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11 Dimensional
Touching on the 11th dimension.
by Parker Emmerson © 2010
We start by examining the wavelength with constant value :
Theorem 4 : The derivative of the height of the cone with respect to time equals the average rate of the circumference of the
initial circle divided by q when q = k t (the angle is a constant function of time like a clock).
(1)
velocity =
wavelength of frequency = v = l ƒ = r ƒ = r ê t = r H1 ê Hq ê H2 pLLL =2 p r
q=
H2 p r1 + q rLq
=2 p q r
q ^ 2=
2 p s
q2
=
2 pH2 p r-2 p r1L
q
q=
2 p2 p r-2 p r
2-h2
q
q=
2 p 2 p r - 2 p r2 - h2
q2
=
2 p 2 p r - 2 p r2 -4 p r2 q-r2 q2
2 p
2
q2
=
H1
ê H1
ê H2 p
LLLD
B
4 p r2 q - r2 q2
2 p
, q
F=
4 p r2 - 2 r2 q
2 4 p r2 q - r2 q2
Theorem 5 : The derivative of the height of the cone with respect to time equals the average rate of the circumference of the
initial circle divided by q when q = k t (the angle is a constant function of time like a clock).
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We Solve for r
SolveB2 p 2 p r - 2 p r2 - HhL2
q2
==4 p r2 - 2 r2 q
2 4 p r2
q - r2
q2
, rF
99r Ø -,I-I256 p7
h2
q3M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10M +
I320 p6
h2
q4M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10M -
I128 p5
h2
q5M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10M +
I16 p4
h2
q6M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10M -
I128 p6 ,I256 p
5h4
q3
- 448 p4
h4
q4
+ 304 p3
h4
q5
- 100 p2
h4
q6
+ 16 p h4
q7
- h4
q8MM ë
I-1024 p7
q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10MM=,
9r Ø ,I-I256 p7
h2
q3M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10M +
I320 p6
h2
q4M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10M -
I128 p5
h2
q5M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10M +
I16 p
4h2
q6
M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10
M-
I128 p6 ,I256 p5 h4 q3 - 448 p4 h4 q4 + 304 p3 h4 q5 - 100 p2 h4 q6 + 16 p h4 q7 - h4 q8MM ëI-1024 p7
q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10MM=,
9r Ø -,I-I256 p7
h2
q3M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10M +
I320 p6
h2
q4M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10M -
I128 p5
h2
q5M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10M +
I16 p4
h2
q6M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10M +
I128 p6 ,I256 p
5h4
q3
- 448 p4
h4
q4
+ 304 p3
h4
q5
- 100 p2
h4
q6
+ 16 p h4
q7
- h4
q8MM ë
I-1024 p7
q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10MM=,
9r Ø ,I-I256 p7
h2
q3M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10M +
I320 p6
h2
q4M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10M -
I128 p
5h2
q5
M ë I-1024 p
7q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10
M+
I16 p4 h2 q6M ë I-1024 p7 q3 + 1280 p6 q4 - 512 p5 q5 + 80 p4 q6 - 32 p3 q7 + 24 p2 q8 - 8 p q9 + q10M +
I128 p6 ,I256 p
5h4
q3
- 448 p4
h4
q4
+ 304 p3
h4
q5
- 100 p2
h4
q6
+ 16 p h4
q7
- h4
q8MM ë
I-1024 p7
q3
+ 1280 p6
q4
- 512 p5
q5
+ 80 p4
q6
- 32 p3
q7
+ 24 p2
q8
- 8 p q9
+ q10MM==
I construct the expression:r 2
q
2 p
(the ratio or rate of r 2 to theta) from the solutions from the
previous section:
r2
q
2 p
ã1
q
2 p
I,I-I256 p 7 h2 q3M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M +
I320 p 6 h2 q4M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M -
I128 p 5 h2 q5M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M +
I16 p 4 h2 q6M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M +
I128 p 6,I256 p 5 h4 q3 - 448 p 4 h4 q4 + 304 p 3 h4 q5 - 100 p 2 h4 q6 + 16 p h4 q7 - h4 q8MM ë
I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10MMM2 =
2 11 Dimensional by Parker Emmerson ©2009-2011.nb
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1
q2 p I-I256 p 7 h2 q3M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M +
I320 p 6 h2 q4M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M -
I128 p 5 h2 q5M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M +
