       surprising comparison of Mathematica 5.2 and 7.0

• To: mathgroup at smc.vnet.net
• Subject: [mg111168] surprising comparison of Mathematica 5.2 and 7.0
• From: mathfanda <KKratky at seznam.cz>
• Date: Thu, 22 Jul 2010 05:44:42 -0400 (EDT)

```Dear Mathematica friends,

the following program runs 4.7 times faster and uses 22.7 times less
memory
in Mathematica 5.2 than in Mathematica 7.0.
Fortunately, it gives the same result.

ClearAll["Global`*"];
c = 2;
Table[
a = Sum[c[i] r^i,{i,1,n}] + O[r]^(n+1);
s = 4(1-1/(1+1/3+r-a*Cos[2t]))//Normal//TrigReduce;
Table [ b[2i]= Coefficient[s,Cos[2i*t]]/2,{i,n}];
b = s-2*Sum[b[2i]*Cos[2i*t],{i,n}]//Simplify;
b[x_?OddQ]=0;
m=Table[If[i==j,b-(n+1-i)^2,b[Abs[i-j]]],{i,2n+1},{j,2n+1}];
m=Simplify[m];
d=Det[m]+O[r]^(n+1)//Simplify//Normal;
c[n-1]=c[n-1]/.First[Solve[d==0,c[n-1]]];
,{n,3,5}];
Print[\$Version];
Print["c=",c];
Print["time=",TimeUsed[]];
Print["memory=",MaxMemoryUsed[]/2^20.," MB"];

Here are the results:

5.2 for Linux x86 (64 bit) (June 20, 2005)
38475
c=-(-----)
16384
time=0.98
memory=6.07137 MB

7.0 for Linux x86 (64-bit) (February 18, 2009)
38475
c=-(-----)
16384
time=4.61
memory=136.313 MB

The conclusion might be: do not uninstall Mathematica 5.2 yet :-)
Or am I wrong?

Pavel

```

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