As for the question html( In which kind of school do they teach
$\\sqrt{-2.4995} = - i 1.58$ ??? );, I think any good school that teaches
about complex numbers should teach that both - i 1.58 and i 1.58
are equally valid (approximate) square roots of -2.4995. One choice is as
good as another. Any choice one makes on the whole complex plane involves
(at least) a branch cut, cutting up the complex plane from the origin
outwards. At the branch cut, the square root function is non-continuous, so
any floating point implementation will be erratic near the branch cut (like
Sage and C are around the negative real axis). If you want to make a choice
that is different from your computer programme (such as mapping all numbers
to numbers with non-negative imaginary part), you will have to add a few
lines to the square root code that check the imaginary part of the output
and change the sign of the number if necessary.
2013/5/13 man...@gmx.net
Could anyone shed a bit of light on this?
The more I try, the more SAGE's types get in my way. It turns out to be
an unpredictable element. Unless I make sure *every* involved function
really returns one specific type, calculations are becoming practically
impossible, because the results are completely random (malfunctions).
Here is just the last and most annoying of my encounters I can't make
heads or tails of, enjoy:
http://alpha.sagenb.org/home/pub/701/
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