I16 p 4 h2 q6M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M +
I128 p 6
,I256 p 5
h4
q3
- 448 p 4
h4
q4
+ 304 p 3
h4
q5
- 100 p 2
h4
q6
+ 16 p h4
q7
- h4
q8
MM ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10MM ==
2 p -1
qI256 p 7 h2 q3M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M +
1
qI320 p 6 h2 q4M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M -
1
qI128 p 5 h2 q5M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M +
1
qI16 p 4 h2 q6M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M +
1
q II128 p 6 ,I256 p 5 h4 q3 - 448 p 4 h4 q4 + 304 p 3 h4 q5 - 100 p 2 h4 q6 + 16 p h4 q7 - h4 q8MM ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10MM =
2 p -256 p 7 h2 q2
- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10
+
320 p 6 h2 q3
- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10
-
128 p 5 h2 q4
- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10
+
16 p
4
h
2
q
5
- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10
+
128 p 6 256 p 5 h4 q3 - 448 p 4 h4 q4 + 304 p 3 h4 q5 - 100 p 2 h4 q6 + 16 p h4 q7 - h4 q8 ì Iq I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10MM =
11 Dimensional by Parker Emmerson ©2009-2011.nb 3
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2 p -I256 p 7 h2 q2M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M +
320 p 6 h2 q3
- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10
-
128 p 5 h2 q4
- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10 +
16 p 4 h2 q5
- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10
+
128 p 6 256 p 5 h4 q3 - 448 p 4 h4 q4 + 304 p 3 h4 q5 - 100 p 2 h4 q6 + 16 p h4 q7 - h4 q8 ì I I- 1024 p 7 q q3 + 1280 p 6 q q4 - 512 p 5 q q5 + 80 p 4 q q6 - 32 p 3 q q7 + 24 p 2 q q8 - 8 p q q9 + q q10MM =
2 p -256 p7 h2 q2
-1024 p7 q3 + 1280 p6 q4 - 512 p5 q5 + 80 p4 q6 - 32 p3 q7 + 24 p2 q8 - 8 p q9 + q10
+
320 p6 h2 q3
-1024 p7 q3 + 1280 p6 q4 - 512 p5 q5 + 80 p4 q6 - 32 p3 q7 + 24 p2 q8 - 8 p q9 + q10
-
128 p5 h2 q4
-1024 p7 q3 + 1280 p6 q4 - 512 p5 q5 + 80 p4 q6 - 32 p3 q7 + 24 p2 q8 - 8 p q9 + q10
+
16 p4 h2 q5
-1024 p7 q3 + 1280 p6 q4 - 512 p5 q5 + 80 p4 q6 - 32 p3 q7 + 24 p2 q8 - 8 p q9 + q10
+
128 p6
256 p5
h4
q3
- 448 p4
h4
q4
+ 304 p3
h4
q5
- 100 p2
h4
q6
+ 16 p h4
q7
- h4
q8 ì
I-1024 p7
q4
+ 1280 p6
q5
- 512 p5
q6
+ 80 p4
q7
- 32 p3
q8
+ 24 p2
q9
- 8 p q10
+ q11M
r2
q
2 p
== 2 p -256 p 7 h2 q2
- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10
+
320 p 6 h2 q3
- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10
-
128 p 5 h2 q4
- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10
+
16 p 4 h2 q5
- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10
+
128 p 6 256 p 5 h4 q3 - 448 p 4 h4 q4 + 304 p 3 h4 q5 - 100 p 2 h4 q6 + 16 p h4 q7 - h4 q8 ì
I- 1024 p 7 q4 + 1280 p 6 q5 - 512 p 5 q6 + 80 p 4 q7 - 32 p 3 q8 + 24 p 2 q9 - 8 p q10 + q11
M
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SolveB r2
q
2 p
==
2 p I-I256 p 7
h2
q2M ë I- 1024 p
7q3
+ 1280 p 6
q4
- 512 p 5
q5
+ 80 p 4
q6
- 32 p 3
q7
+ 24 p 2
q8
- 8 p q9
+ q10M +
I320 p 6 h2 q3M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M -
I128 p 5 h2 q4
M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10
M+
I16 p 4 h2 q5M ë I- 1024 p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 + q10M +
I128 p 6,I256 p 5 h4 q3 - 448 p 4 h4 q4 + 304 p 3 h4 q5 - 100 p 2 h4 q6 + 16 p h4 q7 - h4 q8MM ë
I- 1024 p 7 q4 + 1280 p 6 q5 - 512 p 5 q6 + 80 p 4 q7 - 32 p 3 q8 + 24 p 2 q9 - 8 p q10 + q11MM, rF::r Ø -
1
2
q ,II512 p7
h2
q2M ë I1024 p
7q3
- 1280 p6
q4
+ 512 p5
q5
- 80 p4
q6
+ 32 p3
q7
- 24 p2
q8
+ 8 p q9
- q10M -
I640 p6
h2
q3M ë I1024 p
7q3
- 1280 p6
q4
+ 512 p5
q5
- 80 p4
q6
+ 32 p3
q7
- 24 p2
q8
+ 8 p q9
- q10M +
I256 p5
h2
q4M ë I1024 p
7q3
- 1280 p6
q4
+ 512 p5
q5
- 80 p4
q6
+ 32 p3
q7
- 24 p2
q8
+ 8 p q9
- q10M -
I32 p4
h2
q5M ë I1024 p
7q3
- 1280 p6
q4
+ 512 p5
q5
- 80 p4
q6
+ 32 p3
q7
- 24 p2
q8
+ 8 p q9
- q10M -
I256 p
6
,I256 p
5h4
q3
- 448 p4
