Bug#326720: carg(3) man page error
tags 326720 fixed-upstream thanks > Ramiro is right - that is, his text is much better than the > present text. However normalizations differ. > > It is true that tan(carg(z)) = cimag(z) / creal(z), > almost by definition. Taking atan() on both sides yields > atan(tan(carg(z))) = atan(cimag(z) / creal(z)) > but it is not precisely true that atan(tan(x)) = x. > The tan() function is periodic with period pi, and > atan() returns an answer in (-pi/2,pi/2], so atan(tan(x)) > returns the value that is congruent x mod pi and lies in > this interval. > In particular, atan(tan(carg(z))) returns a value that > is congruent carg(z) mod pi and lies in (-pi/2,pi/2]. > On the other hand, carg returns a value in [-pi,pi] > and if that return value does not lie in (-pi/2,pi/2] > then carg(z) and atan(cimag(z) / creal(z)) will differ by pi. > > In other words: you may write > "One has tan(carg(z)) = cimag(z) / creal(z)." Okay -- that is what will appear in man-pages-2.08 -- Michael Kerrisk maintainer of Linux man pages Sections 2, 3, 4, 5, and 7 Want to help with man page maintenance? Grab the latest tarball at ftp://ftp.win.tue.nl/pub/linux-local/manpages/ and grep the source files for 'FIXME'. -- To UNSUBSCRIBE, email to [EMAIL PROTECTED] with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED]
Bug#326720: carg(3) man page error
> > > Ramiro is right - that is, his text is much better than the > present text. However normalizations differ. > > It is true that tan(carg(z)) = cimag(z) / creal(z), > almost by definition. Taking atan() on both sides yields > atan(tan(carg(z))) = atan(cimag(z) / creal(z)) > but it is not precisely true that atan(tan(x)) = x. > The tan() function is periodic with period pi, and > atan() returns an answer in (-pi/2,pi/2], so atan(tan(x)) > returns the value that is congruent x mod pi and lies in > this interval. > In particular, atan(tan(carg(z))) returns a value that > is congruent carg(z) mod pi and lies in (-pi/2,pi/2]. > On the other hand, carg returns a value in [-pi,pi] > and if that return value does not lie in (-pi/2,pi/2] > then carg(z) and atan(cimag(z) / creal(z)) will differ by pi. > > In other words: you may write > "One has tan(carg(z)) = cimag(z) / creal(z)." > > Andries > > Hello Andries, your explanation is superb and very accurate. You are completely right. I never thought I could find a bug.;-) Free software and Debian are marvellous. Thank you very much. Ramiro. -- To UNSUBSCRIBE, email to [EMAIL PROTECTED] with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED]
Bug#326720: carg(3) man page error
On Mon, Sep 19, 2005 at 02:04:00PM +0200, Michael Kerrisk wrote: > Andries, > > Could you comment on the following please -- I don't remember > enough of my maths... > > Cheers, > > Michael Ramiro is right - that is, his text is much better than the present text. However normalizations differ. It is true that tan(carg(z)) = cimag(z) / creal(z), almost by definition. Taking atan() on both sides yields atan(tan(carg(z))) = atan(cimag(z) / creal(z)) but it is not precisely true that atan(tan(x)) = x. The tan() function is periodic with period pi, and atan() returns an answer in (-pi/2,pi/2], so atan(tan(x)) returns the value that is congruent x mod pi and lies in this interval. In particular, atan(tan(carg(z))) returns a value that is congruent carg(z) mod pi and lies in (-pi/2,pi/2]. On the other hand, carg returns a value in [-pi,pi] and if that return value does not lie in (-pi/2,pi/2] then carg(z) and atan(cimag(z) / creal(z)) will differ by pi. In other words: you may write "One has tan(carg(z)) = cimag(z) / creal(z)." Andries >> Von: Ramiro Aceves <[EMAIL PROTECTED]> >> An: [EMAIL PROTECTED] >> Betreff: Bug#326720: carg(3) man page error >> Datum: Mon, 05 Sep 2005 12:19:14 +0200 >> >> Package: manpages-dev >> Version: 1.70-1 >> >> There seems to be en error in carg(3) man page, DESCRIPTION chapter. >> >> "One has carg(z) = atan(creal(z) / cimag(z))" >> >> is wrong and should be : >> >> "One has carg(z) = atan(cimag(z) / creal(z))" >> >> Hope this helps. >> >> Thank you very much. >> >> Ramiro. -- To UNSUBSCRIBE, email to [EMAIL PROTECTED] with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED]
