[om] Algebraic Numbers
Paul Libbrecht
paul at activemath.org
Sat Nov 29 21:06:21 CET 2003
Funnily the new defmp, if through in OpenMath 2 allows exactly the same
thing if your algebraic number is as much valuable as needing to be put
into a content-dictionary.
Paul
Bill Naylor wrote:
> 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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