h4
q4
+ 304 p3
h4
q5
- 100 p2
h4
q6
+ 16 p h4
q7
- h4
q8
MM ëI1024 p7
q4
- 1280 p6
q5
+ 512 p5
q6
- 80 p4
q7
+ 32 p3
q8
- 24 p2
q9
+ 8 p q10
- q11MM>,
:r Ø1
2
q . 512 p7 h2 q2
1024 p7 q3 - 1280 p6 q4 + 512 p5 q5 - 80 p4 q6 + 32 p3 q7 - 24 p2 q8 + 8 p q9 - q10
-
I640 p6
h2
q3M ë I1024 p
7q3
- 1280 p6
q4
+ 512 p5
q5
- 80 p4
q6
+ 32 p3
q7
- 24 p2
q8
+ 8 p q9
- q10M +
I256 p5
h2
q4M ë I1024 p
7q3
- 1280 p6
q4
+ 512 p5
q5
- 80 p4
q6
+ 32 p3
q7
- 24 p2
q8
+ 8 p q9
- q10M -
I32 p4
h2
q5M ë I1024 p
7q3
- 1280 p6
q4
+ 512 p5
q5
- 80 p4
q6
+ 32 p3
q7
- 24 p2
q8
+ 8 p q9
- q10M -
I256 p6 ,I256 p
5h4
q3
- 448 p4
h4
q4
+ 304 p3
h4
q5
- 100 p2
h4
q6
+ 16 p h4
q7
- h4
q8MM ë
I1024 p7
q4
- 1280 p6
q5
+ 512 p5
q6
- 80 p4
q7
+ 32 p3
q8
- 24 p2
q9
+ 8 p q10
- q11M >>
RevolutionPlot3DB:-1
2
q
,II512 p 7 h2 q2M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10M -
I640 p 6 h2 q3M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10M +
I256 p 5 h2 q4M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10M -
I32 p 4 h2 q5M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10M -
I256 p 6,I256 p 5 h4 q3 - 448 p 4 h4 q4 + 304 p 3 h4 q5 - 100 p 2 h4 q6 + 16 p h4 q7 - h4 q8MM ë
I1024 p 7 q4 - 1280 p 6 q5 + 512 p 5 q6 - 80 p 4 q7 + 32 p 3 q8 - 24 p 2 q9 + 8 p q10 - q11MM,1
2
q
,II512 p 7 h2 q2M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10M -
I640 p 6 h2 q3
M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10
M+
I256 p 5 h2 q4M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10M -
I32 p 4 h2 q5M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10M -
I256 p 6,I256 p 5 h4 q3 - 448 p 4 h4 q4 + 304 p 3 h4 q5 - 100 p 2 h4 q6 + 16 p h4 q7 - h4 q8MM ë
I1024 p 7 q4 - 1280 p 6 q5 + 512 p 5 q6 - 80 p 4 q7 + 32 p 3 q8 -
24 p 2 q9 + 8 p q10 - q11MM>, 8h, - 1, 1<, 8q, - 2 p , 2 p <FComputationalGeometry`Methods`SpatialSearch::spoutbounds :
-- Message text not found -- H8-5.98759, -42.1091<L
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ComputationalGeometry`Methods`SpatialSearch::spoutbounds :
-- Message text not found -- H85.55128, -39.8165<L
ComputationalGeometry`Methods`SpatialSearch::spoutbounds :
-- Message text not found -- H85.98759, -42.1091<L
General::stop :
Further output of ComputationalGeometry`Methods`SpatialSearch::spoutbounds will be suppressedduring this calculation. à
h :=4 p r2 q - r2 q2
2 p
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r :=2 p H4 p - qL q
H4 p - qL q
q :=
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SphericalPlot3DB:-1
2
q
. I512 p 7 h2 q2M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10M -
I640 p 6 h2 q3
M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10
M+
I256 p 5 h2 q4M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10M -
I32 p 4 h2 q5M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10M -
I256 p 6,I256 p 5 h4 q3 - 448 p 4 h4 q4 + 304 p 3 h4 q5 - 100 p 2 h4 q6 + 16 p h4 q7 - h4 q8MM ì
1024 p 7 q4 - 1280 p 6 q5 + 512 p 5 q6 - 80 p 4 q7 + 32 p 3 q8 -
24 p 2 q9 + 8 p q10 - 2 p + p 2 - p 2 Sin@bD2 11
,1
2
q
. I512 p 7 h2 q2M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10M -
I640 p
6
h
2
q
3
M ë I1024 p
7
q
3
- 1280 p
6
q
4
+ 512 p
5
q
5
- 80 p
4
q
6
+ 32 p
3
q
7
- 24 p
2
q
8
+ 8 p q
9
- q
10
M +I256 p 5 h2 q4M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10M -
I32 p 4 h2 q5M ë I1024 p 7 q3 - 1280 p 6 q4 + 512 p 5 q5 - 80 p 4 q6 + 32 p 3 q7 - 24 p 2 q8 + 8 p q9 - q10M -
I256 p 6,I256 p 5 h4 q3 - 448 p 4 h4 q4 + 304 p 3 h4 q5 - 100 p 2 h4 q6 + 16 p h4 q7 - h4 q8MM ì
1024 p 7 q4 - 1280 p 6 q5 + 512 p 5 q6 - 80 p 4 q7 + 32 p 3 q8 - 24 p 2 q9 + 8 p q10 -
2 p + p 2 - p 2 Sin@bD2 11 >, 8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F
8 11 Dimensional by Parker Emmerson ©2009-2011.nb
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Havingcomposed theexpression for r2
q
2p
in the11th dimension, wesolvefor the11th
imensional position oftheta.T histakestwo"runs through."
Firstrun-through.
