivativeStructure<T> e)` Power operation.
`FieldDerivativeStructure<T>`	`pow(int n)` Integer power operation.
`FieldDerivativeStructure<T>`	`rebase(FieldDerivativeStructure<T>... p)` Rebase instance with respect to low level parameter functions.
`FieldDerivativeStructure<T>`	`reciprocal()` Returns the multiplicative inverse of `this` element.
`FieldDerivativeStructure<T>`	`remainder(double a)` IEEE remainder operator.
`FieldDerivativeStructure<T>`	`remainder(FieldDerivativeStructure<T> a)` IEEE remainder operator.
`FieldDerivativeStructure<T>`	`remainder(T a)` IEEE remainder operator.
`FieldDerivativeStructure<T>`	`rint()` Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
`FieldDerivativeStructure<T>`	`rootN(int n)` N^th root.
`FieldDerivativeStructure<T>`	`scalb(int n)` Multiply the instance by a power of 2.
`FieldDerivativeStructure<T>`	`sign()` Compute the sign of the instance.
`FieldDerivativeStructure<T>`	`sin()` Sine operation.
`FieldSinCos<FieldDerivativeStructure<T>>`	`sinCos()` Combined Sine and Cosine operation.
`FieldDerivativeStructure<T>`	`sinh()` Hyperbolic sine operation.
`FieldSinhCosh<FieldDerivativeStructure<T>>`	`sinhCosh()` Combined hyperbolic sine and sosine operation.
`FieldDerivativeStructure<T>`	`sqrt()` Square root.
`FieldDerivativeStructure<T>`	`subtract(double a)` '-' operator.
`FieldDerivativeStructure<T>`	`subtract(FieldDerivativeStructure<T> a)` Compute this - a.
`FieldDerivativeStructure<T>`	`subtract(T a)` '-' operator.
`FieldDerivativeStructure<T>`	`tan()` Tangent operation.
`FieldDerivativeStructure<T>`	`tanh()` Hyperbolic tangent operation.
`T`	`taylor(double... delta)` Evaluate Taylor expansion of a derivative structure.
`T`	`taylor(T... delta)` Evaluate Taylor expansion of a derivative structure.
`FieldDerivativeStructure<T>`	`toDegrees()` Convert radians to degrees, with error of less than 0.5 ULP
`FieldDerivativeStructure<T>`	`toRadians()` Convert degrees to radians, with error of less than 0.5 ULP
`FieldDerivativeStructure<T>`	`ulp()` Compute least significant bit (Unit in Last Position) for a number.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.hipparchus.CalculusFieldElement
isFinite, isInfinite, isNaN, norm, round

Methods inherited from interface org.hipparchus.FieldElement
isZero

- Method Detail
  - newInstance
```
public FieldDerivativeStructure<T> newInstance(double value)
```
    Create an instance corresponding to a constant real value.
    
    Specified by:
    
    newInstance in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    value - constant real value
    
    Returns:
    
    instance corresponding to a constant real value
  - getFactory
```
public FDSFactory<T> getFactory()
```
    Get the factory that built the instance.
    
    Returns:
    
    factory that built the instance
  - getFreeParameters
```
public int getFreeParameters()
```
    Description copied from interface: FieldDerivative
    
    Get the number of free parameters.
    
    Specified by:
    
    getFreeParameters in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    number of free parameters
  - getOrder
```
public int getOrder()
```
    Description copied from interface: FieldDerivative
    
    Get the derivation order.
    
    Specified by:
    
    getOrder in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    derivation order
  - getReal
```
public double getReal()
```
    Get the real value of the number.
    
    Specified by:
    
    getReal in interface FieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    real value
  - getValue
```
public T getValue()
```
    Get the value part of the derivative structure.
    
    Specified by:
    
    getValue in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    value part of the derivative structure
    
    See Also:
    
    getPartialDerivative(int...)
  - getPartialDerivative
```
public T getPartialDerivative(int... orders)
                       throws MathIllegalArgumentException
```
    Get a partial derivative.
    
