# Interface CalculusFieldElement<T extends FieldElement<T>>

Type Parameters:
T - the type of the field elements
All Superinterfaces:
FieldElement<T>
All Known Subinterfaces:
Derivative<T>, Derivative1<T>, FieldDerivative<S,T>, FieldDerivative1<S,T>
All Known Implementing Classes:
Binary64, Complex, DerivativeStructure, Dfp, DfpDec, FieldComplex, FieldDerivativeStructure, FieldGradient, FieldTuple, FieldUnivariateDerivative, FieldUnivariateDerivative1, FieldUnivariateDerivative2, Gradient, SparseGradient, Tuple, UnivariateDerivative, UnivariateDerivative1, UnivariateDerivative2

public interface CalculusFieldElement<T extends FieldElement<T>> extends FieldElement<T>
Interface representing a field with calculus capabilities (sin, cos, ...).
Since:
1.7
• ## Method Summary

Modifier and Type
Method
Description
T
abs()
absolute value.
T
acos()
Arc cosine operation.
T
acosh()
Inverse hyperbolic cosine operation.
default T
add(double a)
'+' operator.
T
asin()
Arc sine operation.
T
asinh()
Inverse hyperbolic sine operation.
T
atan()
Arc tangent operation.
T
atan2(T x)
Two arguments arc tangent operation.
T
atanh()
Inverse hyperbolic tangent operation.
default T
cbrt()
Cubic root.
default T
ceil()
Get the smallest whole number larger than instance.
default T
copySign(double sign)
Returns the instance with the sign of the argument.
T
copySign(T sign)
Returns the instance with the sign of the argument.
T
cos()
Cosine operation.
T
cosh()
Hyperbolic cosine operation.
default T
divide(double a)
'÷' operator.
default T
divide(T a)
Compute this ÷ a.
T
exp()
Exponential.
T
expm1()
Exponential minus 1.
default T
floor()
Get the largest whole number smaller than instance.
default int
getExponent()
Return the exponent of the instance, removing the bias.
default T
getPi()
Get the Archimedes constant π.
T
hypot(T y)
Returns the hypotenuse of a triangle with sides this and y - sqrt(this2 +y2) avoiding intermediate overflow or underflow.
default boolean
isFinite()
Check if the instance is finite (neither infinite nor NaN).
default boolean
isInfinite()
Check if the instance is infinite.
default boolean
isNaN()
Check if the instance is Not a Number.
default T
linearCombination(double[] a, T[] b)
Compute a linear combination.
default T
linearCombination(double a1, T b1, double a2, T b2)
Compute a linear combination.
default T
linearCombination(double a1, T b1, double a2, T b2, double a3, T b3)
Compute a linear combination.
default T
linearCombination(double a1, T b1, double a2, T b2, double a3, T b3, double a4, T b4)
Compute a linear combination.
T
linearCombination(T[] a, T[] b)
Compute a linear combination.
T
linearCombination(T a1, T b1, T a2, T b2)
Compute a linear combination.
T
linearCombination(T a1, T b1, T a2, T b2, T a3, T b3)
Compute a linear combination.
T
linearCombination(T a1, T b1, T a2, T b2, T a3, T b3, T a4, T b4)
Compute a linear combination.
T
log()
Natural logarithm.
T
log10()
Base 10 logarithm.
T
log1p()
Shifted natural logarithm.
default T
multiply(double a)
'×' operator.
default T
multiply(int n)
Compute n × this.
T
newInstance(double value)
Create an instance corresponding to a constant real value.
default double
norm()
norm.
default T
pow(double p)
Power operation.
default T
pow(int n)
Integer power operation.
T
pow(T e)
Power operation.
T
remainder(double a)
IEEE remainder operator.
T
remainder(T a)
IEEE remainder operator.
default 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.
default T
rootN(int n)
Nth root.
default long
round()
Get the closest long to instance real value.
T
scalb(int n)
Multiply the instance by a power of 2.
default T
sign()
Compute the sign of the instance.
T
sin()
Sine operation.
default FieldSinCos<T>
sinCos()
Combined Sine and Cosine operation.
T
sinh()
Hyperbolic sine operation.
default FieldSinhCosh<T>
sinhCosh()
Combined hyperbolic sine and cosine operation.
default T
sqrt()
Square root.
default T
square()
Compute this × this.
default T
subtract(double a)
'-' operator.
default T
subtract(T a)
Compute this - a.
default T
tan()
Tangent operation.
default T
tanh()
Hyperbolic tangent operation.
default T
toDegrees()
Convert radians to degrees, with error of less than 0.5 ULP
default T
toRadians()
Convert degrees to radians, with error of less than 0.5 ULP
default T
ulp()
Compute least significant bit (Unit in Last Position) for a number.

