Add exact division for fmpz

fmpz(4) / fmpz(2) -> fmpz(2)
fmpz(5) / fmpz(2) -> DomainError

Author: oscarbenjamin

src/flint/test/test.py

@@ -90,6 +90,7 @@ def test_fmpz():
         assert int(f) == i
         assert flint.fmpz(f) == f
         assert flint.fmpz(str(i)) == f
+    assert raises(lambda: flint.fmpz(1,2), TypeError)
     assert raises(lambda: flint.fmpz("qwe"), ValueError)
     assert raises(lambda: flint.fmpz([]), TypeError)
     for s in L:
@@ -162,6 +163,9 @@ def test_fmpz():
     # XXX: Handle negative modulus like int?
     assert raises(lambda: pow(flint.fmpz(2), 2, -1), ValueError)
 
+    assert raises(lambda: pow(flint.fmpz(2), "asd", 2), TypeError)
+    assert raises(lambda: pow(flint.fmpz(2), 2, "asd"), TypeError)
+
     f = flint.fmpz(2)
     assert f.numerator == f
     assert type(f.numerator) is flint.fmpz
@@ -2276,6 +2280,44 @@ def test_fmpz_mod_mat():
     assert raises(lambda: flint.fmpz_mod_mat(A, c11), TypeError)
 
 
+def test_division_scalar():
+    Z = flint.fmpz
+    Q = flint.fmpq
+    F17 = lambda x: flint.nmod(x, 17)
+    ctx = flint.fmpz_mod_ctx(163)
+    F163 = lambda a: flint.fmpz_mod(a, ctx)
+    # fmpz exact division
+    for (a, b) in [(Z(4), Z(2)), (Z(4), 2), (4, Z(2))]:
+        assert a / b == Z(2)
+    for (a, b) in [(Z(5), Z(2)), (Z(5), 2), (5, Z(2))]:
+        assert raises(lambda: a / b, DomainError)
+    # fmpz Euclidean division
+    for (a, b) in [(Z(5), Z(2)), (Z(5), 2), (5, Z(2))]:
+        assert a // b == 2
+        assert a % b == 1
+        assert divmod(a, b) == (2, 1)
+    # field division
+    for (a, b) in [(Q(5), Q(2)), (Q(5), 2), (5, Q(2))]:
+        assert a / b == Q(5,2)
+    for (a, b) in [(F17(5), F17(2)), (F17(5), 2), (5, F17(2))]:
+        assert a / b == F17(11)
+    for (a, b) in [(F163(5), F163(2)), (F163(5), 2), (5, F163(2))]:
+        assert a / b == F163(84)
+    # divmod with fields - should this give remainder zero instead of error?
+    for K in [Q, F17, F163]:
+        for (a, b) in [(K(5), K(2)), (K(5), 2), (5, K(2))]:
+            assert raises(lambda: divmod(a, b), TypeError)
+    # Zero division
+    for R in [Z, Q, F17, F163]:
+        assert raises(lambda: R(5) / 0, ZeroDivisionError)
+        assert raises(lambda: R(5) / R(0), ZeroDivisionError)
+        assert raises(lambda: 5 / R(0), ZeroDivisionError)
+    # Bad types
+    for R in [Z, Q, F17, F163]:
+        assert raises(lambda: R(5) / "AAA", TypeError)
+        assert raises(lambda: "AAA" / R(5), TypeError)
+
+
 def _all_polys():
     return [
         # (poly_type, scalar_type, is_field)
@@ -3023,7 +3065,7 @@ def test_all_tests():
     test_fmpz_mod_poly,
     test_fmpz_mod_mat,
 
-    test_arb,
+    test_division_scalar,
 
     test_polys,
 
@@ -3048,7 +3090,9 @@ def test_all_tests():
     test_matrices_rref,
     test_matrices_solve,
 
+    test_arb,
+
     test_pickling,
-    test_all_tests,
 
+    test_all_tests,
 ]

src/flint/types/fmpz.pyx

@@ -1,5 +1,3 @@
-from cpython.version cimport PY_MAJOR_VERSION
-
 from flint.flint_base.flint_base cimport flint_scalar
 from flint.utils.typecheck cimport typecheck
 from flint.utils.conversion cimport chars_from_str
@@ -12,6 +10,9 @@ from flint.flintlib.fmpz_factor cimport *
 from flint.flintlib.arith cimport *
 from flint.flintlib.partitions cimport *
 
