.gitignore

@@ -0,0 +1,145 @@
+data
+data.zip
+*.kate-swp
+tags.json
+
+# ---> Python
+# Byte-compiled / optimized / DLL files
+__pycache__/
+*.py[cod]
+*$py.class
+
+# C extensions
+*.so
+
+# Distribution / packaging
+.Python
+build/
+develop-eggs/
+dist/
+downloads/
+eggs/
+.eggs/
+lib/
+lib64/
+parts/
+sdist/
+var/
+wheels/
+share/python-wheels/
+*.egg-info/
+.installed.cfg
+*.egg
+MANIFEST
+
+# PyInstaller
+#  Usually these files are written by a python script from a template
+#  before PyInstaller builds the exe, so as to inject date/other infos into it.
+*.manifest
+*.spec
+
+# Installer logs
+pip-log.txt
+pip-delete-this-directory.txt
+
+# Unit test / coverage reports
+htmlcov/
+.tox/
+.nox/
+.coverage
+.coverage.*
+.cache
+nosetests.xml
+coverage.xml
+*.cover
+*.py,cover
+.hypothesis/
+.pytest_cache/
+cover/
+
+# Translations
+*.mo
+*.pot
+
+# Django stuff:
+*.log
+local_settings.py
+db.sqlite3
+db.sqlite3-journal
+
+# Flask stuff:
+instance/
+.webassets-cache
+
+# Scrapy stuff:
+.scrapy
+
+# Sphinx documentation
+docs/_build/
+
+# PyBuilder
+.pybuilder/
+target/
+
+# Jupyter Notebook
+.ipynb_checkpoints
+
+# IPython
+profile_default/
+ipython_config.py
+
+# pyenv
+#   For a library or package, you might want to ignore these files since the code is
+#   intended to run in multiple environments; otherwise, check them in:
+# .python-version
+
+# pipenv
+#   According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
+#   However, in case of collaboration, if having platform-specific dependencies or dependencies
+#   having no cross-platform support, pipenv may install dependencies that don't work, or not
+#   install all needed dependencies.
+#Pipfile.lock
+
+# PEP 582; used by e.g. github.com/David-OConnor/pyflow
+__pypackages__/
+
+# Celery stuff
+celerybeat-schedule
+celerybeat.pid
+
+# SageMath parsed files
+*.sage.py
+
+# Environments
+.env
+.venv
+env/
+venv/
+ENV/
+env.bak/
+venv.bak/
+
+# Spyder project settings
+.spyderproject
+.spyproject
+
+# Rope project settings
+.ropeproject
+
+# mkdocs documentation
+/site
+
+# mypy
+.mypy_cache/
+.dmypy.json
+dmypy.json
+
+# Pyre type checker
+.pyre/
+
+# pytype static type analyzer
+.pytype/
+
+# Cython debug symbols
+cython_debug/
+

README.md

@@ -1,4 +1,9 @@
-# p-adic-numbers
+# p-adic-numbers
-
+
 class for p-adic number fields
-fork from https://github.com/meagtan/p-adic-numbers
+fork from https://github.com/meagtan/p-adic-numbers
+
+Thank you meagtan. He told me by mail, that I can release this project as GPL3+.
+
+This repository is hosted and maintained on https://git.jdmweb2.ch/beat/p-adic-numbers
+If you have questions feel free to send me an Email. My address is in the commits.

hensel.py

@@ -0,0 +1,42 @@
+# Finding roots of polynomials in p-adic integers using Hensel's lemma
+
+from padic import *
+from poly import *
+
+def roots(p, poly):
+    'Yield all roots of polynomial in the given p-adic integers.'
+    for root in xrange(p):
+        try:
+            yield PAdicPoly(p, poly, root)
+        except ValueError:
+            pass
+
+class PAdicPoly(PAdic):
+    'Result of lifting a root of a polynomial in the integers mod p to the p-adic integers.'
+    def __init__(self, p, poly, root):
+        PAdic.__init__(self, p)
+        self.root = root
+        self.poly = poly
+        self.deriv = derivative(poly)
+        
+        # argument checks for the algorithm to work
+        if poly(root) % p:
+            raise ValueError("%d is not a root of %s modulo %d" % (root, poly, p))
+        if self.deriv(root) % p == 0:
+            raise ValueError("Polynomial %s is not separable modulo %d" % (poly, p))
+        
+        # take care of trailing zeros
+        digit = self.root
+        self.val = str(digit)
+        self.exp = self.p
+        while digit == 0:
+            self.order += 1
+            digit = self._nextdigit()
+            # self.prec += 1
+
+    def _nextdigit(self):
+        self.root = ModP(self.exp * self.p, self.root)
+        self.root = self.root - self.poly(self.root) / self.deriv(self.root) # coercions automatically taken care of
+        digit = self.root // self.exp
+        self.exp *= self.p
+        return digit

modp.py

@@ -0,0 +1,50 @@
+class ModP(int):
+    'Integers mod p, p a prime power.'
+    def __new__(cls, p, num):
+        self = int.__new__(cls, int(num) % p)
+        self.p = p
+        return self
+    
+    def __str__(self):
+        return "%d (mod %d)" % (self, self.p)
+    def __repr__(self):
+        return "%d %% %d" % (self, self.p)
+    
+    # arithmetic
+    def __neg__(self):
+        return ModP(self.p, self.p - int(self))
+    def __add__(self, other):
+        return ModP(self.p, int(self) + int(other))
+    def __radd__(self, other):
+        return ModP(self.p, int(other) + int(self))
+    def __sub__(self, other):
+        return ModP(self.p, int(self) - int(other))
+    def __rsub__(self, other):
+        return ModP(self.p, int(other) - int(self))
+    def __mul__(self, other):
+        return ModP(self.p, int(self) * int(other))
+    def __rmul__(self, other):
+        return ModP(self.p, int(other) * int(self))
+    def __div__(self, other):
+        if not isinstance(other, ModP):
+            other = ModP(self.p, other)
+        return self * other._inv()
+    def __rdiv__(self, other):
+        return other * self._inv()
+    
+    def _inv(self):
+        'Find multiplicative inverse of self in Z mod p.'
+        # extended Euclidean algorithm
+        rcurr = self.p
+        rnext = int(self)
+        tcurr = 0
+        tnext = 1
+        
+        while rnext:
+            q = rcurr // rnext
+            rcurr, rnext = rnext, rcurr - q * rnext
+            tcurr, tnext = tnext, tcurr - q * tnext
+        
+        if rcurr != 1:
+            raise ValueError("%d not a unit modulo %d" % (self, self.p))
+        return ModP(self.p, tcurr)

