Re: [SOSlib-devel] MathML Piecewise function[Scanned]

[Rainer M. <ra...@tb...>]

I can't really find a nice description of piecewise. There are only two 
examples, one is the simple case piece/otherwise:

  piecewise(0, lt(x, 0), x)

the other one is the case with three pieces:

  piecewise(-x, lt(x, 0), 0, eq(x, 0), x, gt(x, 0))

(which is a definition of abs(x)).

Can there also be cases with e.g. two pieces and one otherwise?
Or only two pieces?

Can the following distinction:

* odd number of AST children indicates that the last expression is an 
otherwise expression

* even number of AST children indicates that all children a pairs of 
pieces

solve it generally or are there other cases?

Rainer

On Fri, 16 Jun 2006, Rainer Machne wrote:

>
>> You are right this is a bug in the test suite
>
> Ok. We have implemented this bug in SOSlib :)
>
> i guess i have done the piecewise function when going through the tests
> and used these examples as a template for implementation :)
>
> r
>
>
> On Fri, 16 Jun 2006, Andrew Finney wrote:
>
>> Rainer
>>
>> You are right this is a bug in the test suite
>>
>> Andrew
>>
>>> -----Original Message-----
>>> From: Rainer Machne [mailto:ra...@tb...]
>>> Sent: 16 June 2006 12:23
>>> To: Andrew Finney
>>> Cc: SOSlib Development
>>> Subject: MathML Piecewise function[Scanned]
>>>
>>> hi Andrew,
>>>
>>> The use of piecewise in the semantic test suite seems to
>>> differ from official definitions:
>>>
>>> E.g. in discontinuityTimeAndDelay-geq-l2.xml
>>> it's:
>>>
>>>   <piecewise>
>>>     <piece>
>>>       <apply>
>>>         <geq/>
>>>         <ci> s2 </ci>
>>>         <cn> 4 </cn>
>>>       </apply>
>>>       <cn>1.5</cn>
>>>     </piece>
>>>     <otherwise>
>>>        <cn>0.05</cn>
>>>     </otherwise>
>>> </piecewise>
>>>
>>> which is
>>>
>>> piecewise(geq(s2, 4), 1.5, 0.05)
>>>
>>> in libSBML infix and interpreted as
>>>
>>> 1.5 if s2 >= 4
>>> and
>>> 0.05 otherwise
>>>
>>> by SOSlib.
>>> SOSlib produces the results required by the testsuite.
>>>
>>>
>>> However, at
>>> http://www.w3.org/TR/MathML2/chapter4.html#contm.piecewise
>>> the definition is slightly different:
>>>
>>> <piecewise>
>>>    <piece>
>>>        <cn> 0 </cn>
>>>        <apply><lt/><ci> x </ci> <cn> 0 </cn></apply>
>>>    </piece>
>>>    <otherwise>
>>>        <ci> x </ci>
>>>    </otherwise>
>>> </piecewise>
>>>
>>> in libSBML infix
>>> piecewise(0, lt(x, 0), x)
>>>
>>> interpreted as
>>> 0 if x < 0
>>> and x otherwise.
>>>
>>> Note, that the if condition of the piece element is BEFORE
>>> the associated result, while it is AFTER the result in the
>>> test suite example.
>>>
>>> The same ordering is found in the piecewise example for more
>>> pieces - see below. The result associated with a piece is
>>> always BEFORE the condition.
>>>
>>> Am i missing something or is the test suite example (and
>>> SOSlib) wrong?
>>>
>>> Rainer
>>>
>>>
>>>
>>> The general example with more pieces:
>>>
>>> <piecewise>
>>>    <piece>
>>>        <apply><minus/><ci> x </ci></apply>
>>>        <apply><lt/><ci> x </ci> <cn> 0 </cn></apply>
>>>    </piece>
>>>    <piece>
>>>        <cn> 0 </cn>
>>>        <apply><eq/><ci> x </ci> <cn> 0 </cn></apply>
>>>    </piece>
>>>    <piece>
>>>        <ci> x </ci>
>>>        <apply><gt/><ci> x </ci> <cn> 0 </cn></apply>
>>>    </piece>
>>> </piecewise>
>>>
>>
>
>
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