WeierstrassInvariants

WeierstrassInvariants[{ω1,ω3}]

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

Details

Examples

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Basic Examples  (3)

Evaluate numerically:

This list contains and :

Plot the invariants over a subset of the reals:

Given the half‐periods, calculate a value of a Weierstrass function:

Scope  (4)

Evaluate to high precision:

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

Symbolic evaluation of the equianharmonic case of WeierstrassInvariants:

Symbolic evaluation of the lemniscatic case of WeierstrassInvariants:

WeierstrassInvariants can be used with CenteredInterval objects:

Applications  (1)

Plot an elliptic function over a period parallelogram:

Properties & Relations  (2)

For numerical inputs, WeierstrassInvariants[{omega_1,omega_3}]={TemplateBox[{{omega, _, 1}, {omega, _, 3}}, WeierstrassInvariantG2],TemplateBox[{{omega, _, 1}, {omega, _, 3}}, WeierstrassInvariantG3]}:

WeierstrassInvariants is effectively the inverse of WeierstrassHalfPeriods:

Possible Issues  (1)

Assignment of invariants corresponding to symbolic or exact half‐periods is impossible as the right‐hand side is not a list:

Use WeierstrassInvariantG2 and WeierstrassInvariantG3 instead:

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

Text

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

CMS

Wolfram Language. 1996. "WeierstrassInvariants." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/WeierstrassInvariants.html.

APA

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

BibTeX

@misc{reference.wolfram_2025_weierstrassinvariants, author="Wolfram Research", title="{WeierstrassInvariants}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/WeierstrassInvariants.html}", note=[Accessed: 25-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_weierstrassinvariants, organization={Wolfram Research}, title={WeierstrassInvariants}, year={2023}, url={https://reference.wolfram.com/language/ref/WeierstrassInvariants.html}, note=[Accessed: 25-May-2025 ]}