FW: dummy indices / variables
- To: mathgroup@smc.vnet.net
- Subject: [mg11212] FW: [mg11145] dummy indices / variables
- From: Ersek_Ted%PAX1A@mr.nawcad.navy.mil
- Date: Mon, 2 Mar 1998 23:11:04 -0500
Richard Easther wrote:
|
| ...... coming up with a method to let Mathematica recognize (and then
perform
| simplifications upon) equivalent expressions with dummy indices. |
| For instance,
|
| Sum[f[a],{a,1,m}] + Sum[f[b],{b,1,m}] // FullSimplify |
| does not recognise that the two sums are identical, and misses what
(to | a human being, at least!) is a trivial simplification. |
( sections deleted )
|
| PS If anyone is keeping track, I would add the ability to recognize |
dummy indices to the wish-list for the next version of mathematica! |
Consider the following.
In[1]:=
f[x_]:=If[Abs[x]<1,x+2,x+3]
g[x_]:=If[Abs[x]<1,-x+4,-x+5]
In[3]:=
(f[t]+g[t])//FullSimplify
Out[3]=
If[Abs[t]<1,t+2,t+3]+If[Abs[t]<1,-t+4,-t+5]
I am not surprised FullSimplify didn't simplify the line above, but the
expression in Out[3] is obviously equivalent to ( If[Abs[t]<1, 6,
8]
).
Including a rule under FullSimplify to make the simplification above
would be equally useful as the simplification on Richard's wish list.
We could also sit around for years making a very long list of
simplifications we want FullSimplify to handle. Before long the list
of rules used by FullSimplify would get so long it would run at a
snails pace using even the fastest workstation.
FullSimplify can take a very long time as it is. Adding more rules to
the list will make it take even longer, so Wolfram Research should
carefully weigh the pros and cons before giving FullSimplify more
knowledge.
Ted Ersek