Allowing instantiation of PAdic from floats, if the corresponding rat…

…ional can be identified with confidence. Fixed issue where multivariate newton used the same sequence of pseudo random numbers for all variables, causing issues if something special (e.g. a pole) appears when they are all equal.

pyadic/interpolation.py

@@ -84,7 +84,7 @@ def multivariate_Newton_polynomial_interpolation(f, prime, seed=0, depth=0, verb
         tpoly = tpoly.subs({'t': 't1', })
         return tpoly
 
-    t_sequence_generator = FFSequenceGenerator(prime, seed)
+    t_sequence_generator = FFSequenceGenerator(prime, seed=seed + depth)  # do not use same sequence for all variables!!!
     avals, tvals, subtracted = [], [], [f]
 
     dynamic_fsubtracted_string = f"""def fsubtracted(i, {''.join([f't{i}, ' for i in range(1, num_args + 1)])}):

pyadic/padic.py

@@ -1,11 +1,12 @@
-import fractions
 import functools
 import math
 import numbers
 import numpy
 import random
 import re
 
+from fractions import Fraction as Q
+
 from .finite_field import ModP, finite_field_sqrt, isinteger
 from .field_extension import FieldExtension
 
@@ -55,7 +56,7 @@ def wrapper_padicfy(self, other):
             if self.p != other.p:
                 raise ValueError(f"Can't cast a {other.p}-adic to a {self.p}-adic.")
             return func(self, other)
-        elif isinteger(other) or isinstance(other, ModP) or isinstance(other, fractions.Fraction) or (hasattr(other, "imag") and not isinstance(other, numpy.ndarray)):
+        elif isinteger(other) or isinstance(other, ModP) or isinstance(other, Q) or (hasattr(other, "imag") and not isinstance(other, numpy.ndarray)):
             return func(self, PAdic(other, self.p, max((self.n + self.k, self.k))))
         else:
             return NotImplemented
@@ -116,11 +117,19 @@ def __init__(self, num, p=None, k=None, n=0, from_addition=False):
                 self.k = self.k + factors_of_p
             if all_precision_loss_warning and self.k == 0:
                 print("Lost all precision @", self)
-        elif isinstance(num, fractions.Fraction):
+        elif isinstance(num, Q):
             res = PAdic(num.numerator, p, k, n, from_addition) / PAdic(num.denominator, p, k, n, from_addition)
             self.num, self.p, self.k, self.n = res.num, res.p, res.k, res.n
         elif isinstance(num, PAdic):
             self.num, self.p, self.k, self.n = num.num, num.p, num.k, num.n
+        elif isinstance(num, float):
+            if not (Q(num).limit_denominator(10 ** 3) == Q(num).limit_denominator(10 ** 5) == Q(num).limit_denominator(10 ** 8)):
+                raise ValueError(f"PAdic instantiation from float failed. It's unclear to which rational {num} corresponds to.")
+            res = PAdic(Q(num).limit_denominator(10 ** 3), p, k, n, from_addition)
+            self.p = res.p
+            self.k = res.k
+            self.n = res.n
+            self.num = res.num
         elif hasattr(num, "imag"):
             res = PAdic(num.real, p, k, n, from_addition)
             if num.imag != 0:
@@ -136,7 +145,7 @@ def __init__(self, num, p=None, k=None, n=0, from_addition=False):
         elif p is None and k is None and isinstance(num, str):
             self.num, self.p, self.k, self.n = self.__rstr__(num)
         elif isinstance(num, str):
-            num = fractions.Fraction(num)
+            num = Q(num)
             res = PAdic(num.numerator, p, k, n, from_addition) / PAdic(num.denominator, p, k, n, from_addition)
             self.num, self.p, self.k, self.n = res.num, res.p, res.k, res.n
         else: