This debate has been going on for as long as computers have been in
existence. Yes, there is a case to be made the odd roots of negative
reals should return a negative real instead of the principal complex
root. But that leads to more subtle problems in other places. If all
of mathematica,
On Thu, May 14, 2009 at 1:56 AM, Robert Bradshaw wrote:
On May 13, 2009, at 9:11 PM, Bill Page wrote:
On Wed, May 13, 2009 at 11:54 PM, Robert Bradshaw wrote:
This is because the branch in which the positive real root is real is
taken. We're opting for continuity and consistency with
On Thu, May 14, 2009 at 4:59 AM, John Cremona wrote:
This debate has been going on for as long as computers have been in
existence. Yes, there is a case to be made the odd roots of negative
reals should return a negative real instead of the principal complex
root. But that leads to more
Bill Page wrote:
On Thu, May 14, 2009 at 4:59 AM, John Cremona wrote:
This debate has been going on for as long as computers have been in
existence. Yes, there is a case to be made the odd roots of negative
reals should return a negative real instead of the principal complex
root. But that
On Thu, May 14, 2009 at 11:06 AM, Jason Grout wrote:
Bill Page wrote:
Consider the problem to define
f(x) = x^(1/3)
so that it takes the real branch for x 0. The best I have been able
to come up with so far is:
sage: f = lambda x:
Bill Page wrote:
On Thu, May 14, 2009 at 11:06 AM, Jason Grout wrote:
Bill Page wrote:
Consider the problem to define
f(x) = x^(1/3)
so that it takes the real branch for x 0. The best I have been able
to come up with so far is:
sage: f = lambda x:
On Thu, May 14, 2009 at 12:34 PM, Jason Grout wrote:
Bill Page wrote:
Ok thanks. I recall the discussion and I can indeed write:
sage: f=lambda x:RR(x).nth_root(3)
sage: f(-2.0)
-1.25992104989487
but I think I'll let my earlier comment stand:
I think there should be a more obvious way.
I like Jason's idea (specifically real_nth_root) as a method.
However, to me the real issue is plotting. If someone tries to get a
cube root of -1 and gets a complex number, at least they see there is
an output! And then someone can help them understand why they get
that answer.
But there is
On Wed, May 13, 2009 at 6:58 PM, Bill Page bill.p...@newsynthesis.org wrote:
Can someone explain this apparently inconsistent result?
It's just operator precedence:
sage: -(2.0^(1/3))
-1.25992104989487
sage: (-2.0)^(1/3)
0.629960524947437 + 1.09112363597172*I
--Mike
On Wed, May 13, 2009 at 10:46 PM, Mike Hansen wrote:
On Wed, May 13, 2009 at 6:58 PM, Bill Page wrote:
Can someone explain this apparently inconsistent result?
It's just operator precedence:
sage: -(2.0^(1/3))
-1.25992104989487
sage: (-2.0)^(1/3)
0.629960524947437 + 1.09112363597172*I
On Thu, May 14, 2009 at 1:19 PM, Bill Page bill.p...@newsynthesis.org wrote:
On Wed, May 13, 2009 at 10:46 PM, Mike Hansen wrote:
On Wed, May 13, 2009 at 6:58 PM, Bill Page wrote:
Can someone explain this apparently inconsistent result?
It's just operator precedence:
sage: -(2.0^(1/3))
On Wed, May 13, 2009 at 11:23 PM, Alex Ghitza wrote:
On Thu, May 14, 2009 at 1:19 PM, Bill Page wrote:
On Wed, May 13, 2009 at 10:46 PM, Mike Hansen wrote:
On Wed, May 13, 2009 at 6:58 PM, Bill Page wrote:
Can someone explain this apparently inconsistent result?
It's just operator
On May 13, 2009, at 8:49 PM, Bill Page wrote:
On Wed, May 13, 2009 at 11:23 PM, Alex Ghitza wrote:
On Thu, May 14, 2009 at 1:19 PM, Bill Page wrote:
On Wed, May 13, 2009 at 10:46 PM, Mike Hansen wrote:
On Wed, May 13, 2009 at 6:58 PM, Bill Page wrote:
Can someone explain this apparently
On Wed, May 13, 2009 at 11:54 PM, Robert Bradshaw wrote:
This is because the branch in which the positive real root is real is
taken. We're opting for continuity and consistency with complex numbers.
If I wrote:
sage: ComplexField(53)(-2.0)^(1/3)
0.629960524947437 + 1.09112363597172*I
that
On May 13, 2009, at 9:11 PM, Bill Page wrote:
On Wed, May 13, 2009 at 11:54 PM, Robert Bradshaw wrote:
This is because the branch in which the positive real root is real is
taken. We're opting for continuity and consistency with complex
numbers.
If I wrote:
sage:
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