WeierstrassHalfPeriods

WeierstrassHalfPeriods[{g2,g3}]

gives the halfperiods {ω1,ω3} for Weierstrass elliptic functions corresponding to the invariants {g2,g3}.

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The halfperiods {ω1,ω3} define the fundamental period parallelogram for the Weierstrass elliptic functions.
  • WeierstrassHalfPeriods is the inverse of WeierstrassInvariants.
  • WeierstrassHalfPeriods can be evaluated to arbitrary numerical precision.

Examples

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Basic Examples  (3)

Evaluate numerically:

Given the halfperiods, calculate a value of a Weierstrass function:

Scope  (2)

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Applications  (1)

Plot an elliptic function over a period parallelogram:

Properties & Relations  (1)

WeierstrassHalfPeriods is effectively the inverse of WeierstrassInvariants:

Possible Issues  (1)

Assignment to halfperiods with symbolic or exact invariants is impossible as the righthand side is not a list:

Neat Examples  (1)

A doubly periodic function over the complex plane:

Wolfram Research (1996), WeierstrassHalfPeriods, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassHalfPeriods.html.

Text

Wolfram Research (1996), WeierstrassHalfPeriods, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassHalfPeriods.html.

BibTeX

@misc{reference.wolfram_2021_weierstrasshalfperiods, author="Wolfram Research", title="{WeierstrassHalfPeriods}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/WeierstrassHalfPeriods.html}", note=[Accessed: 18-October-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_weierstrasshalfperiods, organization={Wolfram Research}, title={WeierstrassHalfPeriods}, year={1996}, url={https://reference.wolfram.com/language/ref/WeierstrassHalfPeriods.html}, note=[Accessed: 18-October-2021 ]}

CMS

Wolfram Language. 1996. "WeierstrassHalfPeriods." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WeierstrassHalfPeriods.html.

APA

Wolfram Language. (1996). WeierstrassHalfPeriods. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WeierstrassHalfPeriods.html