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last edited 10 years ago by Bill Page |
Edit detail for SandBoxLorentzTransformation revision 3 of 30
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Editor: Bill Page
Time: 2013/09/22 04:14:34 GMT+0 |
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| Note: | ||
changed: -vect [a1,a2,a3] vect [a1,a2,a3,a4] changed: -transpose(vect [a1,a2,a3]) transpose(vect [a1,a2,a3,a4]) removed: -Tensor product is -\begin{axiom} -tensor(v,w) == v*transpose(w) -tensor(vect [a1,a2,a3], vect [b1,b2,b3]) -\end{axiom} added: Tensor product is \begin{axiom} tensor(v,w) == v*g(w) tensor(vect [a1,a2,a3,a4], vect [b1,b2,b3,b4]) \end{axiom} added: v:=w(Q,P) g(Q,v) added: L(P,P) L(P,Q)*Q-P changed: -L(R,P)*R L(P,Q)*u + v
Lorentz transformations.
Book by T. Matolcsi
Mathematical Preliminaries
A vector is represented as a nx1 matrix (column vector)
fricas
vect(x:List Expression Integer):Matrix Expression Integer == matrix map(y+->[y],x)
Function declaration vect : List(Expression(Integer)) -> Matrix( Expression(Integer)) has been added to workspace.
Type: Void
fricas
vect [a1,a2, a3, a4]
fricas
Compiling function vect with type List(Expression(Integer)) ->
Matrix(Expression(Integer))![\label{eq1}\left[
\begin{array}{c}
a 1
\
a 2
\
a 3
\
a 4](images/2198737460665284646-16.0px.png "\label{eq1}\left[
\begin{array}{c}
a 1
\
a 2
\
a 3
\
a 4") | (1) |
Type: Matrix(Expression(Integer))
Then a row vector is
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transpose(vect [a1,a2, a3, a4])
 | (2) |
Type: Matrix(Expression(Integer))
Applying the Lorentz form produces a row vector
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g(x)==transpose(x)*diagonalMatrix [-1,1, 1, 1]
Type: Void
or a scalar
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g(x,y)== (transpose(x)*diagonalMatrix([-1, 1, 1, 1])*y)::EXPR INT
Type: Void
Tensor product is
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tensor(v,w) == v*g(w)
Type: Void
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tensor(vect [a1,a2, a3, a4], vect [b1, b2, b3, b4])
fricas
Compiling function g with type Matrix(Expression(Integer)) -> Matrix
(Expression(Integer))fricas
Compiling function tensor with type (Matrix(Expression(Integer)),Matrix(Expression(Integer))) -> Matrix(Expression(Integer))
![\label{eq3}\left[
\begin{array}{cccc}
-{a 1 \ b 1}&{a 1 \ b 2}&{a 1 \ b 3}&{a 1 \ b 4}
\
-{a 2 \ b 1}&{a 2 \ b 2}&{a 2 \ b 3}&{a 2 \ b 4}
\
-{a 3 \ b 1}&{a 3 \ b 2}&{a 3 \ b 3}&{a 3 \ b 4}
\
-{a 4 \ b 1}&{a 4 \ b 2}&{a 4 \ b 3}&{a 4 \ b 4}](images/8089115829163637274-16.0px.png "\label{eq3}\left[
\begin{array}{cccc}
-{a 1 \ b 1}&{a 1 \ b 2}&{a 1 \ b 3}&{a 1 \ b 4}
\
-{a 2 \ b 1}&{a 2 \ b 2}&{a 2 \ b 3}&{a 2 \ b 4}
\
-{a 3 \ b 1}&{a 3 \ b 2}&{a 3 \ b 3}&{a 3 \ b 4}
\
-{a 4 \ b 1}&{a 4 \ b 2}&{a 4 \ b 3}&{a 4 \ b 4}") | (3) |
Type: Matrix(Expression(Integer))
For difficult verifications it is sometimes convenient to replace symbols by random numerical values.
fricas
possible(x)==subst(x,map(y+->(y=(random(100) - random(100))), variables x) )
Type: Void
fricas
Is?(eq:Equation EXPR INT):Boolean == (lhs(eq)-rhs(eq)=0)::Boolean
Function declaration Is? : Equation(Expression(Integer)) -> Boolean has been added to workspace.
Type: Void
fricas
Is2?(eq:Equation(Matrix(EXPR(INT)))):Boolean == _ ( (lhs(eq)-rhs(eq)) :: Matrix Expression AlgebraicNumber = _ zero(nrows(lhs(eq)),ncols(lhs(eq)))$Matrix Expression AlgebraicNumber )::Boolean
Function declaration Is2? : Equation(Matrix(Expression(Integer))) -> Boolean has been added to workspace.
Type: Void
The AlgebraicNumber? domain can test for numerical equality of complicated
expressions involving 
.
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IsPossible?(eq:Equation EXPR INT):Boolean == _ (possible(lhs(eq)-rhs(eq)) :: Expression AlgebraicNumber=0)::Boolean
Function declaration IsPossible? : Equation(Expression(Integer)) -> Boolean has been added to workspace.
Type: Void
fricas
IsPossible2?(eq:Equation(Matrix(EXPR(INT)))):Boolean == _ ( map(possible,(lhs(eq)-rhs(eq))) :: Matrix Expression AlgebraicNumber = _ zero(nrows(lhs(eq)), ncols(lhs(eq)))$Matrix Expression AlgebraicNumber )::Boolean
Function declaration IsPossible2? : Equation(Matrix(Expression( Integer))) -> Boolean has been added to workspace.
Type: Void
Massive Objects
An object (also referred to as an obserser) is represented by a time-like 4-vector
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P:=vect [sqrt(p1^2+p2^2+p3^2+1),p1, p2, p3];
Type: Matrix(Expression(Integer))
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g(P,P)
fricas
Compiling function g with type (Matrix(Expression(Integer)),Matrix( Expression(Integer))) -> Expression(Integer)
 | (4) |
Type: Expression(Integer)
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Q:=vect [sqrt(q1^2+q2^2+q3^2+1),q1, q2, q3];
Type: Matrix(Expression(Integer))
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g(Q,Q)
 | (5) |
Type: Expression(Integer)
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R:=vect [1,0, 0, 0]
![\label{eq6}\left[
\begin{array}{c}
1
\
0
\
0
\
0](images/6345508732508486706-16.0px.png "\label{eq6}\left[
\begin{array}{c}
1
\
0
\
0
\
0") | (6) |
Type: Matrix(Expression(Integer))
fricas
g(R,R)
 | (7) |
Type: Expression(Integer)
Associated with each such vector is the orthogonal 3-d Euclidean subspace
Relative Velocity
An object Q has a unique relative velocity w(P,Q) with respect to object P given by
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w(P,Q)==-Q/g(P, Q)-P
Type: Void
Lorentz factor
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gamma(v)==1/sqrt(1-g(v,v))
Type: Void
Binary Boost
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b(P,v)==gamma(v)*(P+v)
Type: Void
Observer P measures velocity u. u is space-like and in 
.
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u:=w(P,Q);
fricas
Compiling function w with type (Matrix(Expression(Integer)),Matrix( Expression(Integer))) -> Matrix(Expression(Integer))
Type: Matrix(Expression(Integer))
fricas
g(P,u)
 | (8) |
Type: Expression(Integer)
fricas
v:=w(Q,P)
![\label{eq9}\left[
\begin{array}{c}
{{{{\left({p 3 \ q 3}+{p 2 \ q 2}+{p 1 \ q 1}\right)}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{{q 3}^{2}}-{{q 2}^{2}}-{{q 1}^{2}}\right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}}}\over{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}-{p 3 \ q 3}-{p 2 \ q 2}-{p 1 \ q 1}}}
\
{{-{q 1 \ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{p 3 \ q 1 \ q 3}+{p 2 \ q 1 \ q 2}+{p 1 \ {{q 1}^{2}}}+ p 1}\over{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}-{p 3 \ q 3}-{p 2 \ q 2}-{p 1 \ q 1}}}
\
{{-{q 2 \ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{p 3 \ q 2 \ q 3}+{p 2 \ {{q 2}^{2}}}+{p 1 \ q 1 \ q 2}+ p 2}\over{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}-{p 3 \ q 3}-{p 2 \ q 2}-{p 1 \ q 1}}}
\
{{-{q 3 \ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{p 3 \ {{q 3}^{2}}}+{{\left({p 2 \ q 2}+{p 1 \ q 1}\right)}\ q 3}+ p 3}\over{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}-{p 3 \ q 3}-{p 2 \ q 2}-{p 1 \ q 1}}}](images/2227620814854408821-16.0px.png "\label{eq9}\left[
\begin{array}{c}
{{{{\left({p 3 \ q 3}+{p 2 \ q 2}+{p 1 \ q 1}\right)}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{{q 3}^{2}}-{{q 2}^{2}}-{{q 1}^{2}}\right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}}}\over{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}-{p 3 \ q 3}-{p 2 \ q 2}-{p 1 \ q 1}}}
\
{{-{q 1 \ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{p 3 \ q 1 \ q 3}+{p 2 \ q 1 \ q 2}+{p 1 \ {{q 1}^{2}}}+ p 1}\over{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}-{p 3 \ q 3}-{p 2 \ q 2}-{p 1 \ q 1}}}
\
{{-{q 2 \ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{p 3 \ q 2 \ q 3}+{p 2 \ {{q 2}^{2}}}+{p 1 \ q 1 \ q 2}+ p 2}\over{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}-{p 3 \ q 3}-{p 2 \ q 2}-{p 1 \ q 1}}}
\
{{-{q 3 \ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{p 3 \ {{q 3}^{2}}}+{{\left({p 2 \ q 2}+{p 1 \ q 1}\right)}\ q 3}+ p 3}\over{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}-{p 3 \ q 3}-{p 2 \ q 2}-{p 1 \ q 1}}}") | (9) |
Type: Matrix(Expression(Integer))
fricas
g(Q,v)
 | (10) |
Type: Expression(Integer)
fricas
possible(g(u,u))::EXPR Float
fricas
Compiling function possible with type Expression(Integer) ->
Expression(Integer) | (11) |
Type: Expression(Float)
fricas
L(P,Q) == diagonalMatrix([1, 1, 1, 1]) + tensor(P+Q, P+Q)/(1-g(P, Q)) - 2*tensor(P, Q)
Type: Void
fricas
L(P,P)
fricas
Compiling function L with type (Matrix(Expression(Integer)),Matrix( Expression(Integer))) -> Matrix(Expression(Integer))
![\label{eq12}\left[
\begin{array}{cccc}
1 & 0 & 0 & 0
\
0 & 1 & 0 & 0
\
0 & 0 & 1 & 0
\
0 & 0 & 0 & 1](images/7258234151035562175-16.0px.png "\label{eq12}\left[
\begin{array}{cccc}
1 & 0 & 0 & 0
\
0 & 1 & 0 & 0
\
0 & 0 & 1 & 0
\
0 & 0 & 0 & 1") | (12) |
Type: Matrix(Expression(Integer))
fricas
L(P,Q)*Q-P
![\label{eq13}\left[
\begin{array}{c}
0
\
0
\
0
\
0](images/5701575585267440490-16.0px.png "\label{eq13}\left[
\begin{array}{c}
0
\
0
\
0
\
0") | (13) |
Type: Matrix(Expression(Integer))
fricas
L(R,P)
![\label{eq14}\left[
\begin{array}{cccc}