    Specified by:
    
    getPartialDerivative in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    orders - derivation orders with respect to each variable (if all orders are 0, the value is returned)
    
    Returns:
    
    partial derivative
    
    Throws:
    
    MathIllegalArgumentException - if the numbers of variables does not match the instance
    
    See Also:
    
    FieldDerivative.getValue()
  - getAllDerivatives
```
public T[] getAllDerivatives()
```
    Get all partial derivatives.
    
    Returns:
    
    a fresh copy of partial derivatives, in an array sorted according to DSCompiler.getPartialDerivativeIndex(int...)
  - add
```
public FieldDerivativeStructure<T> add(T a)
```
    '+' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this+a
  - add
```
public FieldDerivativeStructure<T> add(double a)
```
    '+' operator.
    
    Specified by:
    
    add in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this+a
  - add
```
public FieldDerivativeStructure<T> add(FieldDerivativeStructure<T> a)
                                throws MathIllegalArgumentException
```
    Compute this + a.
    
    Specified by:
    
    add in interface FieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a - element to add
    
    Returns:
    
    a new element representing this + a
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - subtract
```
public FieldDerivativeStructure<T> subtract(T a)
```
    '-' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this-a
  - subtract
```
public FieldDerivativeStructure<T> subtract(double a)
```
    '-' operator.
    
    Specified by:
    
    subtract in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this-a
  - subtract
```
public FieldDerivativeStructure<T> subtract(FieldDerivativeStructure<T> a)
                                     throws MathIllegalArgumentException
```
    Compute this - a.
    
    Specified by:
    
    subtract in interface FieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a - element to subtract
    
    Returns:
    
    a new element representing this - a
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - multiply
```
public FieldDerivativeStructure<T> multiply(T a)
```
    '×' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this×a
  - multiply
```
public FieldDerivativeStructure<T> multiply(int n)
```
    Compute n × this. Multiplication by an integer number is defined as the following sum n × this = ∑_i=1ⁿ this.
    
    Specified by:
    
    multiply in interface FieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    n - Number of times this must be added to itself.
    
    Returns:
    
    A new element representing n × this.
  - multiply
```
public FieldDerivativeStructure<T> multiply(double a)
```
    '×' operator.
    
    Specified by:
    
    multiply in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this×a
  - multiply
```
public FieldDerivativeStructure<T> multiply(FieldDerivativeStructure<T> a)
                                     throws MathIllegalArgumentException
```
    Compute this × a.
    
    Specified by:
    
    multiply in interface FieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a - element to multiply
    
    Returns:
    
    a new element representing this × a
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - divide
```
public FieldDerivativeStructure<T> divide(T a)
```
    '÷' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this÷a
  - divide
```
public FieldDerivativeStructure<T> divide(double a)
```
    '÷' operator.
    
    Specified by:
    
    divide in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this÷a
  - divide
```
public FieldDerivativeStructure<T> divide(FieldDerivativeStructure<T> a)
                                   throws MathIllegalArgumentException
```
    Compute this ÷ a.
    
    Specified by:
    
    divide in interface FieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a - element to divide by
    
    Returns:
    
    a new element representing this ÷ a
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - remainder
```
public FieldDerivativeStructure<T> remainder(T a)
```
    IEEE remainder operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a (the even integer is chosen for n if this/a is halfway between two integers)
  - remainder
```
public FieldDerivativeStructure<T> remainder(double a)
```
    IEEE remainder operator.
    
    Specified by:
    
    remainder in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
  - remainder
```
public FieldDerivativeStructure<T> remainder(FieldDerivativeStructure<T> a)
                                      throws MathIllegalArgumentException
```
    IEEE remainder operator.
    
    Specified by:
    
    remainder in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - negate
```
public FieldDerivativeStructure<T> negate()
```
    Returns the additive inverse of this element.
    
    Specified by:
    
    negate in interface FieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    the opposite of this.
  - abs
```
public FieldDerivativeStructure<T> abs()
```
    absolute value.
    Just another name for CalculusFieldElement.norm()
    
    Specified by:
    
    abs in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    abs(this)
  - ceil
```
public FieldDerivativeStructure<T> ceil()
```
    Get the smallest whole number larger than instance.
    
    Specified by:
    
    ceil in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    ceil(this)
  - floor
```
public FieldDerivativeStructure<T> floor()
```
    Get the largest whole number smaller than instance.
    
