From cd8741690efb0b8f60ce16aec6373c28c7942d28 Mon Sep 17 00:00:00 2001
From: GDeLaurentis <g.dl@hotmail.it>
Date: Mon, 14 Oct 2024 16:57:29 +0100
Subject: [PATCH] Improved stability of point_on_variety with arbitrary
 precision complex floats (retrying on NoConvergence and AssertionError, the
 latter sometimes being triggered by an innacurate Grobner basis computation);
 fixed issue in Polynomial with parsing of arbitrary precision complex floats
 where the imaginary part is written in scientific notation (was failing to
 include 'e+' or 'e-' in the pattern matching).

---
 syngular/polynomial.py | 2 +-
 syngular/variety.py    | 8 +++++---
 2 files changed, 6 insertions(+), 4 deletions(-)

diff --git a/syngular/polynomial.py b/syngular/polynomial.py
index 711f518..e73c13d 100644
--- a/syngular/polynomial.py
+++ b/syngular/polynomial.py
@@ -167,7 +167,7 @@ def reduce(self):
     @staticmethod
     def __rstr__(polynomial, field):
         polynomial = polynomial.replace(" ", "").replace("+-", "-")
-        polynomial = re.sub(r"(\+|\-)I\*{0,1}([\d\.]+)", r"\1\2j", polynomial)  # format complex nbrs
+        polynomial = re.sub(r"(\+|\-)I\*{0,1}([\d\.e\+\-]+)", r"\1\2j", polynomial)  # format complex nbrs
         parentheses = [(("(", ), (")", )), (("{", ), ("}", )), (("[", "⟨", "<", ), ("]", "⟩", ">"))]
         lopen_parentheses = [parenthesis[0] for parenthesis in parentheses]
         lclos_parentheses = [parenthesis[1] for parenthesis in parentheses]
diff --git a/syngular/variety.py b/syngular/variety.py
index e3ff516..6453e45 100644
--- a/syngular/variety.py
+++ b/syngular/variety.py
@@ -9,6 +9,8 @@
 from copy import copy, deepcopy
 from pyadic import ModP
 
+from mpmath.libmp.libhyper import NoConvergence
+
 from .tools import RootNotInFieldError, RootPrecisionError
 from .field import Field
 from .polynomial import Monomial, Polynomial
@@ -32,10 +34,10 @@ def wrapper(self, field, base_point={}, directions=None, valuations=tuple(), ind
                         res = func(self, field, base_point=base_point, directions=directions, valuations=valuations,
                                    indepSetNbr=indepSetNbr, seed=seed, verbose=verbose)
                         break
-                    except (RootNotInFieldError, RootPrecisionError) as e:
+                    except (RootNotInFieldError, RootPrecisionError, NoConvergence, AssertionError) as e:
                         if try_nbr != max_tries - 1:
                             if verbose:
-                                print(f"Caught {type(e).__name__}, retrying...")
+                                print(f"Caught {type(e).__name__} at try number {try_nbr}, retrying...")
                             if seed is not None:  # maintain pseudo-randomness, but change seed, else retring has no effect.
                                 random.seed(seed)
                                 seed += random.randint(10 ** 5, 10**6)
@@ -157,7 +159,7 @@ def point_on_variety(self, field, base_point={}, directions=None, valuations=tup
             if prime is None and oSemiNumericalIdeal.groebner_basis == ['1']:
                 raise RootPrecisionError
             if not oSemiNumericalIdeal.dim == 0:
-                raise Exception("The dimension of the semi-numerical ideal was not zero.")
+                raise AssertionError("The dimension of the semi-numerical ideal was not zero.")
 
             root_dicts = lex_groebner_solve(oSemiNumericalIdeal.groebner_basis, prime=prime)
             check_solutions(oSemiNumericalIdeal.groebner_basis, root_dicts, field)  # they may be stricter then wanted for mpc.