{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}& - p 1 & - p 2 & - p 3
\
- p 1 &{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+{{p 1}^{2}}+ 1}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}&{{p 1 \ p 2}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}&{{p 1 \ p 3}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}
\
- p 2 &{{p 1 \ p 2}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}&{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+{{p 2}^{2}}+ 1}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}&{{p 2 \ p 3}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}
\
- p 3 &{{p 1 \ p 3}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}&{{p 2 \ p 3}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}&{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+{{p 3}^{2}}+ 1}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}](images/3659931444992713636-16.0px.png "\label{eq14}\left[
\begin{array}{cccc}
{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}& - p 1 & - p 2 & - p 3
\
- p 1 &{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+{{p 1}^{2}}+ 1}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}&{{p 1 \ p 2}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}&{{p 1 \ p 3}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}
\
- p 2 &{{p 1 \ p 2}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}&{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+{{p 2}^{2}}+ 1}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}&{{p 2 \ p 3}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}
\
- p 3 &{{p 1 \ p 3}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}&{{p 2 \ p 3}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}&{{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+{{p 3}^{2}}+ 1}\over{{\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}+ 1}}") | (14) |
Type: Matrix(Expression(Integer))
fricas
L(P,Q)*u + v
![\label{eq15}\left[
\begin{array}{c}
{{{{\left({{\left({{16}\ {{p 3}^{5}}}+{{\left({{24}\ {{p 2}^{2}}}+{{24}\ {{p 1}^{2}}}+{24}\right)}\ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{4}}}+{{\left({{16}\ {{p 1}^{2}}}+{16}\right)}\ {{p 2}^{2}}}+{8 \ {{p 1}^{4}}}+{{16}\ {{p 1}^{2}}}+ 8 \right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left({{32}\ p 2 \ {{p 3}^{4}}}+{{\left({{4
0}\ {{p 2}^{3}}}+{{\left({{40}\ {{p 1}^{2}}}+{40}\right)}\ p 2}\right)}\ {{p 3}^{2}}}+{8 \ {{p 2}^{5}}}+{{\left({{16}\ {{p 1}^{2}}}+{16}\right)}\ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{4}}}+{{16}\ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ q 2}+{{\left({{3
2}\ p 1 \ {{p 3}^{4}}}+{{\left({{40}\ p 1 \ {{p 2}^{2}}}+{{4
0}\ {{p 1}^{3}}}+{{40}\ p 1}\right)}\ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{4}}}+{{\left({{16}\ {{p 1}^{3}}}+{{16}\ p 1}\right)}\ {{p 2}^{2}}}+{8 \ {{p 1}^{5}}}+{{16}\ {{p 1}^{3}}}+{8 \ p 1}\right)}\ q 1}-{8 \ {{p 3}^{4}}}+{{\left(-{{10}\ {{p 2}^{2}}}-{{10}\ {{p 1}^{2}}}-{10}\right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{q 3}^{2}}}+{{\left({{\left({8 \ {{p 3}^{5}}}+{{\left({{40}\ {{p 2}^{2}}}+{{16}\ {{p 1}^{2}}}+{16}\right)}\ {{p 3}^{3}}}+{{\left({{32}\ {{p 2}^{4}}}+{{\left({{4
0}\ {{p 1}^{2}}}+{40}\right)}\ {{p 2}^{2}}}+{8 \ {{p 1}^{4}}}+{{16}\ {{p 1}^{2}}}+ 8 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{\left({{48}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left({{4
8}\ p 1 \ {{p 2}^{3}}}+{{\left({{48}\ {{p 1}^{3}}}+{{48}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 1}-{{12}\ p 2 \ {{p 3}^{3}}}+{{\left(-{{12}\ {{p 2}^{3}}}+{{\left(-{{12}\ {{p 1}^{2}}}-{12}\right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left({8 \ {{p 3}^{5}}}+{{\left({{16}\ {{p 2}^{2}}}+{{40}\ {{p 1}^{2}}}+{16}\right)}\ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{4}}}+{{\left({{4
0}\ {{p 1}^{2}}}+{16}\right)}\ {{p 2}^{2}}}+{{32}\ {{p 1}^{4}}}+{{40}\ {{p 1}^{2}}}+ 8 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left(-{{12}\ p 1 \ {{p 3}^{3}}}+{{\left(-{{12}\ p 1 \ {{p 2}^{2}}}-{{12}\ {{p 1}^{3}}}-{{12}\ p 1}\right)}\ p 3}\right)}\ q 1}+{8 \ {{p 3}^{5}}}+{{\left({{16}\ {{p 2}^{2}}}+{{16}\ {{p 1}^{2}}}+{12}\right)}\ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{4}}}+{{\left({{16}\ {{p 1}^{2}}}+{12}\right)}\ {{p 2}^{2}}}+{8 \ {{p 1}^{4}}}+{{12}\ {{p 1}^{2}}}+ 4 \right)}\ p 3}\right)}\ q 3}+{{\left({8 \ p 2 \ {{p 3}^{4}}}+{{\left({{24}\ {{p 2}^{3}}}+{{\left({{16}\ {{p 1}^{2}}}+{16}\right)}\ p 2}\right)}\ {{p 3}^{2}}}+{{16}\ {{p 2}^{5}}}+{{\left({{24}\ {{p 1}^{2}}}+{24}\right)}\ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{4}}}+{{16}\ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left({8 \ p 1 \ {{p 3}^{4}}}+{{\left({{40}\ p 1 \ {{p 2}^{2}}}+{{16}\ {{p 1}^{3}}}+{{16}\ p 1}\right)}\ {{p 3}^{2}}}+{{32}\ p 1 \ {{p 2}^{4}}}+{{\left({{40}\ {{p 1}^{3}}}+{{40}\ p 1}\right)}\ {{p 2}^{2}}}+{8 \ {{p 1}^{5}}}+{{16}\ {{p 1}^{3}}}+{8 \ p 1}\right)}\ q 1}-{2 \ {{p 3}^{4}}}+{{\left(-{{10}\ {{p 2}^{2}}}-{4 \ {{p 1}^{2}}}- 4 \right)}\ {{p 3}^{2}}}-{8 \ {{p 2}^{4}}}+{{\left(-{{1
0}\ {{p 1}^{2}}}-{10}\right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{q 2}^{2}}}+{{\left({{\left({8 \ p 2 \ {{p 3}^{4}}}+{{\left({{16}\ {{p 2}^{3}}}+{{\left({{4
0}\ {{p 1}^{2}}}+{16}\right)}\ p 2}\right)}\ {{p 3}^{2}}}+{8 \ {{p 2}^{5}}}+{{\left({{40}\ {{p 1}^{2}}}+{16}\right)}\ {{p 2}^{3}}}+{{\left({{32}\ {{p 1}^{4}}}+{{40}\ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{{\left(-{{12}\ p 1 \ p 2 \ {{p 3}^{2}}}-{{12}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{12}\ {{p 1}^{3}}}-{{12}\ p 1}\right)}\ p 2}\right)}\ q 1}+{8 \ p 2 \ {{p 3}^{4}}}+{{\left({{16}\ {{p 2}^{3}}}+{{\left({{16}\ {{p 1}^{2}}}+{12}\right)}\ p 2}\right)}\ {{p 3}^{2}}}+{8 \ {{p 2}^{5}}}+{{\left({{1
6}\ {{p 1}^{2}}}+{12}\right)}\ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{4}}}+{{12}\ {{p 1}^{2}}}+ 4 \right)}\ p 2}\right)}\ q 2}+{{\left({8 \ p 1 \ {{p 3}^{4}}}+{{\left({{16}\ p 1 \ {{p 2}^{2}}}+{{24}\ {{p 1}^{3}}}+{{16}\ p 1}\right)}\ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{4}}}+{{\left({{24}\ {{p 1}^{3}}}+{{16}\ p 1}\right)}\ {{p 2}^{2}}}+{{16}\ {{p 1}^{5}}}+{{24}\ {{p 1}^{3}}}+{8 \ p 1}\right)}\ {{q 1}^{3}}}+{{\left(-{2 \ {{p 3}^{4}}}+{{\left(-{4 \ {{p 2}^{2}}}-{{10}\ {{p 1}^{2}}}- 4 \right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{4}}}+{{\left(-{{10}\ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{2}}}-{8 \ {{p 1}^{4}}}-{{10}\ {{p 1}^{2}}}- 2 \right)}\ {{q 1}^{2}}}+{{\left({8 \ p 1 \ {{p 3}^{4}}}+{{\left({{16}\ p 1 \ {{p 2}^{2}}}+{{16}\ {{p 1}^{3}}}+{{12}\ p 1}\right)}\ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{4}}}+{{\left({{16}\ {{p 1}^{3}}}+{{12}\ p 1}\right)}\ {{p 2}^{2}}}+{8 \ {{p 1}^{5}}}+{{12}\ {{p 1}^{3}}}+{4 \ p 1}\right)}\ q 1}-{2 \ {{p 3}^{4}}}+{{\left(-{4 \ {{p 2}^{2}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{2 \ {{p 1}^{2}}}\right)}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left({{\left(-{{16}\ {{p 3}^{4}}}+{{\left(-{{16}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{2}}}-{16}\right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{q 3}^{4}}}+{{\left({{\left(-{{32}\ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{24}\right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left(-{{32}\ p 1 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{2}}}-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 3}\right)}\ q 1}+{8 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{2}}}+{6 \ {{p 1}^{2}}}+ 6 \right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{{16}\ {{p 3}^{4}}}+{{\left(-{{44}\ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}-{20}\right)}\ {{p 3}^{2}}}-{{16}\ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{20}\right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{4}}}-{8 \ {{p 1}^{2}}}- 4 \right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{48}\ p 1 \ p 2 \ {{p 3}^{2}}}-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ q 1}+{{12}\ p 2 \ {{p 3}^{2}}}+{6 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ q 2}+{{\left(-{{16}\ {{p 3}^{4}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{{44}\ {{p 1}^{2}}}-{20}\right)}\ {{p 3}^{2}}}-{4 \ {{p 2}^{4}}}+{{\left(-{{2
