Python API

PARI/GP interop API

Optional exact-object interop with PARI/GP (pari). Pure Python; needs a separately installed cypari or cypari2 because PARI is GPL and is never bundled or imported by import alkahest. Every result is re-verified with Alkahest's own exact arithmetic where that is cheap; see the PARI/GP interop chapter of the user guide.

function

available() → bool

No docstring.

function

backend() → str | None

No docstring.

function

pari_version() → str | None

No docstring.

function

number_field_invariants(
    field_or_poly,
    *,
    primes=(),
    class_group=True,
    galois=True,
    certify="auto"
) → NumberFieldData

Ring of integers, discriminant, class group, units, prime-ideal factorisation and Galois group of a monic number field. certification is "certified" or "grh_conditional".

function

elliptic_curve_invariants(
    ainvs,
    *,
    ap_bound=100,
    rank=True,
    l_value=True
) → EllipticCurveData

Conductor, a_p, torsion (checked in Pic⁰), root number, analytic rank, L(E,1) / L'(E,1) as an ArbBall and 2-descent rank bounds with Mordell–Weil points.

function

modular_forms(N, k, *, nmax=20) → ModularFormsData

q-expansion basis of S_k(Γ0(N)) and the new subspace's Hecke eigenform orbits with exact (number-field) eigenvalues.

function

ramanujan_tau(n) → int

No docstring.

function

PrimeIdeal

No docstring.

function

NumberFieldData

No docstring.

function

EllipticCurveData

No docstring.

function

EigenformOrbit

No docstring.

function

ModularFormsData

No docstring.

Errors: PariError (E-PARI-002/003/004) and PariUnavailable (E-PARI-001).