# User:Tohline/Appendix/ComputerAlgorithms/Riemann

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# Riemann Algorithms

These are algorithms that I have stored under the directory, …/numRecipes/EllipticIntegrals/Riemann

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## Riemann02 (12 June 2020)

Basically the same as "Riemann01," but with the output formatted more clearly. The example output file shown immediately below refers to …

**TEST (part 1)**, which is in the context of our discussion of*General Coefficient Expressions*.**TEST (part 2)**, which is in the context of the evaluation of several*Virial-Equilibrium-based*expressions.**Table 2**, which contains*Other Parameter Determinations*.

**Example Output File**

Riemann S-type Ellipsoid having: (b/a,c/a) = (9.000000000000D-01,6.410000000000D-01) ************* TEST (part 1): Elliptic Integrals of the 1st and 2nd kinds: phi(deg) (rad) asin(k) (deg) (rad) F(phi,k) E(phi,k) 5.013357254094D+01 8.749959066267D-01 3.253852919374D+01 5.679044681871D-01 9.090259485521D-01 8.431180475729D-01 A1 A2 A3 5.214502732782D-01 5.951310119083D-01 8.834187148135D-01 ************* TEST (part 2): a2A12 B12 alpha beta 3.877933612108D-01 2.073376506975D-01 2.472452000855D-01 3.797483470425D+00 f omega f_Ad omega_Ad -2.680088866444D-01 1.131374738327D+00 -1.509117086331D+01 -1.507716218767D-01 ************* Table 2: Direct (omega,lambda,zeta,f): 1.131374738327 0.150771621841 -0.303218483925 -0.268008886644 Adjoint (omega,lambda,zeta,f): -0.150771621877 -1.131374730590 2.275320291519 -15.091170863305 *************

## Riemann01 (21 August 2019)

Evaluate terms associated with construction of various Riemann S-type Ellipsoids, especially for comparison with work by Ou (2006). Enter two axis-ratio values: bovera covera (separated by space).

# See Also

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