Add Q, R, C, and GF2 fields

- add `lalib.fields.base.Field`, a blueprint for all concrete fields,
  providing a unified interface to be used outside of the
  `lalib.fields` sub-package
- implement `lalib.fields.complex_.ComplexField`, or `C` for short,
  the field over the complex numbers (modeled as `complex` numbers)
- implement `lalib.fields.galois.GaloisField2`, or `GF2` for short,
  the (finite) field over the two elements `one` and `zero`
  + adapt `lalib.elements.galois.GF2Element.__eq__()` to return
    `NotImplemented` instead of `False` for non-castable `other`s
    => this fixes a minor issue with `pytest.approx()`
- implement `lalib.fields.rational.RationalField`, or `Q` for short,
  the field over the rational numbers (modeled as `fractions.Fraction`s)
- implement `lalib.fields.real.RealField`, or `R` for short,
  the field over the real numbers (modeled as `float`s)
- organize top-level imports for `lalib.fields`,
  making `Q`, `R`, `C`, and `GF2` importable with
  `from lalib.fields import *`
- provide extensive unit and integration tests for the new objects:
  + test generic and common behavior in `tests.fields.test_base`
  + test specific behavior is other modules
  + test the well-known math axioms for all fields (integration tests)
  + test the new objects' docstrings
  + add "pytest-repeat" to run randomized tests many times

tests/fields/utils.py

@@ -0,0 +1,75 @@
+"""Utilities to test the `lalib.fields` sub-package."""
+
+import decimal
+import fractions
+import os
+
+import pytest
+
+from lalib import config
+from lalib import elements
+from lalib import fields
+
+
+ALL_FIELDS = (fields.Q, fields.R, fields.C, fields.GF2)
+NON_10_FIELDS = (fields.Q, fields.R, fields.C)
+
+ONES = (
+    1,
+    1.0,
+    fractions.Fraction(1, 1),
+    decimal.Decimal("1.0"),
+    elements.one,
+    True,
+)
+
+ZEROS = (
+    0,
+    0.0,
+    fractions.Fraction(0, 1),
+    decimal.Decimal("+0.0"),
+    decimal.Decimal("-0.0"),
+    elements.zero,
+    False,
+)
+
+ONES_N_ZEROS = ONES + ZEROS
+
+NON_ONES_N_ZEROS = (
+    +42,
+    +42.0,
+    fractions.Fraction(+42, 1),
+    decimal.Decimal("+42.0"),
+    -42,
+    -42.0,
+    fractions.Fraction(-42, 1),
+    decimal.Decimal("-42.0"),
+)
+
+NUMBERS = ONES_N_ZEROS + NON_ONES_N_ZEROS
+
+DEFAULT_THRESHOLD = config.THRESHOLD
+WITHIN_THRESHOLD = config.THRESHOLD / 10
+NOT_WITHIN_THRESHOLD = config.THRESHOLD * 10
+
+N_RANDOM_DRAWS = os.environ.get("N_RANDOM_DRAWS") or 1
+
+
+def is_field_element(field, value):
+    """Utility method to avoid redundant logic in tests."""
+    element = field.cast(value)
+
+    assert element == value
+    assert field.validate(value)
+
+
+def is_not_field_element(field, value):
+    """Utility method to avoid redundant logic in tests."""
+    with pytest.raises(ValueError, match="not an element of the field"):
+        field.cast(value)
+
+    assert not field.validate(value)
+    assert not field.validate(value, silent=True)
+
+    with pytest.raises(ValueError, match="not an element of the field"):
+        field.validate(value, silent=False)