holomorphicFactorQuantTetra.sagews

# -*- coding: utf-8 -*-
"""
Created on Mon Feb 10 20:05:11 2014

@author: David Horgan
"""

from scipy.optimize import fsolve
import math



#scene.range = 10

#cylinder(pos=(0,0,0), radius=1.0,axis=(0,0,1), color=color.white)

#scene2 = display(title='Examples of Tetrahedrons',
    # x=0, y=0, width=600, height=600,
    # center=(0,0,0), background=(1,1,1))

#scene2.visible = True
#scene2.range = 10




#unit circle plot
C = circle((0,0), 1)





#input points from unit circle

p1=0.6
p2=0.7


#face1
a1=(((1 - p2**2)/(2*(1 + p1)))**(1/4), (1/2)*(p2 + 1)*((2*(1 + p1))/(1 - p2**2))**(1/4), 0)
a2=(((1 - p2**2)/(2*(1 + p1)))**(1/4),  (1/2)*(p2 - 1)*((2*(1 + p1))/(1 - p2**2))**(1/4), 0 )
a3=(((1/2)*( (1 + p1)**3)* (1 - p2**2))**(1/4),p2*((2*(1 + p1))/(1 - p2**2))**(1/4), sqrt(1 - p1**2)*((1 - p2**2)/(2*(1 + p1)))**(1/4) )
a=[a1,a2,a3]


#face2

b1=(0, 0, 0)
b2=(((1 - p2**2)/(2*(1 + p1)))**(1/4), (1/2)*(p2 - 1)*((2*(1 + p1))/(1 - p2**2))**(1/4), 0)
b3=(((1/2)*((1 + p1)**3)*(1 - p2**2))**(1/4),p2*((2*(1 + p1))/(1 - p2**2))**(1/4), sqrt(1-p1**2)*((1-p2**2)/(2*(1+p1)))**(1/4)  )
b=[b1,b2,b3]

#face3
c1=(0, 0, 0)
c2=( ((1 - p2**2)/(2*(1 + p1)))**(1/4), (1/2)*(p2 + 1)*((2*(1 + p1))/(1 - p2**2))**(1/4), 0)
c3=(((1/2)*((1 + p1)**3)*(1 - p2**2))**(1/4), p2*((2*(1 + p1))/(1 - p2**2))**(1/4),  sqrt(1 - p1**2)*((1 - p2**2)/(2*(1 + p1)))**(1/4) )
c=[c1,c2,c3]


#face4
d1=(0, 0, 0)
d2=(((1 - p2**2)/(2*(1 + p1)))**(1/4), (1/2)*(p2 + 1)*((2*(1 + p1))/(1 - p2**2))**(1/4), 0)
d3 =(((1 - p2**2)/(2*(1 + p1)))**(1/4), (1/2)*(p2 - 1)*((2*(1 + p1))/(1 - p2**2))**(1/4), 0)
d=[d1,d2,d3]

#printresults
print 'a1=', a1
print 'a2=', a2
print 'a3=', a3

print 'b1=', b1
print 'b2=', b2
print 'b3=', b3

print 'c1=', c1
print 'c2=', c2
print 'c3=', c3

print 'd1=', d1
print 'd2=', d2
print 'd3=', d3



G = Graphics()

#tetrahedron faces - coloured
P1=polygon([a1,a2, a3], color='red')
P2=polygon([b1,b2, b3],color='yellow')
P3=polygon([c1,c2, c3],color='blue')
P4=polygon([d1,d2, d3],color='green')

#polygon faces
#P1=polygon([a1,a2, a3])
#P2=polygon([b1,b2, b3])
#P3=polygon([c1,c2, c3])
#P4=polygon([d1,d2, d3])

#polygon([a1,a2, a3])
#polygon([b1,b2, b3])
#polygon([c1,c2, c3])
#polygon([d1,d2, d3])

g=G+P1+P2+P3+P4
show(g, title='tet(w)', viewer='tachyon')
show(C, title='w plane')

'\nCreated on Mon Feb 10 20:05:11 2014\n\n@author: David Horgan\n' a1= (0.631836992876155, 1.34528368801383, 0) a2= (0.631836992876155, -0.237403003767146, 0) a3= (1.01093918860185, 1.10788068424668, 0.505469594300924) b1= (0, 0, 0) b2= (0.631836992876155, -0.237403003767146, 0) b3= (1.01093918860185, 1.10788068424668, 0.505469594300924) c1= (0, 0, 0) c2= (0.631836992876155, 1.34528368801383, 0) c3= (1.01093918860185, 1.10788068424668, 0.505469594300924) d1= (0, 0, 0) d2= (0.631836992876155, 1.34528368801383, 0) d3= (0.631836992876155, -0.237403003767146, 0)