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Maintaining the order of terms when adding symbolic expressions

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  Maintaining the order of terms when adding symbolic expressions Andrew DeYoung <adeyoung@andrew.cmu.edu> - 2011-05-14 07:10 +0000
    Re: Maintaining the order of terms when adding symbolic expressions Ray Koopman <koopman@sfu.ca> - 2011-05-15 11:03 +0000
    Re: Maintaining the order of terms when adding symbolic expressions Peter Pein <petsie@dordos.net> - 2011-05-15 11:05 +0000
    Re: Maintaining the order of terms when adding symbolic expressions Peter Breitfeld <phbrf@t-online.de> - 2011-05-17 11:48 +0000

#2351 — Maintaining the order of terms when adding symbolic expressions

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

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#2387

On May 14, 12:10 am, Andrew DeYoung <adeyo...@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]}

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#2396

Am 14.05.2011 09:10, schrieb Andrew DeYoung:
> 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]];
> 
...

> Many thanks for all your time and help!  I really appreciate it.
> 
> Sincerely,
> 
> Andrew DeYoung
> Carnegie Mellon University
> 

Hi Andrew,

TraditionalForm does this. Replace  Print[numlist] by  Print[numlist //
TraditionalForm].

Peter

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#2430

You have two (maybe more) possibilities:

1. Replace Print[numlist] with Print[numlist//TraditionalForm].
2. If you don't want the output in TraditionalForm, you can use
   PolynomialForm instead, with Option TraditionalOrdering->True. I use to make
   this setting the default, because otherwise PolynomialForm seems to
   do nothing. 

   SetOptions[PolynomialForm,TraditionalOrder->True], then again:
   Print[numlist//PolynomialForm]

   But beware: PolynomialForm is a form similar to NumberForm,
   MatrixForm, etc, so can't be used for further calculations, compare

   expr = (Expand[(x - 2)^3]) // PolynomialForm
   expr^2 // Expand
   expr[[1]]^2 // Expand


//Peter   
   

Andrew DeYoung 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
>

-- 
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de

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