# source:sage/databases/db_modular_polynomials.py@908:f4032d22f197

Revision 908:f4032d22f197, 4.9 KB checked in by David Kohel <kohel@…>, 7 years ago (diff)

[project @ Modular polynomial databases]

Line
1"""
2Database of Modular Polynomials
3"""
4
5#######################################################################
6#
7#  SAGE: System for Algebra and Geometry Experimentation
8#
9#       Copyright (C) 2006 William Stein <wstein@gmail.com>
10#       Copyright (C) 2006 David Kohel <kohel@maths.usyd.edu.au>
11#
12#  Distributed under the terms of the GNU General Public License (GPL)
13#
14#  The full text of the GPL is available at:
15#
17#######################################################################
18
19
20import bz2, os
21import sage.misc.misc
22import sage.rings.polydict as polydict # internal representation may change!!!
23from sage.rings.integer import Integer
24from sage.rings.integer_ring import IntegerRing
25from sage.rings.multi_polynomial_ring import MPolynomialRing
26
27DB_HOME = '%s/kohel'%sage.misc.misc.SAGE_DATA
28
29def _dbz_to_integer_list(name):
30    file = '%s/%s'%(DB_HOME, name)
31    if not os.path.exists(file):
32        raise RuntimeError, "Modular polynomial database file %s not available"%file
33    data = bz2.decompress(open(file).read())
34    data = "[[" + data.replace("\n","],[").replace(" ",",")[:-2] + "]"
35    return eval(data)
36
38    return "0"*(n-len(str(s))) + str(s)
39
40class ModularPolynomialDatabase:
41    def _dbpath(self,level):
42        return "PolMod/%s/pol.%s.dbz"%(self.model, _pad_int(level,3))
43
44    def __repr__(self):
45        if self.model == "Cls":
46            head = "Classical"
47            poly = "polynomial"
48        elif self.model == "Atk":
49            head = "Atkin"
50            poly = "polynomial"
51        elif self.model == "AtkCrr":
52            head = "Atkin"
53            poly = "correspondence"
54        elif self.model == "Eta":
55            head = "Dedekind eta"
56            poly = "polynomial"
57        elif self.model == "EtaCrr":
58            head = "Dedekind eta"
59            poly = "correspondence"
60        return "%s modular %s database"%(head,poly)
61
62    def __getitem__(self,level):
63        if self.model != "Cls":
64            level = Integer(level)
65            if not level.is_prime():
66                raise TypeError, "Argument level (= %s) must be prime."%level
67        modpol = self._dbpath(level)
68        try:
69            coeff_list = _dbz_to_integer_list(modpol)
70        except RuntimeError, msg:
71            print msg
72            raise RuntimeError, \
73                  "No database entry for modular polynomial of level %s"%level
74        if self.model == "Cls":
75            P = MPolynomialRing(IntegerRing(),2,"j")
76        else:
77            P = MPolynomialRing(IntegerRing(),2,"x,j")
78        poly = {}
79        if self.model == "Cls":
80            if level == 1:
81                return P(polydict.PolyDict({(1,0):1,(0,1):-1}))
82            for cff in coeff_list:
83                i = cff[0]
84                j = cff[1]
85                poly[(i,j)] = Integer(cff[2])
86                if i != j:
87                    poly[(j,i)] = Integer(cff[2])
88        else:
89            for cff in coeff_list:
90                poly[(cff[0],cff[1])] = Integer(cff[2])
91        return P(polydict.PolyDict(poly))
92
93class ModularCorrespondenceDatabase(ModularPolynomialDatabase):
94    def _dbpath(self,level):
95        (Nlevel,crrlevel) = level
96        return "PolMod/%s/corr.%s.%s.dbz"%(
98
99class ClassicalModularPolynomialDatabase(ModularPolynomialDatabase):
100    """
101    The database of classical modular polynomials, i.e. the polynomials
102    Phi_N(X,Y) relating the j-functions j(q) and j(q^N).
103    """
104    def __init__(self):
105        """
106        Initialize the database.
107        """
108        self.model = "Cls"
109
110class DedekindEtaModularPolynomialDatabase(ModularPolynomialDatabase):
111    """
112    The database of modular polynomials Phi_N(X,Y) relating a quotient
113    of Dedekind eta functions, well-defined on X_0(N), relating x(q) and
114    the j-function j(q).
115    """
116    def __init__(self):
117        """
118        Initialize the database.
119        """
120        self.model = "Eta"
121
122class DedekindEtaModularCorrespondenceDatabase(ModularCorrespondenceDatabase):
123    """
124    The database of modular correspondences in $X_0(p) \times X_0(p)$, where
125    the model of the curves $X_0(p) = \PP^1$ are specified by quotients of
126    Dedekind's eta function.
127    """
128    def __init__(self):
129        """
130        Returns the
131        """
132        self.model = "EtaCrr"
133
134class AtkinModularPolynomialDatabase(ModularPolynomialDatabase):
135    """
136    The database of modular polynomials Phi(x,j) for $X_0(p)$, where
137    x is a function on invariant under the Atkin-Lehner invariant,
138    with pole of minimal order at infinity.
139    """
140    def __init__(self):
141        """
142        Initialize the database.
143        """
144        self.model = "Atk"
145
146class AtkinModularCorrespondenceDatabase(ModularCorrespondenceDatabase):
147    def __init__(self):
148        """
149        Initialize the database.
150        """
151        self.model = "AtkCrr"
Note: See TracBrowser for help on using the repository browser.