Welcome to pyweierstrass’s documentation!

Indices and tables

Members functions

pyweierstrass.weierstrass.eisensenteinE4(tau)

Eisenstein E-series of weight 4.

Parameters:

tau (complex) – A complex number.

Returns:

The value of the Eisenstein E4 series at tau.

Return type:

complex

pyweierstrass.weierstrass.eisensenteinE6(tau)

Eisenstein E-series of weight 6.

Parameters:

tau (complex) – A complex number.

Returns:

The value of the Eisenstein E6 series at tau.

Return type:

complex

pyweierstrass.weierstrass.eisensteinG4(tau)

Eisenstein G-series of weight 4.

Parameters:

tau (complex) – A complex number.

Returns:

The value of the Eisenstein G4 series at tau.

Return type:

complex

pyweierstrass.weierstrass.eisensteinG6(tau)

Eisenstein G-series of weight 6.

Parameters:

tau (complex) – A complex number.

Returns:

The value of the Eisenstein G6 series at tau.

Return type:

complex

pyweierstrass.weierstrass.g_from_omega(omega1, omega2)

Elliptical invariants from half periods.

Parameters:
  • omega1 (complex) – A complex number.

  • omega2 (complex) – A complex number.

Returns:

The elliptical invariants g2 and g3.

Return type:

complex pair

pyweierstrass.weierstrass.invwp(w, omega)

Inverse Weierstrass p-function.

Parameters:
  • w (complex) – A complex number.

  • omega (complex pair) – A pair of complex numbers, the half-periods.

Returns:

The inverse Weierstrass p-function evaluated at w.

Return type:

complex

pyweierstrass.weierstrass.kleinjinv(z)

Inverse of the klein-j invariant function (the one with the 1728 factor).

Parameters:

z (complex) – A complex number.

Returns:

The value of the inverse of the klein-j invariant function at z.

Return type:

complex

pyweierstrass.weierstrass.omega_from_g(g2, g3)

Half-periods from elliptical invariants.

Parameters:
  • g2 (complex) – A complex number.

  • g3 (complex) – A complex number.

Returns:

The two half-periods corresponding to the elliptical invariants g2 and g3.

Return type:

complex pair

pyweierstrass.weierstrass.wp(z, omega)

Weierstrass p-function.

Parameters:
  • z (complex) – A complex number.

  • omega (complex pair) – A pair of complex numbers, the half-periods.

Returns:

The Weierstrass p-function evaluated at z.

Return type:

complex

pyweierstrass.weierstrass.wpprime(z, omega)

Derivative of Weierstrass p-function.

Parameters:
  • z (complex) – A complex number.

  • omega (complex pair) – A pair of complex numbers, the half-periods.

Returns:

The derivative of the Weierstrass p-function evaluated at z.

Return type:

complex

pyweierstrass.weierstrass.wsigma(z, omega)

Weierstrass sigma function.

Parameters:
  • z (complex) – A complex number.

  • omega (complex pair) – A pair of complex numbers, the half-periods.

Returns:

The Weierstrass sigma function evaluated at z.

Return type:

complex

pyweierstrass.weierstrass.wzeta(z, omega)

Weierstrass zeta function.

Parameters:
  • z (complex) – A complex number.

  • omega (complex pair) – A pair of complex numbers, the half-periods.

Returns:

The Weierstrass zeta function evaluated at z.

Return type:

complex