Plotting script for Programming Blockchain ch2

ECPlotting.py

# coding: utf-8

# In[81]:


#EC Addition Plot
import math
import numpy as np

class EC:
    def __init__(self, a, b, c, d):
        self.a = a
        self.b = b
        self.c = c
        self.d = d
    
    def yspace (self, xspace):
        ypos=[]
        yneg=[]
        xSpace=[]
        for x in xspace:
            exp = self.a*x**3 + self.b*x**2 + self.c*x + self.d
            if exp >= 0:
                ypos += [math.sqrt(exp)]
                yneg += [-math.sqrt(exp)]
                xSpace += [x]
        return [xSpace, ypos, yneg]
    
    def y (self, x):
        exp = self.a*x**3 + self.b*x**2 + self.c*x + self.d
        if exp >= 0:
            ypos = math.sqrt(exp)
            return ypos
        if exp < 0:
            return None
    
    def tangent (self, x):
        exp = self.a*x**3 + self.b*x**2 + self.c*x + self.d
        if exp > 0:
            ypos = math.sqrt(exp)
            m =(3 * x**2 + self.a) / (2 * ypos)
            return m
        if exp == 0:
            m = 'infinity'
            return m
            return m
        if exp < 0:
            return None        
    
    def add (self, x1, x2, y1_sign, y2_sign):
    #this requires numpy
        y1 = self.y(x1) * y1_sign
        y2 = self.y(x2) * y2_sign
        if y1 != None and y2 != None:
            
            if y1 == y2:
                if y1 == 'infinity':
                    return "Infinity, no intersection"
                else:    
                #tangent dy/dx=(3x2+a)/(2y)
                    #perhaps c, instead of a
                    m = (3*x1 **2 + self.c) / (2*y1)
                    #x3=s2-x1-x2
                    x3 = m**2 - 2*x1
                    #y3=-(s(x-x1)+y1)=s(x1-x3)-y1
                    y3 = m *(x1-x3)-y1
                    return [x3,y3]
            else:
                m = (y2-y1)/(x2-x1)
            print(m)
            #x3=s2-x1-x2
            x3 = m**2 - x1 - x2
            #y3=-(s(x-x1)+y1)=s(x1-x3)-y1
            y3 = m *(x1-x3)-y1
            return [x3,y3]
        
        else:
            return "point or points not on EC"

        
#define EC for BTC
secp256k1 = EC(1,0,0,7)

#define two EC points
x1 = -1
y1_sign = -1
y1 = secp256k1.y(x1) * y1_sign

x2 = -1
y2_sign = -1
y2 = secp256k1.y(x2) * y2_sign

#calculate result
xy3 = secp256k1.add(x1,x2,y1_sign,y2_sign)
x3 = xy3[0]
y3 = xy3[1]       
print(xy3[1])
print(secp256k1.y(x3))
    
#calculate plot x range
xmin = min([x1,x2,x3]) *1.5
xmax = max([x1,x2,x3]) *1.5

#Plot code below
import plotly.offline as py #no inline possible apparenly
import plotly.graph_objs as go
import numpy as np
import pandas as pd
import scipy

#define the range for the plot
x = np.linspace(-5,xmax,3000)
ypos=secp256k1.yspace(x)[1]
yneg=secp256k1.yspace(x)[2]
xplot = secp256k1.yspace(x)[0]

ySpacePos = go.Scatter(
    x=xplot,
    y=ypos,
    mode='lines',
    name='f(x)',
    marker=dict(
        color='rgb(220, 20, 60)'
    )
)

ySpaceNeg = go.Scatter(
    x=xplot,
    y=yneg,
    mode='lines',
    name='f(x)',
    marker=dict(
        color='rgb(220, 20, 60)'
    )
)

x1x2Line = go.Scatter(
    x=[x1,x2,x3],
    y=[y1,y2,-y3],
    mode='lines',
    name='P1, P2, P3',
    marker=dict(color='rgb(0, 0, 0)')
)

x3Line = go.Scatter(
    x=[x3,x3],
    y=[y3,-y3],
    mode='lines',
    name='P3-Vertical',
    marker=dict(color='rgb(0, 0, 0)')
)   

Points = go.Scatter(
    x = [x1,x2,x3],
    y = [y1,y2,y3],
    mode='markers+text',
    name='Markers and Text',
    text=['P1=P2', '', 'P1+P2'],
    textposition='right',
    marker = dict(
        size = 10,
        color = 'rgba(100, 182, 193, .9)'
    )
)

layout = go.Layout(showlegend=False)
#fig = go.Figure(data=[ySpacePos,ySpaceNeg,Points,x1x2Line,x3Line], layout=layout)
fig = go.Figure(data=[ySpacePos,ySpaceNeg], layout=layout)
py.offline.plot(fig, filename='ECADDplot.html')