+from flint.utils.flint_exceptions import DomainError
+
+
 cdef fmpz_get_intlong(fmpz_t x):
     """
     Convert fmpz_t to a Python int or long.
@@ -29,10 +30,6 @@ cdef int fmpz_set_any_ref(fmpz_t x, obj):
     if typecheck(obj, fmpz):
         x[0] = (<fmpz>obj).val[0]
         return FMPZ_REF
-    if PY_MAJOR_VERSION < 3 and PyInt_Check(obj):
-        fmpz_init(x)
-        fmpz_set_si(x, PyInt_AS_LONG(obj))
-        return FMPZ_TMP
     if PyLong_Check(obj):
         fmpz_init(x)
         fmpz_set_pylong(x, obj)
@@ -103,9 +100,6 @@ cdef class fmpz(flint_scalar):
     def __int__(self):
         return fmpz_get_intlong(self.val)
 
-    def __long__(self):
-        return long(fmpz_get_intlong(self.val))
-
     def __index__(self):
         return fmpz_get_intlong(self.val)
 
@@ -134,27 +128,18 @@ cdef class fmpz(flint_scalar):
         cdef fmpz_struct * sval
         cdef int ttype
         sval = &((<fmpz>s).val[0])
-        if PY_MAJOR_VERSION < 3 and PyInt_Check(t):
-            tl = PyInt_AS_LONG(t)
-            if   op == 2: res = fmpz_cmp_si(sval, tl) == 0
-            elif op == 3: res = fmpz_cmp_si(sval, tl) != 0
-            elif op == 0: res = fmpz_cmp_si(sval, tl) < 0
-            elif op == 1: res = fmpz_cmp_si(sval, tl) <= 0
-            elif op == 4: res = fmpz_cmp_si(sval, tl) > 0
-            elif op == 5: res = fmpz_cmp_si(sval, tl) >= 0
-        else:
-            ttype = fmpz_set_any_ref(tval, t)
-            if ttype != FMPZ_UNKNOWN:
-                if   op == 2: res = fmpz_equal(sval, tval)
-                elif op == 3: res = not fmpz_equal(sval, tval)
-                elif op == 0: res = fmpz_cmp(sval, tval) < 0
-                elif op == 1: res = fmpz_cmp(sval, tval) <= 0
-                elif op == 4: res = fmpz_cmp(sval, tval) > 0
-                elif op == 5: res = fmpz_cmp(sval, tval) >= 0
-            if ttype == FMPZ_TMP:
-                fmpz_clear(tval)
-            if ttype == FMPZ_UNKNOWN:
-                return NotImplemented
+        ttype = fmpz_set_any_ref(tval, t)
+        if ttype != FMPZ_UNKNOWN:
+            if   op == 2: res = fmpz_equal(sval, tval)
+            elif op == 3: res = not fmpz_equal(sval, tval)
+            elif op == 0: res = fmpz_cmp(sval, tval) < 0
+            elif op == 1: res = fmpz_cmp(sval, tval) <= 0
+            elif op == 4: res = fmpz_cmp(sval, tval) > 0
+            elif op == 5: res = fmpz_cmp(sval, tval) >= 0
+        if ttype == FMPZ_TMP:
+            fmpz_clear(tval)
+        if ttype == FMPZ_UNKNOWN:
+            return NotImplemented
         return res
 
     def bit_length(self):
@@ -265,6 +250,39 @@ cdef class fmpz(flint_scalar):
         if ttype == FMPZ_TMP: fmpz_clear(tval)
         return u
 
+    def __truediv__(s, t):
+        cdef fmpz_struct tval[1]
+        cdef fmpz_struct rval[1]
+        cdef int ttype
+
+        ttype = fmpz_set_any_ref(tval, t)
+        if ttype == FMPZ_UNKNOWN:
+            return NotImplemented
+
+        if fmpz_is_zero(tval):
+            if ttype == FMPZ_TMP:
+                fmpz_clear(tval)
+            raise ZeroDivisionError("fmpz division by zero")
+
+        q = fmpz.__new__(fmpz)
+        fmpz_init(rval)
+        fmpz_fdiv_qr((<fmpz>q).val, rval, (<fmpz>s).val, tval)
+        exact = fmpz_is_zero(rval)
+        fmpz_clear(rval)
+
+        if ttype == FMPZ_TMP: fmpz_clear(tval)
+
+        if exact:
+            return q
+        else:
+            raise DomainError("fmpz division is not exact")
+
+    def __rtruediv__(s, t):
+        t = any_as_fmpz(t)
+        if t is NotImplemented:
+            return t
+        return t.__truediv__(s)
+
     def __floordiv__(s, t):
         cdef fmpz_struct tval[1]
         cdef int ttype = FMPZ_UNKNOWN