    Specified by:
    
    floor in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    floor(this)
  - rint
```
public FieldDerivativeStructure<T> rint()
```
    Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
    
    Specified by:
    
    rint in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5
  - sign
```
public FieldDerivativeStructure<T> sign()
```
    Compute the sign of the instance. The sign is -1 for negative numbers, +1 for positive numbers and 0 otherwise, for Complex number, it is extended on the unit circle (equivalent to z/|z|, with special handling for 0 and NaN)
    
    Specified by:
    
    sign in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
  - copySign
```
public FieldDerivativeStructure<T> copySign(T sign)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    Parameters:
    
    sign - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
  - copySign
```
public FieldDerivativeStructure<T> copySign(double sign)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    Specified by:
    
    copySign in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    sign - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
  - copySign
```
public FieldDerivativeStructure<T> copySign(FieldDerivativeStructure<T> sign)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    Specified by:
    
    copySign in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    sign - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
  - getExponent
```
public int getExponent()
```
    Return the exponent of the instance value, removing the bias.
    For double numbers of the form 2^x, the unbiased exponent is exactly x.
    
    Specified by:
    
    getExponent in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    exponent for instance in IEEE754 representation, without bias
  - scalb
```
public FieldDerivativeStructure<T> scalb(int n)
```
    Multiply the instance by a power of 2.
    
    Specified by:
    
    scalb in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    n - power of 2
    
    Returns:
    
    this × 2ⁿ
  - ulp
```
public FieldDerivativeStructure<T> ulp()
```
    Compute least significant bit (Unit in Last Position) for a number.
    The ulp function is a step function, hence all its derivatives are 0.
    
    Specified by:
    
    ulp in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    ulp(this)
    
    Since:
    
    2.0
  - hypot
```
public FieldDerivativeStructure<T> hypot(FieldDerivativeStructure<T> y)
                                  throws MathIllegalArgumentException
```
    Returns the hypotenuse of a triangle with sides this and y - sqrt(this² +y²) avoiding intermediate overflow or underflow.
    - If either argument is infinite, then the result is positive infinity.
    - else, if either argument is NaN then the result is NaN.
    Specified by:
    
    hypot in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    y - a value
    
    Returns:
    
    sqrt(this² +y²)
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - hypot
```
public static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T> hypot(FieldDerivativeStructure<T> x,
                                                                                    FieldDerivativeStructure<T> y)
                                                                             throws MathIllegalArgumentException
```
    Returns the hypotenuse of a triangle with sides x and y - sqrt(x² +y²) avoiding intermediate overflow or underflow.
    - If either argument is infinite, then the result is positive infinity.
    - else, if either argument is NaN then the result is NaN.
    Type Parameters:
    
    T - the type of the field elements
    
    Parameters:
    
    x - a value
    
    y - a value
    
    Returns:
    
    sqrt(x² +y²)
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - compose
```
@SafeVarargs
public final FieldDerivativeStructure<T> compose(T... f)
                                                       throws MathIllegalArgumentException
```
    Compute composition of the instance by a univariate function.
    
    Parameters:
    
    f - array of value and derivatives of the function at the current point (i.e. [f(getValue()), f'(getValue()), f''(getValue())...]).
    
    Returns:
    
    f(this)
    
    Throws:
    
    MathIllegalArgumentException - if the number of derivatives in the array is not equal to order + 1
  - compose
```
public FieldDerivativeStructure<T> compose(double... f)
                                    throws MathIllegalArgumentException
```
    Compute composition of the instance by a univariate function.
    
    Parameters:
    
    f - array of value and derivatives of the function at the current point (i.e. [f(getValue()), f'(getValue()), f''(getValue())...]).
    
    Returns:
    
    f(this)
    
    Throws:
    
    MathIllegalArgumentException - if the number of derivatives in the array is not equal to order + 1
