Re: Re: canonical mathematical expression represenation?

*To*: mathgroup at smc.vnet.net*Subject*: [mg52548] Re: [mg52511] Re: [mg52484] canonical mathematical expression represenation?*From*: DrBob <drbob at bigfoot.com>*Date*: Wed, 1 Dec 2004 05:58:46 -0500 (EST)*References*: <200411301024.FAA01367@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

To use that kind of solution, you'd probably have to look at FullForm to decide what indices to use in MapAt. In this case, for instance: Sum[a^k,{k,0,M}]//FullForm Times[Power[Plus[-1,a],-1],Plus[-1,Power[a,Plus[1,M]]]] The denominator is Plus[-1,a] at position {1,1} in the expression, and the numerator is Plus[-1, Power[a, Plus[1, M]]] at position {2}. A more automatic but somewhat bulky option is: expr /. {Denominator[expr] -> -Denominator[expr], Numerator[expr] -> -Numerator[expr]} (1 - a^(1 + M))/(1 - a) Here's a simpler solution, though not as general: expr /. {-1 + x_ :> 1 - x} (1 - a^(1 + M))/(1 - a) And finally, try this one: expr /. {x_ + y_ /; x < 0 -> (-x) + (-y)} (1 - a^(1 + M))/(1 - a) That's less general than the Numerator/Denominator solution, but more general than the others. Bobby On Tue, 30 Nov 2004 05:24:27 -0500 (EST), David Park <djmp at earthlink.net> wrote: > > Yes it is annoying the way Mathematica tends to get the minus signs where we > would prefer not to have them. One way to fix this, in simple expressions at > least, is to Map Minus to the two factors you would wish to change. > > Sum[a^k, {k, 0, M}] > MapAt[Minus, %, {{1, 1}, {2}}] > (-1 + a^(1 + M))/(-1 + a) > (1 - a^(1 + M))/(1 - a) > > I find that it is almost always possible to manipulate expressions to the > form you want, textbook form say, but it is a bit of an art and sometimes > even I have to come to MathGroup to learn the trick. > > > David Park > djmp at earthlink.net > http://home.earthlink.net/~djmp/ > > From: nospam nospam [mailto:nospam_please at nospam.com] To: mathgroup at smc.vnet.net > > I noticed that Mathematica represents expressions with > some specific 'way' or order. > > For example, > > Sum[a^k, {k, 0, M}] > > gives > -1 + a^(1+M) > ------------- > -1 + a > > > How can I make it display the expression, in what I would consider > a more 'natural' way, as follows > > 1 - a^(1+M) > ------------- > 1 - a > > I am sure there is a way to do, and why do you think > Mathematica does it the way it does? what is the logic > of how it represents things? is there a command to convert > the first output to the second? I tried few commands, but > can not figure it out. > > thank you, > --nospam > > > > > > -- DrBob at bigfoot.com www.eclecticdreams.net