Ralf Hemmecke wrote:
>
> > I just commited fix for the bug to the repository, but note then
> > even with fix you may prefer to use 'sqrt(-1)' insted of '%i' in
> > rules, because '%i' does not match imaginary part of '2 + %i':
> > complex pattern matching considers '%i' and '2 + %i' to be to
> > distinct complex constants. OTOH 'sqrt(-1)' is considered "kernel"
> > and is matched separately form constants.
>
> My first thought about this problem was to replace %i by sqrt(-1) within
> the rule command. But then there would be two issues.
> 1) Probably small waste of time to scan the pattern and do the replacement.
> 2) The equation x^2+1 has two solutions %i and -%i. Everyone seems to
> believe that sqrt(-1)=%i, but in fact that choice is arbitrary. Is
> sqrt(-2 %i) equal to (1+%i) or to (-1+%i)? Maybe for sqrt(-1) FriCAS
> makes this fixed choice or maybe not. I haven't checked.
FriCAS treats '%i' and 'sqrt(-1)' as two almost unrelated things:
'%i' is just a constant from base ring, while 'sqrt(-1)' is
a kernel. So '%i*%i' gets passed to Complex and evaluated here.
OTOH 'sqrt(-1)' is an algebraic kernel and 'sqrt(-1)*sqrt(-1)'
is handled by Expression. One visible difference is type:
(3) -> exp(%i)
%i
(3) %e
Type: Expression(Complex(Integer))
(4) -> exp(sqrt(-1))
+---+
\|- 1
(4) %e
Type: Expression(Integer)
--
Waldek Hebisch
[email protected]
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