[Om] Tutorial or example collection for OpenMath?

[Alberto González Palomo]

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,
-- 
     Alberto González Palomo
     Toledo, España / Saarbrücken, Deutschland
     http://www.matracas.org