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[Axiom-mail] Ugly representation of square roots in console mode
From: |
Francois Maltey |
Subject: |
[Axiom-mail] Ugly representation of square roots in console mode |
Date: |
Sat, 24 May 2008 14:04:57 +0200 |
User-agent: |
Thunderbird 2.0.0.14 (X11/20080502) |
Dear Alasdair, and all !
you write you use root.
What roots do you use : from AlgebraicNumber, Expression or RealClosure.
Can you explain how you understand theses roots ?
I feel (but I can't be sure) that roots in algebraicNumber can be seen
as the FractionField over polynoms, with some bugs and inconsistencies.
realClosure only handles real roots, and positive root for even radix.
RCFI => RealClosureFractionInteger
(-2::RCFI)^(1/3) + (2::RCFI)^(1/2) --- is zero.
But there are also surprising results :
(4::RCFI)^(1/3) + (2::RFCI)^(2/3)
I can't get the numeric value, and this domain can't be use in
Expression Integer.
You find some don't so funny results in :
http://axiom-wiki.newsynthesis.org/285EqualInAlgebraicNumberFails
Other CAS compute over usual complex roots with the first positive argument.
(-1)^(1/2) = e^(%i*%pi)^(1/2) = e^(%i*%pi/2) = %i.
What roots do you use with your students ? What point of view do you
explain ?
The only sens my students have about root is the real root,
they learn the complex ones, but I can't expose AlgebraicNumber.
The exercice I like to solve with axiom :
P(z)=z^4 + 2*m*z^2 + 1, with m real.
solve P(z)=0, (with 4 radix expressions)
find limits for the 4 expressions when m is near of +/-1 or +/-%infinity
and plot with 4 colors the 4 roots. You get a circle and the 2 axes.
You may change z^4 and z^2 by z^6 and z^3, and +1 by -1, for other
pretty plots.
François
Have a nice day !
F.