CoCalc Public Fileselliptic.sagews
Author: Paul Zeitz
Views : 38
ec1=plot(sqrt(x^3+17),(x,-17^(1/3),5),aspect_ratio=1)
ec2=plot(-sqrt(x^3+17),(x,-17^(1/3),5),aspect_ratio=1)

pt = point((-1,4))
(ec1+ec2+pt).show()

def plus(p,q):
x1,y1 = p[0],p[1]
x2,y2 = q[0],q[1]
if p==q:  #compute 2p
m = (3*x1^2+4)/(2*y1)
b = y1-m*x1
x3= m^2-2*x1
y3= m*x3+b

else: #compute p+q
m=(y2-y1)/(x2-x1)
b= y1-m*x1
x3 = m^2-x1-x2
y3= m*x3+b
return (x3, -y3)

@interact
def _(u= input_box(1,width=12),
up=checkbox(),
lines=checkbox(False),
n=[1,2,3,4,5,6,7,8,9,10]):

if up:
v=sqrt(u^3+4*u)
else:
v=-sqrt(u^3+4*u)

#define the list of points to be generated
pt0 = (u,v)
allPoints = [pt0]
for _ in range(n):
lastPt=allPoints[-1]

allPoints.append(plus(pt0,lastPt))

ptsToPlot = point(allPoints)
linesToPlot=line(allPoints,color='red')
xmx=max([allPoints[i][0] for i in range(n+1)])
xmx=max(xmx,5)
ymx=max([allPoints[i][1] for i in range(n+1)])
ymx=max(ymx,10)
ec1=plot(sqrt(x^3+4*x),(x,0,xmx))
ec2=plot(-sqrt(x^3+4*x),(x,0,xmx))
print(float(xmx))
print(float(ymx))
print(allPoints)
if lines:
(ec1+ec2+ptsToPlot+linesToPlot).show(xmax=xmx)
else:
(ec1+ec2+ptsToPlot).show(xmax=xmx)











p2=point((9,3))

p2

mylist=[1,2,3]
max(6,8)

8
point([(1,1),(2,2)])


mylist[-1]

3


a,b=p1[0],p1[1]

a

9
b

3
@interact(layout={'top': [['f', 'color']],'left': [['axes'],['fill']],'bottom':[['zoom']]})
def _(f=input_box(x^2,width=20),
color=color_selector(widget='colorpicker', label="color"),
axes=True,
fill=True,
zoom=range_slider(-3,3, default=(-3,3))):
show(plot(f,(x,zoom[0], 4), color=color, axes=axes,fill=fill,xmax=3))





layout(??







@interact(layout={'top': [['a', 'b']], 'left': [['c']], 'right': [['d']]})
def _(a=input_box(x^2, width=12), b=(0..20), c=100, d=x+1):
html('')
show(a+b+c+d)




@interact
def _(m=('matrix', identity_matrix(5))):
print m.eigenvalues()
print m

line([(0,0),(1,1)])



z=6.001+ -17*I
n= 20000
s=0
for k in range(n):
s += (-1)^k/(z-k)
s

0.00985596612271962 + 0.0256688110729291*I