Re: Simplifying expression involving Log and I
- To: mathgroup at smc.vnet.net
- Subject: [mg38052] Re: Simplifying expression involving Log and I
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Thu, 28 Nov 2002 14:07:47 -0500 (EST)
- References: <arv2ai$ar4$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Andrzej, You write: > It seems related to the following behaviour, that certianly suggests a > bug: > > FullSimplify[ArcTan[x, y], {x > 0, y < 0}] > > ArcTan[x, y] > > > FullSimplify[ArcTan[2*x, 2*y], {x > 0, y < 0}] > > ArcTan[y/x] Both results are correct. The difference seems to be due to the complexity test used and, maybe, the order of simplification. FullSimplify[ArcTan[x, y], {x > 0, y < 0}, ComplexityFunction -> Length] ArcTan[y/x] -- Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "Andrzej Kozlowski" <andrzej at tuins.ac.jp> wrote in message news:arv2ai$ar4$1 at smc.vnet.net... > This will take you pretty close: > > FullSimplify[ComplexExpand[ > d*Pi + I*d*(Log[M] - 2*Log[(-I)*Sqrt[(M*r)/d] + > Sqrt[M - (M*r)/d]]), TargetFunctions -> {Re, Im}], > M > 0 && 0 < r < d] > > > d*(Pi + 2*ArcTan[Sqrt[M - (M*r)/d], -Sqrt[(M*r)/d]]) > > Still, there appears to be something missing among the rules > FullSimplify is applying. > It seems related to the following behaviour, that certianly suggests a > bug: > > FullSimplify[ArcTan[x, y], {x > 0, y < 0}] > > > ArcTan[x, y] > > > FullSimplify[ArcTan[2*x, 2*y], {x > 0, y < 0}] > > > ArcTan[y/x] > > On Monday, November 25, 2002, at 03:58 PM, Dave Snead wrote: > > > Hi, > > > > I'm trying to simplify (M, r, d are positive reals with r<d) > > d*Pi + I*d*(Log[M] - 2*Log[(-I)*Sqrt[(M*r)/d] + Sqrt[M - (M*r)/d]]) > > > > to > > > > 2*d*ArcCos[Sqrt[r/d]] > > > > I've tried applying > > > > FullSimplify[#,M>0 && 0<r<d]& > > > > and > > > > ExpToTrig > > > > but Mathematica won't get rid of the Log and the I and give me the > > ArcCos. > > > > Does anyone know which Mathematica functions to apply to my expression > > to > > give me the simplification I want? > > > > Thanks in advance. > > > > > > > > > > > > > > > Andrzej Kozlowski > Yokohama, Japan > http://www.mimuw.edu.pl/~akoz/ > http://platon.c.u-tokyo.ac.jp/andrzej/ > >