Drop igcd(), use math.gcd()

A partial fix for #839

diofant/__init__.py

@@ -14,7 +14,7 @@
                    cacheit, comp, count_ops, diff, evaluate, expand,
                    expand_complex, expand_func, expand_log, expand_mul,
                    expand_multinomial, expand_power_base, expand_power_exp,
-                   expand_trig, factor_nc, factor_terms, gcd_terms, igcd,
+                   expand_trig, factor_nc, factor_terms, gcd_terms,
                    integer_digits, integer_nthroot, mod_inverse, nan, nfloat,
                    oo, pi, preorder_traversal, symbols, sympify, var,
                    vectorize, zoo)
@@ -179,7 +179,7 @@
     'cacheit', 'comp', 'count_ops', 'diff', 'evaluate', 'expand',
     'expand_complex', 'expand_func', 'expand_log', 'expand_mul',
     'expand_multinomial', 'expand_power_base', 'expand_power_exp',
-    'expand_trig', 'factor_nc', 'factor_terms', 'gcd_terms', 'igcd',
+    'expand_trig', 'factor_nc', 'factor_terms', 'gcd_terms',
     'integer_digits', 'integer_nthroot', 'mod_inverse', 'nan', 'nfloat',
     'oo', 'pi', 'preorder_traversal', 'symbols', 'sympify', 'var',
     'vectorize', 'zoo', 'ITE', 'And', 'Equivalent', 'Implies', 'Nand', 'Nor',

diofant/core/__init__.py

@@ -8,8 +8,8 @@
 from .expr import Expr, AtomicExpr
 from .symbol import Symbol, Wild, Dummy, symbols, var
 from .numbers import (Number, Float, Rational, Integer,
-                      NumberSymbol, igcd, E, I, nan, oo,
-                      pi, zoo, comp, mod_inverse, integer_digits)
+                      NumberSymbol, E, I, nan, oo, pi, zoo, comp,
+                      mod_inverse, integer_digits)
 from .power import Pow, integer_nthroot
 from .mul import Mul
 from .add import Add
@@ -37,7 +37,7 @@
 __all__ = ('sympify', 'SympifyError', 'cacheit', 'Basic', 'Atom',
            'preorder_traversal', 'S', 'Expr', 'AtomicExpr', 'Symbol',
            'Wild', 'Dummy', 'symbols', 'var', 'Number', 'Float', 'Rational',
-           'Integer', 'NumberSymbol', 'igcd', 'E', 'I', 'nan', 'oo',
+           'Integer', 'NumberSymbol', 'E', 'I', 'nan', 'oo',
            'pi', 'zoo', 'comp', 'mod_inverse', 'integer_digits', 'Pow',
            'integer_nthroot', 'Mul', 'Add', 'Mod', 'Rel', 'Eq', 'Ne',
            'Lt', 'Le', 'Gt', 'Ge', 'Equality', 'GreaterThan', 'LessThan',

diofant/core/add.py

@@ -6,7 +6,7 @@
 from .cache import cacheit
 from .compatibility import is_sequence
 from .logic import _fuzzy_group
-from .numbers import Integer, igcd, nan, oo, zoo
+from .numbers import Integer, nan, oo, zoo
 from .operations import AssocOp
 
 
@@ -724,10 +724,10 @@ def primitive(self):
             terms.append((c.numerator, c.denominator, m))
 
         if not inf:
-            ngcd = functools.reduce(igcd, [t[0] for t in terms], 0)
+            ngcd = functools.reduce(math.gcd, [t[0] for t in terms], 0)
             dlcm = functools.reduce(math.lcm, [t[1] for t in terms], 1)
         else:
-            ngcd = functools.reduce(igcd, [t[0] for t in terms if t[1]], 0)
+            ngcd = functools.reduce(math.gcd, [t[0] for t in terms if t[1]], 0)
             dlcm = functools.reduce(math.lcm, [t[1] for t in terms if t[1]], 1)
 
         if ngcd == dlcm == 1:
@@ -812,7 +812,7 @@ def as_content_primitive(self, radical=False):
                 # find the gcd of bases for each q
                 G = []
                 for q in common_q:
-                    g = functools.reduce(igcd, [r[q] for r in rads], 0)
+                    g = functools.reduce(math.gcd, [r[q] for r in rads], 0)
                     if g != 1:
                         G.append(root(g, q))
                 if G:

diofant/core/numbers.py

@@ -96,28 +96,6 @@ def _str_to_Decimal_dps(s):
         return num, len(num.as_tuple().digits)
 
 
-@cacheit
-def igcd(*args):
-    """Computes positive integer greatest common divisor.
-
-    Examples
-    ========
-
-    >>> igcd(2, 4)
-    2
-    >>> igcd(5, 10, 15)
-    5
-
-    """
-    args = map(as_int, args)
-    a = next(args)
-    for b in args:
-        if a == 1:
-            break
-        a = math.gcd(a, b)
-    return a
-
-
 def igcdex(a, b):
     """Returns x, y, g such that g = x*a + y*b = gcd(a, b).
 

diofant/integrals/transforms.py

@@ -450,7 +450,6 @@ def _rewrite_gamma(f, s, a, b):
     (([], []), ([], []), 1/2, 1, 8)
 
     """
-    from ..core import igcd
     from ..functions import cos, cot, exp_polar, gamma, re, sin, tan
     from ..polys import Poly, RootOf, roots
 
@@ -522,7 +521,7 @@ def left(c, is_numer):
             s_multiplier = common_coefficient
         else:
             s_multiplier = common_coefficient \
-                * functools.reduce(igcd, [Integer(x.numerator) for x in s_multipliers])
+                * functools.reduce(math.gcd, [Integer(x.numerator) for x in s_multipliers])
 
     exponent = Integer(1)
     fac = Integer(1)

diofant/ntheory/modular.py

@@ -3,7 +3,6 @@
 
 import mpmath
 
-from ..core import igcd
 from ..core.compatibility import as_int
 from ..core.numbers import igcdex
 from .primetest import isprime
@@ -216,7 +215,7 @@ def combine(c1, c2):
         a1, m1 = c1
         a2, m2 = c2
         a, b, c = m1, a2 - a1, m2
-        g = functools.reduce(igcd, [a, b, c])
+        g = functools.reduce(math.gcd, [a, b, c])
         a, b, c = [i//g for i in [a, b, c]]
         if a != 1:
             inv_a, _, g = igcdex(a, c)

diofant/polys/polyroots.py

@@ -4,7 +4,7 @@
 import math
 
 from ..core import (Dummy, Eq, Float, I, Integer, Rational, Symbol, comp,
-                    factor_terms, igcd, pi, symbols)
+                    factor_terms, pi, symbols)
 from ..core.mul import expand_2arg
 from ..core.sympify import sympify
 from ..domains.compositedomain import CompositeDomain
@@ -646,7 +646,7 @@ def _integer_basis(poly):
     monoms = monoms[:-1]
     coeffs = coeffs[:-1]
 
-    divs = reversed(divisors(igcd(*coeffs))[1:])
+    divs = reversed(divisors(math.gcd(*coeffs))[1:])
 
     try:
         div = next(divs)

diofant/simplify/trigsimp.py

@@ -1,9 +1,10 @@
 import functools
+import math
 from collections import defaultdict
 
 from ..core import (Add, Basic, Dummy, E, Expr, FunctionClass, I, Integer, Mul,
                     Pow, Rational, Wild, cacheit, count_ops, expand,
-                    expand_mul, factor_terms, igcd, symbols)
+                    expand_mul, factor_terms, symbols)
 from ..core.compatibility import iterable
 from ..core.function import _mexpand
 from ..core.strategies import greedy, identity
@@ -289,7 +290,7 @@ def analyse_gens(gens, hints):
             # from this list.
             fns = [x[1] for x in val]
             val = [x[0] for x in val]
-            gcd = functools.reduce(igcd, val)
+            gcd = functools.reduce(math.gcd, val)
             terms = [(fn, v/gcd) for (fn, v) in zip(fns, val)]
             fs = set(funcs + fns)
             for c, s, t in ([cos, sin, tan], [cosh, sinh, tanh]):

diofant/solvers/diophantine.py

@@ -1,6 +1,6 @@
 import math
 
-from ..core import (Add, Eq, Integer, Rational, Symbol, factor_terms, igcd,
+from ..core import (Add, Eq, Integer, Rational, Symbol, factor_terms,
                     integer_nthroot, oo, symbols, sympify)
 from ..core.assumptions import check_assumptions
 from ..core.compatibility import as_int, is_sequence
@@ -48,9 +48,9 @@ def _sorted_tuple(*i):
 
 def _remove_gcd(*x):
     try:
-        g = igcd(*x)
+        g = math.gcd(*x)
         return tuple(i//g for i in x)
-    except ValueError:
+    except (TypeError, ValueError):
         return x
 
