On Feb 12, 2:07 am, bill purvis <[EMAIL PROTECTED]> wrote:
> I wanted to make a plot of x^3+y^3=1729 (the well-known taxicab problem).
> I'm sure there are better ways of acieving this but I opted for a naive
> approach:
>
> {{{
> def sng(x):
> if x < 0:
> return -1
> return 1
>
> def f(x):
> y3 = 1729 - x^3
> return sgn(y3) * abs(y3)^(1/3)
>
> }}}
>
> {{{
> c = parametric_plot((x,f(x)),-15,15)
> c.show()
>
> }}}
>
> (I want to add other things to the plot).
> However, when I run this in the notebook, the plot has a cusp at x=12+
> and behaves as if the sgn(x) has been taken as +1. I tried evaluating
> f(x) at 12 and 13 and the result changes sign as I'd expect.
The problem is here:
sage: sgn(1729-x^3)
1
sage: 1729-x^3 < 0
1729 - x^3 < 0
sage: bool(1729-x^3 < 0)
False
You're applying the Python function f to the symbolic variable x,
which calls sgn(1729-x^3). Then sgn(x) checks whether 1729-x^3<0,
which is taken to mean "Can you prove that 1729-x^3 is always less
than 0"? Since the answer is no, sgn() returns 1.
The fix is easy: instead of passing the symbolic expression f(x) to
parametric_plot, pass the function f.
c = parametric_plot((x,f),-15,15)
Or even easier, there's no reason for this to be a parametric plot:
c = plot(f,-15,15)
As to whether there's a bug here... I don't know how to decide if any
of the above should count as a bug. (I use the symbolic part of Sage
very seldom.) If there is a bug, it may be difficult to fix. The
thing I can see to do would be to make bool(x<0) signal an error,
instead of just returning False; but I don't know how much that would
break.
Carl
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