Re: Re: How to simplify to a result that is real
- To: mathgroup at smc.vnet.net
- Subject: [mg50788] Re: [mg50735] Re: How to simplify to a result that is real
- From: Richard Chen <richard at doubleprime.com>
- Date: Tue, 21 Sep 2004 03:49:05 -0400 (EDT)
- References: <cidt38$brv$1@smc.vnet.net> <200409180948.FAA00572@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I have seen quite a few responses here. I'll just Thank all of you with one response. I still feel that at this stage, simplifying expressions in mathematica is still a kind of art and requires intimate knowledge of how esoteric mathematica options work. For example, I just tried this technique on a problem which is essentially the same: ch = Integrate[1/(a + b Cos[t]), {t, 0, c}, Assumptions -> {a > b > 0, 0 < c < Pi}] FullSimplify[ComplexExpand[ch, TargetFunctions -> {Re, Im}], { a > b > 0, 0 < c < Pi}] This time, mathematica comes back with an expression involving ArcTan[u,v] which is just ArcTan[v/u], by direct inspection. So the 2 terms involving different ArcTan are actually the same. But I cannot easily make Mathematica to recognize that they are the same. Even if I use the rule ArcTan[u_,v_]->ArcTan[v/u] it still does not think the 2 expressions are the same. It is easier to simply copy and paste an anwser than manipulate mathematica to get a simpler result. Perhaps future versions of mathematica will be smarter and does not require as much intervention from the user. Thanks Richard On Sat, Sep 18, 2004 at 05:48:55AM -0400, Peter Valko wrote: > Richard Chen <richard at doubleprime.com> wrote in message news:<cidt38$brv$1 at smc.vnet.net>... > > The command: > > > > Integrate[1/(1 + e Cos[t]), {t, 0, a}, > > Assumptions -> {-1 < e < 1, 0 < a < Pi}] > > > > leads to a complex valued result. I could not make > > mathematica to render the result in a form that is > > purely real. ComplexExpand, Refine all do not seem to work. > > > > Does anyone know how to make mathematica to simplify this > > result into a real form? > > > > Thanks for any info. > > > > Richard > > > > Richard, > > I think this will work: > > > ch = Integrate[1/(1 + e Cos[t]), {t, 0, a}, Assumptions -> {-1 < e < > 1, 0 < a < Pi}] > > FullSimplify[ComplexExpand[ch, TargetFunctions -> {Re, Im}], {-1 < e < > 1, 0 < a < Pi}] > > > The result is > > (-2*ArcTan[((-1 + e)*Tan[a/2])/Sqrt[1 - e^2]])/Sqrt[1 - e^2] > > > Peter >
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- Re: How to simplify to a result that is real
- From: p-valko@tamu.edu (Peter Valko)
- Re: How to simplify to a result that is real