bug in divides

[williamstein]

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. It may not be able to handle all cases but classes who need a more clever function should do their own implementation anyways.

Greetings,
Kilian.

Component: basic arithmetic

Author: Luis Felipe Tabera

Reviewer: John Cremona

Merged: sage-4.6.alpha3

Issue created by migration from https://trac.sagemath.org/ticket/5759

[sagetrac-kkilger]

Description changed:

--- 
+++ 
@@ -1,21 +1,11 @@
+The function "divides" does not work for generic commutative rings.
 
-```
-sage: Zmod(2)(0).divides(Zmod(2)(1))
----------------------------------------------------------------------------
-ZeroDivisionError                         Traceback (most recent call last)
+1. it is not checked that the elements are in the same space, i.e.
 
-/Users/wstein/.sage/temp/teragon.local/50691/_Users_wstein__sage_init_sage_0.py in <module>()
+Zmod(5)(1).divides(Zmod(2)(1)) is "True"
 
-/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)()
+2. No division by zero checking is done! This gives for example an error if you type
 
-/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)
+Zmod(2).zero_ideal() == Zmod(2).zero_ideal() Zmod(2).zero_ideal() == Zmod(2).unit_ideal()
 
-ZeroDivisionError: integer division or modulo by zero
-
-Found by  kilian__ on irc.
-```
+This patch should fix this.

[sagetrac-kkilger]

comment:1

Attachment: divides.patch.gz

[sagetrac-kkilger]

Description changed:

--- 
+++ 
@@ -6,6 +6,7 @@
 
 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()
+    -> Zmod(2).zero_ideal() == Zmod(2).zero_ideal() 
+    -> Zmod(2).zero_ideal() == Zmod(2).unit_ideal()
 
 This patch should fix this.

[sagetrac-kkilger]

Description changed:

--- 
+++ 
@@ -7,6 +7,10 @@
 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.
+
+Greetings,
+Kilian. 

[sagetrac-kkilger]

Description changed:

--- 
+++ 
@@ -10,7 +10,7 @@
 
     -> Zmod(2).zero_ideal() == Zmod(2).unit_ideal()
 
-This patch should fix this.
+This patch should fix this. It may not be able to handle all cases but classes who need a more clever function should do their own implementation anyways.
 
 Greetings,
 Kilian. 

[sagetrac-kkilger]

comment:7

Attachment: 5759-doctests.patch.gz