You can subscribe to this list here.
2000 
_{Jan}
(16) 
_{Feb}
(21) 
_{Mar}
(49) 
_{Apr}
(35) 
_{May}
(25) 
_{Jun}
(15) 
_{Jul}
(17) 
_{Aug}
(15) 
_{Sep}
(12) 
_{Oct}
(18) 
_{Nov}
(42) 
_{Dec}
(31) 

2001 
_{Jan}
(35) 
_{Feb}
(24) 
_{Mar}
(53) 
_{Apr}
(59) 
_{May}
(124) 
_{Jun}
(134) 
_{Jul}
(92) 
_{Aug}
(74) 
_{Sep}
(75) 
_{Oct}
(95) 
_{Nov}
(47) 
_{Dec}
(32) 
2002 
_{Jan}
(191) 
_{Feb}
(143) 
_{Mar}
(279) 
_{Apr}
(287) 
_{May}
(106) 
_{Jun}
(96) 
_{Jul}
(95) 
_{Aug}
(126) 
_{Sep}
(184) 
_{Oct}
(152) 
_{Nov}
(84) 
_{Dec}
(136) 
2003 
_{Jan}
(170) 
_{Feb}
(64) 
_{Mar}
(202) 
_{Apr}
(142) 
_{May}
(103) 
_{Jun}
(145) 
_{Jul}
(56) 
_{Aug}
(204) 
_{Sep}
(130) 
_{Oct}
(91) 
_{Nov}
(32) 
_{Dec}
(130) 
2004 
_{Jan}
(89) 
_{Feb}
(208) 
_{Mar}
(190) 
_{Apr}
(61) 
_{May}
(111) 
_{Jun}
(126) 
_{Jul}
(121) 
_{Aug}
(90) 
_{Sep}
(65) 
_{Oct}
(80) 
_{Nov}
(90) 
_{Dec}
(95) 
2005 
_{Jan}
(63) 
_{Feb}
(106) 
_{Mar}
(105) 
_{Apr}
(90) 
_{May}
(99) 
_{Jun}
(96) 
_{Jul}
(197) 
_{Aug}
(144) 
_{Sep}
(128) 
_{Oct}
(123) 
_{Nov}
(232) 
_{Dec}
(153) 
2006 
_{Jan}
(210) 
_{Feb}
(69) 
_{Mar}
(37) 
_{Apr}
(74) 
_{May}
(123) 
_{Jun}
(51) 
_{Jul}
(91) 
_{Aug}
(25) 
_{Sep}
(98) 
_{Oct}
(98) 
_{Nov}
(87) 
_{Dec}
(33) 
2007 
_{Jan}
(43) 
_{Feb}
(41) 
_{Mar}
(27) 
_{Apr}
(18) 
_{May}
(20) 
_{Jun}
(18) 
_{Jul}
(35) 
_{Aug}
(35) 
_{Sep}
(21) 
_{Oct}
(75) 
_{Nov}
(41) 
_{Dec}
(28) 
2008 
_{Jan}
(34) 
_{Feb}
(28) 
_{Mar}
(33) 
_{Apr}
(26) 
_{May}
(45) 
_{Jun}
(35) 
_{Jul}
(36) 
_{Aug}
(32) 
_{Sep}
(87) 
_{Oct}
(70) 
_{Nov}
(98) 
_{Dec}
(96) 
2009 
_{Jan}
(94) 
_{Feb}
(79) 
_{Mar}
(9) 
_{Apr}
(10) 
_{May}
(5) 
_{Jun}
(54) 
_{Jul}
(49) 
_{Aug}
(65) 
_{Sep}
(61) 
_{Oct}
(16) 
_{Nov}
(61) 
_{Dec}
(70) 
2010 
_{Jan}
(2) 
_{Feb}
(67) 
_{Mar}
(8) 
_{Apr}
(30) 
_{May}
(19) 
_{Jun}
(2) 
_{Jul}
(17) 
_{Aug}
(30) 
_{Sep}
(23) 
_{Oct}
(20) 
_{Nov}
(47) 
_{Dec}
(12) 
2011 
_{Jan}
(44) 
_{Feb}
(46) 
_{Mar}
(20) 
_{Apr}
(74) 
_{May}
(35) 
_{Jun}
(37) 
_{Jul}
(5) 
_{Aug}
(14) 
_{Sep}

_{Oct}
(8) 
_{Nov}
(6) 
_{Dec}
(1) 
2012 
_{Jan}
(18) 
_{Feb}
(12) 
_{Mar}
(22) 
_{Apr}
(6) 
_{May}
(16) 
_{Jun}
(17) 
_{Jul}
(10) 
_{Aug}
(13) 
_{Sep}
(2) 
_{Oct}
(8) 
_{Nov}
(10) 
_{Dec}
(1) 
2013 
_{Jan}
(19) 
_{Feb}
(14) 
_{Mar}
(12) 
_{Apr}
(3) 
_{May}
(33) 
_{Jun}
(12) 
_{Jul}
(20) 
_{Aug}
(5) 
_{Sep}
(5) 
_{Oct}
(17) 
_{Nov}
(15) 
_{Dec}
(4) 
2014 
_{Jan}
(8) 
_{Feb}
(4) 
_{Mar}
(17) 
_{Apr}

_{May}
(16) 
_{Jun}
(10) 
_{Jul}
(7) 
_{Aug}

_{Sep}
(1) 
_{Oct}
(25) 
_{Nov}
(6) 
_{Dec}
(1) 
2015 
_{Jan}
(1) 
_{Feb}
(3) 
_{Mar}
(9) 
_{Apr}
(1) 
_{May}
(8) 
_{Jun}

