 |
WeierstrassInvariants
WeierstrassInvariants[
,
] gives the invariants 
,
 for Weierstrass elliptic functions corresponding to the half-periods 
,
 .
Mathematical function (see Section A.3.10).
WeierstrassInvariants is the inverse of WeierstrassHalfPeriods.
See the Mathematica book: Section 3.2.11.
See also: WeierstrassP, InverseWeierstrassP, KleinInvariantJ.
Further Examples
From two complex numbers  and  that are not linearly dependent over the reals, we can form the two Weierstrass invariants  and  , where both sums are over the nonzero elements  of the lattice generated by  and  . The quotient of the complex plane by this lattice is equivalent, as a complex curve, to the elliptic curve with equation  .
WeierstrassInvariants returns  and  , given  and  .
In[1]:= 
Out[1]= 
The Weierstrass invariants depend only on the lattice, not on the particular generators.
In[2]:= 
Out[2]= 
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT. SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION. | | | |
| |
|
