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diff --git a/src/sage/rings/integer.pyx b/src/sage/rings/integer.pyx
index 4c835d0..77a3a18 100644
--- a/src/sage/rings/integer.pyx
+++ b/src/sage/rings/integer.pyx
@@ -4414,6 +4414,29 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
sig_off()
return z
+ def _gcd(self, Integer n):
+ """
+ Return the greatest common divisor of self and `n`.
+
+ EXAMPLES::
+
+ sage: 1._gcd(-1)
+ 1
+ sage: 0._gcd(1)
+ 1
+ sage: 0._gcd(0)
+ 0
+ sage: 2._gcd(2^6)
+ 2
+ sage: 21._gcd(2^6)
+ 1
+ """
+ cdef Integer z = PY_NEW(Integer)
+ sig_on()
+ mpz_gcd(z.value, self.value, n.value)
+ sig_off()
+ return z
+
def denominator(self):
"""
Return the denominator of this integer, which of course is
@@ -6736,33 +6759,6 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
raise ZeroDivisionError(f"inverse of Mod({self}, {m}) does not exist")
return ans
- def gcd(self, n):
- """
- Return the greatest common divisor of self and `n`.
-
- EXAMPLES::
-
- sage: gcd(-1,1)
- 1
- sage: gcd(0,1)
- 1
- sage: gcd(0,0)
- 0
- sage: gcd(2,2^6)
- 2
- sage: gcd(21,2^6)
- 1
- """
- if not isinstance(n, Integer) and not isinstance(n, int):
- left, right = coercion_model.canonical_coercion(self, n)
- return left.gcd(right)
- cdef Integer m = as_Integer(n)
- cdef Integer g = PY_NEW(Integer)
- sig_on()
- mpz_gcd(g.value, self.value, m.value)
- sig_off()
- return g
-
def crt(self, y, m, n):
"""
Return the unique integer between `0` and `mn` that is congruent to
diff --git a/src/sage/structure/element.pyx b/src/sage/structure/element.pyx
index f145e66..1cf634e 100644
--- a/src/sage/structure/element.pyx
+++ b/src/sage/structure/element.pyx
@@ -3908,16 +3908,79 @@ def is_PrincipalIdealDomainElement(x):
return isinstance(x, PrincipalIdealDomainElement)
cdef class PrincipalIdealDomainElement(DedekindDomainElement):
+ def gcd(self, right):
+ r"""
+ Return the greatest common divisor of ``self`` and ``other``.
+
+ TESTS:
+
+ :trac:`30849`::
+
+ sage: 2.gcd(pari(3))
+ 1
+ sage: type(2.gcd(pari(3)))
+ <class 'sage.rings.integer.Integer'>
+
+ sage: 2.gcd(pari('1/3'))
+ 1/3
+ sage: type(2.gcd(pari('1/3')))
+ <class 'sage.rings.rational.Rational'>
+
+ sage: import gmpy2
+ sage: 2.gcd(gmpy2.mpz(3))
+ 1
+ sage: type(2.gcd(gmpy2.mpz(3)))
+ <class 'sage.rings.integer.Integer'>
+
+ sage: 2.gcd(gmpy2.mpq(1,3))
+ 1/3
+ sage: type(2.gcd(pari('1/3')))
+ <class 'sage.rings.rational.Rational'>
+ """
+ # NOTE: in order to handle nicely pari or gmpy2 integers we do not rely only on coercion
+ if not isinstance(right, Element):
+ right = py_scalar_to_element(right)
+ if not isinstance(right, Element):
+ right = right.sage()
+ if not ((<Element>right)._parent is self._parent):
+ from sage.arith.all import gcd
+ return coercion_model.bin_op(self, right, gcd)
+ return self._gcd(right)
+
def lcm(self, right):
"""
Return the least common multiple of ``self`` and ``right``.
- """
- if not isinstance(right, Element) or not ((<Element>right)._parent is self._parent):
+
+ TESTS:
+
+ :trac:`30849`::
+
+ sage: 2.lcm(pari(3))
+ 6
+ sage: type(2.lcm(pari(3)))
+ <class 'sage.rings.integer.Integer'>
+
+ sage: 2.lcm(pari('1/3'))
+ 2
+ sage: type(2.lcm(pari('1/3')))
+ <class 'sage.rings.rational.Rational'>
+
+ sage: import gmpy2
+ sage: 2.lcm(gmpy2.mpz(3))
+ 6
+ sage: type(2.lcm(gmpy2.mpz(3)))
+ <class 'sage.rings.integer.Integer'>
+ """
+ # NOTE: in order to handle nicely pari or gmpy2 integers we do not rely only on coercion
+ if not isinstance(right, Element):
+ right = py_scalar_to_element(right)
+ if not isinstance(right, Element):
+ right = right.sage()
+ if not ((<Element>right)._parent is self._parent):
from sage.arith.all import lcm
return coercion_model.bin_op(self, right, lcm)
return self._lcm(right)
-
# This is pretty nasty low level stuff. The idea is to speed up construction
# of EuclideanDomainElements (in particular Integers) by skipping some tp_new
# calls up the inheritance tree.
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