In[25]:=
SetDirectory @"~Factorisation"D;
<< kappaLib.m
<< helper.m
KappaLib v1.1
Loading helper.m ..
vp = 80.37157301445131136`, - 2.9222500600197514`, 1.6650489727470879`<;
vv = 80.6474540481976111`, - 0.18015053062800562`, 0.7405059363617374`<;
sub = 8a1 ® a2, b1 ® b2<;
vars = 8x0, x1, x2, x3<;
a1 - b1 0
0
0
0
b1 a1 0
0
0
0
0
0
a2 0
0 - b2
kappa = emMatrixToKappaB
F;
0
1
0
a1 b1 0
1
0
0 - b1 a1 0
0
0
b2 0
0
a2
fr = emKappaToFresnel@kappa, varsD . sub;
AA =
1
0
0
b1
0 - b1 0
0
;
0
0 - b1 0
b1 0
0
0
BB =
-1 0
0
b1
0 - b1 0
0
;
0
0 - b1 0
b1
0
0
0
f1 = Simplify @vars.AA .varsD;
f2 = Simplify @vars.BB.varsD;
verify = b1 f1 f2;
Simplify @fr - verify . subD
0
Ÿ Fresnel polynomial depends on x0, x1^2+x2^2, x3
f1
f2
x0 2 - b1 Ix1 2 + x2 2 M + 2 b1 x0 x3
- x0 2 - b1 Ix1 2 + x2 2 M + 2 b1 x0 x3
f@b1_ D := toEqsA9x0 2 - b1 x1 2 + 2 b1 x0 x3, - x0 2 - b1 x1 2 + 2 b1 x0 x3=E
2
Plot_II.nb
Ÿ Image 1: b1 = 1/5 = 0.2
[email protected]
9x0 2 - 0.2 x1 2 + 0.4 x0 x3 Š 0, - x0 2 - 0.2 x1 2 + 0.4 x0 x3 Š 0=
p1 = ContourPlot3DA9x0 2 - 0.2` x1 2 + 0.4` x0 x3 Š 0, - x0 2 - 0.2` x1 2 + 0.4` x0 x3 Š 0=,
8x0, - 1, 1<, 8x1, - 1, 1<, 8x3, - 1, 1<,
Axes ® False, Boxed ® False, ViewPoint ® vp, ViewVertical ® vv E
Ÿ Image 2: b1 = 4/5 =0.8
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9x0 2 - 0.8 x1 2 + 1.6 x0 x3 Š 0, - x0 2 - 0.8 x1 2 + 1.6 x0 x3 Š 0=
p2 = ContourPlot3DA9x0 2 - 0.8` x1 2 + 1.6` x0 x3 Š 0, - x0 2 - 0.8` x1 2 + 1.6` x0 x3 Š 0=,
8x0, - 1, 1.59<, 8x1, - 1, 1<, 8x3, - 1, 1<,
Axes ® False, Boxed ® False, ViewPoint ® vp, ViewVertical ® vv E
f@5D
9x0 2 - 5 x1 2 + 10 x0 x3 Š 0, - x0 2 - 5 x1 2 + 10 x0 x3 Š 0=
p3 = ContourPlot3DA9x0 2 - 5 x1 2 + 10 x0 x3 Š 0, - x0 2 - 5 x1 2 + 10 x0 x3 Š 0=,
8x0, - 1.9, 2.1<, 8x1, - 1, 2<, 8x3, - 1, 1.1<,
Axes ® False, Boxed ® False, ViewPoint ® vp, ViewVertical ® vv E
all = Show @GraphicsGrid @88p1, p2, p3<<DD
In[29]:=
printNotebook@"Plot_II.pdf"D