SolveB r2
q
2 p
==
2 p I-I256p 7 h2 q2Më I-1024p 7 q3 + 1280 p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 +q10M+
I320p 6 h2 q3Më I-1024p 7 q3 + 1280 p 6 q4 - 512p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 +q 10M-
I128p 5 h2 q4Më I-1024p 7 q3 + 1280 p 6 q4 - 512p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q9 +q 10M+
I16 p 4 h2 q5Më I- 1024 p 7 q3 + 1280p 6 q4 - 512 p 5 q5 + 80 p 4 q6 - 32 p 3 q7 + 24 p 2 q8 - 8 p q 9 +q 10M +
I128p 6,I256p 5 h4 q3 - 448p 4 h4 q4 + 304 p 3 h4 q5 - 100 p 2 h4 q6 + 16 p h4 q7 -h 4 q8MMë I-1024p 7 q4 + 1280p 6 q5 - 512p 5 q6 + 80 p 4 q7 - 32 p 3 q8 + 24 p 2 q9 - 8 p q10 + xMM, xF
:: Ø - 262144p12r2
q4
+65536 p12
h2
q4
+393216 p11r2
q5
-98304 p11
h2
q5
-212992 p10r2
q6
+
53248 p10
h2
q6
+57344 p9r2
q7
-13312 p9
h2
q7
-22528 p8r2
q8
+3328p8
h2
q8
+
16384 p7r2 q
9-2048p
7h2
q9
-7232p6r2 q
10+ 896p
6h2
q10
+1472p5r2 q
11- 128p
5h2
q11
-
304 p4 r2 q
12+160 p
3 r2 q13
-56 p2 r2 q
14+8 pr
2q15
-32768 p11
q h4 H2 p-q L2 H4 p-q L3 q
3+
8192p10
q2
h4H2 p-q L2H4 p-q L3 q
3+512 p
8q4
h4 H2 p-q L2 H4 p-q L3 q
3-
512 p7
q5
h4 H2 p-q L2 H4 p-q L3 q
3+ 128p
6q6
h4H2 p-q L2H4 p-q L3 q
3 ì I-256 p
5 r2 +64 p5
h2
+64 p4 r2 q- 16 p
4h2
q+ 4 p2 r2 q
3- 4 p r2 q
4+ r2 q
5M>>
11DimensionalbyParker Emmerson©2009-2011.nb 9
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ContourPlot3DB - 262144 p 12 r2 q4 + 65 536 p 12 h2 q4 + 393216 p 11 r2 q5 - 98304 p 11 h2 q5 - 212992 p 10 r2 q6 +
53 248 p 10 h2 q6 + 57 344 p 9 r2 q7 - 13 312 p 9 h2 q7 - 22 528 p 8 r2 q8 + 3328 p 8 h2 q8 +
16 384 p 7 r2 q9 - 2048 p 7 h2 q9 - 7232 p 6 r2 q10 + 896 p 6 h2 q10 + 1472 p 5 r2 q11 - 128 p 5 h2 q11 -
304 p 4 r2 q12 + 160 p 3 r2 q13 - 56 p 2 r2 q14 + 8 p r2 q15 - 32768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3 +
8192 p 10
q2
h4
H2 p - qL2
H4 p - qL3
q3
+ 512 p 8
q4
h4
H2 p - qL2
H4 p - qL3
q3
-
512 p 7 q5 h4 H2 p - qL2 H4 p - qL3 q3 + 128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3 ì I- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5M,
8r, - 1, 1<, 8h, - 1, 1<, 8q, - 2 p , 2 p <F
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In[1]:= AnimateBPlot3DB - 262144 p 12 r2 q4 + 65536 p 12 h2 q4 + 393216 p 11 r2 q5 - 98 304 p 11 h2 q5 - 212992 p 10 r2 q6 +
53248 p 10 h2 q6 + 57 344 p 9 r2 q7 - 13 312 p 9 h2 q7 - 22 528 p 8 r2 q8 + 3328 p 8 h2 q8 +
16384 p 7 r2 q9 - 2048 p 7 h2 q9 - 7232 p 6 r2 q10 + 896 p 6 h2 q10 + 1472 p 5 r2 q11 - 128 p 5 h2 q11 -
304 p 4
r2
q12
+ 160 p 3
r2
q13
- 56 p 2
r2
q14
+ 8 p r2
q15
- 32768 p 11
q h4
H2 p - qL2
H4 p - qL3
q3
+
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3 + 512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3 -
512 p 7 q5 h4 H2 p - qL2 H4 p - qL3 q3 + 128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3 ì I- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5M,
8r, - 1, 1<, 8h, - 1, 1<, AxesLabel Ø AutomaticF, 8q, - 2 p , 2 p <F
Out[1]=
q
h :=4 p r2 q - r2 q2
2 p
11 Dimensional by Parker Emmerson ©2009-2011.nb 11
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RevolutionPlot3DB- 262144 p 12 r2 q4 + 65 536 p 12 h2 q4 + 393216 p 11 r2 q5 - 98 304 p 11 h2 q5 - 212992 p 10 r2 q6 +
53 248 p 10 h2 q6 + 57 344 p 9 r2 q7 - 13 312 p 9 h2 q7 - 22 528 p 8 r2 q8 + 3328 p 8 h2 q8 +
16 384 p 7 r2 q9 - 2048 p 7 h2 q9 - 7232 p 6 r2 q10 + 896 p 6 h2 q10 + 1472 p 5 r2 q11 - 128 p 5 h2 q11 -
304 p 4
r2
q12
+ 160 p 3
r2
q13
- 56 p 2
r2
q14
+ 8 p r2
q15
- 32768 p 11
q h4
H2 p - qL2
H4 p - qL3
q3
+
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3 + 512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3 -
512 p 7 q5 h4 H2 p - qL2 H4 p - qL3 q3 + 128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3 ì I- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5M, 8r, - 1, 1<, 8q, - 2 p , 2 p <F
r :=2 p H4 p - qL q
H4 p - q
Lq
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RevolutionPlot3DB- 262144 p 12 r2 q4 + 65 536 p 12 h2 q4 + 393216 p 11 r2 q5 - 98 304 p 11 h2 q5 - 212992 p 10 r2 q6 +
53 248 p 10 h2 q6 + 57 344 p 9 r2 q7 - 13 312 p 9 h2 q7 - 22 528 p 8 r2 q8 + 3328 p 8 h2 q8 +
16 384 p 7 r2 q9 - 2048 p 7 h2 q9 - 7232 p 6 r2 q10 + 896 p 6 h2 q10 + 1472 p 5 r2 q11 - 128 p 5 h2 q11 -
304 p 4
r2
q12
+ 160 p 3
r2
q13
- 56 p 2
r2
q14
+ 8 p r2
q15
- 32768 p 11
q h4
H2 p - qL2
H4 p - qL3
q3
+
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3 + 512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3 -
512 p 7 q5 h4 H2 p - qL2 H4 p - qL3 q3 + 128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3 ì I- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5M, 8q, - 2 p , 2 p <F
11 Dimensional by Parker Emmerson ©2009-2011.nb 13
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SphericalPlot3DB- 262144 p 12 r2 q4 + 65 536 p 12 h2 q4 + 393216 p 11 r2 q5 - 98 304 p 11 h2 q5 - 212992 p 10 r2 q6 +
53 248 p 10 h2 q6 + 57 344 p 9 r2 q7 - 13 312 p 9 h2 q7 - 22 528 p 8 r2 q8 +
3328 p 8 h2 q8 + 16384 p 7 r2 q9 - 2048 p 7 h2 q9 - 7232 p 6 r2 q10 + 896 p 6 h2 q10 +
1472 p 5 r2 2 p + p 2 - p 2 Sin@bD211
- 128 p 5 h2 2 p + p 2 - p 2 Sin@bD211
-
304 p 4 r2 q12 + 160 p 3 r2 q13 - 56 p 2 r2 q14 + 8 p r2 q15 - 32768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3 +
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3 + 512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3 -
512 p 7 q5 h4 H2 p - qL2 H4 p - qL3 q3 + 128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3 ì I- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5M,
8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F
14 11 Dimensional by Parker Emmerson ©2009-2011.nb
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SphericalPlot3DB
- 262144 p 12 r2 q4 + 65 536 p 12 h2 q4 + 393216 p 11 r2 q5 - 98 304 p 11 h2 2 p + p 2 - p 2 Sin@bD2 5
-
212992 p 10 r2 q6 + 53 248 p 10 h2 q6 + 57 344 p 9 r2 q7 - 13 312 p 9 h2 q7 - 22 528 p 8 r2 q8 +
3328 p 8 h2 2 p + p 2 - p 2 Sin@bD2 8
+ 16 384 p 7 r2 q9 - 2048 p 7 h2 q9 - 7232 p 6 r2 q10 +
896 p 6 h2 q10 + 1472 p 5 r2 HqL11 - 128 p 5 h2 2 p + p 2 - p 2 Sin@bD2 11
-
304 p 4 r2 q12 + 160 p 3 r2 q13 - 56 p 2 r2 q14 + 8 p r2 2 p + p 2 - p 2 Sin@bD2 15
-
32 768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3 + 8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3 +
512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3 - 512 p 7 q5 h4 H2 p - qL2 4 p - 2 p + p 2 - p 2 Sin@bD2 3
q3 +
128 p 6 q6 h4 2 p - 2 p + p 2 - p 2 Sin@bD2 2 H4 p - qL3 q3 ì
I- 256 p 5 r2
+ 64 p 5
h2
+ 64 p 4 r2
q - 16 p 4
h2
q + 4 p 2 r2
q3
- 4 p r2q4
+ r2q5M,
8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<F
