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From: Christoph on 3 Mar 2005 07:21
Hi,

I've got a question concerning notation. Given a binary vector xi with
i=1,...,n: how can I show with a notation symbol that I just want to
address a part of the vector, for example the elements x3,...,x5 of
this vector?

Given also a boolean function: F: {0,1}^n -> {0,1}

How can I for example formally express F(x3,...,x5)=1?

Thanks in advance.

Maybe you can sent me an email with an attachment, if it's too
difficult to show the solution with the ASCII symbols.

Regards, Christoph
From: Lynn Kurtz on 3 Mar 2005 22:11
On 3 Mar 2005 04:21:32 -0800, christoph.stich(a)gmx.de (Christoph)
wrote:

>Hi,
>
>I've got a question concerning notation. Given a binary vector xi with
>i=1,...,n: how can I show with a notation symbol that I just want to
>address a part of the vector, for example the elements x3,...,x5 of
>this vector?
>

If e_1 = < 1, 0, 0, ...,0 >
e_2 = < 0, 1, 0, ..., 0 >
etc. so your vector is sum[k = 1 .. n] x_k * e_k
you could let M = { 3, 4, 5} and write y = sum[ k in M] x_k * e_k.
This would give you y = < 0, 0, x_3, x_4, x_5, 0, 0, ... 0 >
I'm not sure if that is what you mean by "addressing" those parts of
the vector.

--Lynn


>Given also a boolean function: F: {0,1}^n -> {0,1}
>
>How can I for example formally express F(x3,...,x5)=1?
>
>Thanks in advance.
>
>Maybe you can sent me an email with an attachment, if it's too
>difficult to show the solution with the ASCII symbols.
>
>Regards, Christoph

From: Christoph on 5 Mar 2005 12:12
Lynn Kurtz <kurtzDELETE-THIS(a)asu.edu> wrote in message news:<fNInQtL0MHxceQZm2ITPvcfvWGEi(a)4ax.com>...
> On 3 Mar 2005 04:21:32 -0800, christoph.stich(a)gmx.de (Christoph)
> wrote:
>
> >Hi,
> >
> >I've got a question concerning notation. Given a binary vector xi with
> >i=1,...,n: how can I show with a notation symbol that I just want to
> >address a part of the vector, for example the elements x3,...,x5 of
> >this vector?
> >
>
> If e_1 = < 1, 0, 0, ...,0 >
> e_2 = < 0, 1, 0, ..., 0 >
> etc. so your vector is sum[k = 1 .. n] x_k * e_k
> you could let M = { 3, 4, 5} and write y = sum[ k in M] x_k * e_k.
> This would give you y = < 0, 0, x_3, x_4, x_5, 0, 0, ... 0 >
> I'm not sure if that is what you mean by "addressing" those parts of
> the vector.
>
> --Lynn
>
> I meant, how can I express that I want to extract 3 elements of the vector in a general way. something like: F(x,[3:5]). What is an official mathemathical synthax?

--Christoph
From: A N Niel on 5 Mar 2005 16:48
> I meant, how can I express that I want to extract 3 elements of the vector
> in a general way. something like: F(x,[3:5]). What is an official mathemathical synthax?

Wny would you imagine that there exists such a thing as "official
mathematical syntax"? Computer languages have official syntax:
so for example in Maple op(3..5,x) or something. But "mathematics"
does not have official syntax.
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