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