11 Dimensional by Parker Emmerson ©2009-2011.nb 15
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ü Second run-through
SolveBx == - 262144 p 12 r2 q4 + 65 536 p 12 h2 q4 + 393216 p 11 r2 q5 - 98 304 p 11 h2 q5 - 212992 p 10 r2 q6 +
53248 p 10 h2 q6 + 57 344 p 9 r2 q7 - 13 312 p 9 h2 q7 - 22 528 p 8 r2 q8 + 3328 p 8 h2 q8 +
16384 p 7
r2
q9
- 2048 p 7
h2
q9
- 7232 p 6
r2
q10
+ 896 p 6
h2
q10
+ 1472 p 5
r2
x - 128 p 5
h2
x -
304 p 4 r2 q12 + 160 p 3 r2 q13 - 56 p 2 r2 q14 + 8 p r2 q15 - 32768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3 +
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3 + 512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3 -
512 p 7 q5 h4 H2 p - qL2 H4 p - qL3 q3 + 128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3 ì I- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5M, xF
::x Ø -262144 p12 r2 q4
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
+
65536 p12 h2 q4
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
+
393216 p11 r2 q5
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
-
98304 p11 h2 q5
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
-
212992 p10 r2 q6
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
+
53248 p10 h2 q6
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
+
57344p9 r2 q7
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5-
13312p9 h2 q7
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
-
22528p8 r2 q8
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
+
3328 p8 h2 q8
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
+
16 11 Dimensional by Parker Emmerson ©2009-2011.nb
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16384p7 r2 q9
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
-
2048 p7 h2 q9
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
-
7232 p6 r2 q10
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5+
896 p6 h2 q10
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
-
304 p4 r2 q12
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
+
160 p3 r2 q13
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
-
56 p2 r2 q14
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
+
8 p r2
q15
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
-
32768p11 q h4 H2 p - qL2 H4 p - qL3 q3
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
+
8192 p10 q2 h4 H2 p - qL2 H4 p - qL3 q3
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
+
512 p8 q4 h4 H2 p - qL2 H4 p - qL3 q3
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
-
512 p7
q5
h4
H2 p - qL2
H4 p - qL3
q3
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p6 q6 h4 H2 p - qL2 H4 p - qL3 q3
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
ì
1 -1472 p5 r2
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p5 h2
-256 p5 r2 + 64 p5 h2 + 64 p4 r2 q - 16 p4 h2 q + 4 p2 r2 q3 - 4 p r2 q4 + r2 q5
>>
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ContourPlot3DB -262144 p 12 r2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
65 536 p 12 h2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
393216 p 11 r2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
98 304 p 11 h2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
212992 p 10 r2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
53 248 p 10 h2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
57 344 p 9 r2 q7
- 256 p
5
r
2
+ 64 p
5
h
2
+ 64 p
4
r
2
q - 16 p
4
h
2
q + 4 p
2
r
2
q
3
- 4 p r
2
q
4
+ r
2
q
5
-
13 312 p 9 h2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
22 528 p 8 r2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
3328 p 8 h2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
16 384 p 7 r2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
2048 p 7 h2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
7232 p 6 r2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
896 p 6 h2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
304 p 4 r2 q12
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
18 11 Dimensional by Parker Emmerson ©2009-2011.nb
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160 p 3 r2 q13
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
56 p 2 r2 q14
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8 p r2 q15
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5-
32 768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
512 p 7 q5 h4
H2 p - q
L2
H4 p - q
L3
q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
ì
1 -1472 p 5 r2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 5 h2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
,
8r, - 1, 1<, 8h, - 1, 1<, 8q, - 2 p , 2<F
11 Dimensional by Parker Emmerson ©2009-2011.nb 19
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h := r Sin@bD
ContourPlot3DB -262144 p 12 r2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
65 536 p 12 h2 q4
- 256 p 5
r2
+ 64 p 5
h2
+ 64 p 4
r2
q - 16 p 4
h2
q + 4 p 2
r2
q3
- 4 p r2
q4
+ r2
q5
+
393216 p 11 r2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
98 304 p 11 h2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
212992 p 10 r2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
53 248 p 10 h2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
20 11 Dimensional by Parker Emmerson ©2009-2011.nb
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57 344 p 9 r2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
13 312 p 9 h2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
22 528 p 8 r2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5+
3328 p 8 h2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
16 384 p 7 r2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
2048 p 7 h2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
7232 p 6 r2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
896 p 6
h2
q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
304 p 4 r2 q12
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
160 p 3 r2 q13
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
56 p 2 r2 q14
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8 p r2 q15
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
32 768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
11 Dimensional by Parker Emmerson ©2009-2011.nb 21
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512 p 7 q5 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
ì
1 -1472 p 5 r2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 5 h2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
,
8r, - 1, 1<, 8b, - p ê 2, p ê 2<, 8q, - 2 p , 2<F