  - reciprocal
```
public FieldDerivativeStructure<T> reciprocal()
```
    Returns the multiplicative inverse of this element.
    
    Specified by:
    
    reciprocal in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Specified by:
    
    reciprocal in interface FieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    the inverse of this.
  - sqrt
```
public FieldDerivativeStructure<T> sqrt()
```
    Square root.
    
    Specified by:
    
    sqrt in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    square root of the instance
  - cbrt
```
public FieldDerivativeStructure<T> cbrt()
```
    Cubic root.
    
    Specified by:
    
    cbrt in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    cubic root of the instance
  - rootN
```
public FieldDerivativeStructure<T> rootN(int n)
```
    N^th root.
    
    Specified by:
    
    rootN in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    n - order of the root
    
    Returns:
    
    n^th root of the instance
  - getField
```
public Field<FieldDerivativeStructure<T>> getField()
```
    Get the Field to which the instance belongs.
    
    Specified by:
    
    getField in interface FieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    Field to which the instance belongs
  - pow
```
public static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T> pow(double a,
                                                                                  FieldDerivativeStructure<T> x)
```
    Compute a^x where a is a double and x a FieldDerivativeStructure
    
    Type Parameters:
    
    T - the type of the field elements
    
    Parameters:
    
    a - number to exponentiate
    
    x - power to apply
    
    Returns:
    
    a^x
  - pow
```
public FieldDerivativeStructure<T> pow(double p)
```
    Power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    p - power to apply
    
    Returns:
    
    this^p
  - pow
```
public FieldDerivativeStructure<T> pow(int n)
```
    Integer power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    n - power to apply
    
    Returns:
    
    thisⁿ
  - pow
```
public FieldDerivativeStructure<T> pow(FieldDerivativeStructure<T> e)
                                throws MathIllegalArgumentException
```
    Power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    e - exponent
    
    Returns:
    
    this^e
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - exp
```
public FieldDerivativeStructure<T> exp()
```
    Exponential.
    
    Specified by:
    
    exp in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    exponential of the instance
  - expm1
```
public FieldDerivativeStructure<T> expm1()
```
    Exponential minus 1.
    
    Specified by:
    
    expm1 in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    exponential minus one of the instance
  - log
```
public FieldDerivativeStructure<T> log()
```
    Natural logarithm.
    
    Specified by:
    
    log in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    logarithm of the instance
  - log1p
```
public FieldDerivativeStructure<T> log1p()
```
    Shifted natural logarithm.
    
    Specified by:
    
    log1p in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    logarithm of one plus the instance
  - log10
```
public FieldDerivativeStructure<T> log10()
```
    Base 10 logarithm.
    
    Specified by:
    
    log10 in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    base 10 logarithm of the instance
  - cos
```
public FieldDerivativeStructure<T> cos()
```
    Cosine operation.
    
    Specified by:
    
    cos in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    cos(this)
  - sin
```
public FieldDerivativeStructure<T> sin()
```
    Sine operation.
    
    Specified by:
    
    sin in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    sin(this)
  - sinCos
```
public FieldSinCos<FieldDerivativeStructure<T>> sinCos()
```
    Combined Sine and Cosine operation.
    
    Specified by:
    
    sinCos in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    [sin(this), cos(this)]
  - tan
```
public FieldDerivativeStructure<T> tan()
```
    Tangent operation.
    
    Specified by:
    
    tan in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    tan(this)
  - acos
```
public FieldDerivativeStructure<T> acos()
```
    Arc cosine operation.
    
    Specified by:
    
    acos in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    acos(this)
  - asin
```
public FieldDerivativeStructure<T> asin()
```
    Arc sine operation.
    
    Specified by:
    
    asin in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    asin(this)
  - atan
```
public FieldDerivativeStructure<T> atan()
```
    Arc tangent operation.
    
    Specified by:
    
    atan in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    atan(this)
  - atan2
```
public FieldDerivativeStructure<T> atan2(FieldDerivativeStructure<T> x)
                                  throws MathIllegalArgumentException
