[Trac] [OpenMath] #59: CD minmax1

[OpenMath]

#59: CD minmax1
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     Reporter:  jauecker      |          Owner:  kohlhase  
         Type:  proposal      |         Status:  new       
     Priority:  major         |      Milestone:  CD3 Draft1
    Component:  OM3 Standard  |        Version:            
   Resolution:                |       Keywords:            
Include_gantt:  0             |   Dependencies:            
   Due_assign:  YYYY/MM/DD    |      Due_close:  YYYY/MM/DD
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Comment (by jauecker):

 '''David:'''


 >>If I remember correctly, Maple and Mathematica differ on where they do
 branch cuts.  Do we want to favor one over the other?  have two sets of
 arc trig functions?  Maybe NAG uses even different branch cuts...

 >But take care: this is precisely Dr Carlisle's exquisite reasoning in
 favour of full specification here (although he omits to tell even me if
 these are functions on the reals or the complexes before worrying about
 whether cuts are the way to describe this).

 You can always read the CDs to see whether the functions are defined
 over the complexes:-)

 As to my "exquisite reasoning" It was mainly a statement of my
 recollection of the reasons why the OM CDs reference an explict version
 of A&S for these functions. It wasn't necessarily an argument that
 chapter 4 should do the same. It's a matter of judgement though.

 I think that most people would agree that you want 1.0 + 2.0 to be
 understood as "addition" whatever your system means by that (whether
 that is BCD based arithemetic or some system based on interval
 arithmetic, or IEEE double arithemetic or whatever. To do otherwise
 would make it essentially impossible to transfer any expressions from
 one system to another.

 Howver given that it is known that (say) arccot(-1) has multiple
 definitions in different systems (and different books) One has to take a
 judjement whether it's best to let arccot mean "arccot on your system" or
 "arccot as normalised in some reference text" Note that in this case, if
 you do say it means a specific version, then systems using a different
 version
 only need to typically add a special case conditional normalising the
 arguments, it's not like systems that are using different underlying
 arithemtic systems or integration methods where, if we are explict about
 the exact semantics it would make it essentially impossible to use on
 systems that are not built with that semantics.



 see for example the table on page 12 of

 http://www.openmath.org/projects/thematic/tools-2.pdf



 Table 1: Different values of arccot(-1)
 This table is taken from [2], with the addition of the Maxima line.

 Source       Detail          arccot(-1) Comments
 [1]          1st printing    3pi/4      inconsistent
 [1]          9th printing   -pi/4
 [6]          5th edition     ?          inconsistent
 [10]         30th edition    3pi/4      inconsistent
 Maple        V release 5     3pi/4
 Axiom        2.1             3pi/4
 Mathematica  [9]             -pi/4
 Maxima       5.5             -pi/4
 Reduce       3.4.1           -pi/4      in floating point
 Matlab       5.3.0           -pi/4      in floating point
 Matlab       5.3.0           3pi/4      symbolic toolbox

 The note "inconsistent" means that, although the source quotes, or
 clearly lets be inferred, a value for arccot(-1), there are enough
 inconsistencies in the definition of arccot that one could infer a
 different value. For [6], 3pi/4 and -pi/4 are equally inferable.

-- 
Ticket URL: <https://trac.kwarc.info/OM3/ticket/59#comment:8>
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