--- In

primenumbers@yahoogroups.com, Edwin Clark <eclark@m...> wrote:

>

> Actually one can solve the system eqn with Maple (in two ways):

>

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Very perceptive Edwin. I didn't know we had any Maple users

in this group. You are correct that if you copy/paste the

following lines into a Maple worksheet:

c1:=a1*b1:

c2:=(a2+a1*b1+b2)*c1+1+(a2*a1*b1+1)*(a2*b2+1)*(a1*b1*b2+1):

c3:=(a2+a1*b1+b2)*c1*(1+(a2*a1*b1+1)*(a2*b2+1)*(a1*b1*b2+1)):

c4:=1+(a2*b1*a1*b2+1)*(a2*b1*c2+1)*(a1*b2*c2+1):

c5:=1+(a2*b2*c3+1)*(a2*b2*c4+1)*(c3*c4+1):

eqn := {a1+b1 = 1,

a2+a1*b1+b2+c1 = 1,

a2*b1+a1*b2+c2 = 1,

a2*b2+c3+c4 = 0,

c5 = 0}:

Sol:=msolve(eqn,2);

Maple provides the solutions immediately:

Sol := {a1 = 0, b1 = 1, a2 = 1, b2 = 0},

{a1 = 1, b1 = 0, a2 = 0, b2 = 1}

I should have used "msolve()" in my example instead of

"solve()." *However*, if you use the actual RSA-640 carry

definitions and equations (all 135MB of them!) instead of the

equations in this simple example, Maple's "msolve()" also fails.

If you don't include the carry definitions it fails immediately,

and if you include them it runs for awhile (hours) and then

terminates with an "Out of Memory" error while trying to expand

the carry definitions (if I recall correctly). If anyone wants

to try it themselves, you can download the carry definition file

(Carries.txt) and the equation file (equ.dat) as a single gzipped

tar file from:

http://snipurl.com/6uqu/rsa640.tar.gz
or as a Windows ZIP file from:

http://snipurl.com/6uqu/rsa640.zip
(They are both about 10MB in size)

To have Maple try to solve them, paste the following

into a Maple worksheet and execute it from the same directory

you unzipped "equ.dat" and "Carries.txt" into:

restart:

print("Reading Equations");

read "equ.dat":

print("Reading Carries");

read "Carries.txt":

print("Solving");

Sol:=msolve(equ,2);

Maybe it will work on a computer that's faster than

mine and has more RAM, but I doubt it. I have

an Athlon 1.1 GHz AMD processor with 1 GB RAM.

Ron Dotson

6/04/2004

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