```
    Two arguments arc tangent operation.
    Beware of the order or arguments! As this is based on a two-arguments functions, in order to be consistent with arguments order, the instance is the first argument and the single provided argument is the second argument. In order to be consistent with programming languages atan2, this method computes atan2(this, x), i.e. the instance represents the y argument and the x argument is the one passed as a single argument. This may seem confusing especially for users of Wolfram alpha, as this site is not consistent with programming languages atan2 two-arguments arc tangent and puts x as its first argument.
    
    Specified by:
    
    atan2 in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    x - second argument of the arc tangent
    
    Returns:
    
    atan2(this, x)
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders are inconsistent
  - atan2
```
public static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T> atan2(FieldDerivativeStructure<T> y,
                                                                                    FieldDerivativeStructure<T> x)
                                                                             throws MathIllegalArgumentException
```
    Two arguments arc tangent operation.
    
    Type Parameters:
    
    T - the type of the field elements
    
    Parameters:
    
    y - first argument of the arc tangent
    
    x - second argument of the arc tangent
    
    Returns:
    
    atan2(y, x)
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - cosh
```
public FieldDerivativeStructure<T> cosh()
```
    Hyperbolic cosine operation.
    
    Specified by:
    
    cosh in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    cosh(this)
  - sinh
```
public FieldDerivativeStructure<T> sinh()
```
    Hyperbolic sine operation.
    
    Specified by:
    
    sinh in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    sinh(this)
  - sinhCosh
```
public FieldSinhCosh<FieldDerivativeStructure<T>> sinhCosh()
```
    Combined hyperbolic sine and sosine operation.
    
    Specified by:
    
    sinhCosh in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    [sinh(this), cosh(this)]
  - tanh
```
public FieldDerivativeStructure<T> tanh()
```
    Hyperbolic tangent operation.
    
    Specified by:
    
    tanh in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    tanh(this)
  - acosh
```
public FieldDerivativeStructure<T> acosh()
```
    Inverse hyperbolic cosine operation.
    
    Specified by:
    
    acosh in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    acosh(this)
  - asinh
```
public FieldDerivativeStructure<T> asinh()
```
    Inverse hyperbolic sine operation.
    
    Specified by:
    
    asinh in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    asin(this)
  - atanh
```
public FieldDerivativeStructure<T> atanh()
```
    Inverse hyperbolic tangent operation.
    
    Specified by:
    
    atanh in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    atanh(this)
  - toDegrees
```
public FieldDerivativeStructure<T> toDegrees()
```
    Convert radians to degrees, with error of less than 0.5 ULP
    
    Specified by:
    
    toDegrees in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    instance converted into degrees
  - toRadians
```
public FieldDerivativeStructure<T> toRadians()
```
    Convert degrees to radians, with error of less than 0.5 ULP
    
    Specified by:
    
    toRadians in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    instance converted into radians
  - integrate
```
public FieldDerivativeStructure<T> integrate(int varIndex,
                                             int integrationOrder)
```
    Integrate w.r.t. one independent variable.
    Rigorously, if the derivatives of a function are known up to order N, the ones of its M-th integral w.r.t. a given variable (seen as a function itself) are actually known up to order N+M. However, this method still casts the output as a DerivativeStructure of order N. The integration constants are systematically set to zero.
    
    Parameters:
    
    varIndex - Index of independent variable w.r.t. which integration is done.
    
    integrationOrder - Number of times the integration operator must be applied. If non-positive, call the differentiation operator.
    
    Returns:
    
    DerivativeStructure on which integration operator has been applied a certain number of times.
    
    Since:
    
    2.2
  - differentiate
```
public FieldDerivativeStructure<T> differentiate(int varIndex,
                                                 int differentiationOrder)
```
    Differentiate w.r.t. one independent variable.
    Rigorously, if the derivatives of a function are known up to order N, the ones of its M-th derivative w.r.t. a given variable (seen as a function itself) are only known up to order N-M. However, this method still casts the output as a DerivativeStructure of order N with zeroes for the higher order terms.
    
