sorry, I just use the google groups interface, didn't realise that I
just can reply to a thread like an email.
I'll just try it with an attached .txt file.
/David
On Jan 28, 7:47 pm, William Stein <wst...@gmail.com> wrote:
> On Wed, Jan 28, 2009 at 9:05 AM, David Møller Hansen
>
>
>
> <da...@mollerhansen.com> wrote:
>
> > Hi
>
> > I've made an interact on elliptic curve point addition, see below.
> > When I run it in notebook() mode I get an error:
>
> > Traceback (click to the left for traceback)
> > ...
> > AttributeError: 'SymbolicEquation' object has no attribute
> > '_fast_float_'
>
> > It worked in sage 3.1.1. I can't figure out how to fix it. Help is
> > much appreciated since I want to add this to the wiki and my thesis
> > presentation.
>
> Hi,
>
> Even using "Show Original" the code below is too mangled by email to
> work. Try it? Pull up your sent email and paste the code into sage.
> You should send your code as an email attachment (e.g., a sws file, or
> just paste your code into a .txt file and attach), or post it online
> e.g., pastebin and post a link to that.
>
> William
>
>
>
> > ______________
>
> > def point_txt(P,name,rgbcolor):
> > if (P.xy()[1]) < 0:
> > r = text(name,[float(P.xy()[0]),float(P.xy()
> > [1])-1],rgbcolor=rgbcolor)
> > elif P.xy()[1] == 0:
> > r = text(name,[float(P.xy()[0]),float(P.xy()[1])
> > +1],rgbcolor=rgbcolor)
> > else:
> > r = text(name,[float(P.xy()[0]),float(P.xy()[1])
> > +1],rgbcolor=rgbcolor)
> > return r
>
> > E = EllipticCurve('37a')
> > list_of_points = E.integral_points()
> > html("Graphical addition of two points $P$ and $Q$ on the curve $ E:
> > %s $"%latex(E))
> > @interact
> > def _(P=selector(list_of_points,label='Point P'),Q=selector
> > (list_of_points,label='Point Q'), marked_points = checkbox
> > (default=True,label = 'Points'), Lines = selector([0..2],nrows=1),
> > Axes=True):
> > curve = plot(E,rgbcolor = (0,0,1),xmin=25,xmax=25)
> > #Q = list_of_points[Q]
> > #P = list_of_points[P]
> > R = P + Q
> > Rneg = -R
> > #html("$P=(%s:%s:%s)$, $Q=(%s:%s:%s)$\n"%(latex(P[0]),latex(P
> > [1]),latex(P[2]),latex(Q[0]),latex(Q[1]),latex(Q[2])))
> > #html("Graphical addition of points $P$ and $Q$ \non the curve $ E:
> > %s $ \n\n$P + Q = (%s:%s:%s)$"%(latex(E),latex(R[0]),latex(R[1]),latex
> > (R[2]))) # $P + Q$ = $%s + %s = %s"%(P,Q,R)
> > l1 = line_from_curve_points(E,P,Q)
> > l2 = line_from_curve_points(E,R,Rneg,style='--')
> > p1 = point(P,rgbcolor=(1,0,0),pointsize=40)
> > p2 = plot(Q,rgbcolor=(1,0,0),pointsize=40)
> > p3 = plot(R,rgbcolor=(1,0,0),pointsize=40)
> > p4 = plot(Rneg,rgbcolor=(1,0,0),pointsize=40)
> > textp1 = point_txt(P,"$P$",rgbcolor=(0,0,0))
> > textp2 = point_txt(Q,"$Q$",rgbcolor=(0,0,0))
> > textp3 = point_txt(R,"$P+Q$",rgbcolor=(0,0,0))
> > if Lines==0:
> > g=curve
> > elif Lines ==1:
> > g=curve+l1
> > elif Lines == 2:
> > g=curve+l1+l2
> > if marked_points:
> > g=g+p1+p2+p3+p4
> > if P != Q:
> > g=g+textp1+textp2+textp3
> > else:
> > g=g+textp1+textp3
> > g.axes_range(xmin=-5,xmax=5,ymin=-13,ymax=13)
> > show(g,axes = Axes)
>
> > def line_from_curve_points(E,P,Q,style='-',rgb=(1,0,0),length=25):
> > """
> > P,Q two points on an elliptic curve.
> > Output is a graphic representation of the straight line intersecting
> > with P,Q.
> > """
> > # The function tangent to P=Q on E
> > if P == Q:
> > if P[2]==0:
> > return
> > line([(1,-length),(1,length)],linestyle=style,rgbcolor=rgb)
> > else:
> > # Compute slope of the curve E in P
> > l=-(3*P[0]^2 + 2*E.a2()*P[0] + E.a4() -
> > E.a1()*P[1])/((-2)*P[1] -
> > E.a1()*P[0] - E.a3())
> > f(x) = l * (x - P[0]) + P[1]
> > return
> > plot(f(x),-length,length,linestyle=style,rgbcolor=rgb)
> > # Trivial case of P != R where P=O or R=O then we get the vertical
> > line from the other point
> > elif P[2] == 0:
> > return line([(Q[0],-length),(Q
> > [0],length)],linestyle=style,rgbcolor=rgb)
> > elif Q[2] == 0:
> > return line([(P[0],-length),(P
> > [0],length)],linestyle=style,rgbcolor=rgb)
> > # Non trivial case where P != R
> > else:
> > # Case where x_1 = x_2 return vertical line evaluated in Q
> > if P[0] == Q[0]:
> > return line([(P[0],-length),(P
> > [0],length)],linestyle=style,rgbcolor=rgb)
>
> > #Case where x_1 != x_2 return line trough P,R evaluated in Q"
> > l=(Q[1]-P[1])/(Q[0]-P[0])
> > f(x) = l * (x - P[0]) + P[1]
> > return plot(f(x),-length,length,linestyle=style,rgbcolor=rgb)
>
> --
> William Stein
> Associate Professor of Mathematics
> University of Washingtonhttp://wstein.org
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