### Methods inherited from interface org.hipparchus.FieldElement

add, getField, getReal, isZero, multiply, negate, reciprocal
• ## Method Details

• ### getPi

default T getPi()
Get the Archimedes constant π.

Archimedes constant is the ratio of a circle's circumference to its diameter.

Returns:
Archimedes constant π
Since:
2.0
• ### newInstance

T newInstance(double value)
Create an instance corresponding to a constant real value.
Parameters:
value - constant real value
Returns:
instance corresponding to a constant real value

'+' operator.
Parameters:
a - right hand side parameter of the operator
Returns:
this+a
• ### subtract

default T subtract(double a)
'-' operator.
Parameters:
a - right hand side parameter of the operator
Returns:
this-a
• ### subtract

default T subtract(T a)
Compute this - a.
Specified by:
subtract in interface FieldElement<T extends FieldElement<T>>
Parameters:
a - element to subtract
Returns:
a new element representing this - a
• ### multiply

default T multiply(double a)
'×' operator.
Parameters:
a - right hand side parameter of the operator
Returns:
this×a
• ### multiply

default T multiply(int n)
Compute n × this. Multiplication by an integer number is defined as the following sum $n \times \mathrm{this} = \sum_{i=1}^n \mathrm{this}$
Specified by:
multiply in interface FieldElement<T extends FieldElement<T>>
Parameters:
n - Number of times this must be added to itself.
Returns:
A new element representing n × this.
• ### divide

default T divide(double a)
'÷' operator.
Parameters:
a - right hand side parameter of the operator
Returns:
this÷a
• ### getExponent

default int getExponent()
Return the exponent of the instance, removing the bias.

For double numbers of the form 2x, the unbiased exponent is exactly x.

Returns:
exponent for the instance, without bias
• ### scalb

T scalb(int n)
Multiply the instance by a power of 2.
Parameters:
n - power of 2
Returns:
this × 2n
• ### ulp

default T ulp()
Compute least significant bit (Unit in Last Position) for a number.
Returns:
ulp(this)
Since:
2.0
• ### hypot

T hypot(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.
Parameters:
y - a value
Returns:
sqrt(this2 +y2)
Throws:
MathIllegalArgumentException - if number of free parameters or orders are inconsistent
• ### divide

default T divide(T a)
Compute this ÷ a.
Specified by:
divide in interface FieldElement<T extends FieldElement<T>>
Parameters:
a - element to divide by
Returns:
a new element representing this ÷ a
• ### sqrt

default T sqrt()
Square root.
Returns:
square root of the instance
• ### cbrt

default T cbrt()
Cubic root.
Returns:
cubic root of the instance
• ### rootN

default T rootN(int n)
Nth root.
Parameters:
n - order of the root
Returns:
nth root of the instance
• ### square

default T square()
Compute this × this.
Returns:
a new element representing this × this
Since:
3.1
• ### pow

default T pow(double p)
Power operation.
Parameters:
p - power to apply
Returns:
thisp
• ### pow

default T pow(int n)
Integer power operation.
Parameters:
n - power to apply
Returns:
thisn
• ### pow

Power operation.
Parameters:
e - exponent
Returns:
thise
Throws:
MathIllegalArgumentException - if number of free parameters or orders are inconsistent
• ### exp

T exp()
Exponential.
Returns:
exponential of the instance
• ### expm1

T expm1()
Exponential minus 1.
Returns:
exponential minus one of the instance
• ### log

T log()
Natural logarithm.
Returns:
logarithm of the instance
• ### log1p

T log1p()
Shifted natural logarithm.
Returns:
logarithm of one plus the instance
• ### log10

T log10()
Base 10 logarithm.
Returns:
base 10 logarithm of the instance
• ### cos

T cos()
Cosine operation.
Returns:
cos(this)
• ### sin

T sin()
Sine operation.
Returns:
sin(this)
• ### sinCos

default  sinCos()
Combined Sine and Cosine operation.
Returns:
[sin(this), cos(this)]
Since:
1.4
• ### tan

default T tan()
Tangent operation.
Returns:
tan(this)
• ### acos

T acos()
Arc cosine operation.
Returns:
acos(this)
• ### asin

T asin()
Arc sine operation.
Returns:
asin(this)
• ### atan

T atan()
Arc tangent operation.
Returns:
atan(this)
• ### atan2

T atan2(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.