 

diofant/tests/core/test_numbers.py

@@ -7,7 +7,7 @@
 
 from diofant import (Catalan, E, EulerGamma, Float, Ge, GoldenRatio, Gt, I,
                      Integer, Le, Lt, Mul, Number, Pow, Rational, Symbol, cbrt,
-                     comp, cos, exp, factorial, false, igcd, integer_digits,
+                     comp, cos, exp, factorial, false, integer_digits,
                      integer_nthroot, latex, log, mod_inverse, nan, nextprime,
                      oo, pi, root, sin, sqrt, true, zoo)
 from diofant.core.cache import clear_cache
@@ -169,30 +169,6 @@ def test_divmod():
     assert divmod(Integer(4), Rational(f)) == divmod(4, f)
 
 
-def test_igcd():
-    assert igcd(0, 0) == 0
-    assert igcd(0, 1) == 1
-    assert igcd(1, 0) == 1
-    assert igcd(0, 7) == 7
-    assert igcd(7, 0) == 7
-    assert igcd(7, 1) == 1
-    assert igcd(1, 7) == 1
-    assert igcd(-1, 0) == 1
-    assert igcd(0, -1) == 1
-    assert igcd(-1, -1) == 1
-    assert igcd(-1, 7) == 1
-    assert igcd(7, -1) == 1
-    assert igcd(8, 2) == 2
-    assert igcd(4, 8) == 4
-    assert igcd(8, 16) == 8
-    assert igcd(7, -3) == 1
-    assert igcd(-7, 3) == 1
-    assert igcd(-7, -3) == 1
-    assert igcd(*[10, 20, 30]) == 10
-    pytest.raises(ValueError, lambda: igcd(45.1, 30))
-    pytest.raises(ValueError, lambda: igcd(45, 30.1))
-
-
 def test_igcdex():
     assert igcdex(0, 0) == (0, 1, 0)
     assert igcdex(-2, 0) == (-1, 0, 2)

diofant/tests/test_wester.py

@@ -6,6 +6,7 @@
 each tested system.
 """
 import itertools
+import math
 
 import pytest
 
@@ -26,15 +27,14 @@
                      exp, expand, expand_func, eye, factor, factorial,
                      factorial2, factorint, fibonacci, floor,
                      fourier_transform, gamma, gcd, groebner, hessian, hyper,
-                     hyperexpand, igcd, im, integrate,
-                     inverse_laplace_transform, laplace_transform,
-                     legendre_poly, limit, log, logcombine, maximize,
-                     mellin_transform, minimize, nan, npartitions, oo, pi,
-                     polygamma, polylog, powdenest, powsimp, primerange,
-                     primitive, primitive_root, product, radsimp, re,
-                     reduce_inequalities, residue, resultant, rf, root, rsolve,
-                     sec, series, sign, simplify, sin, sinh, solve, sqrt,
-                     sqrtdenest, summation, symbols, tan, tanh, totient,
+                     hyperexpand, im, integrate, inverse_laplace_transform,
+                     laplace_transform, legendre_poly, limit, log, logcombine,
+                     maximize, mellin_transform, minimize, nan, npartitions,
+                     oo, pi, polygamma, polylog, powdenest, powsimp,
+                     primerange, primitive, primitive_root, product, radsimp,
+                     re, reduce_inequalities, residue, resultant, rf, root,
+                     rsolve, sec, series, sign, simplify, sin, sinh, solve,
+                     sqrt, sqrtdenest, summation, symbols, tan, tanh, totient,
                      trigsimp, trunc, wronskian, zeta, zoo)
 from diofant.abc import a, b, c, s, t, w, x, y, z
 from diofant.functions.combinatorial.numbers import stirling
@@ -100,7 +100,7 @@ def test_C8():
 
 
 def test_C9():
-    assert igcd(1776, 1554, 5698) == 74
+    assert math.gcd(1776, 1554, 5698) == 74
 
 
 def test_C10():

docs/modules/core.rst

@@ -115,10 +115,6 @@ NumberSymbol
 .. autoclass:: NumberSymbol
    :members:
 
-igcd
-^^^^
-.. autofunction:: igcd
-
 mod_inverse
 ^^^^^^^^^^^
 .. autofunction:: mod_inverse

docs/release/notes-0.13.rst

@@ -19,7 +19,7 @@ Compatibility breaks
 * Renamed ``Ring`` as :class:`~diofant.domains.ring.CommutativeRing`, see :pull:`1123`.
 * Removed support for Python 3.7 and 3.8, see :pull:`1118` and :pull:`1124`.
 * ``FiniteRing`` renamed to :class:`~diofant.domains.IntegerModRing`, see :pull:`1124`.
-* Removed ``ilcm()`` and ``prod()`` functions, see :pull:`1125`.
+* Removed ``igcd()``, ``ilcm()`` and ``prod()`` functions, see :pull:`1125`.
 
 Minor changes
 =============