..nodoctest

Basic

x.__init__(...) initializes x; see help(type(x)) for signature

recip.basic.lift_small(a)

Given a in Z/muZ, output b in ZZ with |b| <= mu/2 and (b mod mu) = a. Given a in Z, output a.

EXAMPLES:

sage: from recip import *
sage: lift_small(Zmod(8)(7))
-1
sage: lift_small(Zmod(7)(10))
3
sage: lift_small(Zmod(12)(20))
-4
sage: lift_small(-501)
-501
sage: lift_small(QQ(7))     
7

recip.basic.mat_convert(M, ring_or_map)

Applies \(ring_or_map\) to the coefficients of M, i.e. given M = (m_ij)_ij, returns (ring_or_map(m_ij))_ij

EXAMPLES:

sage: from recip import *
sage: M = Matrix([[1/2, 1/5], [7, 9/2]])
sage: mat_convert(M, floor)
[0 0]
[7 4]
sage: mat_convert(M, GF(3))
[2 2]
[1 0]

recip.basic.uniformizer(p)

Given a prime ideal p, returns a uniformizer.

EXAMPLES:

sage: from recip import *
sage: P = QuadraticField(-5,'a').ideal(5).factor()[0][0]
sage: uniformizer(P)
a