[om] Algebraic Numbers

[Mike Dewar]

Hi Claire,

In OpenMath 1.1 you either have to use the second approach or create a
new symbol to contain the last two children in your OMBIND.  As Andreas
pointed out you need to be careful about whether you mean a particular
root or not.

Michael Kohlhase has proposed an extension to OMBIND in OpenMath 2 which
might do what you want.  His presentation from the Bremen meeting is at
http://www.openmath.org/meetings/bremen2003/binary_OMBIND.pdf .  Does
his proposal meet your needs?

Cheers, Mike.

On Fri, Nov 28, 2003 at 11:51:21AM -0500, Clare So wrote:
> Dear OpenMathers,
> 
> The MONET group at ORCCA is trying to figure out the appropriate
> OpenMath representation for algebraic numbers.  We propose two
> approaches.  Let's say we would like to encode $ {\alpha}{x^2} + 
> (\alpha - 1)x + (1 + \alpha )y $ in OpenMath where \alpha is
> the algebraic expression representing RootOf(z^2+z+1):
> 
> * First Approach *
> 
> <OMA>
>   <OMS cd="algext1" name="algebraicnumber"/>
>   <OMBIND>
>     <OMS cd="fns1" name="lambda"/>
>     <OMBVAR>
>       <OMV name="alpha"/>
>     </OMBVAR>
>     <OMA>
>       [$ {\alpha ^ 2} + \alpha + 1 $ in OpenMath]
>     </OMA>
>     <OMA>
>       [$ {\alpha}{x^2} + (\alpha - 1)x + (1 + \alpha )y $ in OpenMath]
>     </OMA>
>   </OMBIND>
> </OMA>
> 
> For this approach, alpha is defined in the second argument of of
> <OMS cd="fns1" name="lambda"/> and is used in the expression in the
> third argument.
> 
> 
> * Second Approach *
> 
> <OMA>
>   <OMS cd ="arith1" name="plus"/>
>   <OMA>
>     <OMS cd="arith1" name="times"/>
>     <OMA>
>       <OMS cd="algext1" name="algebraicnumber"/>
>       [$ {\alpha ^ 2} + \alpha + 1 $ in OpenMath]
>     </OMA>
>     <OMA>
>       <OMS cd="arith1" name="power"/>
>       <OMV name="x"/>
>       <OMI> 2 </OMI>
>     </OMA>
>   </OMA>
>   <OMA>
>     <OMS cd="arith1" name="times"/>
>     <OMA>    
>       <OMS cd="arith1" name="minus"/>
>       <OMA>
>         <OMS cd="algext1" name="algebraicnumber"/>
>         [$ {\alpha ^ 2} + \alpha + 1 $ in OpenMath]
>       </OMA>
>       <OMI> 1 </OMI>
>     </OMA>
>     <OMV name="x"/>
>   </OMA>
>   <OMA>
>     <OMS cd="arith1" name="times"/>
>     <OMA>
>       <OMS cd="arith1" name="plus"/>
>       <OMA>
>         <OMS cd="algext1" name="algebraicnumber"/>
>         [$ {\alpha ^ 2} + \alpha + 1 $ in OpenMath]
>       </OMA>
>       <OMI> 1 </OMI>
>     </OMA>
>     <OMV name="y"/>
>   </OMA>
> </OMA>
> 
> The algebraic number is defined every time we need it.
> 
> 
> First approach is a compact way to express algebraic number because
> alpha is defined once for the entire expression.  Second approach is
> a straight-forward way because alpha is defined exactly the place we
> need it.
> 
> Please let us know which approach you think should be used for this
> purpose.
> 
> 
> Clare & MONET group at UWO
> --
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