#5759: bug in divides
------------------------------+---------------------------------------------
Reporter: was | Owner: somebody
Type: defect | Status: new
Priority: major | Milestone: sage-3.4.2
Component: basic arithmetic | Keywords:
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Changes (by kkilger):
* priority: minor => major
Old description:
> {{{
> sage: Zmod(2)(0).divides(Zmod(2)(1))
> ---------------------------------------------------------------------------
> ZeroDivisionError Traceback (most recent call
> last)
>
> /Users/wstein/.sage/temp/teragon.local/50691/_Users_wstein__sage_init_sage_0.py
> in <module>()
>
> /Users/wstein/build/sage-3.4.1.rc2/local/lib/python2.5/site-
> packages/sage/structure/element.so in
> sage.structure.element.CommutativeRingElement.divides
> (sage/structure/element.c:12423)()
>
> /Users/wstein/build/sage-3.4.1.rc2/local/lib/python2.5/site-
> packages/sage/rings/integer_mod.so in
> sage.rings.integer_mod.IntegerMod_int.__mod__
> (sage/rings/integer_mod.c:17834)()
> 1867 def __mod__(IntegerMod_int self, right):
> 1868 right = int(right)
> -> 1869 if self.__modulus.int32 % right != 0:
> 1870 raise ZeroDivisionError, "reduction modulo right not
> defined."
> 1871 return integer_mod_ring.IntegerModRing(right)(self)
>
> ZeroDivisionError: integer division or modulo by zero
>
> Found by kilian__ on irc.
> }}}
New description:
The function "divides" does not work for generic commutative rings.
1. it is not checked that the elements are in the same space, i.e.
Zmod(5)(1).divides(Zmod(2)(1)) is "True"
2. No division by zero checking is done! This gives for example an error
if you type
Zmod(2).zero_ideal() == Zmod(2).zero_ideal() Zmod(2).zero_ideal() ==
Zmod(2).unit_ideal()
This patch should fix this.
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5759#comment:1>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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