h := r Sin@bD
r :=2 p H4 p - qL q
H4 p - qL q
22 11 Dimensional by Parker Emmerson ©2009-2011.nb
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SphericalPlot3DB -262144 p 12 r2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
65 536 p 12 h2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
393216 p 11 r2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
98 304 p 11 h2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
212992 p 10 r2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
53 248 p 10 h2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
57 344 p 9 r2 q7
- 256 p
5
r
2
+ 64 p
5
h
2
+ 64 p
4
r
2
q - 16 p
4
h
2
q + 4 p
2
r
2
q
3
- 4 p r
2
q
4
+ r
2
q
5
-
13 312 p 9 h2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
22 528 p 8 r2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
3328 p 8 h2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
16 384 p 7 r2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
2048 p 7 h2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
7232 p 6 r2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
896 p 6 h2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
304 p 4 r2 q12
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
11 Dimensional by Parker Emmerson ©2009-2011.nb 23
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160 p 3 r2 q13
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
56 p 2 r2 q14
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8 p r2 q15
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5-
32 768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
512 p 7 q5 h4
H2 p - q
L2
H4 p - q
L3
q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
ì
1 -1472 p 5 r2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 5 h2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
,
8b, - p ê 2, p ê 2<, 8q, - 2 p , 2<F
24 11 Dimensional by Parker Emmerson ©2009-2011.nb
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SphericalPlot3DB -262144 p 12 r2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
65 536 p 12 h2 q4
- 256 p
5
r
2
+ 64 p
5
h
2
+ 64 p
4
r
2
q - 16 p
4
h
2
q + 4 p
2
r
2
q
3
- 4 p r
2
q
4
+ r
2
q
5
+
393216 p 11 r2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
98 304 p 11 h2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
212992 p 10 r2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
53 248 p 10 h2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
11 Dimensional by Parker Emmerson ©2009-2011.nb 25
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57 344 p 9 r2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
13 312 p 9 h2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
22 528 p 8 r2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5+
3328 p 8 h2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
16 384 p 7 r2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
2048 p 7 h2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
7232 p 6 r2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
896 p 6
h2
q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
304 p 4 r2 q12
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
160 p 3 r2 q13
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
56 p 2 r2 q14
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8 p r2 q15
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
32 768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
26 11 Dimensional by Parker Emmerson ©2009-2011.nb
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512 p 7 q5 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
ì
1 -1472 p 5 r2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
I128 p 5 h2M ì - 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 -
4 p r2 q4 + r2 2 p + p 2 - p 2 Sin@bD2 5
, 8b, - p ê 2, p ê 2<, 8q, - 2 p , 2<F
11 Dimensional by Parker Emmerson ©2009-2011.nb 27
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ArcCosB1
2‰-2 Â p 1-Sin@bD2 1 + ‰4 Â p 1-Sin@bD2 F ==
-262144 p 12 r2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
65 536 p 12 h2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
393216 p 11 r2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
98 304 p 11 h2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
212992 p 10 r2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
53 248 p 10 h2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
57 344 p 9 r2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
13 312 p 9 h2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
22 528 p 8 r2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
3328 p 8 h2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
16 384 p 7 r2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
2048 p 7 h2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
7232 p 6 r2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
896 p 6 h2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
11 Dimensional by Parker Emmerson ©2009-2011.nb 29
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304 p 4 r2 q12
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
160 p 3 r2 q13
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
56 p 2 r2 q14
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5+
8 p r2 q15
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
32 768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
512 p 8 q4 h4
H2 p - q
L2
H4 p - q
L3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5 -
512 p 7 q5 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
ì
1 -1472 p 5 r2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 5 h2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
SphericalPlot3DB 2 p + p 2 - p 2 Sin@bD2 2 2 p 2 - p 2 Sin@bD2 + 2 p 2 1 - Sin@bD2
2 2 p -p 2 Sin@bD2
p + p 1 - Sin@bD22 p +
p 2 Sin@bD2 - p 2 Sin@bD3 Sin@bD2Sin@bD2
30 11 Dimensional by Parker Emmerson ©2009-2011.nb
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98304 p 11 h2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
212992 p 10 r2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
53248 p 10 h2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5+
57 344 p 9 r2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
13 312 p 9 h2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
22 528 p 8 r2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
3328 p 8 h2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
16 384 p 7
r2
q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
2048 p 7 h2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