    Parameters:
    
    varIndex - Index of independent variable w.r.t. which differentiation is done.
    
    differentiationOrder - Number of times the differentiation operator must be applied. If non-positive, call the integration operator instead.
    
    Returns:
    
    DerivativeStructure on which differentiation operator has been applied a certain number of times
    
    Since:
    
    2.2
  - taylor
```
@SafeVarargs
public final T taylor(T... delta)
                            throws MathRuntimeException
```
    Evaluate Taylor expansion of a derivative structure.
    
    Parameters:
    
    delta - parameters offsets (Δx, Δy, ...)
    
    Returns:
    
    value of the Taylor expansion at x + Δx, y + Δy, ...
    
    Throws:
    
    MathRuntimeException - if factorials becomes too large
  - taylor
```
public T taylor(double... delta)
         throws MathRuntimeException
```
    Evaluate Taylor expansion of a derivative structure.
    
    Parameters:
    
    delta - parameters offsets (Δx, Δy, ...)
    
    Returns:
    
    value of the Taylor expansion at x + Δx, y + Δy, ...
    
    Throws:
    
    MathRuntimeException - if factorials becomes too large
  - rebase
```
public FieldDerivativeStructure<T> rebase(FieldDerivativeStructure<T>... p)
```
    Rebase instance with respect to low level parameter functions.
    The instance is considered to be a function of n free parameters up to order o \(f(p_0, p_1, \ldots p_{n-1})\). Its partial derivatives are therefore \(f, \frac{\partial f}{\partial p_0}, \frac{\partial f}{\partial p_1}, \ldots \frac{\partial^2 f}{\partial p_0^2}, \frac{\partial^2 f}{\partial p_0 p_1}, \ldots \frac{\partial^o f}{\partial p_{n-1}^o}\). The free parameters \(p_0, p_1, \ldots p_{n-1}\) are considered to be functions of \(m\) lower level other parameters \(q_0, q_1, \ldots q_{m-1}\).
    \( \begin{align} p_0 & = p_0(q_0, q_1, \ldots q_{m-1})\\ p_1 & = p_1(q_0, q_1, \ldots q_{m-1})\\ p_{n-1} & = p_{n-1}(q_0, q_1, \ldots q_{m-1}) \end{align}\)
    This method compute the composition of the partial derivatives of \(f\) and the partial derivatives of \(p_0, p_1, \ldots p_{n-1}\), i.e. the partial derivatives of the value returned will be \(f, \frac{\partial f}{\partial q_0}, \frac{\partial f}{\partial q_1}, \ldots \frac{\partial^2 f}{\partial q_0^2}, \frac{\partial^2 f}{\partial q_0 q_1}, \ldots \frac{\partial^o f}{\partial q_{m-1}^o}\).
    
    The number of parameters must match getFreeParameters() and the derivation orders of the instance and parameters must also match.
    
    Parameters:
    
    p - base parameters with respect to which partial derivatives were computed in the instance
    
    Returns:
    
    derivative structure with partial derivatives computed with respect to the lower level parameters used in the \(p_i\)
    
    Since:
    
    2.2
  - linearCombination
```
public FieldDerivativeStructure<T> linearCombination(FieldDerivativeStructure<T>[] a,
                                                     FieldDerivativeStructure<T>[] b)
                                              throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - linearCombination
```
public FieldDerivativeStructure<T> linearCombination(T[] a,
                                                     FieldDerivativeStructure<T>[] b)
                                              throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
    
    Throws:
    
    MathIllegalArgumentException - if arrays dimensions don't match
  - linearCombination
```
public FieldDerivativeStructure<T> linearCombination(double[] a,
                                                     FieldDerivativeStructure<T>[] b)
                                              throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - linearCombination
```
public FieldDerivativeStructure<T> linearCombination(FieldDerivativeStructure<T> a1,
                                                     FieldDerivativeStructure<T> b1,
                                                     FieldDerivativeStructure<T> a2,
                                                     FieldDerivativeStructure<T> b2)
                                              throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    Returns:
    
    a₁×b₁ + a₂×b₂
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
    
    See Also:
    
    CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement), CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
  - linearCombination
```
public FieldDerivativeStructure<T> linearCombination(T a1,
                                                     FieldDerivativeStructure<T> b1,
                                                     T a2,
                                                     FieldDerivativeStructure<T> b2)
                                              throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    Returns:
    
