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## Re: [Axiom-developer] Bug in complexForm : complexForm(log(%i) - log(-%i

**From**: |
Martin Rubey |

**Subject**: |
Re: [Axiom-developer] Bug in complexForm : complexForm(log(%i) - log(-%i)) -> 0 |

**Date**: |
Wed, 19 Jan 2005 16:55:21 +0100 |

Dear Vladimir,
Vladimir Bondarenko writes:
>* AXIOM -> complexForm(log(%i) - log(-%i))*
>* *
>* 0*
could you please file this as a bug on issuetracker? The problem is in the
operation "argument":
(8) -> argument(%i)
%pi
(8) ---
2
Type: Expression Integer
(9) -> argument(-%i)
%pi
(9) ---
2
Type: Expression Integer
the latter should be -pi/2, of course. The problem is in gaussian.spad,
COMPCAT:
if R has TranscendentalFunctionCategory then
half := recip(2::R)::R
if R has RealNumberSystem then
atan2loc(y: R, x: R): R ==
pi1 := pi()$R
pi2 := pi1 * half
x = 0 => if y >= 0 then pi2 else -pi2
-- Atan in (-pi/2,pi/2]
theta := atan(y * recip(x)::R)
while theta <= -pi2 repeat theta := theta + pi1
while theta > pi2 repeat theta := theta - pi1
x >= 0 => theta -- I or IV
if y >= 0 then
theta + pi1 -- II
else
theta - pi1 -- III
argument x == atan2loc(imag x, real x)
else
-- Not ordered so dictate two quadrants
argument x ==
zero? real x => pi()$R * half
atan(imag(x) * recip(real x)::R)
so the problem occurs if R does not have "RealNumberSystem":
(15) -> argument(-%i*1.0)
(15) - 1.5707963267 948966192
since Float does have RNS, but INT does not. I'm not quite sure what the
condition should be. OrderedSet?
Martin