WeierstrassHalfPeriods

WeierstrassHalfPeriods[{g2,g3}]

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

Details

Examples

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Basic Examples  (2)

Evaluate numerically:

This list contains and :

Plot the half-periods over a subset of the reals:

Scope  (4)

Evaluate to high precision:

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

Symbolic evaluation of the equianharmonic case of WeierstrassHalfPeriods:

Symbolic evaluation of the lemniscatic case of WeierstrassHalfPeriods:

WeierstrassHalfPeriods can be used with CenteredInterval objects:

Applications  (1)

Plot an elliptic function over a period parallelogram:

Properties & Relations  (2)

For numerical inputs, WeierstrassHalfPeriods[{g_2,g_3}]={TemplateBox[{{g, _, 2}, {g, _, 3}}, WeierstrassHalfPeriodW1],TemplateBox[{{g, _, 2}, {g, _, 3}}, WeierstrassHalfPeriodW3]}:

WeierstrassHalfPeriods is effectively the inverse of WeierstrassInvariants:

Possible Issues  (1)

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

Use WeierstrassHalfPeriodW1 and WeierstrassHalfPeriodW3 instead:

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 (updated 2023).

Text

Wolfram Research (1996), WeierstrassHalfPeriods, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassHalfPeriods.html (updated 2023).

CMS

Wolfram Language. 1996. "WeierstrassHalfPeriods." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. 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

BibTeX

@misc{reference.wolfram_2024_weierstrasshalfperiods, author="Wolfram Research", title="{WeierstrassHalfPeriods}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/WeierstrassHalfPeriods.html}", note=[Accessed: 29-May-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_weierstrasshalfperiods, organization={Wolfram Research}, title={WeierstrassHalfPeriods}, year={2023}, url={https://reference.wolfram.com/language/ref/WeierstrassHalfPeriods.html}, note=[Accessed: 29-May-2024 ]}