0}\ {{p 1}^{2}}}- 8 \right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}- 4 \right)}\ {{q 1}^{2}}}+{{\left({{12}\ p 1 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ q 1}-{{16}\ {{p 3}^{4}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}-{16}\right)}\ {{p 3}^{2}}}-{4 \ {{p 2}^{4}}}+{{\left(-{8 \ {{p 1}^{2}}}- 6 \right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{4}}}-{6 \ {{p 1}^{2}}}- 2 \right)}\ {{q 3}^{2}}}+{{\left({{\left(-{{24}\ p 2 \ {{p 3}^{3}}}+{{\left(-{{32}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{24}\right)}\ p 2}\right)}\ p 3}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{{24}\ p 1 \ {{p 3}^{3}}}+{{\left(-{{48}\ p 1 \ {{p 2}^{2}}}-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 3}\right)}\ q 1}+{6 \ {{p 3}^{3}}}+{{\left({{12}\ {{p 2}^{2}}}+{6 \ {{p 1}^{2}}}+ 6 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 2}^{3}}}+{{\left(-{{48}\ {{p 1}^{2}}}-{24}\right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{12}\ p 1 \ p 2 \ p 3 \ q 1}-{{24}\ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{20}\right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left(-{{24}\ p 1 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{2}}}-{{32}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 3}\right)}\ {{q 1}^{3}}}+{{\left({6 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{2}}}+{{12}\ {{p 1}^{2}}}+ 6 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ p 1 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{2}}}-{{24}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ p 3}\right)}\ q 1}+{6 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{2}}}+{6 \ {{p 1}^{2}}}+ 4 \right)}\ p 3}\right)}\ q 3}+{{\left(-{2 \ {{p 3}^{4}}}+{{\left(-{{16}\ {{p 2}^{2}}}-{4 \ {{p 1}^{2}}}- 4 \right)}\ {{p 3}^{2}}}-{{16}\ {{p 2}^{4}}}+{{\left(-{{16}\ {{p 1}^{2}}}-{16}\right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{q 2}^{4}}}+{{\left({{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{2}}}-{{32}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ q 1}+{6 \ p 2 \ {{p 3}^{2}}}+{8 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{4 \ {{p 3}^{4}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}- 8 \right)}\ {{p 3}^{2}}}-{{16}\ {{p 2}^{4}}}+{{\left(-{{44}\ {{p 1}^{2}}}-{20}\right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}- 4 \right)}\ {{q 1}^{2}}}+{{\left({6 \ p 1 \ {{p 3}^{2}}}+{{12}\ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ q 1}-{4 \ {{p 3}^{4}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{8 \ {{p 1}^{2}}}- 6 \right)}\ {{p 3}^{2}}}-{{16}\ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{16}\right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{4}}}-{6 \ {{p 1}^{2}}}- 2 \right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{2}}}-{{2
4}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{32}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ {{q 1}^{3}}}+{{\left({6 \ p 2 \ {{p 3}^{2}}}+{6 \ {{p 2}^{3}}}+{{\left({{12}\ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{2}}}-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ p 2}\right)}\ q 1}+{6 \ p 2 \ {{p 3}^{2}}}+{6 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 4 \right)}\ p 2}\right)}\ q 2}+{{\left(-{2 \ {{p 3}^{4}}}+{{\left(-{4 \ {{p 2}^{2}}}-{{16}\ {{p 1}^{2}}}- 4 \right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{4}}}+{{\left(-{{16}\ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{16}\ {{p 1}^{2}}}- 2 \right)}\ {{q 1}^{4}}}+{{\left({6 \ p 1 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ {{q 1}^{3}}}+{{\left(-{4 \ {{p 3}^{4}}}+{{\left(-{8 \ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}- 6 \right)}\ {{p 3}^{2}}}-{4 \ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{2}}}- 6 \right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{16}\ {{p 1}^{2}}}- 2 \right)}\ {{q 1}^{2}}}+{{\left({6 \ p 1 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ q 1}-{2 \ {{p 3}^{4}}}+{{\left(-{4 \ {{p 2}^{2}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{2 \ {{p 1}^{2}}}\right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}}}\over{{{\left({{\left({4 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({6 \ p 2 \ p 3 \ q 2}+{6 \ p 1 \ p 3 \ q 1}-{2 \ p 3}\right)}\ q 3}+{{\left({{p 3}^{2}}+{4 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({6 \ p 1 \ p 2 \ q 1}-{2 \ p 2}\right)}\ q 2}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{4 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}-{2 \ p 1 \ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{4 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{6 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{6 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{2 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{6 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left(-{6 \ p 1 \ p 2 \ p 3 \ q 1}+{2 \ p 2 \ p 3}\right)}\ q 2}+{{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 3 \ q 1}-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ q 3}+{{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{4 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{6 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{2 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 2 \ q 1}-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{4 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ {{q 1}^{3}}}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{2 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}
\
{{{{\left({{\left({{16}\ p 1 \ {{p 3}^{3}}}+{{\left({8 \ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left({{32}\ p 1 \ p 2 \ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 2}\right)}\ q 2}+{{\left({{32}\ {{p 1}^{2}}\ {{p 3}^{2}}}+{8 \ {{p 1}^{2}}\ {{p 2}^{2}}}+{8 \ {{p 1}^{4}}}+{8 \ {{p 1}^{2}}}\right)}\ q 1}-{8 \ p 1 \ {{p 3}^{2}}}-{2 \ p 1 \ {{p 2}^{2}}}-{2 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 3}^{2}}}+{{\left({{\left({8 \ p 1 \ {{p 3}^{3}}}+{{\left({{32}\ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{4
8}\ {{p 1}^{2}}\ p 2 \ p 3 \ q 1}-{{12}\ p 1 \ p 2 \ p 3}\right)}\ q 2}+{{\left({8 \ p 1 \ {{p 3}^{3}}}+{{\left({8 \ p 1 \ {{p 2}^{2}}}+{{32}\ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 3}\right)}\ {{q 1}^{2}}}-{{12}\ {{p 1}^{2}}\ p 3 \ q 1}+{8 \ p 1 \ {{p 3}^{3}}}+{{\left({8 \ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 3}\right)}\ q 3}+{{\left({8 \ p 1 \ p 2 \ {{p 3}^{2}}}+{{16}\ p 1 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left({8 \ {{p 1}^{2}}\ {{p 3}^{2}}}+{{32}\ {{p 1}^{2}}\ {{p 2}^{2}}}+{8 \ {{p 1}^{4}}}+{8 \ {{p 1}^{2}}}\right)}\ q 1}-{2 \ p 1 \ {{p 3}^{2}}}-{8 \ p 1 \ {{p 2}^{2}}}-{2 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 2}^{2}}}+{{\left({{\left({8 \ p 1 \ p 2 \ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{3}}}+{{\left({{3
2}\ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 2}\right)}\ {{q 1}^{2}}}-{{12}\ {{p 1}^{2}}\ p 2 \ q 1}+{8 \ p 1 \ p 2 \ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 2}\right)}\ q 2}+{{\left({8 \ {{p 1}^{2}}\ {{p 3}^{2}}}+{8 \ {{p 1}^{2}}\ {{p 2}^{2}}}+{{16}\ {{p 1}^{4}}}+{8 \ {{p 1}^{2}}}\right)}\ {{q 1}^{3}}}+{{\left(-{2 \ p 1 \ {{p 3}^{2}}}-{2 \ p 1 \ {{p 2}^{2}}}-{8 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 1}^{2}}}+{{\left({8 \ {{p 1}^{2}}\ {{p 3}^{2}}}+{8 \ {{p 1}^{2}}\ {{p 2}^{2}}}+{8 \ {{p 1}^{4}}}+{4 \ {{p 1}^{2}}}\right)}\ q 1}-{2 \ p 1 \ {{p 3}^{2}}}-{2 \ p 1 \ {{p 2}^{2}}}-{2 \ {{p 1}^{3}}}\right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{{16}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{16}\ p 1 \ {{p 2}^{2}}}-{{16}\ {{p 1}^{3}}}-{{16}\ p 1}\right)}\ {{p 3}^{2}}}-{2 \ p 1 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{3}}}-{4 \ p 1}\right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{5}}}-{4 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 3}^{4}}}+{{\left({{\left(-{{32}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left(-{{32}\ {{p 1}^{2}}\ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}\ {{p 2}^{2}}}-{{24}\ {{p 1}^{4}}}-{{24}\ {{p 1}^{2}}}\right)}\ p 3}\right)}\ q 1}+{8 \ p 1 \ {{p 3}^{3}}}+{{\left({6 \ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{{16}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{44}\ p 1 \ {{p 2}^{2}}}-{{20}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ {{p 3}^{2}}}-{{16}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{5}}}-{8 \ {{p 1}^{3}}}-{4 \ p 1}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{48}\ {{p 1}^{2}}\ p 2 \ {{p 3}^{2}}}-{{24}\ {{p 1}^{2}}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{4}}}-{{24}\ {{p 1}^{2}}}\right)}\ p 2}\right)}\ q 1}+{{12}\ p 1 \ p 2 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 2}\right)}\ q 2}+{{\left(-{{1
6}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{20}\ p 1 \ {{p 2}^{2}}}-{{4
4}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ {{p 3}^{2}}}-{4 \ p 1 \ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{3}}}-{8 \ p 1}\right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{5}}}-{{20}\ {{p 1}^{3}}}-{4 \ p 1}\right)}\ {{q 1}^{2}}}+{{\left({{12}\ {{p 1}^{2}}\ {{p 3}^{2}}}+{6 \ {{p 1}^{2}}\ {{p 2}^{2}}}+{6 \ {{p 1}^{4}}}+{6 \ {{p 1}^{2}}}\right)}\ q 1}-{{16}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{20}\ p 1 \ {{p 2}^{2}}}-{{20}\ {{p 1}^{3}}}-{{16}\ p 1}\right)}\ {{p 3}^{2}}}-{4 \ p 1 \ {{p 2}^{4}}}+{{\left(-{8 \ {{p 1}^{3}}}-{6 \ p 1}\right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{5}}}-{6 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 3}^{2}}}+{{\left({{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{32}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{{24}\ {{p 1}^{2}}\ {{p 3}^{3}}}+{{\left(-{{48}\ {{p 1}^{2}}\ {{p 2}^{2}}}-{{24}\ {{p 1}^{4}}}-{{24}\ {{p 1}^{2}}}\right)}\ p 3}\right)}\ q 1}+{6 \ p 1 \ {{p 3}^{3}}}+{{\left({{12}\ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{48}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{12}\ {{p 1}^{2}}\ p 2 \ p 3 \ q 1}-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left(-{{24}\ {{p 1}^{2}}\ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}\ {{p 2}^{2}}}-{{32}\ {{p 1}^{4}}}-{{24}\ {{p 1}^{2}}}\right)}\ p 3}\right)}\ {{q 1}^{3}}}+{{\left({6 \ p 1 \ {{p 3}^{3}}}+{{\left({6 \ p 1 \ {{p 2}^{2}}}+{{12}\ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ {{p 