Kummer: SeqEnum Default: [1,0]
Tate: RngIntElt Default: 0
Weight: RngIntElt Default:
Given two sequences of rationals, corresponding to positive and negative
elements in the free group on (Q)/(Z), create the resulting
Jacobi motive. This requires that the signed sum of the rationals is
an integer. The optional Kummer vararg can specify a Kummer twist,
and similarly with the Tate vararg. Alternatively, the desired Tate twist
can be obtained by giving and integral argument to the Weight vararg,
and the effective Tate twist can be obtained by setting Weight as true.
A variant with only one argument (B is empty) is also available.
Similar to above, this intrinsic spells out the Jacobi summands (A, B),
the Kummer twist tρ, and the Tate twist j explicitly.
Given a Jacobi motive J, return its Kummer twist by tρ,
where ρ is rational and t is a nonzero rational.
Given a Jacobi motive J and an integer j, return the jth
Tate twist of J.
Given two Jacobi motives, take their tensor product, eliminating any
rationals common to the positive and negative parts.
Given two Jacobi motives, take their tensor quotient, eliminating any
rationals common to the positive and negative parts.
J1 ne J2 : JacketMot, JacketMot -> JacketMot
Whether two Jacobi motives are equal, that is, whether they have the
same positive and negative parts, their tρ Kummer twists are
the same, and they have the same Tate twist parameter.
Given a Jacobi motive, scale all the rational numbers defined the datum
by the given rational q. The denominator of q must be coprime to m,
and q must be invertible mod m. The resulting motive will be identical
over (Q) but need only be conjugate over Kθ.
The field of definition of a Jacobi motive.
The motivic weight of a Jacobi motive.
The effective motivic weight of a Jacobi motive,
that is, the width of its Hodge structure.
HodgeVector(J) : JacketMot -> HodgeStruc, RngIntElt
EffectiveHodgeStructure(J) : JacketMot -> HodgeStruc
The Hodge structure of a Jacobi motive.
Degree: RngIntElt Default:
Roots: BoolElt Default: false
Given a good prime p, that is, one which is coprime to m and
the Kummer twisting parameter t, compute its Euler factor.
The Roots vararg also returns as a second argument the
p-adic approximations to the roots (associated to the prime ideals
above p). The Degree vararg can be used when the full Euler
factor is not needed, though it is often still just as easily computed.
It is often easier to first identify the Jacobi motive
as a Grossencharacter, and then compute its Euler factors.
Precision: RngIntElt Default:
Given a Jacobi motive and a good degree 1 prime over Kθ
that splits completely over the cyclotomic field,
compute the associated Jacobi sum as a complex number.
This is used to identify motives that are equivalent over (Q)
but not over Kθ in some examples.
Given a Jacobi motive, identify it as a Grössencharacter.
This uses the Weil bound on the conductor, and then tries enough
good primes to distinguish the character. This is now the preferred
way to compute the LSeries of a Jacobi motive (though the latter
still exists).
V2.28, 13 July 2023