Parameters:
x - second argument of the arc tangent
Returns:
atan2(this, x)
Throws:
MathIllegalArgumentException - if number of free parameters or orders are inconsistent
• ### cosh

T cosh()
Hyperbolic cosine operation.
Returns:
cosh(this)
• ### sinh

T sinh()
Hyperbolic sine operation.
Returns:
sinh(this)
• ### sinhCosh

default  sinhCosh()
Combined hyperbolic sine and cosine operation.
Returns:
[sinh(this), cosh(this)]
Since:
2.0
• ### tanh

default T tanh()
Hyperbolic tangent operation.
Returns:
tanh(this)
• ### acosh

T acosh()
Inverse hyperbolic cosine operation.
Returns:
acosh(this)
• ### asinh

T asinh()
Inverse hyperbolic sine operation.
Returns:
asin(this)
• ### atanh

T atanh()
Inverse hyperbolic tangent operation.
Returns:
atanh(this)
• ### toDegrees

default T toDegrees()
Convert radians to degrees, with error of less than 0.5 ULP
Returns:
instance converted into degrees

Convert degrees to radians, with error of less than 0.5 ULP
Returns:
• ### linearCombination

T linearCombination(T[] a, T[] b) throws MathIllegalArgumentException
Compute a linear combination.
Parameters:
a - Factors.
b - Factors.
Returns:
Σi ai bi.
Throws:
MathIllegalArgumentException - if arrays dimensions don't match
• ### linearCombination

default T linearCombination(double[] a, T[] b) throws MathIllegalArgumentException
Compute a linear combination.
Parameters:
a - Factors.
b - Factors.
Returns:
Σi ai bi.
Throws:
MathIllegalArgumentException - if arrays dimensions don't match
• ### linearCombination

T linearCombination(T a1, T b1, T a2, T b2)
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
• ### linearCombination

default T linearCombination(double a1, T b1, double a2, T b2)
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
• ### linearCombination

T linearCombination(T a1, T b1, T a2, T b2, T a3, T b3)
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
• ### linearCombination

default T linearCombination(double a1, T b1, double a2, T b2, double a3, T b3)
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
• ### linearCombination

T linearCombination(T a1, T b1, T a2, T b2, T a3, T b3, T a4, T b4)
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 fourth term
b4 - second factor of the fourth term
Returns:
a1×b1 + a2×b2 + a3×b3 + a4×b4
• ### linearCombination

default T linearCombination(double a1, T b1, double a2, T b2, double a3, T b3, double a4, T b4)
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 fourth term
b4 - second factor of the fourth term
Returns:
a1×b1 + a2×b2 + a3×b3 + a4×b4
• ### ceil

default T ceil()
Get the smallest whole number larger than instance.
Returns:
ceil(this)
• ### floor

default T floor()
Get the largest whole number smaller than instance.
Returns:
floor(this)
• ### rint

default 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.
Returns:
a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5
• ### remainder

T remainder(double 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
• ### remainder

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
• ### sign

default 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)
Returns:
-1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
• ### copySign

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

default T copySign(double 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
• ### isInfinite

default boolean isInfinite()
Check if the instance is infinite.
Returns:
true if the instance is infinite
• ### isFinite

default boolean isFinite()
Check if the instance is finite (neither infinite nor NaN).
Returns:
true if the instance is finite (neither infinite nor NaN)
Since:
2.0
• ### isNaN

default boolean isNaN()
Check if the instance is Not a Number.
Returns:
true if the instance is Not a Number
• ### norm

default double norm()
norm.
Returns:
norm(this)
Since:
2.0
• ### abs

T abs()
absolute value.
Returns:
abs(this)
• ### round

default long round()
Get the closest long to instance real value.
Returns:
closest long to FieldElement.getReal()