1}^{2}}\ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}\ {{p 2}^{2}}}-{{24}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}\right)}\ p 3}\right)}\ q 1}+{6 \ p 1 \ {{p 3}^{3}}}+{{\left({6 \ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 3}\right)}\ q 3}+{{\left(-{2 \ p 1 \ {{p 3}^{4}}}+{{\left(-{{16}\ p 1 \ {{p 2}^{2}}}-{4 \ {{p 1}^{3}}}-{4 \ p 1}\right)}\ {{p 3}^{2}}}-{{16}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{16}\ {{p 1}^{3}}}-{{16}\ p 1}\right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{5}}}-{4 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 2}^{4}}}+{{\left({{\left(-{{24}\ {{p 1}^{2}}\ p 2 \ {{p 3}^{2}}}-{{32}\ {{p 1}^{2}}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{4}}}-{{24}\ {{p 1}^{2}}}\right)}\ p 2}\right)}\ q 1}+{6 \ p 1 \ p 2 \ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{4 \ p 1 \ {{p 3}^{4}}}+{{\left(-{{20}\ p 1 \ {{p 2}^{2}}}-{{20}\ {{p 1}^{3}}}-{8 \ p 1}\right)}\ {{p 3}^{2}}}-{{16}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{44}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{5}}}-{{20}\ {{p 1}^{3}}}-{4 \ p 1}\right)}\ {{q 1}^{2}}}+{{\left({6 \ {{p 1}^{2}}\ {{p 3}^{2}}}+{{12}\ {{p 1}^{2}}\ {{p 2}^{2}}}+{6 \ {{p 1}^{4}}}+{6 \ {{p 1}^{2}}}\right)}\ q 1}-{4 \ p 1 \ {{p 3}^{4}}}+{{\left(-{{20}\ p 1 \ {{p 2}^{2}}}-{8 \ {{p 1}^{3}}}-{6 \ p 1}\right)}\ {{p 3}^{2}}}-{{16}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{3}}}-{{16}\ p 1}\right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{5}}}-{6 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ {{p 1}^{2}}\ p 2 \ {{p 3}^{2}}}-{{24}\ {{p 1}^{2}}\ {{p 2}^{3}}}+{{\left(-{{32}\ {{p 1}^{4}}}-{{24}\ {{p 1}^{2}}}\right)}\ p 2}\right)}\ {{q 1}^{3}}}+{{\left({6 \ p 1 \ p 2 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{3}}}+{{\left({{1
2}\ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 2}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ {{p 1}^{2}}\ p 2 \ {{p 3}^{2}}}-{{24}\ {{p 1}^{2}}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}\right)}\ p 2}\right)}\ q 1}+{6 \ p 1 \ p 2 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 2}\right)}\ q 2}+{{\left(-{2 \ p 1 \ {{p 3}^{4}}}+{{\left(-{4 \ p 1 \ {{p 2}^{2}}}-{{16}\ {{p 1}^{3}}}-{4 \ p 1}\right)}\ {{p 3}^{2}}}-{2 \ p 1 \ {{p 2}^{4}}}+{{\left(-{{16}\ {{p 1}^{3}}}-{4 \ p 1}\right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{5}}}-{{16}\ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 1}^{4}}}+{{\left({6 \ {{p 1}^{2}}\ {{p 3}^{2}}}+{6 \ {{p 1}^{2}}\ {{p 2}^{2}}}+{8 \ {{p 1}^{4}}}+{6 \ {{p 1}^{2}}}\right)}\ {{q 1}^{3}}}+{{\left(-{4 \ p 1 \ {{p 3}^{4}}}+{{\left(-{8 \ p 1 \ {{p 2}^{2}}}-{{20}\ {{p 1}^{3}}}-{6 \ p 1}\right)}\ {{p 3}^{2}}}-{4 \ p 1 \ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{3}}}-{6 \ p 1}\right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{5}}}-{{16}\ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 1}^{2}}}+{{\left({6 \ {{p 1}^{2}}\ {{p 3}^{2}}}+{6 \ {{p 1}^{2}}\ {{p 2}^{2}}}+{6 \ {{p 1}^{4}}}+{4 \ {{p 1}^{2}}}\right)}\ q 1}-{2 \ p 1 \ {{p 3}^{4}}}+{{\left(-{4 \ p 1 \ {{p 2}^{2}}}-{4 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{p 3}^{2}}}-{2 \ p 1 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{5}}}-{2 \ {{p 1}^{3}}}}\over{{{\left({{\left({4 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({6 \ p 2 \ p 3 \ q 2}+{6 \ p 1 \ p 3 \ q 1}-{2 \ p 3}\right)}\ q 3}+{{\left({{p 3}^{2}}+{4 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({6 \ p 1 \ p 2 \ q 1}-{2 \ p 2}\right)}\ q 2}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{4 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}-{2 \ p 1 \ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{4 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{6 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{6 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{2 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{6 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left(-{6 \ p 1 \ p 2 \ p 3 \ q 1}+{2 \ p 2 \ p 3}\right)}\ q 2}+{{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 3 \ q 1}-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ q 3}+{{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{4 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{6 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{2 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 2 \ q 1}-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{4 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ {{q 1}^{3}}}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{2 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}
\
{{{{\left({{\left({{16}\ p 2 \ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left({{32}\ {{p 2}^{2}}\ {{p 3}^{2}}}+{8 \ {{p 2}^{4}}}+{{\left({8 \ {{p 1}^{2}}}+ 8 \right)}\ {{p 2}^{2}}}\right)}\ q 2}+{{\left({{32}\ p 1 \ p 2 \ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 2}\right)}\ q 1}-{8 \ p 2 \ {{p 3}^{2}}}-{2 \ {{p 2}^{3}}}+{{\left(-{2 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 3}^{2}}}+{{\left({{\left({8 \ p 2 \ {{p 3}^{3}}}+{{\left({{32}\ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{48}\ p 1 \ {{p 2}^{2}}\ p 3 \ q 1}-{{12}\ {{p 2}^{2}}\ p 3}\right)}\ q 2}+{{\left({8 \ p 2 \ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{3}}}+{{\left({{32}\ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{2}}}-{{12}\ p 1 \ p 2 \ p 3 \ q 1}+{8 \ p 2 \ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{2}}}+ 4 \right)}\ p 2}\right)}\ p 3}\right)}\ q 3}+{{\left({8 \ {{p 2}^{2}}\ {{p 3}^{2}}}+{{1
6}\ {{p 2}^{4}}}+{{\left({8 \ {{p 1}^{2}}}+ 8 \right)}\ {{p 2}^{2}}}\right)}\ {{q 2}^{3}}}+{{\left({{\left({8 \ p 1 \ p 2 \ {{p 3}^{2}}}+{{32}\ p 1 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 2}\right)}\ q 1}-{2 \ p 2 \ {{p 3}^{2}}}-{8 \ {{p 2}^{3}}}+{{\left(-{2 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 2}^{2}}}+{{\left({{\left({8 \ {{p 2}^{2}}\ {{p 3}^{2}}}+{8 \ {{p 2}^{4}}}+{{\left({{32}\ {{p 1}^{2}}}+ 8 \right)}\ {{p 2}^{2}}}\right)}\ {{q 1}^{2}}}-{{12}\ p 1 \ {{p 2}^{2}}\ q 1}+{8 \ {{p 2}^{2}}\ {{p 3}^{2}}}+{8 \ {{p 2}^{4}}}+{{\left({8 \ {{p 1}^{2}}}+ 4 \right)}\ {{p 2}^{2}}}\right)}\ q 2}+{{\left({8 \ p 1 \ p 2 \ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{3}}}+{{\left({{1
6}\ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 2}\right)}\ {{q 1}^{3}}}+{{\left(-{2 \ p 2 \ {{p 3}^{2}}}-{2 \ {{p 2}^{3}}}+{{\left(-{8 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{{\left({8 \ p 1 \ p 2 \ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 2}\right)}\ q 1}-{2 \ p 2 \ {{p 3}^{2}}}-{2 \ {{p 2}^{3}}}-{2 \ {{p 1}^{2}}\ p 2}\right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{{16}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{16}\ {{p 2}^{3}}}+{{\left(-{{16}\ {{p 1}^{2}}}-{16}\right)}\ p 2}\right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{5}}}+{{\left(-{4 \ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{3}}}+{{\left(-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 3}^{4}}}+{{\left({{\left(-{{32}\ {{p 2}^{2}}\ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 2}^{4}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{24}\right)}\ {{p 2}^{2}}}\right)}\ p 3}\right)}\ q 2}+{{\left(-{{32}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 1}+{8 \ p 2 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{{16}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{44}\ {{p 2}^{3}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{20}\right)}\ p 2}\right)}\ {{p 3}^{2}}}-{{16}\ {{p 2}^{5}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{20}\right)}\ {{p 2}^{3}}}+{{\left(-{4 \ {{p 1}^{4}}}-{8 \ {{p 1}^{2}}}- 4 \right)}\ p 2}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{48}\ p 1 \ {{p 2}^{2}}\ {{p 3}^{2}}}-{{24}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{2
4}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ {{p 2}^{2}}}\right)}\ q 1}+{{12}\ {{p 2}^{2}}\ {{p 3}^{2}}}+{6 \ {{p 2}^{4}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ {{p 2}^{2}}}\right)}\ q 2}+{{\left(-{{16}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{20}\ {{p 2}^{3}}}+{{\left(-{{44}\ {{p 1}^{2}}}-{20}\right)}\ p 2}\right)}\ {{p 3}^{2}}}-{4 \ {{p 2}^{5}}}+{{\left(-{{20}\ {{p 1}^{2}}}- 8 \right)}\ {{p 2}^{3}}}+{{\left(-{{16}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}- 4 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{{\left({{12}\ p 1 \ p 2 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 2}\right)}\ q 1}-{{16}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{20}\ {{p 2}^{3}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{16}\right)}\ p 2}\right)}\ {{p 3}^{2}}}-{4 \ {{p 2}^{5}}}+{{\left(-{8 \ {{p 1}^{2}}}- 6 \right)}\ {{p 2}^{3}}}+{{\left(-{4 \ {{p 1}^{4}}}-{6 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 3}^{2}}}+{{\left({{\left(-{{24}\ {{p 2}^{2}}\ {{p 3}^{3}}}+{{\left(-{{32}\ {{p 2}^{4}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{24}\right)}\ {{p 2}^{2}}}\right)}\ p 3}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{48}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 1}+{6 \ p 2 \ {{p 3}^{3}}}+{{\left({{1