7232 p 6 r2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
896 p 6 h2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
304 p 4 r2 q12
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
160 p 3 r2 q13
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
56 p 2 r2 q14
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8 p r2 q15
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
32 11 Dimensional by Parker Emmerson ©2009-2011.nb
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32 768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
512 p 7 q5 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
ì
1 -1472 p 5 r2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 5 h2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
,
8q, - 2 p , 2 p <, 8b, - p ê 2, p ê 2<FPower::infy : Infinite expression
1
0.encountered. à
Power::infy : Infinite expression1
0.encountered. à
Power::infy : Infinite expression1
0.encountered. à
General::stop : Further output of Power::infy will be suppressed during this calculation. à
11 Dimensional by Parker Emmerson ©2009-2011.nb 33
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D-Brane Mechanics
The D - Brane theta moves in the following manners :
AnimateBContourPlot3DB -262144 p 12 r2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
65536 p 12 h2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
393216 p 11 r2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
98304 p 11 h2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
212992 p 10 r2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
53248 p 10 h2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
57 344 p 9 r2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
13 312 p 9 h2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
22 528 p 8 r2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
3328 p 8 h2 q8
- 256 p 5
r2
+ 64 p 5
h2
+ 64 p 4
r2
q - 16 p 4
h2
q + 4 p 2
r2
q3
- 4 p r2
q4
+ r2
q5
+
16 384 p 7 r2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
2048 p 7 h2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
7232 p 6 r2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
34 11 Dimensional by Parker Emmerson ©2009-2011.nb
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896 p 6 h2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
304 p 4 r2 q12
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
160 p 3 r2 q13
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5-
56 p 2 r2 q14
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8 p r2 q15
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
32 768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5
r2
+ 64 p 5
h2
+ 64 p 4
r2
q - 16 p 4
h2
q + 4 p 2
r2
q3
- 4 p r2
q4
+ r2
q5
+
512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
512 p 7 q5 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
ì
1 -1472 p 5 r2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
I128 p 5 h2M ì - 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q +
4 p 2 r2 q3 - 4 p r2 q4 + r2 2 p + p 2 - p 2 Sin@bD2 5
,
8b, - p ê 2, p ê 2<, 8h, - 1, 1<, 8r, - 1, 1<, AxesLabel Ø AutomaticF, 8q,
- 2 p , 2 p <F
11 Dimensional by Parker Emmerson ©2009-2011.nb 35
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AnimateBContourPlot3DB -262144 p 12 r2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
65536 p 12 h2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
393216 p 11 r2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
98304 p 11 h2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
212992 p 10 r2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
53248 p 10 h2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
57 344 p 9 r2 q7
- 256 p
5
r
2
+ 64 p
5
h
2
+ 64 p
4
r
2
q - 16 p
4
h
2
q + 4 p
2
r
2
q
3
- 4 p r
2
q
4
+ r
2
q
5
-
13 312 p 9 h2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
22 528 p 8 r2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
3328 p 8 h2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
16 384 p 7 r2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
2048 p 7 h2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
7232 p 6 r2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
896 p 6 h2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
304 p 4 r2 q12
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
11 Dimensional by Parker Emmerson ©2009-2011.nb 37
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160 p 3 r2 q13
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
56 p 2 r2 q14
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8 p r2 q15
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5-
32 768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
512 p 7 q5 h4
H2 p - q
L2
H4 p - q
L3
q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
ì
1 -1472 p 5 r2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
I128 p 5 h2M ì - 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q +
4 p 2 r2 q3 - 4 p r2 q4 + r2 2 p + p 2 - p 2 Sin
@b
D2
5
,
8b, - p ê 2, p ê 2<, 8q, - 2 p , 2<, 8r, - 1, 1<, AxesLabel Ø AutomaticF, 8h,
- 1, 1<F
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11 Dimensional by Parker Emmerson ©2009-2011.nb 39
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AnimateBContourPlot3DB -262144 p 12 r2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
65536 p 12 h2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
393216 p 11 r2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
98304 p 11 h2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
212992 p 10 r2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
53248 p 10 h2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
57 344 p 9 r2 q7
- 256 p
5
r
2
+ 64 p
5
h
2
+ 64 p
4
r
2
q - 16 p
4
h
2
q + 4 p
2
r
2
q
3
- 4 p r
2
q
4
+ r
2
q
5
-
13 312 p 9 h2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
22 528 p 8 r2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
3328 p 8 h2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
16 384 p 7 r2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
2048 p 7 h2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
7232 p 6 r2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
896 p 6 h2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
304 p 4 r2 q12
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
40 11 Dimensional by Parker Emmerson ©2009-2011.nb
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160 p 3 r2 q13
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
56 p 2 r2 q14
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8 p r2 q15