_{Jul}
(16) 
_{Aug}
(13) 
_{Sep}

_{Oct}
(44) 
_{Nov}
(1) 
_{Dec}
(4) 
2016 
_{Jan}
(1) 
_{Feb}
(1) 
_{Mar}

_{Apr}
(3) 
_{May}

_{Jun}
(8) 
_{Jul}

_{Aug}

_{Sep}

_{Oct}

_{Nov}

_{Dec}

S  M  T  W  T  F  S 



1
(6) 
2
(5) 
3
(5) 
4
(1) 
5

6
(1) 
7
(4) 
8
(10) 
9
(2) 
10
(5) 
11
(2) 
12
(1) 
13
(1) 
14
(4) 
15

16

17
(2) 
18
(1) 
19

20
(2) 
21

22
(1) 
23

24
(1) 
25

26

27

28

29

30
(2) 
31



From: Pascal Bourguignon <pascal@af...>  20030717 14:24:46

lin8080 wrote: > >Kaz Kylheku schrieb: > > > >This is what HyperSpec says in section SQRT, ISQRT (file >/body/fun_sqrtcm_isqrt.html.) "... if the number is not a complex but is >negative, then the result is a complex" (12.1. ff). This case seems to >be clear. > >The mathematicans also say that a negativ sqrt is complex (right?), but >the same mathematicans say that (sqrt) is the reverse function of (* >zahl zahl) (which will returned only positiv numbers) and they also >describe for what kind of numbers this is valid. > You have to take into account the domain of the function. To take the reverse function, you must consider the function only on a subdomain where it's a bijection. For example, if you consider: f : ]infinity, 0] > [0, +infinity[ x > x*x then the reverse is: f^1 : [0, +infinity[ > ]infinity, 0] x >  sqrt(x) Note that this other function: g : [0, +infinity[ > [0, +infinity[ x > x*x which looks a lot like f, has not the same reverse function! And of course, a function square : R > R, x > x*x is not a bijection, so it has no reverse. So you see, you cannot expect the operators implemented in Lisp to correspond to the mathematical function you're manipulating. In maths, there are a lot of square root function, all defined on a different domain, and with a different image set. In computer languages we choose to implement one specific function, with a domain and image set considered useful. Since Lisp knows about complex, it naturally defines sqrt over the complexes and returns a complex (unless the imaginary part is null, in which case it's a real). > > >The practical reason why there is +, in trigononic functions, is to say >where the point of the graph is in the xysystem. And for that no >complex is needed, only 2 values. > >So the question should be: is there a way to suppress the complex number >representation in negative trigonomic values, when a sqrt is involved? > Yes, define properly your functions, and implement them accordingly. (defun mysquareoverRplus (x) (assert (and (realp x) (<= 0 x))) (* x x)) (defun mysquarerootoverRplus (x) (assert (and (realp x) (<= 0 x))) (sqrt x))  __Pascal Bourguignon__ mailto:pascal@... mailto:pjb@... 
From: lin8080 <lin8080@fr...>  20030717 06:52:35

Kaz Kylheku schrieb: > On Mon, 14 Jul 2003, lin8080 wrote: > > Now, when I type in (rechne (sin 30)) it returns some numbers in the way > > like complex numbers are shown. And I think there is something going > > wrong ... > Radians are units based on the idea that the radius of a circle > represents one unit going around the circle. Hence there are (* 2 pi) > radians to 360 degrees, and 30 degrees is (/ pi 6) radians or > about 0.524. Yes, I know. I normaly use 57.3 to transform Grad in Radians. (x[rad] = x * 57.3 [grad], y[grad] = y / 57.3 [rad]). Doing so, I get other results (sin (/ 30 57.3)) vs (sin 30). > The reason some numbers coming out of your program are shown in complex > notation is because they really *are* complex. The value of (sin 30) is > approx 0.988. The square root of that is a negative number. This is what HyperSpec says in section SQRT, ISQRT (file /body/fun_sqrtcm_isqrt.html.) "... if the number is not a complex but is negative, then the result is a complex" (12.1. ff). This case seems to be clear. The mathematicans also say that a negativ sqrt is complex (right?), but the same mathematicans say that (sqrt) is the reverse function of (* zahl zahl) (which will returned only positiv numbers) and they also describe for what kind of numbers this is valid. The practical reason why there is +, in trigononic functions, is to say where the point of the graph is in the xysystem. And for that no complex is needed, only 2 values. So the question should be: is there a way to suppress the complex number representation in negative trigonomic values, when a sqrt is involved? > In some programming languages, taking the square root of a negative > number triggers an error. Lisp is different and better; it produces a > complex number. This is one of the advantages of dynamic typing. Yes, right. I also see simple 0 instead of an error (some small schemelisps). > > (setq rechen (makearray '(9 3))) > This works as casual use in CLISP and other Lisp implementations, but > in serious Lisp programs you should use DEFVAR, DEFPARAMETER for > defining global variables. > It's not welldefined behavior to SETQ or SETF a symbol which has no > previously defined variable binding. Oh, this is more like my privat convention. For variables/symbols that will not change I use the old SETQ. The rest is SETF. And don't worry, this code will not find a way into a package. It is only a quick hack to see a series of digits is equal or not. The file names "zahl5.lsp" and is executed as needed with (load ".."). Only when playing around I realised the complex representation in trigonomic functions and I reported this, because it makes me wonder how to interpret complex (sin x) values and while there is a similar mail with maxima (sin x) here. stefan 