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eYc @ s� d d l Z d d l Z d d l m Z d d l m Z m Z e j Z d � Z d � Z d � Z
d � Z d d � Z d
� Z
d d � Z d d � Z d d
� Z d d d � Z d d � Z d d l m Z d d l m Z d � Z d S( i����N( t cputime( t Integert ZZc C sA t g t j | � j � D] \ } } | d k r | ^ q g � S( Ni ( t sumt Ft ideals_of_bdd_normt iteritems( t Bt nt v( ( s% psage/modform/hilbert/sqrt5/tables.pyt ideals_of_bounded_norm s c C sx y t | � } Wn t k
r2 t | � g } n Xt j t | � � } t g | D] } | d k rR | | ^ qR g � S( Ni ( t listt TypeErrorR R R t maxR ( R t zR ( ( s% psage/modform/hilbert/sqrt5/tables.pyt ideals_of_norm
s
c C sd yE | j � j | j � � j � } t | � d k s< t � | d SWn t k
r_ t | � SXd S( s�
Return a canonical choice of generator for this ideal I (of a
PID).
The implementation computes the Hermite normal form (HNF) basis of
the ideal, which is canonical, then finds a generator for the
ideal it defines.
EXAMPLES::
sage: import psage.modform.hilbert.sqrt5.tables as tables
sage: a = tables.F.gen()
sage: z = a^30 * (-45*a+28); z
-37284985*a - 23043388
sage: tables.canonical_gen(tables.F.ideal(z))
-45*a + 28
i i N( t ringt idealt basist gens_reducedt lent AssertionErrort AttributeErrorR ( t It g( ( s% psage/modform/hilbert/sqrt5/tables.pyt
canonical_gen s !
c C s t | j � j | � � S( s}
Return canonical generator for the ideal generated by z. See the
documentation for the canonical_gen function.
( R t parentR ( R ( ( s% psage/modform/hilbert/sqrt5/tables.pyt
canonical_rep- s i2 c C sm t j � } d | d } g t | | � D] } t | | | � ^ q+ } t t | � � d k si t � d S( Ni����i i ( R t gent rangeR R t setR ( R t aR t iR ( ( s% psage/modform/hilbert/sqrt5/tables.pyt test_canonical_gen4 s 1c C s t | � j d d � S( Nt t ( t strt replace( t s( ( s% psage/modform/hilbert/sqrt5/tables.pyt no_space; s c C s� | r t | d � n d } x� t | � D]� } t � } t j | � } t | � } d | j � | j � t t | � � | f } | GH| r( | j
| d � | j � q( q( Wd S( s�
Compute dimensions of spaces of Hilbert modular forms for all the levels in v.
The format is:
Norm dimension generator time
R s %s %s %s %ss
N( t opent NoneR R t
sqrt5_fastt IcosiansModP1ModNt normt cardinalityR' R t writet flush( R t filenameR t Nt tt Ht tmR& ( ( s% psage/modform/hilbert/sqrt5/tables.pyt
dimensions> s .c C s= | r t | d � n d } g t | � D] } | j � r( | ^ q( } x� t | � D]� } t � } t j | � } g | D]T } t t | j
� � t | j
� � � d k rx | j � | j | � j
� f ^ qx } t | � }
d | j
� t t | � � |
t | � f } | GH| rS | j | d � | j � qS qS Wd S( s�
Compute characteristic polynomials of T_P for primes P with norm <= B
for spaces of Hilbert modular forms for all the levels in v.
R i s %s %s %s %ss
N( R( R) R
t is_primeR R R* R+ t gcdR R, t smallest_integert hecke_matrixt fcpR' R R. R/ ( R R R0 R t pt PR1 R2 R3 t TR4 R& ( ( s% psage/modform/hilbert/sqrt5/tables.pyt charpolysP s +
T .c
C s� | r t | d � n d } g t d � D] } | j � r( | ^ q( } x:t | � D],} t | j � � } t � } t j | � } t | � } x3 | D]+ } t | j � � j
| � d k r� Pq� q� Wt � } | j | � }
t | � } t � } |
j � } t | � }
d | j � t
t | � � | j � t
t | � � t
| � | | |
f } | GH| rS | j | d � | j � qS qS Wd S( s�
Compute and factor one characteristic polynomials for all the
levels in v. Always compute the charpoly of T_P where P is the
smallest prime not dividing the level.
