Damn. What if they type i? I have to create an instance of i, the square
root of -1... super, but where does that go in the taxonomy of things??
I'm not smart like you people... is it a number? Oh, we have number then
real and imaginary then rational and irrational unde real.. how'm I doin?
kenny
On 2008-07-02 19:58:37 -0400, Kenny <·········@gmail.com> said:
> Oh, we have number then real and imaginary then rational and irrational
> unde real.. how'm I doin?
What was the question again?
Raffael Cavallaro wrote:
> On 2008-07-02 19:58:37 -0400, Kenny <·········@gmail.com> said:
>
>> Oh, we have number then real and imaginary then rational and
>> irrational unde real.. how'm I doin?
>
> What was the question again?
>
Too late, already implemented.
kt
On Wed, 02 Jul 2008 19:58:37 -0400, Kenny <·········@gmail.com> said:
| ...
| number then real and imaginary then rational and irrational under
| real.. how'm I doin?
1-800-ONE=EIPI
---Vassil,
who couldn't resist...
--
Peius melius est. ---Ricardus Gabriel.
From: Paul Tarvydas
Subject: Re: Imagine All the Numbers, Living For...
Date:
Message-ID: <g4hh69$k05$1@aioe.org>
Kenny wrote:
> Damn. What if they type i? I have to create an instance of i, the square
> root of -1... super, but where does that go in the taxonomy of things??
> I'm not smart like you people... is it a number? Oh, we have number then
> real and imaginary then rational and irrational unde real.. how'm I doin?
Start with Quaternions. Then specialize.
Paul Tarvydas wrote:
> Kenny wrote:
>
>> Damn. What if they type i? I have to create an instance of i, the square
>> root of -1... super, but where does that go in the taxonomy of things??
>> I'm not smart like you people... is it a number? Oh, we have number then
>> real and imaginary then rational and irrational unde real.. how'm I doin?
>
> Start with Quaternions. Then specialize.
>
Next question: where did I leave that killfile?
:)
I was wondering what had happened to this ng, then I noticed, it's
northern hemi summer! Without the academics this place goes to hell...
:)
kt
On Jul 2, 7:58 pm, Kenny <·········@gmail.com> wrote:
> where does that go in the taxonomy of things??
I usually look at other complex things like,
the hierarchy of smalltalk classes.
Oh! did I just admit to cheating?
> I'm not smart like you people...
But I thought you were the math teacher?
btw...
·····@yahoo.com wrote:
> On Jul 2, 7:58 pm, Kenny <·········@gmail.com> wrote:
>> where does that go in the taxonomy of things??
>
> I usually look at other complex things like,
> the hierarchy of smalltalk classes.
>
> Oh! did I just admit to cheating?
I love cheating!! But Lisp is buddhist, it does not have i. It has
complex numbers as an atomic type, from which one gets two reals, one of
which is merely understood to be a multiplier for i: one can never
isolate the little critter itself to ask its type-of. I tried. :(
kt
On Jul 3, 10:45 am, Kenny <·········@gmail.com> wrote:
> I love cheating!! But Lisp is buddhist, it does not have i. It has
> complex numbers as an atomic type, from which one gets two reals, one of
> which is merely understood to be a multiplier for i: one can never
> isolate the little critter itself to ask its type-of. I tried. :(
What's wrong with something like the following?
(defun pure-imaginary-p (num)
(and (complexp num)
(zerop (realpart num))
(not (zerop (imagpart num)))
The only thing I can think of is that you're trying to do some sort of
CLOS method dispatch on the class of the number, which strikes me as
the wrong way to go.
Cheers,
Pillsy
Pillsy wrote:
> On Jul 3, 10:45 am, Kenny <·········@gmail.com> wrote:
>
>> I love cheating!! But Lisp is buddhist, it does not have i. It has
>> complex numbers as an atomic type, from which one gets two reals, one of
>> which is merely understood to be a multiplier for i: one can never
>> isolate the little critter itself to ask its type-of. I tried. :(
>
> What's wrong with something like the following?
>
> (defun pure-imaginary-p (num)
> (and (complexp num)
> (zerop (realpart num))
> (not (zerop (imagpart num)))
>
> The only thing I can think of is that you're trying to do some sort of
> CLOS method dispatch on the class of the number, which strikes me as
> the wrong way to go.
>
?? No, I am using CLOS to model mathematics to in turn shape my Algebra
tutorial software. So I have a class for the sum operator that has
nothing to do with Lisp's +. ie, this was a math question, not a Lisp
question, but I tried to get some guidance from Lisp.
kt
On Thu, 3 Jul 2008 09:11:50 -0700 (PDT), Pillsy <·········@gmail.com> said:
| ...
| What's wrong with something like the following?
| (defun pure-imaginary-p (num)
| (and (complexp num)
| (zerop (realpart num))
| (not (zerop (imagpart num)))
Again, its "interaction" with computer arithmetic.
For example, the result of (PURE-IMAGINARY-P (EXPT -1 1/2)) is
implementation-dependent. We have to at least consider replacing
ZEROP with a proximity-to-0 test; and then it is not clear to me if
there is much demand for PURE-IMAGINARY-P at all, however it is
implemented.
