I'm sure its omission is just an oversight. For fractional ideals in number fields it is defined:
sage: K.<r>=QuadraticField(7) sage: I=K.fractional_ideal(5) sage: J=K.fractional_ideal(3) sage: I.intersection(J) Fractional ideal (15) I doubt that just knowing a ring is a PID makes computing intersections of ideals easy. So the omission may be because there doesn't seem to be ZZ-specific (or euclidean ring-specific) ideal code. And with lcm around, the need for it has been low, I expect. On Saturday, 28 October 2023 at 02:36:51 UTC-7 G. M.-S. wrote: > > I wonder why SageMath cannot compute the intersection of 2 ideals in ZZ. > > Is this due to the fact that ZZ would "only" be a PID? > > Guillermo > > ┌────────────────────────────────────────────────────────────────────┐ > > │ SageMath version 10.1, Release Date: 2023-08-20 │ > > │ Using Python 3.11.1. Type "help()" for help. │ > > └────────────────────────────────────────────────────────────────────┘ > > sage: n1,n2=720,756 > > sage: d,m=gcd(n1,n2),lcm(n1,n2) > > sage: n1,n2,d,m > > (720, 756, 36, 15120) > > sage: I1,I2=ZZ.ideal(n1),ZZ.ideal(n2) > > sage: I1,I2 > > (Principal ideal (720) of Integer Ring, Principal ideal (756) of Integer > Ring) > > sage: I1+I2 > > Principal ideal (36) of Integer Ring > > sage: I1.intersection(I2) > > --------------------------------------------------------------------------- > > AttributeError Traceback (most recent call > last) > > Cell In [7], line 1 > > ----> 1 I1.intersection(I2) > > > File > /private/var/tmp/sage-10.1-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/structure/element.pyx:488, > > in sage.structure.element.Element.__getattr__ > (build/cythonized/sage/structure/element.c:4846)() > > * 486* AttributeError: > 'LeftZeroSemigroup_with_category.element_class' object has no attribute > 'blah_blah' > > * 487* """ > > --> 488 return self.getattr_from_category(name) > > * 489* > > * 490* cdef getattr_from_category(self, name): > > > File > /private/var/tmp/sage-10.1-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/structure/element.pyx:501, > > in sage.structure.element.Element.getattr_from_category > (build/cythonized/sage/structure/element.c:4958)() > > * 499* else: > > * 500* cls = P._abstract_element_class > > --> 501 return getattr_from_other_class(self, cls, name) > > * 502* > > * 503* def __dir__(self): > > > File > /private/var/tmp/sage-10.1-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/cpython/getattr.pyx:362, > > in sage.cpython.getattr.getattr_from_other_class > (build/cythonized/sage/cpython/getattr.c:2773)() > > * 360* dummy_error_message.cls = type(self) > > * 361* dummy_error_message.name = name > > --> 362 raise AttributeError(dummy_error_message) > > * 363* attribute = <object>attr > > * 364* # Check for a descriptor (__get__ in Python) > > > AttributeError: 'Ideal_pid' object has no attribute 'intersection' > > sage: > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/f54544d4-93f5-4411-99c9-335a67de25f3n%40googlegroups.com.