Bug#326720: carg(3) man page error
tags 326720 fixed-upstream thanks Hello Ramiro, [Original CC list restored...] > > Andries, > > > > Could you comment on the following please -- I don't remember > > enough of my maths... > > > > Cheers, > > > > Michael > > > Hello Michael, > > I am Ramiro. Yes, a complex number z has got two componets: a real part > (creal(z)) and an imaginary part (cimag(z)). I attach a home made ascii > drawing. > > > > imaginary axis > ^ > | >| > | *| > | *| > | z *| > | *|cimag(z) > | *| > | *| > |* \ angle=carg(z)| > ||_|_> real axis > creal(z) > > > Carg(z) is the angle between the complex number z and the real axis, > measured counterclockwise. > > tan(angle)= cimag(z)/creal(z) > > angle=carg(z)= atan(cimag(z)/creal(z)) > > Hope this helps. Pictures always help :-). When you put it like that, I'm convinced. I've changed the page as you suggest. The change will appear in man-pages-2.08. Cheers, Michael > >>--- Ursprüngliche Nachricht --- > >>Von: Ramiro Aceves <[EMAIL PROTECTED]> > >>An: [EMAIL PROTECTED] > >>Betreff: Bug#326720: carg(3) man page error > >>Datum: Mon, 05 Sep 2005 12:19:14 +0200 > >> > >>Package: manpages-dev > >>Version: 1.70-1 > >> > >>There seems to be en error in carg(3) man page, DESCRIPTION chapter. > >> > >>"One has carg(z) = atan(creal(z) / cimag(z))" > >> > >> is wrong and should be : > >> > >>"One has carg(z) = atan(cimag(z) / creal(z))" > >> > >>Hope this helps. > >> > >>Thank you very much. > >> > >>Ramiro. > >> > >> > > > > > -- Michael Kerrisk maintainer of Linux man pages Sections 2, 3, 4, 5, and 7 Want to help with man page maintenance? Grab the latest tarball at ftp://ftp.win.tue.nl/pub/linux-local/manpages/ and grep the source files for 'FIXME'. -- To UNSUBSCRIBE, email to [EMAIL PROTECTED] with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED]
Bug#326720: carg(3) man page error
Andries, Could you comment on the following please -- I don't remember enough of my maths... Cheers, Michael > --- Ursprüngliche Nachricht --- > Von: Ramiro Aceves <[EMAIL PROTECTED]> > An: [EMAIL PROTECTED] > Betreff: Bug#326720: carg(3) man page error > Datum: Mon, 05 Sep 2005 12:19:14 +0200 > > Package: manpages-dev > Version: 1.70-1 > > There seems to be en error in carg(3) man page, DESCRIPTION chapter. > > "One has carg(z) = atan(creal(z) / cimag(z))" > > is wrong and should be : > > "One has carg(z) = atan(cimag(z) / creal(z))" > > Hope this helps. > > Thank you very much. > > Ramiro. > > -- Michael Kerrisk maintainer of Linux man pages Sections 2, 3, 4, 5, and 7 Want to help with man page maintenance? Grab the latest tarball at ftp://ftp.win.tue.nl/pub/linux-local/manpages/ and grep the source files for 'FIXME'. -- To UNSUBSCRIBE, email to [EMAIL PROTECTED] with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED]
Bug#326720: carg(3) man page error
Package: manpages-dev Version: 1.70-1 There seems to be en error in carg(3) man page, DESCRIPTION chapter. "One has carg(z) = atan(creal(z) / cimag(z))" is wrong and should be : "One has carg(z) = atan(cimag(z) / creal(z))" Hope this helps. Thank you very much. Ramiro. -- To UNSUBSCRIBE, email to [EMAIL PROTECTED] with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED]