# In[77]:


#EC Plot

#Plotting EC Curve
import math
import numpy as np

class EC:
    def __init__(self, a, b, c, d):
        self.a = a
        self.b = b
        self.c = c
        self.d = d
    
    def yspace (self, xspace):
        ypos=[]
        yneg=[]
        xSpace=[]
        for x in xspace:
            exp = self.a*x**3 + self.b*x**2 + self.c*x + self.d
            if exp >= 0:
                ypos += [math.sqrt(exp)]
                yneg += [-math.sqrt(exp)]
                xSpace += [x]
        return [xSpace, ypos, yneg]
    
    def y (self, x):
        exp = self.a*x**3 + self.b*x**2 + self.c*x + self.d
        if exp >= 0:
            ypos = math.sqrt(exp)
            return ypos
        if exp < 0:
            return None
    
    def tangent (self, x):
        exp = self.a*x**3 + self.b*x**2 + self.c*x + self.d
        if exp > 0:
            ypos = math.sqrt(exp)
            m =(3 * x**2 + self.a) / (2 * ypos)
            return m
        if exp == 0:
            m = 'infinity'
            return m
            return m
        if exp < 0:
            return None        
    
    def add (self, x1, x2, y1_sign, y2_sign):
    #this requires numpy
        y1 = self.y(x1) * y1_sign
        y2 = self.y(x2) * y2_sign
        if y1 != None and y2 != None:
            
            if y1 == y2:
                if y1 == 'infinity':
                    return "Infinity, no intersection"
                else:    
                #tangent dy/dx=(3x2+a)/(2y)
                    m = (3*x1 **2 + self.a) / (2*y1)
                    #x3=s2-x1-x2
                    x3 = m**2 - 2*x1
                    #y3=-(s(x-x1)+y1)=s(x1-x3)-y1
                    y3 = m *(x1-x3)-y1
                    return [x3,y3]
            else:
                m = (y2-y1)/(x2-x1)
            
            #x3=s2-x1-x2
            x3 = m**2 - x1 - x2
            #y3=-(s(x-x1)+y1)=s(x1-x3)-y1
            y3 = m *(x1-x3)-y1
            return [x3,y3]
        
        else:
            return "point or points not on EC"

        
#define EC for BTC
#ECInstance = EC(1,0,0,7)
#disjoint example
#ECInstance = EC(1,0,-4,0)
#Another example
ECInstance = EC(1,0,-3,3)

#Plot code below
import plotly.offline as py #no inline possible apparenly
import plotly.graph_objs as go
import numpy as np
import pandas as pd
import scipy

#define the range for the plot
x = np.linspace(-5,14,3000)
ypos=ECInstance.yspace(x)[1]
yneg=ECInstance.yspace(x)[2]
xplot = ECInstance.yspace(x)[0]

ySpacePos = go.Scatter(
    x=xplot,
    y=ypos,
    mode='lines',
    name='f(x)',
    marker=dict(
        color='rgb(220, 20, 60)'
    )
)

ySpaceNeg = go.Scatter(
    x=xplot,
    y=yneg,
    mode='lines',
    name='f(x)',
    marker=dict(
        color='rgb(220, 20, 60)'
    )
)

layout = go.Layout(showlegend=False)
fig = go.Figure(data=[ySpacePos,ySpaceNeg], layout=layout)
py.offline.plot(fig, filename='ECplot.html')


# In[78]:


#Linear Plot
#Plot code below
import plotly.offline as py #no inline possible apparenly
import plotly.graph_objs as go
import numpy as np
import pandas as pd
import scipy

#define the range for the plot
x = np.linspace(-7,7,3000)
m = 0.7
b = 4
y = x * a + b

yData = go.Scatter(
    x=x,
    y=y,
    mode='lines',
    name='f(x)',
    marker=dict(
        color='rgb(220, 20, 60)'
    )
)
layout = go.Layout(showlegend=False)
fig = go.Figure(data=[yData], layout=layout)
py.offline.plot(fig, filename='linear.html')


# In[57]:


#Quadratic Plot
#Plot code below
import plotly.offline as py #no inline possible apparenly
import plotly.graph_objs as go
import numpy as np
import pandas as pd
import scipy

#define the range for the plot
x = np.linspace(-10,10,3000)
m = 1
a = 1
b = 0
c = 3

y = x**2 * a + x *b + c
yData = go.Scatter(
    x=x,
    y=y,
    mode='lines',
    name='f(x)',
    marker=dict(
        color='rgb(220, 20, 60)'
    )
)
layout = go.Layout(showlegend=False)
fig = go.Figure(data=[yData], layout=layout)
py.offline.plot(fig, filename='quadratic.html')


# In[ ]:


#Quadratic Plot
#Plot code below
import plotly.offline as py #no inline possible apparenly
import plotly.graph_objs as go
import numpy as np
import pandas as pd
import scipy

#define the range for the plot
x = np.linspace(-10,10,3000)
a = 1
b = 0
c = 0
y = x**2 * a + x *b + c
yData = go.Scatter(
    x=x,
    y=y,
    mode='lines',
    name='f(x)',
    marker=dict(
        color='rgb(220, 20, 60)'
    )
)
layout = go.Layout(showlegend=False)
fig = go.Figure(data=[yData], layout=layout)
py.offline.plot(fig, filename='quadratic.html')



# In[60]:


#Cubic Plot
#Plot code below
import plotly.offline as py #no inline possible apparenly
import plotly.graph_objs as go
import numpy as np
import pandas as pd
import scipy

#define the range for the plot
x = np.linspace(-10,10,3000)
a = 1
b = 2
c = 1
d = 200

y = x**3 * a + x**2 *b + x * c + d
yData = go.Scatter(
    x=x,
    y=y,
    mode='lines',
    name='f(x)',
    marker=dict(
        color='rgb(220, 20, 60)'
    )
)
layout = go.Layout(showlegend=False)
fig = go.Figure(data=[yData], layout=layout)
py.offline.plot(fig, filename='cubic.html')