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Mathematica > Mathematics and Algorithms > Mathematical Functions > Special Functions > Elliptic Functions >

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WeierstrassInvariants

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gives the invariants {g₂, g₃} for Weierstrass elliptic functions corresponding to the half-periods {

For certain special arguments, WeierstrassInvariants automatically evaluates to exact values.

Evaluate numerically:

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: