diff --git a/README.md b/README.md
index 887a69c..be00a38 100644
--- a/README.md
+++ b/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
\ No newline at end of file
+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.
diff --git a/padic.py b/padic.py
index 90d680d..d448c66 100644
--- a/padic.py
+++ b/padic.py
@@ -1,46 +1,122 @@
+#!/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):
+    def __init__(self, p, printInvers=False):
         self.p = p
-        self.val = ''  # current known value
+
+        # 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
-        pass  # initialize object as subclass perhaps
+        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.'
-        while self.prec < prec:
-            # update val based on value
-            self.val = str(int(self._nextdigit())) + self.val
-            self.prec += 1
-        if self.order < 0:
-            return (
-                self.val[:self.order] + ('.' if decimal else '') +
-                self.val[self.order:])[-prec-1:]
-        return (self.val + self.order * '0')[-prec:]
+        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):
-        'Return digit at given index.'
-        return int(self.get(index + 1, False)[0])
-        # int(
-        #    self.get(index+1+int(index < -self.order)
-        # )[-int(index < -self.order)])
+        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)
@@ -74,20 +150,36 @@ class PAdic:
             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):
-        PAdic.__init__(self, p)
+    def __init__(self, p, value, printInvers=False):
+        super().__init__(p, printInvers)
         value = Fraction(value)
 
         # calculate valuation
         if value == 0:
             self.value = value
-            self.val = '0'
-            self.order = maxsize
-            return
+            self.order = float('inf')
+            self.zero = True
+            return None
 
-        self.order = 0
         while not value.numerator % self.p:
             self.order += 1
             value /= self.p
@@ -95,8 +187,7 @@ class PAdicConst(PAdic):
             self.order -= 1
             value *= self.p
         self.value = value
-
-        self.zero = not value
+        return None
 
     def get(self, prec, decimal=True):
         if self.zero:
@@ -105,18 +196,21 @@ class PAdicConst(PAdic):
 
     def _nextdigit(self):
         'Calculate next digit of p-adic number.'
-        rem = ModP(self.p, self.value.numerator) /\
-            ModP(self.p, self.value.denominator)
-        self.value -= int(rem)
+        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):
-        PAdic.__init__(self, p)
+    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
@@ -124,16 +218,17 @@ class PAdicAdd(PAdic):
         arg1.order -= self.order
         arg2.order -= self.order
         # loop until first nonzero digit is found
-        self.index = 0
+        self.index = self.order
         digit = self._nextdigit()
         while digit == 0:
             self.index += 1
-            self.order += 1
             digit = self._nextdigit()
-        self.val += str(int(digit))
-        self.prec = 1
+        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
@@ -143,16 +238,16 @@ class PAdicAdd(PAdic):
 
 class PAdicNeg(PAdic):
     'Negation of a p-adic number.'
-    def __init__(self, p, arg):
-        PAdic.__init__(self, p)
+    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)
-        return self.p - 1 - self.arg.getdigit(self.prec)
+            return self.p - self.arg.getdigit(0 - self.getOffset())
+        return self.p - 1 - self.arg.getdigit(self.prec - self.getOffset())
 
 
 class PAdicMul(PAdic):