Re: denoting the dimension an implicit equation is plotted in

From: William Elliot (marsh_at_privacy.net)
Date: 01/24/05 

Date: Sun, 23 Jan 2005 19:18:48 -0800

On Sun, 23 Jan 2005, Alex Hunsley wrote:
> William Elliot wrote:
>> On Sun, 23 Jan 2005, Alex Hunsley wrote:
>>
>>> Normally an implicit function like
>>>
>>> f(x, y) = x^2 + y^2 - 1
>>>
>>> is thought of as corresponding to a figure in the amount of dimensions
>>> mentioned in the equation, where we find the zero points:
>>>
>>> 0 = f(x,y)
>>> (So here we have a circle in 2 dimensions.)
>>>
>>> I need some notation, however, to denote the figure produced by solving
>>> the implicit equation in a certain amount of dimensions, since changing
>>> the number of dimensions changes the final figure... e.g. the f(x, y)
>>> given above would be a circle if you plotted it in 2 dimensions, but it
>>> would be a cylinder/tube if you plotted it in three dimensions, and so
>>> on...
>>
>> f(x,y,z) = x^2 + y^2 - 1
>> f(x,y,z) = 0 implies a cylinder
>
> I see what you mean, but the point is that I want to attach the amount of
> dimensions solved for to either just the expression f(x,y,z) or just the
> expression x^2+y^2, and not mention both.
> thanks,

To describe a function, two things are needed, it's domain, and it's value
thruout the domain. x^2 + y^2 doesn't describe the domain.

Relevant Pages

  • Re: denoting the dimension an implicit equation is plotted in
    ... On Sun, 23 Jan 2005, Alex Hunsley wrote: ... > William Elliot wrote: ... > I see what you mean, but the point is that I want to attach the amount of ...
    (sci.math)
  • removing external scsi device without reboot
    ... I have Sun 220R running Solaris 7. ... Unplug the external scsi cable from the 220. ... Attach the external tape drive to another machine, ... SBC Yahoo! ...
    (SunManagers)
  • Re: set theory: definition of dim(S)
    ... On Tue, 29 Nov 2005, Alex Hunsley wrote: ... > William Elliot wrote: ... > thinking along the lines of dimbeing equal to n iff x.memberof ... Prev by Date: ...
    (sci.math)
  • Re: 1/0
    ... On Nov 27, 2005 5:38 AM CT, William Elliot wrote: ... > On Sun, 27 Nov 2005, David Kastrup wrote: ... I'm not quite sure what frightens me more, ...
    (sci.math)
  • Re: uniquely determined
    ... On Sun, 18 Jan 2009, William Elliot wrote: ... bijection though I suspect with fuller context, it could be interpreted to mean that the function f is an injection. ...
    (sci.math)