2}\ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ {{p 2}^{2}}\ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 2}^{4}}}+{{\left(-{{48}\ {{p 1}^{2}}}-{24}\right)}\ {{p 2}^{2}}}\right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{12}\ p 1 \ {{p 2}^{2}}\ p 3 \ q 1}-{{24}\ {{p 2}^{2}}\ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 2}^{4}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{20}\right)}\ {{p 2}^{2}}}\right)}\ p 3}\right)}\ q 2}+{{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{32}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{3}}}+{{\left({6 \ p 2 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{3}}}+{{\left({{12}\ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 1}+{6 \ p 2 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 4 \right)}\ p 2}\right)}\ p 3}\right)}\ q 3}+{{\left(-{2 \ p 2 \ {{p 3}^{4}}}+{{\left(-{{16}\ {{p 2}^{3}}}+{{\left(-{4 \ {{p 1}^{2}}}- 4 \right)}\ p 2}\right)}\ {{p 3}^{2}}}-{{16}\ {{p 2}^{5}}}+{{\left(-{{16}\ {{p 1}^{2}}}-{16}\right)}\ {{p 2}^{3}}}+{{\left(-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 2}^{4}}}+{{\left({{\left(-{{24}\ p 1 \ {{p 2}^{2}}\ {{p 3}^{2}}}-{{32}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ {{p 2}^{2}}}\right)}\ q 1}+{6 \ {{p 2}^{2}}\ {{p 3}^{2}}}+{8 \ {{p 2}^{4}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ {{p 2}^{2}}}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{4 \ p 2 \ {{p 3}^{4}}}+{{\left(-{{2
0}\ {{p 2}^{3}}}+{{\left(-{{20}\ {{p 1}^{2}}}- 8 \right)}\ p 2}\right)}\ {{p 3}^{2}}}-{{16}\ {{p 2}^{5}}}+{{\left(-{{44}\ {{p 1}^{2}}}-{20}\right)}\ {{p 2}^{3}}}+{{\left(-{{16}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}- 4 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{{\left({6 \ p 1 \ p 2 \ {{p 3}^{2}}}+{{12}\ p 1 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 2}\right)}\ q 1}-{4 \ p 2 \ {{p 3}^{4}}}+{{\left(-{{20}\ {{p 2}^{3}}}+{{\left(-{8 \ {{p 1}^{2}}}- 6 \right)}\ p 2}\right)}\ {{p 3}^{2}}}-{{1
6}\ {{p 2}^{5}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{16}\right)}\ {{p 2}^{3}}}+{{\left(-{4 \ {{p 1}^{4}}}-{6 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ p 1 \ {{p 2}^{2}}\ {{p 3}^{2}}}-{{24}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{3
2}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ {{p 2}^{2}}}\right)}\ {{q 1}^{3}}}+{{\left({6 \ {{p 2}^{2}}\ {{p 3}^{2}}}+{6 \ {{p 2}^{4}}}+{{\left({{12}\ {{p 1}^{2}}}+ 6 \right)}\ {{p 2}^{2}}}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{2}}\ {{p 3}^{2}}}-{{2
4}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ {{p 2}^{2}}}\right)}\ q 1}+{6 \ {{p 2}^{2}}\ {{p 3}^{2}}}+{6 \ {{p 2}^{4}}}+{{\left({6 \ {{p 1}^{2}}}+ 4 \right)}\ {{p 2}^{2}}}\right)}\ q 2}+{{\left(-{2 \ p 2 \ {{p 3}^{4}}}+{{\left(-{4 \ {{p 2}^{3}}}+{{\left(-{{16}\ {{p 1}^{2}}}- 4 \right)}\ p 2}\right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{5}}}+{{\left(-{{16}\ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{3}}}+{{\left(-{{16}\ {{p 1}^{4}}}-{{16}\ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 1}^{4}}}+{{\left({6 \ p 1 \ p 2 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 2}\right)}\ {{q 1}^{3}}}+{{\left(-{4 \ p 2 \ {{p 3}^{4}}}+{{\left(-{8 \ {{p 2}^{3}}}+{{\left(-{{20}\ {{p 1}^{2}}}- 6 \right)}\ p 2}\right)}\ {{p 3}^{2}}}-{4 \ {{p 2}^{5}}}+{{\left(-{{20}\ {{p 1}^{2}}}- 6 \right)}\ {{p 2}^{3}}}+{{\left(-{{16}\ {{p 1}^{4}}}-{{16}\ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{{\left({6 \ p 1 \ p 2 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 2}\right)}\ q 1}-{2 \ p 2 \ {{p 3}^{4}}}+{{\left(-{4 \ {{p 2}^{3}}}+{{\left(-{4 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{5}}}+{{\left(-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{p 2}^{3}}}+{{\left(-{2 \ {{p 1}^{4}}}-{2 \ {{p 1}^{2}}}\right)}\ p 2}}\over{{{\left({{\left({4 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({6 \ p 2 \ p 3 \ q 2}+{6 \ p 1 \ p 3 \ q 1}-{2 \ p 3}\right)}\ q 3}+{{\left({{p 3}^{2}}+{4 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({6 \ p 1 \ p 2 \ q 1}-{2 \ p 2}\right)}\ q 2}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{4 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}-{2 \ p 1 \ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{4 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{6 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{6 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{2 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{6 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left(-{6 \ p 1 \ p 2 \ p 3 \ q 1}+{2 \ p 2 \ p 3}\right)}\ q 2}+{{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 3 \ q 1}-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ q 3}+{{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{4 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{6 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{2 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 2 \ q 1}-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{4 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ {{q 1}^{3}}}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{2 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}
\
{{{{\left({{\left({{16}\ {{p 3}^{4}}}+{{\left({8 \ {{p 2}^{2}}}+{8 \ {{p 1}^{2}}}+ 8 \right)}\ {{p 3}^{2}}}\right)}\ {{q 3}^{3}}}+{{\left({{\left({{32}\ p 2 \ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left({{32}\ p 1 \ {{p 3}^{3}}}+{{\left({8 \ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 3}\right)}\ q 1}-{8 \ {{p 3}^{3}}}+{{\left(-{2 \ {{p 2}^{2}}}-{2 \ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 3}^{2}}}+{{\left({{\left({8 \ {{p 3}^{4}}}+{{\left({{32}\ {{p 2}^{2}}}+{8 \ {{p 1}^{2}}}+ 8 \right)}\ {{p 3}^{2}}}\right)}\ {{q 2}^{2}}}+{{\left({{48}\ p 1 \ p 2 \ {{p 3}^{2}}\ q 1}-{{12}\ p 2 \ {{p 3}^{2}}}\right)}\ q 2}+{{\left({8 \ {{p 3}^{4}}}+{{\left({8 \ {{p 2}^{2}}}+{{32}\ {{p 1}^{2}}}+ 8 \right)}\ {{p 3}^{2}}}\right)}\ {{q 1}^{2}}}-{{12}\ p 1 \ {{p 3}^{2}}\ q 1}+{8 \ {{p 3}^{4}}}+{{\left({8 \ {{p 2}^{2}}}+{8 \ {{p 1}^{2}}}+ 4 \right)}\ {{p 3}^{2}}}\right)}\ q 3}+{{\left({8 \ p 2 \ {{p 3}^{3}}}+{{\left({{16}\ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 2}^{3}}}+{{\left({{\left({8 \ p 1 \ {{p 3}^{3}}}+{{\left({{3
2}\ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 3}\right)}\ q 1}-{2 \ {{p 3}^{3}}}+{{\left(-{8 \ {{p 2}^{2}}}-{2 \ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{\left({8 \ p 2 \ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{3}}}+{{\left({{32}\ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{2}}}-{{12}\ p 1 \ p 2 \ p 3 \ q 1}+{8 \ p 2 \ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{2}}}+ 4 \right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left({8 \ p 1 \ {{p 3}^{3}}}+{{\left({8 \ p 1 \ {{p 2}^{2}}}+{{16}\ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 3}\right)}\ {{q 1}^{3}}}+{{\left(-{2 \ {{p 3}^{3}}}+{{\left(-{2 \ {{p 2}^{2}}}-{8 \ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left({8 \ p 1 \ {{p 3}^{3}}}+{{\left({8 \ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 3}\right)}\ q 1}-{2 \ {{p 3}^{3}}}+{{\left(-{2 \ {{p 2}^{2}}}-{2 \ {{p 1}^{2}}}\right)}\ p 3}\right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{{16}\ {{p 3}^{5}}}+{{\left(-{{16}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{2}}}-{16}\right)}\ {{p 3}^{3}}}+{{\left(-{2 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 3}^{4}}}+{{\left({{\left(-{{32}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{24}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{24}\right)}\ p 2}\right)}\ {{p 3}^{2}}}\right)}\ q 2}+{{\left(-{{32}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{2}}}-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ {{p 3}^{2}}}\right)}\ q 1}+{8 \ {{p 3}^{4}}}+{{\left({6 \ {{p 2}^{2}}}+{6 \ {{p 1}^{2}}}+ 6 \right)}\ {{p 3}^{2}}}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{{16}\ {{p 3}^{5}}}+{{\left(-{{44}\ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}-{20}\right)}\ {{p 3}^{3}}}+{{\left(-{{16}\ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{20}\right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{4}}}-{8 \ {{p 1}^{2}}}- 4 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{48}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 1}+{{12}\ p 2 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left(-{{16}\ {{p 3}^{5}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{{44}\ {{p 1}^{2}}}-{20}\right)}\ {{p 3}^{3}}}+{{\left(-{4 \ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{2}}}- 8 \right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}- 4 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left({{12}\ p 1 \ {{p 3}^{3}}}+{{\left({6 \ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 3}\right)}\ q 1}-{{16}\ {{p 3}^{5}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}-{16}\right)}\ {{p 3}^{3}}}+{{\left(-{4 \ {{p 2}^{4}}}+{{\left(-{8 \ {{p 1}^{2}}}- 6 \right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{4}}}-{6 \ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 3}^{2}}}+{{\left({{\left(-{{24}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{3
