How do I really get rid of previous results?

• To: mathgroup at smc.vnet.net
• Subject: [mg29556] How do I really get rid of previous results?
• From: "Fred Simons" <f.h.simons at tue.nl>
• Date: Sun, 24 Jun 2001 22:10:14 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```When studying the very interesting approach of Adam Strzebonski to the
question raised by Maarten van den Burg of finding all real roots of an
equation, I ran into the following problem.

As done by Adam Strzebonski , I define a polynomial and a list of roots.

poly=x/20+Normal[Series[Cos[x],{x,0,100}]];
rts=Table[Root[poly,i],{i,14}];//Timing

{1.82 Second,Null}

Finding the numerical values of the elements of the list takes some time:

N[rts] // Timing

{27.9
Second,{-38.9752,-19.1433,-18.4538,-13.4028,-11.6152,-7.47114,-4.96317,-1.49
593,1.65357,4.48616,8.28087,10.446,14.984,16.324}}

I want to redo this computation.

ClearAll[poly, rts];Remove[poly, rts]

I redefine the polynomial and the table. Now the construction of the table
is more than three times as fast.

poly=x/20+Normal[Series[Cos[x],{x,0,100}]];
rts=Table[Root[poly,i],{i,14}];//Timing

{0.55 Second,Null}

And Mathematica still knows the values of my removed table:

N[rts] // Timing

{0.
Second,{-38.9752,-19.1433,-18.4538,-13.4028,-11.6152,-7.47114,-4.96317,-1.49
593,1.65357,4.48616,8.28087,10.446,14.984,16.324}}

It has nothing to do with the removal of the names, as we see by using
different names:

rts2=Table[Root[poly,i],{i,14}];//Timing

{0.55 Second,Null}

N[rts2] // Timing

{0.
Second,{-38.9752,-19.1433,-18.4538,-13.4028,-11.6152,-7.47114,-4.96317,-1.49
593,1.65357,4.48616,8.28087,10.446,14.984,16.324}}

What is going on here, and how do I avoid this behaviour?

Fred Simons
Eindhoven University of Technology

```

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