[om] Algebraic Numbers

[Bill Naylor]

Hi Clare,

I'm not too sure of how 'official' the OpenMath2 spec. is yet, but if you
are willing to use OpenMath2 features, then you can define your algebraic
number once only, with an id attribute tagged onto it, then if you need
to refer to it again, use OMR xlink:href="id val" to refer to it.

Bill.
>
> In all, though, I think the cleanest approach given the limited ability
> of Openmath to express co-references would be to ask that an OpenMath
> version of the statement "let alpha be the algebraic number defined by
> ..." be wrapped around an expression that uses algebraic numbers, as in
> the first two examples (1) or (2) or via some equation.
>
> This is essentially your approach below, except for noting that one can
> bind the algebraic number to a variable in order to avoid having to
> repeat the algebraic number's definition all the time, and except for
> making explicit the need to use a functional argument for
> "algebraicnumber" below to make explicit the variable with respect to
> which the root is taken.
>
>  -- Andreas
>
> >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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> >
> >
>
>
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