    a₁×b₁ + a₂×b₂
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders are inconsistent
    
    See Also:
    
    linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure), linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure)
  - linearCombination
```
public FieldDerivativeStructure<T> linearCombination(double a1,
                                                     FieldDerivativeStructure<T> b1,
                                                     double a2,
                                                     FieldDerivativeStructure<T> b2)
                                              throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    Returns:
    
    a₁×b₁ + a₂×b₂
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement), CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)
  - linearCombination
```
public FieldDerivativeStructure<T> linearCombination(FieldDerivativeStructure<T> a1,
                                                     FieldDerivativeStructure<T> b1,
                                                     FieldDerivativeStructure<T> a2,
                                                     FieldDerivativeStructure<T> b2,
                                                     FieldDerivativeStructure<T> a3,
                                                     FieldDerivativeStructure<T> b3)
                                              throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
    
    See Also:
    
    CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement), CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
  - linearCombination
```
public FieldDerivativeStructure<T> linearCombination(T a1,
                                                     FieldDerivativeStructure<T> b1,
                                                     T a2,
                                                     FieldDerivativeStructure<T> b2,
                                                     T a3,
                                                     FieldDerivativeStructure<T> b3)
                                              throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders are inconsistent
    
    See Also:
    
    linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure), linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure)
  - linearCombination
```
public FieldDerivativeStructure<T> linearCombination(double a1,
                                                     FieldDerivativeStructure<T> b1,
                                                     double a2,
                                                     FieldDerivativeStructure<T> b2,
                                                     double a3,
                                                     FieldDerivativeStructure<T> b3)
                                              throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement), CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)
  - linearCombination
```
public FieldDerivativeStructure<T> linearCombination(FieldDerivativeStructure<T> a1,
                                                     FieldDerivativeStructure<T> b1,
                                                     FieldDerivativeStructure<T> a2,
                                                     FieldDerivativeStructure<T> b2,
                                                     FieldDerivativeStructure<T> a3,
                                                     FieldDerivativeStructure<T> b3,
                                                     FieldDerivativeStructure<T> a4,
                                                     FieldDerivativeStructure<T> b4)
                                              throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    a4 - first factor of the fourth term
    
    b4 - second factor of the fourth term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
    
    See Also:
    
    CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement), CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
  - linearCombination
```
public FieldDerivativeStructure<T> linearCombination(T a1,
                                                     FieldDerivativeStructure<T> b1,
                                                     T a2,
                                                     FieldDerivativeStructure<T> b2,
                                                     T a3,
                                                     FieldDerivativeStructure<T> b3,
                                                     T a4,
                                                     FieldDerivativeStructure<T> b4)
                                              throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    a4 - first factor of the third term
    
    b4 - second factor of the third term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders are inconsistent
    
    See Also:
    
    linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure), linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure)
  - linearCombination
```
public FieldDerivativeStructure<T> linearCombination(double a1,
                                                     FieldDerivativeStructure<T> b1,
                                                     double a2,
                                                     FieldDerivativeStructure<T> b2,
                                                     double a3,
                                                     FieldDerivativeStructure<T> b3,
                                                     double a4,
                                                     FieldDerivativeStructure<T> b4)
                                              throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    a4 - first factor of the fourth term
    
    b4 - second factor of the fourth term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement), CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)
  - getPi
```
public FieldDerivativeStructure<T> getPi()
```
    Get the Archimedes constant π.
    Archimedes constant is the ratio of a circle's circumference to its diameter.
    
    Specified by:
    
    getPi in interface CalculusFieldElement<FieldDerivativeStructure<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    Archimedes constant π

Class FieldDerivativeStructure<T extends CalculusFieldElement<T>>

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.hipparchus.CalculusFieldElement

Methods inherited from interface org.hipparchus.FieldElement

Method Detail

newInstance

getFactory

getFreeParameters

getOrder

getReal

getValue

getPartialDerivative

getAllDerivatives

add

add

add

subtract

subtract

subtract

multiply

multiply

multiply

multiply

divide

divide

divide

remainder

remainder

remainder

negate

abs

ceil

floor

rint

sign

copySign

copySign

copySign

getExponent

scalb

ulp

hypot

hypot

compose

compose

reciprocal

sqrt

cbrt

rootN

getField

pow

pow

pow

pow

exp

expm1

log

log1p

log10

cos

sin

sinCos

tan

acos

asin

atan

atan2

atan2

cosh

sinh

sinhCosh

tanh

acosh

asinh

atanh

toDegrees

toRadians

integrate

differentiate