Re: Re: Trigonometric simplification

*To*: mathgroup at smc.vnet.net*Subject*: [mg68929] Re: [mg68889] Re: [mg68838] Trigonometric simplification*From*: "Kai Gauer" <kai.g.gauer at gmail.com>*Date*: Wed, 23 Aug 2006 07:16:02 -0400 (EDT)*References*: <200608210727.DAA27449@smc.vnet.net> <200608220920.FAA26965@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

When Mathematica does its simplifications, is there a method to specify for a functional type of return value, rather than just an equation that matches the way that Mathematica returns its numerical sign choice approximations? ie is it possible to set up rules that FullSimplify can act on to try and write the result in the form: ((\[PlusMinus*1])*Cos[a])*Sin[a]^2, rather than the two distinct partial solutions which are given below? The answer in the above form would be a decent method of more efficient return for more general answers that I usually get when using Simplify, etc, and frequently come in pairs like this. However, I am uncertain of how to extend the \[PlusMinus] operator to be extensive enough to allow it to appear as a simplification tool. One idea that comes to mind is to write the above in the form of trying to return a similar idea to: Which[newSimplify[r], Pi/2 < a < 3*(Pi/2), newSimplify[r], -Pi/2 < a < Pi/2] -> Assuming[n \[Element] Integers, ((-1)^n)*Cos[a]*Sin[a]^2] (** untested syntax here - sorry... possibly someone can improve on it?! the idea being that Mathematica should try and take both solutions, and basically union them to look like one solution, subjected to the way that \[PlusMinus is extended to the Mathematica syntax of mathematical simplifications on operators such as Plus and Minus. I also had trouble deciding on whether to write the conditional as a Which, Switch or If type of conditional **), Here, I am guessing that Assuming[n \[Element] Integers, (\[PlusMinus*1])*Cos[a]*Sin[a]^2] would match something like the solution set {+Cos[a]*Sin[a]^2, -Cos[a]*Sin[a]^2} and at this point, I would be not so inclined on what the If-And-Only-If is that is imposed on n for Mathematica's choice of when to pick which function that it should use. Even better, it could even be useful to have an extended definition of n returned as a result that still would stay compatible witht the formula return values if n is not just in Integers, say Rationals or Complex, instead. For me however, such a tool would be beneficial, but not necessary. Does anyone have any packages to recommend that make this easier for the user? I would rather be able to relax the restraints on the interval conditions returned in such a solution than to try and constrain the number of (mostly failed) total simplification attempts as unattempted at Evaluated. This is because it is easier for the user to pick which interval the functional should be in, and, since humans think with human arithmetic rules rather than mathematica arithmetic tries, it would be sensible to allow for such an extension. Much of the time, my access is limited to version 3 syntax, but am wondering hether the latest versions would expect to have such a revised symbolic simplification syntax for regrouping solutions. On 8/22/06, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > > On 21 Aug 2006, at 09:27, carlos at colorado.edu wrote: > > > As an intermediate result of some calculations I have > > the expression > > > > r=Tan[a]^2/(Sec[a]^2)^(3/2) > > > > where a is real. How can I coerce Mathematica into > > simplifying that to > > > > r=Cos[a]*Sin[a]^2 > > > > Both Simplify and FullSimplify with assumptions on a > > fail to get the simpler form. > > > > I would not be very happy if Mathematica did what you seem to want it > to do only under the assumptions that a is real since: > > r = Tan[a]^2/(Sec[a]^2)^(3/2) > > > Assuming[Pi/2 < a < 3*(Pi/2), Simplify[r]] > > > (-Cos[a])*Sin[a]^2 > > On the other hand: > > > Assuming[-Pi/2 < a < Pi/2, Simplify[r]] > > > Cos[a]*Sin[a]^2 > > Andrzej Kozlowski

**Follow-Ups**:**Re: Re: Re: Trigonometric simplification***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**References**:**Trigonometric simplification***From:*carlos@colorado.edu

**Re: Trigonometric simplification***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>