---Vassil.
--
Peius melius est. ---Ricardus Gabriel.
Vassil Nikolov <···············@pobox.com> wrote:
+---------------
| For example, the result of (PURE-IMAGINARY-P (EXPT -1 1/2)) is
| implementation-dependent. We have to at least consider replacing
| ZEROP with a proximity-to-0 test...
+---------------
Indeed! On my favorite implementation, for example:
> (sqrt -1d0)
#C(0.0 1.0)
> (* * *)
#C(-1.0 0.0)
> (pure-imaginary-p **)
T
> (expt -1d0 0.5d0)
#C(6.123031769111886e-17 1.0)
> (* * *)
#C(-1.0 1.2246063538223773e-16)
> (pure-imaginary-p **)
NIL
>
Sure, it might be nice if EXPT special-cased the exponent 0.5 to
use SQRT, but I wouldn't necesarily call the above behavior "wrong".
-Rob
-----
Rob Warnock <····@rpw3.org>
627 26th Avenue <URL:http://rpw3.org/>
San Mateo, CA 94403 (650)572-2607
> I love cheating!! But Lisp is buddhist, it does not have i. It has
> complex numbers as an atomic type, from which one gets two reals, one of
> which is merely understood to be a multiplier for i: one can never
> isolate the little critter itself to ask its type-of. I tried. :(
i'm not sure if I understand what do you mean..
.. but actually "i" is just a shorthand notation for a complex number <0,
1>.
"i" is not a fundamental concept of complex number theory -- it's just a
way to make calculations easier to mimic normal calculations.
if by "little critter" you meant "i", obviosly it's type is complex,
with real part equal to zero and imaginary part equal to 1.
in modern math complex numbers are defined not in terms of being
roots of negative numbers (although they were invented in that way),
but just as pairs of numbers with special rules on addition, multiplication
etc defined on them. according to this rules, <0, 1> * <0, 1> = <-1, 0>,
so we can say that <0, 1> is a square root of <-1, 0>. which is cool,
of course, but that is a result, not a definition. this <0, 1>
complex number happens to be quite useful, so it was labeled as "i",
and we can write down any complex number <a, b> as a + bi, and
have normal arithmetic rules instead of rules defined on pairs.
> But Lisp is buddhist, it does not have i.
obviously computer does not need shorthand notation, it operates
on normal, mathematical one, not a notation for children :)
On Jul 3, 10:20 am, "Alex Mizrahi" <············@gmail.com> wrote:
...
>
> if by "little critter" you meant "i", obviosly it's type is complex,
> with real part equal to zero and imaginary part equal to 1.
>
...
perfecly buddhist description...
On Thu, 03 Jul 2008 10:45:10 -0400, Kenny <·········@gmail.com> said:
| ...
| complex numbers as an atomic type, from which one gets two reals, one
| of which is merely understood to be a multiplier for i: one can never
| isolate the little critter itself to ask its type-of. I tried. :(
Rather than that, owing to the quirks of computer arithmetic, it
isn't a single little creature---there are several of them:
* (let ((i #C(0 1))) (type-of i))
(COMPLEX BIT)
* (let ((i #C(0.0 1.0))) (type-of i))
(COMPLEX (SINGLE-FLOAT 0.0 1.0))
etc. This also shows that, absent some context, it is unclear what
the "best" way of defining a constant with the value of i would be,
if one would need it in lieu of #C syntax.
By the way, looking to mathematical notation for guidance, we can
see that while there are well established symbols for the sets of
natural numbers, integers, rational numbers, real numbers, and
complex numbers, there isn't such a symbol for the set of (pure)
imaginary numbers [*], apparently because one is not needed
(strongly enough), which may be taken to indicate that there isn't
great value in looking for a more specific type of i than COMPLEX
(possibly qualified with the type of the real and imaginary parts as
above).
_________
[*] Meaning, obviously, that even if there are occurrences in
mathematical literature of a symbol for the set of the (pure)
imaginary numbers, that would not be a widely spread or
standardized notation (similary for the sets of the algebraic
numbers, transcendental numbers, irrational numbers).
---Vassil.
--
Peius melius est. ---Ricardus Gabriel.
Vassil Nikolov <···············@pobox.com> writes:
> By the way, looking to mathematical notation for guidance, we can
> see that while there are well established symbols for the sets of
> natural numbers, integers, rational numbers, real numbers, and
> complex numbers, there isn't such a symbol for the set of (pure)
> imaginary numbers [*], apparently because one is not needed
> (strongly enough), which may be taken to indicate that there isn't
> great value in looking for a more specific type of i than COMPLEX
> (possibly qualified with the type of the real and imaginary parts as
> above).
>
> _________
> [*] Meaning, obviously, that even if there are occurrences in
> mathematical literature of a symbol for the set of the (pure)
> imaginary numbers, that would not be a widely spread or
> standardized notation (similary for the sets of the algebraic
> numbers, transcendental numbers, irrational numbers).
It is: iℝ
--
__Pascal Bourguignon__