[Om] Tutorial or example collection for OpenMath?

[Michael Kohlhase]

Dear all,

I made an STS to RelaxNG compiler a couple of years back, I will see if
I can dig that out.

Michael
On 26.2.14 12:01, Alberto González Palomo wrote:
> Konrad Hinsen wrote: (25/02/14 10:07)
>> [...]
>> For the particular case of "sum", I find the definition in arith1 a
>> bit vague:
>>
>>     An operator taking two arguments, the first being the range of
>>     summation, e.g. an integral interval, ...
>>
>> There is no definition of "range of summation", just an example. You
>> use a
>> set in your example, which is fine, but there's nothing in the
>> definition
>> of "sum" that tells me that sets are a valid specification for a
>> "range of
>> summation".
>>
>> Which leads to another question: is there any validation tool for
>> OpenMath that checks the semantics? The XML schemas and the XSLT
>> stylesheet from the OpenMath Web site only check syntactical aspects,
>> they won't stop me from using transc1/sin as a summation range, for
>> example.
>
>   I'm not aware of any validation tool, but you can check the Simple
> Type System (STS) used for symbol signatures in the OM CDs.
> http://www.openmath.org/cd/sts.xhtml
>
>   For instance, arith1:sum has:
>
> http://www.openmath.org/sts/arith1.xhtml#sum
>
>   I always used integer intervals for it in all the OM software I wrote.
>   For instance in Yacas, $\sigma_{i=1}^3 i^2$ is:
>
> http://yacas.sourceforge.net/refchapter6.html#Sum
>
> In> OMForm(Sum(i, 1, 3, i^2));
> <OMOBJ>
>   <OMA>
>     <OMS cd="arith1" name="sum"/>
>     <OMA>
>       <OMS cd="interval1" name="integer_interval"/>
>       <OMI>1</OMI>
>       <OMI>3</OMI>
>     </OMA>
>     <OMBIND>
>       <OMS cd="fns1" name="lambda"/>
>       <OMBVAR>
>         <OMV name="i"/>
>       </OMBVAR>
>       <OMA>
>         <OMS cd="arith1" name="power"/>
>         <OMV name="i"/>
>         <OMI>2</OMI>
>       </OMA>
>     </OMBIND>
>   </OMA>
> </OMOBJ>
> Out> True
> In> N(Sum(i, 1, 3, i^2));
> Out> 14
>
>   For the double sum you mentioned, that would be nested:
>
> In> OMForm(Sum(j, -2, 5, Sum(i, 1, 3, j+i^2)));
> <OMOBJ>
>   <OMA>
>     <OMS cd="arith1" name="sum"/>
>     <OMA>
>       <OMS cd="interval1" name="integer_interval"/>
>       <OMA>
>         <OMS cd="arith1" name="minus"/>
>         <OMI>2</OMI>
>       </OMA>
>       <OMI>5</OMI>
>     </OMA>
>     <OMBIND>
>       <OMS cd="fns1" name="lambda"/>
>       <OMBVAR>
>         <OMV name="j"/>
>       </OMBVAR>
>       <OMA>
>         <OMS cd="arith1" name="sum"/>
>         <OMA>
>           <OMS cd="interval1" name="integer_interval"/>
>           <OMI>1</OMI>
>           <OMI>3</OMI>
>         </OMA>
>         <OMBIND>
>           <OMS cd="fns1" name="lambda"/>
>           <OMBVAR>
>             <OMV name="i"/>
>           </OMBVAR>
>           <OMA>
>             <OMS cd="arith1" name="plus"/>
>             <OMV name="j"/>
>             <OMA>
>               <OMS cd="arith1" name="power"/>
>               <OMV name="i"/>
>               <OMI>2</OMI>
>             </OMA>
>           </OMA>
>         </OMBIND>
>       </OMA>
>     </OMBIND>
>   </OMA>
> </OMOBJ>
> Out> True
> In> N(Sum(j, -2, 5, Sum(i, 1, 3, j+i^2)));
> Out> 148
>
>   In my editor that would be as follows:
> http://matracas.org/sentido/demo/index.xhtml#%E2%88%91%28-2..5,%CE%BBj.%E2%88%91%281..3,%CE%BBi.j+i^2%29%29
>
>
>   You can click twice on the sum button (the palettes will scroll
> down because of the variables added to the expression) to get a
> nested sum, then rename the variables by hand.
>
>   It is possible to enter it in the form described by Lars,
> using a set, but my MathML stylesheets don't support it so far:
> http://matracas.org/sentido/demo/index.xhtml#%E2%88%91%28cartesian_product%28X,Y%29,%CE%BB[i,j].i*j%29
>
>
>   Cheers,

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