padic.py

@@ -0,0 +1,271 @@
+#!/usr/bin/env python3
+# -*- coding: UTF-8 -*-
+#
+#  License: GLP3+
+#  Copyright 2017 meagtan
+#  Copyright 2022 Beat Jäckle <beat@git.jdmweb2.ch>
+
+
+from fractions import Fraction
+from sys import maxsize
+from modp import ModP
+
+
+class PAdic:
+    def __init__(self, p, printInvers=False):
+        self.p = p
+
+        # current known value
+        self.digitP = []  # digitP[0]=c_0; digitP[i]=c_i
+        self.digitN = []  # digitN[0]=c_-1; digitN[i]=c_-1-i
+        self.prec = 0  # current known precision, not containing trailing zeros
+
+        self.order = 0  # order/valuation of number
+        self.printInvers = printInvers
+        return None
+
+    def calc(self, prec):
+        # First calculation
+        if len(self.digitN) + len(self.digitP) == 0:
+            if self.value == 0:
+                self.zero = True
+                self.digitP = [0]
+                return None
+            if self.order < 0:
+                absorder = abs(self.order)
+                self.digitN = [None]*absorder
+                for i in range(absorder):
+                    self.digitN[absorder-i-1] = self._nextdigit()
+                if absorder >= prec:
+                    self.prec = absorder
+                self.digitP.append(self._nextdigit())
+            elif self.order > 0:
+                self.digitP = [0]*self.order
+        while len(self.digitN) + len(self.digitP) < prec:
+            if self.value == 0:
+                break
+            self.digitP.append(self._nextdigit())
+        return None
+
+    def get(self, prec, decimal=True):
+        self.calc(prec)
+        'Return value of number with given precision.'
+        s = ''
+        for d in self.digitP[::-1]:
+            s += str(d)
+        if self.digitN:
+            if decimal:
+                s += '.'
+            for d in self.digitN:
+                s += str(d)
+        return s
+
+    def _nextdigit(self):
+        'Calculate next digit of p-adic number.'
+        raise NotImplementedError
+
+    def getdigit(self, index):
+        if index < self.order:
+            # print('not relevant 0')
+            return 0
+
+        # be sure to calculate the digits
+        prec = index+1
+        if self.order < 0:
+            prec += abs(self.order)
+        self.calc(prec)
+
+        # negative index
+        if index < 0:
+            try:
+                return self.digitN[abs(index)-1]
+            except IndexError:
+                print('Should not happen', index)
+                print('__dict__', self.__dict__())
+                raise IndexError(
+                    f"Digit not Found\n"
+                    f"index: {index}\n"
+                    f"dict: {self.__dict__()}"
+                    )
+
+        # positive index
+        else:
+            try:
+                return self.digitP[index]
+            except IndexError:
+                if self.value == 0:
+                    # print('not significant',0)
+                    return 0
+                else:
+                    print('Logical Error')
+                    print(f'Index = {index}')
+                    print(f'pAdic = {self.__dict__()}')
+                    raise ValueError('Logical Error')
+
+    # return value with precision up to 32 bits
+    def __int__(self):
+        return int(self.get(32), self.p)
+
+    def __getitem__(self, index):
+        return self.getdigit(index)
+
+    def __str__(self):
+        if self.printInvers:
+            return self.get(32)[::-1]
+        return self.get(32)
+
+    def __repr__(self):
+        return str(self)
+
+    # arithmetic operations
+    def __neg__(self):
+        return PAdicNeg(self.p, self)
+
+    def __add__(self, other):
+        return PAdicAdd(self.p, self, other)
+
+    def __radd__(self, other):
+        return PAdicAdd(self.p, other, self)
+
+    def __sub__(self, other):
+        return PAdicAdd(self.p, self, PAdicNeg(self.p, other))
+
+    def __rsub__(self, other):
+        return PAdicAdd(self.p, other, PAdicNeg(self.p, self))
+
+    def __mul__(self, other):
+        return PAdicMul(self.p, self, other)
+
+    def __rmul__(self, other):
+        return PAdicMul(self.p, other, self)
+
+    # p-adic norm
+    def __abs__(self):
+        if self.order == maxsize:
+            return 0
+        numer = denom = 1
+        if self.order > 0:
+            numer = self.p ** self.order
+        if self.order < 0:
+            denom = self.p ** self.order
+        return Fraction(numer, denom)
+
+    # determines the p-value of an p-adic number
+    def pValue(self):
+        return self.order
+
+    def fractionvalue(self):
+        self.calc(1)
+        s = Fraction(0)
+        for (i, d) in enumerate([self.digitP[0]]+self.digitN):
+            s += Fraction(d, self.p**i)
+        return s
+
+    def getOffset(self):
+        if self.order >= 0:
+            return 0
+        else:
+            return -self.order
+
+
+class PAdicConst(PAdic):
+    def __init__(self, p, value, printInvers=False):
+        super().__init__(p, printInvers)
+        value = Fraction(value)
+
+        # calculate valuation
+        if value == 0:
+            self.value = value
+            self.order = float('inf')
+            self.zero = True
+            return None
+
+        while not value.numerator % self.p:
+            self.order += 1
+            value /= self.p
+        while not value.denominator % self.p:
+            self.order -= 1
+            value *= self.p
+        self.value = value
+        return None
+
+    def get(self, prec, decimal=True):
+        if self.zero:
+            return '0' * prec
+        return PAdic.get(self, prec, decimal)
+
+    def _nextdigit(self):
+        'Calculate next digit of p-adic number.'
+        rem = int(
+            ModP(self.p, self.value.numerator) *
+            ModP(self.p, self.value.denominator)._inv()
+            )
+        self.value -= rem
+        self.value /= self.p
+        return rem
+
+
+class PAdicAdd(PAdic):
+    'Sum of two p-adic numbers.'
+    def __init__(self, p, arg1, arg2, printInvers=False):
+        super.__init__(self, p, printInvers)
+        self.carry = 0
+        _nextdigitCache = []
+        self.arg1 = arg1
+        self.arg2 = arg2
+        # might be larger than this
+        self.order = self.prec = min(arg1.order, arg2.order)
+        arg1.order -= self.order
+        arg2.order -= self.order
+        # loop until first nonzero digit is found
+        self.index = self.order
+        digit = self._nextdigit()
+        while digit == 0:
+            self.index += 1
+            digit = self._nextdigit()
+        self.order = self.index
+        _nextdigitCache.append(digit)
+
+    def _nextdigit(self):
+        if _nextdigitCache:
+            return _nextdigitCache.pop()
+        s = self.arg1.getdigit(self.index) + \
+            self.arg2.getdigit(self.index) + self.carry
+        self.carry = s // self.p
+        self.index += 1
+        return s % self.p
+
+
+class PAdicNeg(PAdic):
+    'Negation of a p-adic number.'
+    def __init__(self, p, arg, printInvers=False):
+        super.__init__(self, p, printInvers)
+        self.arg = arg
+        self.order = arg.order
+
+    def _nextdigit(self):
+        if self.prec == 0:
+            # cannot be p, 0th digit of arg must be nonzero
+            return self.p - self.arg.getdigit(0 - self.getOffset())
+        return self.p - 1 - self.arg.getdigit(self.prec - self.getOffset())
+
+
+class PAdicMul(PAdic):
+    'Product of two p-adic numbers.'
+    def __init__(self, p, arg1, arg2):
+        PAdic.__init__(self, p)
+        self.carry = 0
+        self.arg1 = arg1
+        self.arg2 = arg2
+        self.order = arg1.order + arg2.order
+        self.arg1.order = self.arg2.order = 0  # TODO requires copy
+        self.index = 0
+
+    def _nextdigit(self):
+        s = sum(
+            self.arg1.getdigit(i) * self.arg2.getdigit(self.index - i)
+            for i in xrange(self.index + 1)
+            ) + self.carry
+        self.carry = s // self.p
+        self.index += 1
+        return s % self.p