2}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{24}\right)}\ p 2}\right)}\ {{p 3}^{2}}}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{{24}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{48}\ p 1 \ {{p 2}^{2}}}-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ {{p 3}^{2}}}\right)}\ q 1}+{6 \ {{p 3}^{4}}}+{{\left({{12}\ {{p 2}^{2}}}+{6 \ {{p 1}^{2}}}+ 6 \right)}\ {{p 3}^{2}}}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{24}\ {{p 2}^{3}}}+{{\left(-{{48}\ {{p 1}^{2}}}-{24}\right)}\ p 2}\right)}\ {{p 3}^{2}}}\right)}\ {{q 1}^{2}}}+{{12}\ p 1 \ p 2 \ {{p 3}^{2}}\ q 1}-{{24}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{24}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{20}\right)}\ p 2}\right)}\ {{p 3}^{2}}}\right)}\ q 2}+{{\left(-{{24}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{2}}}-{{32}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ {{p 3}^{2}}}\right)}\ {{q 1}^{3}}}+{{\left({6 \ {{p 3}^{4}}}+{{\left({6 \ {{p 2}^{2}}}+{{12}\ {{p 1}^{2}}}+ 6 \right)}\ {{p 3}^{2}}}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{2}}}-{{24}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ {{p 3}^{2}}}\right)}\ q 1}+{6 \ {{p 3}^{4}}}+{{\left({6 \ {{p 2}^{2}}}+{6 \ {{p 1}^{2}}}+ 4 \right)}\ {{p 3}^{2}}}\right)}\ q 3}+{{\left(-{2 \ {{p 3}^{5}}}+{{\left(-{{16}\ {{p 2}^{2}}}-{4 \ {{p 1}^{2}}}- 4 \right)}\ {{p 3}^{3}}}+{{\left(-{{16}\ {{p 2}^{4}}}+{{\left(-{{16}\ {{p 1}^{2}}}-{16}\right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 2}^{4}}}+{{\left({{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{32}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 1}+{6 \ p 2 \ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{4 \ {{p 3}^{5}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}- 8 \right)}\ {{p 3}^{3}}}+{{\left(-{{16}\ {{p 2}^{4}}}+{{\left(-{{44}\ {{p 1}^{2}}}-{20}\right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}- 4 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left({6 \ p 1 \ {{p 3}^{3}}}+{{\left({{12}\ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 3}\right)}\ q 1}-{4 \ {{p 3}^{5}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{8 \ {{p 1}^{2}}}- 6 \right)}\ {{p 3}^{3}}}+{{\left(-{{16}\ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{16}\right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{4}}}-{6 \ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{32}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{3}}}+{{\left({6 \ p 2 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{3}}}+{{\left({{12}\ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 1}+{6 \ p 2 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 4 \right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left(-{2 \ {{p 3}^{5}}}+{{\left(-{4 \ {{p 2}^{2}}}-{{16}\ {{p 1}^{2}}}- 4 \right)}\ {{p 3}^{3}}}+{{\left(-{2 \ {{p 2}^{4}}}+{{\left(-{{16}\ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{16}\ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 1}^{4}}}+{{\left({6 \ p 1 \ {{p 3}^{3}}}+{{\left({6 \ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 3}\right)}\ {{q 1}^{3}}}+{{\left(-{4 \ {{p 3}^{5}}}+{{\left(-{8 \ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}- 6 \right)}\ {{p 3}^{3}}}+{{\left(-{4 \ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{2}}}- 6 \right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{16}\ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left({6 \ p 1 \ {{p 3}^{3}}}+{{\left({6 \ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 3}\right)}\ q 1}-{2 \ {{p 3}^{5}}}+{{\left(-{4 \ {{p 2}^{2}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{p 3}^{3}}}+{{\left(-{2 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{2 \ {{p 1}^{2}}}\right)}\ p 3}}\over{{{\left({{\left({4 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({6 \ p 2 \ p 3 \ q 2}+{6 \ p 1 \ p 3 \ q 1}-{2 \ p 3}\right)}\ q 3}+{{\left({{p 3}^{2}}+{4 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({6 \ p 1 \ p 2 \ q 1}-{2 \ p 2}\right)}\ q 2}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{4 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}-{2 \ p 1 \ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{4 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{6 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{6 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{2 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{6 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left(-{6 \ p 1 \ p 2 \ p 3 \ q 1}+{2 \ p 2 \ p 3}\right)}\ q 2}+{{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 3 \ q 1}-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ q 3}+{{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{4 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{6 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{2 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 2 \ q 1}-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{4 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ {{q 1}^{3}}}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{2 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}](images/2282124654803995266-16.0px.png "\label{eq15}\left[
\begin{array}{c}
{{{{\left({{\left({{16}\ {{p 3}^{5}}}+{{\left({{24}\ {{p 2}^{2}}}+{{24}\ {{p 1}^{2}}}+{24}\right)}\ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{4}}}+{{\left({{16}\ {{p 1}^{2}}}+{16}\right)}\ {{p 2}^{2}}}+{8 \ {{p 1}^{4}}}+{{16}\ {{p 1}^{2}}}+ 8 \right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left({{32}\ p 2 \ {{p 3}^{4}}}+{{\left({{4
0}\ {{p 2}^{3}}}+{{\left({{40}\ {{p 1}^{2}}}+{40}\right)}\ p 2}\right)}\ {{p 3}^{2}}}+{8 \ {{p 2}^{5}}}+{{\left({{16}\ {{p 1}^{2}}}+{16}\right)}\ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{4}}}+{{16}\ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ q 2}+{{\left({{3
2}\ p 1 \ {{p 3}^{4}}}+{{\left({{40}\ p 1 \ {{p 2}^{2}}}+{{4
0}\ {{p 1}^{3}}}+{{40}\ p 1}\right)}\ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{4}}}+{{\left({{16}\ {{p 1}^{3}}}+{{16}\ p 1}\right)}\ {{p 2}^{2}}}+{8 \ {{p 1}^{5}}}+{{16}\ {{p 1}^{3}}}+{8 \ p 1}\right)}\ q 1}-{8 \ {{p 3}^{4}}}+{{\left(-{{10}\ {{p 2}^{2}}}-{{10}\ {{p 1}^{2}}}-{10}\right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{q 3}^{2}}}+{{\left({{\left({8 \ {{p 3}^{5}}}+{{\left({{40}\ {{p 2}^{2}}}+{{16}\ {{p 1}^{2}}}+{16}\right)}\ {{p 3}^{3}}}+{{\left({{32}\ {{p 2}^{4}}}+{{\left({{4
0}\ {{p 1}^{2}}}+{40}\right)}\ {{p 2}^{2}}}+{8 \ {{p 1}^{4}}}+{{16}\ {{p 1}^{2}}}+ 8 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{\left({{48}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left({{4
8}\ p 1 \ {{p 2}^{3}}}+{{\left({{48}\ {{p 1}^{3}}}+{{48}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 1}-{{12}\ p 2 \ {{p 3}^{3}}}+{{\left(-{{12}\ {{p 2}^{3}}}+{{\left(-{{12}\ {{p 1}^{2}}}-{12}\right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left({8 \ {{p 3}^{5}}}+{{\left({{16}\ {{p 2}^{2}}}+{{40}\ {{p 1}^{2}}}+{16}\right)}\ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{4}}}+{{\left({{4
0}\ {{p 1}^{2}}}+{16}\right)}\ {{p 2}^{2}}}+{{32}\ {{p 1}^{4}}}+{{40}\ {{p 1}^{2}}}+ 8 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left(-{{12}\ p 1 \ {{p 3}^{3}}}+{{\left(-{{12}\ p 1 \ {{p 2}^{2}}}-{{12}\ {{p 1}^{3}}}-{{12}\ p 1}\right)}\ p 3}\right)}\ q 1}+{8 \ {{p 3}^{5}}}+{{\left({{16}\ {{p 2}^{2}}}+{{16}\ {{p 1}^{2}}}+{12}\right)}\ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{4}}}+{{\left({{16}\ {{p 1}^{2}}}+{12}\right)}\ {{p 2}^{2}}}+{8 \ {{p 1}^{4}}}+{{12}\ {{p 1}^{2}}}+ 4 \right)}\ p 3}\right)}\ q 3}+{{\left({8 \ p 2 \ {{p 3}^{4}}}+{{\left({{24}\ {{p 2}^{3}}}+{{\left({{16}\ {{p 1}^{2}}}+{16}\right)}\ p 2}\right)}\ {{p 3}^{2}}}+{{16}\ {{p 2}^{5}}}+{{\left({{24}\ {{p 1}^{2}}}+{24}\right)}\ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{4}}}+{{16}\ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left({8 \ p 1 \ {{p 3}^{4}}}+{{\left({{40}\ p 1 \ {{p 2}^{2}}}+{{16}\ {{p 1}^{3}}}+{{16}\ p 1}\right)}\ {{p 3}^{2}}}+{{32}\ p 1 \ {{p 2}^{4}}}+{{\left({{40}\ {{p 1}^{3}}}+{{40}\ p 1}\right)}\ {{p 2}^{2}}}+{8 \ {{p 1}^{5}}}+{{16}\ {{p 1}^{3}}}+{8 \ p 1}\right)}\ q 1}-{2 \ {{p 3}^{4}}}+{{\left(-{{10}\ {{p 2}^{2}}}-{4 \ {{p 1}^{2}}}- 4 \right)}\ {{p 3}^{2}}}-{8 \ {{p 2}^{4}}}+{{\left(-{{1
0}\ {{p 1}^{2}}}-{10}\right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{q 2}^{2}}}+{{\left({{\left({8 \ p 2 \ {{p 3}^{4}}}+{{\left({{16}\ {{p 2}^{3}}}+{{\left({{4
0}\ {{p 1}^{2}}}+{16}\right)}\ p 2}\right)}\ {{p 3}^{2}}}+{8 \ {{p 2}^{5}}}+{{\left({{40}\ {{p 1}^{2}}}+{16}\right)}\ {{p 2}^{3}}}+{{\left({{32}\ {{p 1}^{4}}}+{{40}\ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{{\left(-{{12}\ p 1 \ p 2 \ {{p 3}^{2}}}-{{12}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{12}\ {{p 1}^{3}}}-{{12}\ p 1}\right)}\ p 2}\right)}\ q 1}+{8 \ p 2 \ {{p 3}^{4}}}+{{\left({{16}\ {{p 2}^{3}}}+{{\left({{16}\ {{p 1}^{2}}}+{12}\right)}\ p 2}\right)}\ {{p 3}^{2}}}+{8 \ {{p 2}^{5}}}+{{\left({{1
