WeierstrassInvariants

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

Details

Mathematical function, suitable for both symbolic and numerical manipulation.
WeierstrassInvariants is the inverse of WeierstrassHalfPeriods.
For certain special arguments, WeierstrassInvariants automatically evaluates to exact values.
WeierstrassInvariants can be evaluated to arbitrary numerical precision.

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Evaluate numerically:

Evaluate individual invariants:

Visualize invariants:

Evaluate to high precision:

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

Plot an elliptic function over a period parallelogram:

WeierstrassHalfInvariants is effectively the inverse of WeierstrassHalfPeriods:

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

Introduced in 1996

(3.0)

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