Perry S. Glenn on Sun, 1 Jul 2001 14:55:59 -0700 (PDT) |
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Re Modulus a + b*I |
Hello, thank you for clearing that up for me I did mean abs(z)=sqrt(a^2+b^2). I see I was making assumptions about a and b, and I was not condsidering the validity of this for the general case. The PARI-GP is the best caculator I have come across and I am using it to extend my knowledge in mathematics. I am new to symbolic calculations but I'm interested in increasing my understanding of this and Number Theory. PARI-GP is a very nice tool for this end. Again, thank you very much for your quick response, and please excuse my bumbling. -PSGlenn On Sun, Jul 01, 2001 at 11:31:57AM +0200, Gerhard Niklasch wrote: > In response to: > > Message-ID: <20010701080627.73568.qmail@web13607.mail.yahoo.com> > > Date: Sun, 1 Jul 2001 01:06:27 -0700 (PDT) > > From: "Perry S. Glenn" <psglenn@yahoo.com> > > > I would expect to get the result > > > z=a+b*I > > abs(z)= a^2+b^2 > > I hope not! First, that would be the square of abs(z). Second, > even that only when it is known in advance that a and b stand > for real numbers -- which gp has no reason to assume. > > > ? z=a+I*b > > %1 = a + I*b > > ? abs(z) > > %2 = a + I*b > > As with many other functions, this got applied to each > coefficient of the multivariate polynomial. (The only > surprise here is that it left I alone, whereas abs(I) > returns 1.000000000000000000000000000 .) > > If you intend a and b to stand for real numbers, then > > (12:07) gp > norm(a+b*I) > %1 = a^2 + b^2 > > does what you seem to want: compute the square of the > absolute value. If a and b can themselves be complex > (or if they are indeterminates which can take values > in any old commutative ring containing something which > behaves like I), there is no simple formula - the answer > would depend both on the ring you're working in and on > the precise shape of a and b written as elements of that > ring. > > Enjoy, Gerhard --f61LtHN51936.994024517/big.psf.his.org-- __________________________________________________ Do You Yahoo!? Get personalized email addresses from Yahoo! Mail http://personal.mail.yahoo.com/