6}\ {{p 1}^{2}}}+{12}\right)}\ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{4}}}+{{12}\ {{p 1}^{2}}}+ 4 \right)}\ p 2}\right)}\ q 2}+{{\left({8 \ p 1 \ {{p 3}^{4}}}+{{\left({{16}\ p 1 \ {{p 2}^{2}}}+{{24}\ {{p 1}^{3}}}+{{16}\ p 1}\right)}\ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{4}}}+{{\left({{24}\ {{p 1}^{3}}}+{{16}\ p 1}\right)}\ {{p 2}^{2}}}+{{16}\ {{p 1}^{5}}}+{{24}\ {{p 1}^{3}}}+{8 \ p 1}\right)}\ {{q 1}^{3}}}+{{\left(-{2 \ {{p 3}^{4}}}+{{\left(-{4 \ {{p 2}^{2}}}-{{10}\ {{p 1}^{2}}}- 4 \right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{4}}}+{{\left(-{{10}\ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{2}}}-{8 \ {{p 1}^{4}}}-{{10}\ {{p 1}^{2}}}- 2 \right)}\ {{q 1}^{2}}}+{{\left({8 \ p 1 \ {{p 3}^{4}}}+{{\left({{16}\ p 1 \ {{p 2}^{2}}}+{{16}\ {{p 1}^{3}}}+{{12}\ p 1}\right)}\ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{4}}}+{{\left({{16}\ {{p 1}^{3}}}+{{12}\ p 1}\right)}\ {{p 2}^{2}}}+{8 \ {{p 1}^{5}}}+{{12}\ {{p 1}^{3}}}+{4 \ p 1}\right)}\ q 1}-{2 \ {{p 3}^{4}}}+{{\left(-{4 \ {{p 2}^{2}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{2 \ {{p 1}^{2}}}\right)}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left({{\left(-{{16}\ {{p 3}^{4}}}+{{\left(-{{16}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{2}}}-{16}\right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{q 3}^{4}}}+{{\left({{\left(-{{32}\ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{24}\right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left(-{{32}\ p 1 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{2}}}-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 3}\right)}\ q 1}+{8 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{2}}}+{6 \ {{p 1}^{2}}}+ 6 \right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{{16}\ {{p 3}^{4}}}+{{\left(-{{44}\ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}-{20}\right)}\ {{p 3}^{2}}}-{{16}\ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{20}\right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{4}}}-{8 \ {{p 1}^{2}}}- 4 \right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{48}\ p 1 \ p 2 \ {{p 3}^{2}}}-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ q 1}+{{12}\ p 2 \ {{p 3}^{2}}}+{6 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ q 2}+{{\left(-{{16}\ {{p 3}^{4}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{{44}\ {{p 1}^{2}}}-{20}\right)}\ {{p 3}^{2}}}-{4 \ {{p 2}^{4}}}+{{\left(-{{2
0}\ {{p 1}^{2}}}- 8 \right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}- 4 \right)}\ {{q 1}^{2}}}+{{\left({{12}\ p 1 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ q 1}-{{16}\ {{p 3}^{4}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}-{16}\right)}\ {{p 3}^{2}}}-{4 \ {{p 2}^{4}}}+{{\left(-{8 \ {{p 1}^{2}}}- 6 \right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{4}}}-{6 \ {{p 1}^{2}}}- 2 \right)}\ {{q 3}^{2}}}+{{\left({{\left(-{{24}\ p 2 \ {{p 3}^{3}}}+{{\left(-{{32}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{24}\right)}\ p 2}\right)}\ p 3}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{{24}\ p 1 \ {{p 3}^{3}}}+{{\left(-{{48}\ p 1 \ {{p 2}^{2}}}-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 3}\right)}\ q 1}+{6 \ {{p 3}^{3}}}+{{\left({{12}\ {{p 2}^{2}}}+{6 \ {{p 1}^{2}}}+ 6 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 2}^{3}}}+{{\left(-{{48}\ {{p 1}^{2}}}-{24}\right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{12}\ p 1 \ p 2 \ p 3 \ q 1}-{{24}\ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{20}\right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left(-{{24}\ p 1 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{2}}}-{{32}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 3}\right)}\ {{q 1}^{3}}}+{{\left({6 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{2}}}+{{12}\ {{p 1}^{2}}}+ 6 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ p 1 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{2}}}-{{24}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ p 3}\right)}\ q 1}+{6 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{2}}}+{6 \ {{p 1}^{2}}}+ 4 \right)}\ p 3}\right)}\ q 3}+{{\left(-{2 \ {{p 3}^{4}}}+{{\left(-{{16}\ {{p 2}^{2}}}-{4 \ {{p 1}^{2}}}- 4 \right)}\ {{p 3}^{2}}}-{{16}\ {{p 2}^{4}}}+{{\left(-{{16}\ {{p 1}^{2}}}-{16}\right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{q 2}^{4}}}+{{\left({{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{2}}}-{{32}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ q 1}+{6 \ p 2 \ {{p 3}^{2}}}+{8 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{4 \ {{p 3}^{4}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}- 8 \right)}\ {{p 3}^{2}}}-{{16}\ {{p 2}^{4}}}+{{\left(-{{44}\ {{p 1}^{2}}}-{20}\right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}- 4 \right)}\ {{q 1}^{2}}}+{{\left({6 \ p 1 \ {{p 3}^{2}}}+{{12}\ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ q 1}-{4 \ {{p 3}^{4}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{8 \ {{p 1}^{2}}}- 6 \right)}\ {{p 3}^{2}}}-{{16}\ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{16}\right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{4}}}-{6 \ {{p 1}^{2}}}- 2 \right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{2}}}-{{2
4}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{32}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ {{q 1}^{3}}}+{{\left({6 \ p 2 \ {{p 3}^{2}}}+{6 \ {{p 2}^{3}}}+{{\left({{12}\ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{2}}}-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ p 2}\right)}\ q 1}+{6 \ p 2 \ {{p 3}^{2}}}+{6 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 4 \right)}\ p 2}\right)}\ q 2}+{{\left(-{2 \ {{p 3}^{4}}}+{{\left(-{4 \ {{p 2}^{2}}}-{{16}\ {{p 1}^{2}}}- 4 \right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{4}}}+{{\left(-{{16}\ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{16}\ {{p 1}^{2}}}- 2 \right)}\ {{q 1}^{4}}}+{{\left({6 \ p 1 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ {{q 1}^{3}}}+{{\left(-{4 \ {{p 3}^{4}}}+{{\left(-{8 \ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}- 6 \right)}\ {{p 3}^{2}}}-{4 \ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{2}}}- 6 \right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{16}\ {{p 1}^{2}}}- 2 \right)}\ {{q 1}^{2}}}+{{\left({6 \ p 1 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ q 1}-{2 \ {{p 3}^{4}}}+{{\left(-{4 \ {{p 2}^{2}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{2 \ {{p 1}^{2}}}\right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}}}\over{{{\left({{\left({4 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({6 \ p 2 \ p 3 \ q 2}+{6 \ p 1 \ p 3 \ q 1}-{2 \ p 3}\right)}\ q 3}+{{\left({{p 3}^{2}}+{4 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({6 \ p 1 \ p 2 \ q 1}-{2 \ p 2}\right)}\ q 2}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{4 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}-{2 \ p 1 \ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{4 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{6 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{6 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{2 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{6 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left(-{6 \ p 1 \ p 2 \ p 3 \ q 1}+{2 \ p 2 \ p 3}\right)}\ q 2}+{{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 3 \ q 1}-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ q 3}+{{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{4 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{6 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{2 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 2 \ q 1}-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{4 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ {{q 1}^{3}}}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{2 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}
\
{{{{\left({{\left({{16}\ p 1 \ {{p 3}^{3}}}+{{\left({8 \ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left({{32}\ p 1 \ p 2 \ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 2}\right)}\ q 2}+{{\left({{32}\ {{p 1}^{2}}\ {{p 3}^{2}}}+{8 \ {{p 1}^{2}}\ {{p 2}^{2}}}+{8 \ {{p 1}^{4}}}+{8 \ {{p 1}^{2}}}\right)}\ q 1}-{8 \ p 1 \ {{p 3}^{2}}}-{2 \ p 1 \ {{p 2}^{2}}}-{2 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 3}^{2}}}+{{\left({{\left({8 \ p 1 \ {{p 3}^{3}}}+{{\left({{32}\ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{4
8}\ {{p 1}^{2}}\ p 2 \ p 3 \ q 1}-{{12}\ p 1 \ p 2 \ p 3}\right)}\ q 2}+{{\left({8 \ p 1 \ {{p 3}^{3}}}+{{\left({8 \ p 1 \ {{p 2}^{2}}}+{{32}\ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 3}\right)}\ {{q 1}^{2}}}-{{12}\ {{p 1}^{2}}\ p 3 \ q 1}+{8 \ p 1 \ {{p 3}^{3}}}+{{\left({8 \ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 3}\right)}\ q 3}+{{\left({8 \ p 1 \ p 2 \ {{p 3}^{2}}}+{{16}\ p 1 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left({8 \ {{p 1}^{2}}\ {{p 3}^{2}}}+{{32}\ {{p 1}^{2}}\ {{p 2}^{2}}}+{8 \ {{p 1}^{4}}}+{8 \ {{p 1}^{2}}}\right)}\ q 1}-{2 \ p 1 \ {{p 3}^{2}}}-{8 \ p 1 \ {{p 2}^{2}}}-{2 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 2}^{2}}}+{{\left({{\left({8 \ p 1 \ p 2 \ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{3}}}+{{\left({{3
