Yes, I know :-|.�� Thre is a point where analysis has to finish (== stop pure mathematics) and start the implementation, which bring us back to the constraints of the programming environment.

Otherwise it would prudent to start [to develop] another programming language for that!

Em 15/08/2009 19:06, Igor Stasenko < siguctua@gmail.com > escreveu:

2009/8/16 :
> In the context of Complex numbers scalar can be used to call the Real
> numbers as complex numbers are homomorphous to 2 dimension vectos see:
> http://en.wikipedia.org/wiki/Vector_space. Also a vector space can be
> created starting from a complex Field instead of Real one.
>
> So in this conversation Igor's use of scalar scales well :-)
>
Yup.
But it is unlikely, that in operations where you expecting scalars or
some exact kind (real or complex) ,
you can freely substitute a different kind(s) of scalars - like
n-dimention vectors or even matrices and be sure that your code works
correctly as before.

> Em 15/08/2009 17:49, Igor Stasenko < siguctua@gmail.com > escreveu:
>
> 2009/8/15 Schwab,Wilhelm K :
>> Sig,
>>
>> I don't know in what context you mean "scalars," but complex numbers are
>> indeed used as the scalar field for vector spaces. ��That is done both in
>> (abstract) algegra and functional analysis - see Hilbert Space. ��That said,
>> I see what you mean and generally agree. ��Definitely agreed about the linear
>> dimension; complex does not fit in the magnitude hierarchy.
>
> Yes, the scalar term is a bit ambiguous, so i'd better stop using it.
> The wiki gives a disambiguation (http://en.wikipedia.org/wiki/Scalar)
> and , by scalar i mean Scalar (computing), which defined as:
>
> In computing, a scalar is a variable or field that can hold only one
> value at a time; as opposed to composite variables like array, list,
> record, etc. In some contexts, a scalar value may be understood to be
> nume ric. A scalar data type is the type of a scalar variable . For
> example, char, int, float, and double are the most common scalar data
> types in the C programming language.
>
> The origin of the term "scalar" in computing dates back to the 1970s,
> where the intended meaning was "opposite of vector", so as to
> distinguish from the idea of vector processing in computer processor
> design.
>
>>
>> We also have to remember that there are pgragmatic aspects to this. ��We
>> have been over this several times now, so I think we should table this until
>> Ken has time to write up his proposal.
>>
>> Bill
>>
>>
>> -----Original Message-----
>> From: pharo-project-bounces@lists.gforge.inria.fr
>> [mailto:pharo-project-bounces@lists.gforge.inria.fr] On Behalf Of Igor
>> Stasenko
>> Sent: Saturday, August 15, 2009 3:18 PM
>> To: Pharo-project@lists.gforge.inria.fr
>> Subject: Re: [Pharo-project] Complex number support discussion
>>
>> Btw, here is another argument why Complex is not part of Number class
>> hierarchy.
>>
>> Here what reads the Magnitude class:
>>
>> I'm the abstract class Magnitude that provides common protocol for objects
>> that have the ability to be compared along a ___linear dimension___, such as
>> dates or times.
>> Subclasses of Magnitude include Date, ArithmeticValue, and Time, as well
>> as Character and LookupKey.
>>
>> ---
>>
>> Since complex values is not scalars and hence cannot be compared along a
>> linear dimension, they could not be inherited from a Magnitude.
>>
>> Btw this comment seems veeery dated, because it refers to ArithmeticValue,
>> whi ch not present in current class hierarchy :)
>>
>> As you stated earlier that Real set is a subset of Complex, then if you
>> want to see both of them lying in same class hierarchy, it could require a
>> major redesign the class hierarchy to make Complex a base class, and
>> Float/Integer a subclasses.
>> Since subclasses are specialization of superclasses, and superclass always
>> is more generic than any of its subclass.
>>
>> Others could step up and say: hey scalars could be seen as a specialized
>> kind of vectors, and vectors could be seen as a specialized kind of
>> matrices, so lets make Matrix to be the ultimate superclass, and then
>> Vector, and then Scalar etc etc..
>>
>> I can only guess, how far we can go with such generalization(s).
>>
>> --
>> Best regards,
>> Igor Stasenko AKA sig.
>>
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>
>
> --
> Best regards,
> Igor Stasenko AKA sig.
>
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--
Best regards,
Igor Stasenko AKA sig.

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