Re: Maintaining the order of terms when adding symbolic expressions
- To: mathgroup at smc.vnet.net
- Subject: [mg118901] Re: Maintaining the order of terms when adding symbolic expressions
- From: Ray Koopman <koopman at sfu.ca>
- Date: Sun, 15 May 2011 07:03:55 -0400 (EDT)
- References: <iql9ta$9t2$1@smc.vnet.net>
On May 14, 12:10 am, Andrew DeYoung <adeyo... at andrew.cmu.edu> wrote:
> Hi,
>
> I am writing a function that will print a list of displacements:
>
> tlist = Range[1, 41];
> Do[
> numlist = {};
> dt = m;
> k = First[tlist];
> While[k + dt <= Last[tlist],
> AppendTo[numlist, r[i, k + dt] - r[i, k]];
> k++;
> ]
> Print[numlist],
> {m, 0, 5}]
>
> where r is an undefined function that determines the position vector
> of particle i (the first argument) at the time given by the second
> argument.
>
> In the output, I get lists like the following:
>
> {-r[i,1]+r[i,2],-r[i,2]+r[i,3],-r[i,3]+r[i,4],-r[i,4]+r[i,5],-r[i,
> 5]+r[i,6],-r[i,6]+r[i,7], ... }
>
> Notice how it places the subtracted term first; for example, it prints
> "-r[i,1]+r[i,2]" instead of "r[i,2]-r[i,1]". Of course, addition is
> commutative. Still, for the presentation/report I am trying to make,
> for pedagogical clarity I would prefer that Mathematica keep the order
> of terms exactly how I have specified it in my line of code:
>
> AppendTo[numlist, r[i, k + dt] - r[i, k]];
>
> Is there any way that I can maintain this ordering in the output? It
> seems that I need something like "hold" or similar. So, I tried the
> following:
>
> AppendTo[numlist, Hold[r[i, k + dt] - r[i, k]]];
>
> But then this strictly holds everything and prevents r[i, k + dt] -
> r[i, k] to be evaluated at the various values of k and dt. In other
> words, I get output like this:
>
> {Hold[r[i,k+dt]-r[i,k]],Hold[r[i,k+dt]-r[i,k]],Hold[r[i,k+dt]-
> r[i,k]],Hold[r[i,k+dt]-r[i,k]], ... }
>
> which is not what I would like; I would like the expression to be
> evaluated at the various values of k and dt, but just with the order
> terms held fixed.
>
> I also tried HoldForm:
>
> AppendTo[numlist, HoldForm[r[i, k + dt] - r[i, k]]];
>
> But this also does not allow the expression be evaluated at the
> various values of k and dt:
>
> {r[i,k+dt]-r[i,k],r[i,k+dt]-r[i,k],r[i,k+dt]-r[i,k],r[i,k+dt]-
> r[i,k], ... }
>
> Do you have any ideas how I might be able to maintain the order of
> terms? (One note: while it would be very helpful if the order of
> terms were maintained AND the output kept in Mathematica format, it
> will be okay if the only way to accomplish the maintenance of ordering
> is by converting to a text format.)
>
> Many thanks for all your time and help! I really appreciate it.
>
> Sincerely,
>
> Andrew DeYoung
> Carnegie Mellon University
numlist = {-r[i,1]+r[i,2], -r[i,2]+r[i,3], -r[i,3]+r[i,4],
-r[i,4]+r[i,5], -r[i,5]+r[i,6], -r[i,6]+r[i,7]};
numlist /. -a_ + b_ -> HoldForm[b - a]
{r[i,2]-r[i,1], r[i,3]-r[i,2], r[i,4]-r[i,3],
r[i,5]-r[i,4], r[i,6]-r[i,5], r[i,7]-r[i,6]}