#8378: typo in documentation of crt
---------------------------------------------+------------------------------
   Reporter:  zimmerma                       |       Owner:  AlexGhitza  
       Type:  defect                         |      Status:  needs_review
   Priority:  trivial                        |   Milestone:  sage-4.4.1  
  Component:  basic arithmetic               |    Keywords:              
     Author:  Paul Zimmermann, John Cremona  |    Upstream:  N/A         
   Reviewer:  Minh Van Nguyen                |      Merged:              
Work_issues:                                 |  
---------------------------------------------+------------------------------
Changes (by mvngu):

  * reviewer:  => Minh Van Nguyen


Old description:

> {{{
> sage: crt(15,1,30,4)
> ...
> ValueError: arguments a and b must be coprime
> }}}
> However in the documentation of {{{crt}}} a, b are the residues,
> and the moduli are called m, n. Thus the message should be:
> {{{
> ValueError: arguments m and n must be coprime
> }}}
>
> Additionally, this function should be extended to handle non-coprime
> moduli.

New description:

 {{{
 sage: crt(15,1,30,4)
 ...
 ValueError: arguments a and b must be coprime
 }}}
 However in the documentation of {{{crt}}} a, b are the residues,
 and the moduli are called m, n. Thus the message should be:
 {{{
 ValueError: arguments m and n must be coprime
 }}}

 Additionally, this function should be extended to handle non-coprime
 moduli.

 Apply patches in this order:

  1.
 [http://trac.sagemath.org/sage_trac/attachment/ticket/8378/trac_8378-crt.patch
 trac_8378-crt.patch]
  1.
 
[http://trac.sagemath.org/sage_trac/attachment/ticket/8378/trac_8378-reviewer.patch
 trac_8378-reviewer.patch]

--

Comment:

 Reviewer patch has the following changes:

  * Explicitly mention the default values.
  * Properly typeset `lcm(m,n)`.
  * Clean up code following the conventions of
 [http://www.python.org/dev/peps/pep-0008/ PEP 008].
  * The improved documentation of `crt` says that this function also takes
 a list of residues and a list of moduli. Provide an example to demonstrate
 this usage.
  * Cross-reference the two functions `crt` and `CRT_list`.
  * The patch
 [http://trac.sagemath.org/sage_trac/attachment/ticket/8378/trac_8378-crt.patch
 trac_8378-crt.patch] results in two doctest failures in the English and
 French version of the Sage tutorial. Fix those doctest failures.

 If the reviewer patch gets a positive review, then the whole ticket gets a
 positive review. I'm happy with
 [http://trac.sagemath.org/sage_trac/attachment/ticket/8378/trac_8378-crt.patch
 trac_8378-crt.patch]. Any one but myself could review my reviewer patch.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8378#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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