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As Prof Neubueser has not acknowledged my person-to-person reply to his =
forum message, I hope that I may post a farewell message.
1) Thank you Messrs. Joyner, Hibbard, and Linton for helpful replies.
2) To me, a group of size of 2^7 is large, as I thought I had made clear =
by declaring an interest in "groups with size 2^i *3^j up to 72 =
elements". I can now "formulate" most of the groups of interest to me =
apart from the uninteresting proliferation of groups of size 32 and 64.=20
3) As I only need GAP as a reference atlas for Cayley Tables, I shall =
guard my version with "AsSortedList".
4) The important paper by Formanek and Sibley, (identified by David =
Joyner, GAP forum 15 Aug) follows Dedekind & Frobenius in working with =
the INVERSE of the Cayley table (van der Waarden, History of Algebra, =
p224 et seq). This eliminates the key renormalization cases where one or =
more of the Cayley determinant factors take on the value of zero. =
Incidently, Real, Complex, Quaternion and Octonion algebras are =
degenerate because their tables have only one (repeated) factor - they =
cannot renormalize. =20
4) Prof Neubueser did not understand what I said about "renormalizing =
algebras"; perhaps because I have not published anything about them. I =
had hoped that Gap might provide a pre-publication critique of my work. =
I can e-mail a demonstration GAP session to anyone showing an interest.
5) The most important renormalizing algebras have multi-phase "Polar =
Duals" that cannot be handled as GAP rationals, but are easy in =
Mathematica. E-mail discussions with other Mathematica users will be =
welcomed.
Good-bye.
rogerberesford@supanet.com
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<DIV><FONT face=3DArial size=3D2>As Prof Neubueser has not acknowledged =
my=20
person-to-person reply to his forum message, I hope that I may post a =
farewell=20
message.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>1) Thank you Messrs. Joyner, =
Hibbard</FONT><FONT=20
face=3DArial size=3D2>, and Linton for helpful replies.</DIV>
<DIV>
<DIV><FONT face=3DArial size=3D2>2) To me, a group of size of 2^7 is =
</FONT>large,=20
as I thought I had made clear by declaring an interest in "groups =
with size=20
2^i *3^j up to 72 elements". I can now "formulate" most of the groups of =
interest to me apart from the uninteresting proliferation of groups of =
size 32=20
and 64. </DIV>
<DIV>3) As I only need GAP as a reference atlas for Cayley Tables, I =
shall guard=20
my version with "AsSortedList".</DIV>
<DIV>4) The important paper by Formanek and Sibley, (identified by David =
Joyner,=20
GAP forum 15 Aug) follows Dedekind & Frobenius in working with the =
INVERSE=20
of the Cayley table (van der Waarden, History of Algebra, p224 et seq). =
This=20
eliminates the key renormalization cases where one or more of the Cayley =
determinant factors take on the value of zero. Incidently, Real, =
Complex,=20
Quaternion and Octonion algebras are degenerate because their tables =
have only=20
one (repeated) factor - they cannot renormalize. </DIV>
<DIV></FONT><FONT face=3DArial size=3D2>4) Prof Neubueser did not =
understand what I=20
said about "renormalizing algebras"; perhaps because I have not =
published=20
anything about them. I had hoped that Gap might provide a =
pre-publication=20
critique of my work. I can e-mail a demonstration GAP session to anyone =
showing=20
an interest.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>5) The most important renormalizing =
algebras have=20
multi-phase "Polar Duals" that cannot be handled as GAP rationals, but =
are easy=20
in Mathematica. E-mail discussions with other Mathematica users will be=20
welcomed.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Good-bye.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2><A=20
href=3D"mailto:rogerberesford@supanet.com">rogerberesford@supanet.com</A>=
</FONT></DIV></DIV></BODY></HTML>
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