WeierstrassInvariantG3[{ω,ω′}]
gives the invariant 
for the Weierstrass elliptic functions corresponding to the half‐periods {ω,ω′}.
WeierstrassInvariantG3
WeierstrassInvariantG3[{ω,ω′}]
gives the invariant 
for the Weierstrass elliptic functions corresponding to the half‐periods {ω,ω′}.
Details
- Mathematical function, suitable for both symbolic and numerical manipulation.
- WeierstrassInvariantG3 gives the second invariant from the pair given by WeierstrassInvariants.
- For certain special arguments, WeierstrassInvariantG3 automatically evaluates to exact values.
- WeierstrassInvariantG3 can be evaluated to arbitrary numerical precision.
- WeierstrassInvariantG3 can be used with CenteredInterval objects. »
Examples
open all close allScope (6)
The precision of the output tracks the precision of the input:
Evaluate symbolically for the equianharmonic case:
Evaluate symbolically for the lemniscatic case:
WeierstrassInvariantG3 has both singularities and discontinuities:
WeierstrassInvariantG3 can be used with CenteredInterval objects:
TraditionalForm formatting:
Applications (1)
Define the discriminant of the Weierstrass elliptic curve:
KleinInvariantJ can be computed as the ratio of a power of 
invariant and the discriminant:
Text
Wolfram Research (2017), WeierstrassInvariantG3, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassInvariantG3.html (updated 2023).
CMS
Wolfram Language. 2017. "WeierstrassInvariantG3." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/WeierstrassInvariantG3.html.
APA
Wolfram Language. (2017). WeierstrassInvariantG3. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WeierstrassInvariantG3.html