BTW I run sage 3.2.3 on powerpc in mac os x 10.5
/David
On Jan 28, 6:05 pm, 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.
>
> ______________
>
> 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)
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