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5-
32 768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
512 p 7 q5 h4
H2 p - q
L2
H4 p - q
L3
q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
ì
1 -1472 p 5 r2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
I128 p 5 h2M ì - 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q +
4 p 2 r2 q3 - 4 p r2 q4 + r2 2 p + p 2 - p 2 Sin
@b
D2
5
,
8h, - 1, 1<, 8q, - 2 p , 2<, 8r, - 1, 1<, AxesLabel Ø AutomaticF, 8b,
- p ê 2, p ê 2<F
11 Dimensional by Parker Emmerson ©2009-2011.nb 41
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AnimateBContourPlot3DB -262144 p 12 r2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
65536 p 12 h2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
393216 p 11 r2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
98304 p 11 h2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
212992 p 10 r2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
53248 p 10 h2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
57 344 p 9 r2 q7
- 256 p
5
r
2
+ 64 p
5
h
2
+ 64 p
4
r
2
q - 16 p
4
h
2
q + 4 p
2
r
2
q
3
- 4 p r
2
q
4
+ r
2
q
5
-
13 312 p 9 h2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
22 528 p 8 r2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
3328 p 8 h2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
16 384 p 7 r2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
2048 p 7 h2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
7232 p 6 r2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
896 p 6 h2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
304 p 4 r2 q12
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
11 Dimensional by Parker Emmerson ©2009-2011.nb 43
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160 p 3 r2 q13
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
56 p 2 r2 q14
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8 p r2 q15
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5-
32 768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
512 p 7 q5 h4
H2 p - q
L2
H4 p - q
L3
q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
ì
1 -1472 p 5 r2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
I128 p 5 h2M ì - 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q +
4 p 2 r2 q3 - 4 p r2 q4 + r2 2 p + p 2 - p 2 Sin
@b
D2
5
,
8q, - 2 p , 2<, 8b, - p ê 2, p ê 2<, 8h, - 1, 1<, AxesLabel Ø AutomaticF, 8r,
- 1, 1<F
44 11 Dimensional by Parker Emmerson ©2009-2011.nb
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11 Dimensional by Parker Emmerson ©2009-2011.nb 45
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q11 = -262144 p 12 r2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
65 536 p 12 h2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
393216 p 11 r2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
98 304 p 11 h2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
212992 p 10 r2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
53 248 p 10 h2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
57 344 p 9 r2 q7
- 256 p
5
r
2
+ 64 p
5
h
2
+ 64 p
4
r
2
q - 16 p
4
h
2
q + 4 p
2
r
2
q
3
- 4 p r
2
q
4
+ r
2
q
5
-
13 312 p 9 h2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
22 528 p 8 r2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
3328 p 8 h2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
16 384 p 7 r2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
2048 p 7 h2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
7232 p 6 r2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
896 p 6 h2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
304 p 4 r2 q12
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
46 11 Dimensional by Parker Emmerson ©2009-2011.nb
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160 p 3 r2 q13
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
56 p 2 r2 q14
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8 p r2 q15
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5-
32 768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
512 p 7 q5 h4
H2 p - q
L2
H4 p - q
L3
q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
ì
1 -1472 p 5 r2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 5 h2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
ManipulateBPlot3DB -
262144 p 12 r2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5+
65536 p 12 h2 q4
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
393216 p 11 r2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
98304 p 11 h2 q5
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
11 Dimensional by Parker Emmerson ©2009-2011.nb 47
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212992 p 10 r2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
53248 p 10 h2 q6
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
57 344 p 9 r2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5-
13 312 p 9 h2 q7
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
22 528 p 8 r2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
3328 p 8 h2 q8
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
16 384 p 7 r2 q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
2048 p 7
h2
q9
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
7232 p 6 r2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
896 p 6 h2 q10
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
304 p 4 r2 q12
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
160 p 3 r2 q13
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
56 p 2 r2 q14
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
8 p r2 q15
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
32 768 p 11 q h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
48 11 Dimensional by Parker Emmerson ©2009-2011.nb
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8192 p 10 q2 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
512 p 8 q4 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
-
512 p 7 q5 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 6 q6 h4 H2 p - qL2 H4 p - qL3 q3
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
ì
1 -1472 p 5 r2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
+
128 p 5 h2
- 256 p 5 r2 + 64 p 5 h2 + 64 p 4 r2 q - 16 p 4 h2 q + 4 p 2 r2 q3 - 4 p r2 q4 + r2 q5
,
8r, - 1, 1<, 8h, - 1, 1<F, 8q, - 2 p , 2 p <F
q
11 Dimensional by Parker Emmerson ©2009-2011.nb 49
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54 11 Dimensional by Parker Emmerson ©2009-2011.nb
