de.jtem.ellipticFunctions

## Class Jacobi

• ```public class Jacobi
extends Elliptic```
Implementation for Jacobi's elliptic functions. Attention! This class is not thread save. This is usually no problem, when you do numerics.
Author:
Markus Schmies, Boris Springborn,
• ### Method Summary

All Methods
Modifier and Type Method and Description
`static de.jtem.mfc.field.Complex` ```cn(de.jtem.mfc.field.Complex u, de.jtem.mfc.field.Complex k)```
Returns cn(u,k).
`static void` ```cn(de.jtem.mfc.field.Complex u, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex[] thetaConstants, de.jtem.mfc.field.Complex cnOfU)```
Computes cn(u,k(τ)) for given latiuce paramter τ, and theta constants.
`static double` ```cn(double u, double k)```
Returns cn(u,k).
`static de.jtem.mfc.field.Complex` ```dn(de.jtem.mfc.field.Complex u, de.jtem.mfc.field.Complex k)```
Returns dn(u,k).
`static void` ```dn(de.jtem.mfc.field.Complex u, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex[] thetaConstants, de.jtem.mfc.field.Complex dnOfU)```
Computes dn(u,k(τ)) for given latiuce paramter τ, and theta constants.
`static double` ```dn(double u, double k)```
Returns dn(u,k).
`static de.jtem.mfc.field.Complex` `K_from_k(de.jtem.mfc.field.Complex k)`
Returns quarter period K as function of the modulus k.
`static void` ```K_from_k(de.jtem.mfc.field.Complex k, de.jtem.mfc.field.Complex K)```
Computes quarter period K as function of the modulus k.
`static de.jtem.mfc.field.Complex` ```K_from_KPrime_and_tau(de.jtem.mfc.field.Complex KPrime, de.jtem.mfc.field.Complex tau)```
Returns quarter period K as function of complementary quarter period K' and lattice parameter τ.
`static void` ```K_from_KPrime_and_tau(de.jtem.mfc.field.Complex KPrime, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex K)```
Computes quarter period K as function of complementary quarter period K' and lattice parameter τ.
`static de.jtem.mfc.field.Complex` `k_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants)`
Returns modulus k as function of theta constants.
`static de.jtem.mfc.field.Complex` `K_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants)`
Returns quarter period K as function of theta constants.
`static void` ```k_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants, de.jtem.mfc.field.Complex k)```
Computes modulus k as function of theta constants
`static void` ```K_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants, de.jtem.mfc.field.Complex K)```
Computes quarter period K as function of theta constants.
`static de.jtem.mfc.field.Complex` ```KPrime_from_K_and_tau(de.jtem.mfc.field.Complex K, de.jtem.mfc.field.Complex tau)```
Returns complementary quarter period K' as function of quarter period K and lattice parameter τ.
`static void` ```KPrime_from_K_and_tau(de.jtem.mfc.field.Complex K, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex KPrime)```
Computes complementary quarter period K' as function of quarter period K and lattice parameter τ.
`static de.jtem.mfc.field.Complex` `kPrime_from_k(de.jtem.mfc.field.Complex k)`
Returns complementary modulus k' as function of the modulus.
`static de.jtem.mfc.field.Complex` `KPrime_from_k(de.jtem.mfc.field.Complex k)`
Returns complementary quarter Period K' as function of the modulus k.
`static void` ```kPrime_from_k(de.jtem.mfc.field.Complex k, de.jtem.mfc.field.Complex kPrime)```
Computes complementary modulus k' as function of the modulus.
`static void` ```KPrime_from_k(de.jtem.mfc.field.Complex k, de.jtem.mfc.field.Complex KPrime)```
Computes cmplementary quarter period K' as function of the modulus k.
`static double` `kPrime_from_k(double k)`
Returns complementary modulus k' as function of the modulus.
`static de.jtem.mfc.field.Complex` `kPrime_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants)`
Returns complementary modulus k' as function of theta constants.
`static void` ```kPrime_from_thetaConstants(de.jtem.mfc.field.Complex[] thetaConstants, de.jtem.mfc.field.Complex kPrime)```
Computes complementary modulus k' as function theta constants.
`static de.jtem.mfc.field.Complex` ```sn(de.jtem.mfc.field.Complex u, de.jtem.mfc.field.Complex k)```
Returns sn(u,k).
`static void` ```sn(de.jtem.mfc.field.Complex u, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex[] thetaConstants, de.jtem.mfc.field.Complex snOfU)```
Computes sn(u,k(τ)) for given latiuce paramter τ, and theta constants.
`static double` ```sn(double u, double k)```
Returns sn(u,k).
`static de.jtem.mfc.field.Complex` `tau_from_k(de.jtem.mfc.field.Complex k)`
Computes lattice parameter τ as function of modulus k.
`static void` ```tau_from_k(de.jtem.mfc.field.Complex k, de.jtem.mfc.field.Complex tau)```
Computes lattice parameter τ as function of modulus k.
`static de.jtem.mfc.field.Complex` `tauPrime_from_tau(de.jtem.mfc.field.Complex tau)`
Returns complementary lattice paramter τ' = -1/τ for lattice parameter τ.
`static void` ```tauPrime_from_tau(de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex tauPrime)```
Computes complementary lattice paramter τ' = -1/τ for lattice parameter τ.
• ### Methods inherited from class de.jtem.ellipticFunctions.Elliptic

`theta, theta, theta0, theta0, theta1, theta1, theta2, theta2, theta3, theta3, theta4, theta4, thetaConstants, thetaConstants`
• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

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