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== Quantum tetrahedron volume eigenvalues ==
by David Horgan.
Computes the volume eigenvalues of a quantum tetrahedron.

{{{#!sagecell

html('<h3>Quantum tetrahedron Volume Eigenvalue</h3>')
html('Enter the four J values into the input boxes')
html('k values k ranges from kmin to kmax in integer steps')
html('The dimension d of the Hilbert space H4, d = kmax - kmin + 1')
html('kmin = max(|j1-j2|,|j3 -j4|) kmax = min(j1+j2,j3 +j4)')
html('The the dimension of the hilbert space is given by d = kmax -kmin + 1')
html('V^2 =M = 2/9(real antisymmetrix matrix))')
html('Spins must satisfy (j1+j2)<= (j3+j4)')
html('Reference: Bohr-Sommerfeld Quantization of Space by Eugenio Bianchi and Hal M. Haggard ')






import numpy



@interact




def _(j1 = input_box(6.0, 'J1'),
      j2= input_box(6.0, 'J2'),
      j3= input_box(6.0, 'J3'),
      j4= input_box(7.0, 'J1'), auto_update=False):
    if (j1+j2)<= (j3+j4):
        html('<h3>Values of Volume Eigenvalue</h3>')
        kmin = int(max(abs(j1-j2),abs(j3 -j4)))
        kmax = int(min((j1+j2),(j3 +j4)))
        d = kmax -kmin + 1
        y=numpy.arange(kmin,kmax+1,1)
        kmatrix = matrix(CDF,int(d), int(d))
        r=list()
        for j in range(d):
            k=int(y[j])
            c1 = -i*k
            c2 = sqrt(4*k*k - 1)
            c3 = sqrt(j1*(j1+1))
            c4 = sqrt((2*j1+1))
            c5 = sqrt(j3*(j3+1))
            c6 = sqrt((2*j3+1))
            c7 = wigner_6j(j1,1,j1,k,j2,k-1)
            c8 = wigner_6j(j3,1,j3,k,j4,k-1)
            a = c1*c2*c3*c4*c5*c6*c7*c8
            r.append(a)
            q=numerical_approx(a, digits=10)
            #print r
        for j in range(d-1):
            kmatrix[[j],[j+1]]=r[j+1]
            kmatrix[[j+1],[j]]=-r[j+1]
            #print kmatrix
    
        M = (2/9)*kmatrix
        #print M
        s=M.eigenvalues()
        #print s
    
        for j in range(d):
            e= sqrt(s[j])
            if e.imag() ==0:
                print (e)

}}}

Sage Interactions - Geometry

goto interact main page

Intersecting tetrahedral reflections FIXME

by Marshall Hampton. Inspired by a question from Hans Schepker of Glass Geometry.

tetrareflect.png

Evolutes

by Pablo Angulo. Computes the evolute of a plane curve given in parametric coordinates. The curve must be parametrized from the interval [0,2pi].

evoluta3.png

Geodesics on a parametric surface

by Antonio Valdés and Pablo Angulo. A first interact allows the user to introduce a parametric surface, and draws it. Then a second interact draws a geodesic within the surface. The separation is so that after the first interact, the geodesic equations are "compiled", and then the second interact is faster.

geodesics1.png geodesics2.png

Dimensional Explorer

By Eviatar Bach

Renders 2D images (perspective or spring-layout) and 3D models of 0-10 dimensional hypercubes. It also displays number of edges and vertices.

dimensions.png

Crofton's formula

by Pablo Angulo. Illustrates Crofton's formula by throwing some random lines and computing the intersection number with a given curve. May use either solve for exact computation of the intersections, or may also approximate the curve by straight segments (this is the default).

crofton4.png

Banchoff-Pohl area

by Pablo Angulo. Computes the Banchoff-Pohl "area enclosed by a spatial curve", by throwing some random lines and computing the linking number with the given curve. Lines not linked to the given curve are displayed in red, linked lines are displayed in green.

banchoff-pohl.png

Quantum tetrahedron volume eigenvalues

by David Horgan. Computes the volume eigenvalues of a quantum tetrahedron.

interact/geometry (last edited 2013-11-25 10:30:11 by pang)