R id i s %s %s %s %s %s (%.1f,%.1f,%.1f)s
N( R( R) R
R6 R R R, R R* R+ R7 R9 R: R' R R8 R. R/ ( R R0 R R; R< R1 t NNR2 R3 t t0R= t t1t ft t2R& ( ( s% psage/modform/hilbert/sqrt5/tables.pyt one_charpolyc s. +
! !id c C s� d d l m } | r% t | d � n d } x� t | � D]� } | | � } x� t | j � � D]� \ } } | j | � } d | j � t t
| � � | d j g | D] } t | � ^ q� � f }
|
GH| r] | j |
d � | j
� q] q] Wq8 Wd S( Ni����( t HilbertModularFormsR s %s %s %s %sR" s
( t hmfRE R( R) R t enumeratet elliptic_curve_factorst aplistR, R' R t joinR. R/ ( R R R0 RE R R1 R3 R t Et xR& ( ( s% psage/modform/hilbert/sqrt5/tables.pyt elliptic_curves� s Ji c s d d l m � d d l m } m � d d l � | | � � � � � � f d � � } x | t | � � D] } | GHql Wd S( Ni����( RE ( t parallelt set_random_seedc
s� � d � t t | � � j d d � j d d � } t � j j � d | � d � } � | � } t t | � � } y� | j � } | j d | j � | t | � f � | j
� x� t | � D]y \ } } | j � � } d | j � | | d
j g | D] } t | � ^ q� � f } | GH| j | d � | j
� q� WWn3 t
k
rs}
| j d | j � | |
f � n X| j � d S(
Ni t *R# t -t _s %s.txtt ws count %s %s %s
s %s %s %s %sR" s
s exception %s %s "%s"
( R' R R% R( t pathRJ RH R. R, R R/ RG RI t Exceptiont close( R1 t levelR R3 t DR RK R RL R& t msg( R RE t dirt osRO ( s% psage/modform/hilbert/sqrt5/tables.pyRB � s$
*" &
>$( RF RE t sage.allRN RO R[ R ( R R RZ t ncpuRN RB t X( ( R RE RZ R[ RO s% psage/modform/hilbert/sqrt5/tables.pyt elliptic_curves_parallel� s '( t pari( t primesc C sn g } t j � } x4t | d � D]"} | d k r\ | j d t j d | d � f � q# | d d k r� | | } | | k rE| j | t j | � f � qEq# t d � j | � j � } t d | d j � � } t d | d j � � } | j | | t j | | | g � f � | j | | t j | | | g � f � q# W| j
� g | D] } | d ^ qZS( s
Return the prime ideals of the integers of the field Q(sqrt(5)) of
norm at most B, ordered first by norm, then by the image of the
golden ratio mod the prime in GF(p)={0,1,...,p-1}.
INPUT:
- B -- integer
OUTPUT:
- list of prime ideals
EXAMPLES::
sage: import psage
sage: psage.modform.hilbert.sqrt5.primes_of_bounded_norm(4)
[Fractional ideal (2)]
sage: len(psage.modform.hilbert.sqrt5.primes_of_bounded_norm(10^4))
1233
sage: v = psage.modform.hilbert.sqrt5.primes_of_bounded_norm(11); v
[Fractional ideal (2), Fractional ideal (2*a - 1), Fractional ideal (3), Fractional ideal (3*a - 1), Fractional ideal (3*a - 2)]
Check that the sort order is as claimed::
sage: P0 = v[-2]; P1 = v[-1]
sage: K = P0.number_field(); K
Number Field in a with defining polynomial x^2 - x - 1
sage: P0.residue_field()(K.gen())
4
sage: P1.residue_field()(K.gen()) # yep, 4 < 8
8
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" )-
( t sqrt5R* t
sage.misc.allR t sage.rings.allR R R R
R R R R! R' R) R5 R> RD RM R_ t
sage.libs.allR` Ra Rj ( ( ( s% psage/modform/hilbert/sqrt5/tables.pyt <module> s"