poly.py

@@ -0,0 +1,80 @@
+# Polynomial class on Z or Z_p
+
+from collections import defaultdict
+
+class Poly:
+    'Polynomial class.'
+    def __init__(self, coeffs = None):
+        self.coeffs = defaultdict(int, isinstance(coeffs, int) and {0:coeffs} or coeffs or {})
+        self.deg = int(len(self.coeffs) and max(self.coeffs.keys()))
+    
+    def __call__(self, val):
+        'Evaluate polynomial for a given value.'
+        res = 0
+        for i in xrange(self.deg, -1, -1):
+            res = res * val + self.coeffs[i]
+        return res
+    
+    def __str__(self):
+        def term(coeff, expt):
+            if coeff == 1 and expt == 0:
+                return '1'
+            return ' * '.join(([] if coeff == 1 else [str(coeff)]) + \
+                              ([] if expt == 0 else ['X'] if expt == 1 else ['X ** %d' % expt]))
+            
+        return ' + '.join(term(self.coeffs[i], i) for i in self.coeffs if self.coeffs[i] != 0)
+    def __repr__(self):
+        return str(self)
+    
+    # arithmetic
+    def __neg__(self):
+        return Poly({(i, -self.coeffs[i]) for i in self.coeffs})
+    def __add__(self, other):
+        if not isinstance(other, Poly):
+            other = Poly(other)
+        res = Poly()
+        res.deg = max(self.deg, other.deg)
+        for i in xrange(res.deg+1):
+            res.coeffs[i] = self.coeffs[i] + other.coeffs[i]
+        return res
+    def __radd__(self, other):
+        if not isinstance(other, Poly):
+            other = Poly(other)
+        return other.__add__(self)
+    def __sub__(self, other):
+        if not isinstance(other, Poly):
+            other = Poly(other)
+        return self.__add__(other.__neg__())
+    def __rsub__(self, other):
+        if not isinstance(other, Poly):
+            other = Poly(other)
+        return other.__add__(self.__neg__())
+    
+    def __mul__(self, other):
+        if not isinstance(other, Poly):
+            other = Poly(other)
+        res = Poly()
+        res.deg = self.deg + other.deg # consider case where other is 0
+        for i in xrange(res.deg+1):
+            for j in xrange(i+1):
+                res.coeffs[i] += self.coeffs[j] * other.coeffs[i - j]
+        return res
+    def __rmul__(self, other):
+        if not isinstance(other, Poly):
+            other = Poly(other)
+        return other.__mul__(self)
+        
+    def __pow__(self, other):
+        if not isinstance(other, int) or other < 0:
+            raise ValueError("Exponent %d is not a natural number" % other)
+        res = Poly(1)
+        while other:
+            res *= self
+            other -= 1
+        return res
+
+X = Poly({1:1})
+
+def derivative(p):
+    'Return derivative of polynomial.'
+    return Poly({(i - 1, i * p.coeffs[i]) for i in p.coeffs if i != 0})

pyproject.toml

@@ -0,0 +1,26 @@
+[build-system]
+requires = ["setuptools >= 58.0"]
+build-backend = "setuptools.build_meta"
+
+[project]
+name = "padic"
+version = "0.0.2"
+authors = [
+  { name="Beat Jäckle", email="beat@git.jdmweb2.ch" },
+]
+description = "class for p-adic number fields"
+readme = "README.md"
+license = { file="LICENSE" }
+requires-python = ">=3.7"
+classifiers = [
+    "Programming Language :: Python :: 3",
+    "License :: OSI Approved :: GPL3",
+    "Operating System :: OS Independent",
+]
+
+[project.urls]
+"Homepage" = "https://git.jdmweb2.ch/beat/p-adic-numbers"
+"Bug Tracker" = "https://git.jdmweb2.ch/beat/p-adic-numbers/issues"
+
+[tool.setuptools]
+py-modules = ['hensel', 'modp', 'poly', 'padic']