Sorry, Carl, it's
http://www.billp.org/Fermat_1729.sws
Here's my transcript of the notebook for David. Firefox wouldn't let
me copy/paste from the notebook!
Ended up pressing the 'print' link, then doing File/save-as on that
and then editing out
all the HTML junk.
----------------------------
# We consider a curve x^3+y^3=m
# This can be transformed into Y^2 = X^3 - 432 * m^2
# So for the Taxicab problem, we have m=1729
#
{{{
m = 1729
E=EllipticCurve([0,-432*m^2]);
|
Elliptic Curve defined by y^2 = x^3 - 1291438512 over Rational Field
}}}
{{{
# transforming points using X=12*m/x+y, Y=36*m*(x-y)/(x+y)
# define map and inverse functions
def mymap(x,y):
return (12*m/(x+y), 36*m*(x-y)/(x+y))
# To invert the transformation we use
# x=(36*m + Y)/(6 * X), y = (36*m - Y)/(6 * X)
def unmap(p):
x, y = p
return ((36*m + y)/(6*x), (36*m - y)/(6*x))
|
}}}
# Taking point (12,1)
PP = E(mymap(12,1)); P=PP.xy(); P
|
(1596, 52668)
}}}
{{{
# Taking point (10,9)
QQ = E(mymap(10,9)); Q=QQ.xy(); Q
|
(1092, 3276)
}}}
{{{
R = PP+QQ; R = unmap(R.xy()); R
|
(-37/3, 46/3)
}}}
{{{
S = PP-QQ; S = unmap(S.xy()); S
|
(-397/26, 453/26)
}}}
{{{
T = QQ-PP; T = unmap(T.xy()); T
|
(453/26, -397/26)
}}}
{{{
U=-PP-QQ; U = unmap(U.xy()); U
|
(46/3, -37/3)
}}}
{{{
def sgn(x):
if x < 0:
return -1
return 1
def f(x):
y = 1729 - x^3
return sgn(y) * abs(y)^(1/3)
def line(p,q,x):
x1,y1=p
x2,y2=q
return (x-x1) * (y2-y1)/(x2-x1)
t = (1729/2)^(1/3)
}}}
{{{
c = parametric_plot((x,f(x)),-15,t)
d = parametric_plot((f(x),x),-15,t)
e = parametric_plot((x,line((12,1),(10,9),x)),9,15)
f = parametric_plot((x,line((12,1),(9,10),x)),8,18)
|
Exception (click to the left for traceback): d =
parametric_plot((f(x),x),-15,t)
...
TypeError: 'Graphics' object is not callable
}}}
{{{
g = (c+d+e+f)
g.set_aspect_ratio(1)
g.show()
}}}
(Oh, and the print window shows the graph, but it doesn't get printed)
Bill
On Feb 16, 2:46 pm, Carl Witty <[EMAIL PROTECTED]> wrote:
> On Feb 12, 3:47 am, "bill.p" <[EMAIL PROTECTED]> wrote:
>
> > The Notebook is getting rather long now, so I've saved it to a file:
>
> > http://www.billp.org/Fermat-1729.sws
>
> When I try to download this, I get "ERROR 404: Not Found".
>
> Carl
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