2}\ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 2}\right)}\ {{q 1}^{2}}}-{{12}\ {{p 1}^{2}}\ p 2 \ q 1}+{8 \ p 1 \ p 2 \ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 2}\right)}\ q 2}+{{\left({8 \ {{p 1}^{2}}\ {{p 3}^{2}}}+{8 \ {{p 1}^{2}}\ {{p 2}^{2}}}+{{16}\ {{p 1}^{4}}}+{8 \ {{p 1}^{2}}}\right)}\ {{q 1}^{3}}}+{{\left(-{2 \ p 1 \ {{p 3}^{2}}}-{2 \ p 1 \ {{p 2}^{2}}}-{8 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 1}^{2}}}+{{\left({8 \ {{p 1}^{2}}\ {{p 3}^{2}}}+{8 \ {{p 1}^{2}}\ {{p 2}^{2}}}+{8 \ {{p 1}^{4}}}+{4 \ {{p 1}^{2}}}\right)}\ q 1}-{2 \ p 1 \ {{p 3}^{2}}}-{2 \ p 1 \ {{p 2}^{2}}}-{2 \ {{p 1}^{3}}}\right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{{16}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{16}\ p 1 \ {{p 2}^{2}}}-{{16}\ {{p 1}^{3}}}-{{16}\ p 1}\right)}\ {{p 3}^{2}}}-{2 \ p 1 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{3}}}-{4 \ p 1}\right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{5}}}-{4 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 3}^{4}}}+{{\left({{\left(-{{32}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left(-{{32}\ {{p 1}^{2}}\ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}\ {{p 2}^{2}}}-{{24}\ {{p 1}^{4}}}-{{24}\ {{p 1}^{2}}}\right)}\ p 3}\right)}\ q 1}+{8 \ p 1 \ {{p 3}^{3}}}+{{\left({6 \ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{{16}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{44}\ p 1 \ {{p 2}^{2}}}-{{20}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ {{p 3}^{2}}}-{{16}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{5}}}-{8 \ {{p 1}^{3}}}-{4 \ p 1}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{48}\ {{p 1}^{2}}\ p 2 \ {{p 3}^{2}}}-{{24}\ {{p 1}^{2}}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{4}}}-{{24}\ {{p 1}^{2}}}\right)}\ p 2}\right)}\ q 1}+{{12}\ p 1 \ p 2 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 2}\right)}\ q 2}+{{\left(-{{1
6}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{20}\ p 1 \ {{p 2}^{2}}}-{{4
4}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ {{p 3}^{2}}}-{4 \ p 1 \ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{3}}}-{8 \ p 1}\right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{5}}}-{{20}\ {{p 1}^{3}}}-{4 \ p 1}\right)}\ {{q 1}^{2}}}+{{\left({{12}\ {{p 1}^{2}}\ {{p 3}^{2}}}+{6 \ {{p 1}^{2}}\ {{p 2}^{2}}}+{6 \ {{p 1}^{4}}}+{6 \ {{p 1}^{2}}}\right)}\ q 1}-{{16}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{20}\ p 1 \ {{p 2}^{2}}}-{{20}\ {{p 1}^{3}}}-{{16}\ p 1}\right)}\ {{p 3}^{2}}}-{4 \ p 1 \ {{p 2}^{4}}}+{{\left(-{8 \ {{p 1}^{3}}}-{6 \ p 1}\right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{5}}}-{6 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 3}^{2}}}+{{\left({{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{32}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{{24}\ {{p 1}^{2}}\ {{p 3}^{3}}}+{{\left(-{{48}\ {{p 1}^{2}}\ {{p 2}^{2}}}-{{24}\ {{p 1}^{4}}}-{{24}\ {{p 1}^{2}}}\right)}\ p 3}\right)}\ q 1}+{6 \ p 1 \ {{p 3}^{3}}}+{{\left({{12}\ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{48}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{12}\ {{p 1}^{2}}\ p 2 \ p 3 \ q 1}-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left(-{{24}\ {{p 1}^{2}}\ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}\ {{p 2}^{2}}}-{{32}\ {{p 1}^{4}}}-{{24}\ {{p 1}^{2}}}\right)}\ p 3}\right)}\ {{q 1}^{3}}}+{{\left({6 \ p 1 \ {{p 3}^{3}}}+{{\left({6 \ p 1 \ {{p 2}^{2}}}+{{12}\ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ {{p 1}^{2}}\ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}\ {{p 2}^{2}}}-{{24}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}\right)}\ p 3}\right)}\ q 1}+{6 \ p 1 \ {{p 3}^{3}}}+{{\left({6 \ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 3}\right)}\ q 3}+{{\left(-{2 \ p 1 \ {{p 3}^{4}}}+{{\left(-{{16}\ p 1 \ {{p 2}^{2}}}-{4 \ {{p 1}^{3}}}-{4 \ p 1}\right)}\ {{p 3}^{2}}}-{{16}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{16}\ {{p 1}^{3}}}-{{16}\ p 1}\right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{5}}}-{4 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 2}^{4}}}+{{\left({{\left(-{{24}\ {{p 1}^{2}}\ p 2 \ {{p 3}^{2}}}-{{32}\ {{p 1}^{2}}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{4}}}-{{24}\ {{p 1}^{2}}}\right)}\ p 2}\right)}\ q 1}+{6 \ p 1 \ p 2 \ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{4 \ p 1 \ {{p 3}^{4}}}+{{\left(-{{20}\ p 1 \ {{p 2}^{2}}}-{{20}\ {{p 1}^{3}}}-{8 \ p 1}\right)}\ {{p 3}^{2}}}-{{16}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{44}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{5}}}-{{20}\ {{p 1}^{3}}}-{4 \ p 1}\right)}\ {{q 1}^{2}}}+{{\left({6 \ {{p 1}^{2}}\ {{p 3}^{2}}}+{{12}\ {{p 1}^{2}}\ {{p 2}^{2}}}+{6 \ {{p 1}^{4}}}+{6 \ {{p 1}^{2}}}\right)}\ q 1}-{4 \ p 1 \ {{p 3}^{4}}}+{{\left(-{{20}\ p 1 \ {{p 2}^{2}}}-{8 \ {{p 1}^{3}}}-{6 \ p 1}\right)}\ {{p 3}^{2}}}-{{16}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{3}}}-{{16}\ p 1}\right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{5}}}-{6 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ {{p 1}^{2}}\ p 2 \ {{p 3}^{2}}}-{{24}\ {{p 1}^{2}}\ {{p 2}^{3}}}+{{\left(-{{32}\ {{p 1}^{4}}}-{{24}\ {{p 1}^{2}}}\right)}\ p 2}\right)}\ {{q 1}^{3}}}+{{\left({6 \ p 1 \ p 2 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{3}}}+{{\left({{1
2}\ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 2}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ {{p 1}^{2}}\ p 2 \ {{p 3}^{2}}}-{{24}\ {{p 1}^{2}}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}\right)}\ p 2}\right)}\ q 1}+{6 \ p 1 \ p 2 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 2}\right)}\ q 2}+{{\left(-{2 \ p 1 \ {{p 3}^{4}}}+{{\left(-{4 \ p 1 \ {{p 2}^{2}}}-{{16}\ {{p 1}^{3}}}-{4 \ p 1}\right)}\ {{p 3}^{2}}}-{2 \ p 1 \ {{p 2}^{4}}}+{{\left(-{{16}\ {{p 1}^{3}}}-{4 \ p 1}\right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{5}}}-{{16}\ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 1}^{4}}}+{{\left({6 \ {{p 1}^{2}}\ {{p 3}^{2}}}+{6 \ {{p 1}^{2}}\ {{p 2}^{2}}}+{8 \ {{p 1}^{4}}}+{6 \ {{p 1}^{2}}}\right)}\ {{q 1}^{3}}}+{{\left(-{4 \ p 1 \ {{p 3}^{4}}}+{{\left(-{8 \ p 1 \ {{p 2}^{2}}}-{{20}\ {{p 1}^{3}}}-{6 \ p 1}\right)}\ {{p 3}^{2}}}-{4 \ p 1 \ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{3}}}-{6 \ p 1}\right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{5}}}-{{16}\ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{q 1}^{2}}}+{{\left({6 \ {{p 1}^{2}}\ {{p 3}^{2}}}+{6 \ {{p 1}^{2}}\ {{p 2}^{2}}}+{6 \ {{p 1}^{4}}}+{4 \ {{p 1}^{2}}}\right)}\ q 1}-{2 \ p 1 \ {{p 3}^{4}}}+{{\left(-{4 \ p 1 \ {{p 2}^{2}}}-{4 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{p 3}^{2}}}-{2 \ p 1 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{3}}}-{2 \ p 1}\right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{5}}}-{2 \ {{p 1}^{3}}}}\over{{{\left({{\left({4 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({6 \ p 2 \ p 3 \ q 2}+{6 \ p 1 \ p 3 \ q 1}-{2 \ p 3}\right)}\ q 3}+{{\left({{p 3}^{2}}+{4 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({6 \ p 1 \ p 2 \ q 1}-{2 \ p 2}\right)}\ q 2}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{4 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}-{2 \ p 1 \ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{4 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{6 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{6 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{2 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{6 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left(-{6 \ p 1 \ p 2 \ p 3 \ q 1}+{2 \ p 2 \ p 3}\right)}\ q 2}+{{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 3 \ q 1}-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ q 3}+{{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{4 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{6 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{2 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 2 \ q 1}-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{4 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ {{q 1}^{3}}}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{2 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}
\
{{{{\left({{\left({{16}\ p 2 \ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left({{32}\ {{p 2}^{2}}\ {{p 3}^{2}}}+{8 \ {{p 2}^{4}}}+{{\left({8 \ {{p 1}^{2}}}+ 8 \right)}\ {{p 2}^{2}}}\right)}\ q 2}+{{\left({{32}\ p 1 \ p 2 \ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 2}\right)}\ q 1}-{8 \ p 2 \ {{p 3}^{2}}}-{2 \ {{p 2}^{3}}}+{{\left(-{2 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 3}^{2}}}+{{\left({{\left({8 \ p 2 \ {{p 3}^{3}}}+{{\left({{32}\ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{48}\ p 1 \ {{p 2}^{2}}\ p 3 \ q 1}-{{12}\ {{p 2}^{2}}\ p 3}\right)}\ q 2}+{{\left({8 \ p 2 \ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{3}}}+{{\left({{32}\ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{2}}}-{{12}\ p 1 \ p 2 \ p 3 \ q 1}+{8 \ p 2 \ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{2}}}+ 4 \right)}\ p 2}\right)}\ p 3}\right)}\ q 3}+{{\left({8 \ {{p 2}^{2}}\ {{p 3}^{2}}}+{{1
6}\ {{p 2}^{4}}}+{{\left({8 \ {{p 1}^{2}}}+ 8 \right)}\ {{p 2}^{2}}}\right)}\ {{q 2}^{3}}}+{{\left({{\left({8 \ p 1 \ p 2 \ {{p 3}^{2}}}+{{32}\ p 1 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 2}\right)}\ q 1}-{2 \ p 2 \ {{p 3}^{2}}}-{8 \ {{p 2}^{3}}}+{{\left(-{2 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 2}^{2}}}+{{\left({{\left({8 \ {{p 2}^{2}}\ {{p 3}^{2}}}+{8 \ {{p 2}^{4}}}+{{\left({{32}\ {{p 1}^{2}}}+ 8 \right)}\ {{p 2}^{2}}}\right)}\ {{q 1}^{2}}}-{{12}\ p 1 \ {{p 2}^{2}}\ q 1}+{8 \ {{p 2}^{2}}\ {{p 3}^{2}}}+{8 \ {{p 2}^{4}}}+{{\left({8 \ {{p 1}^{2}}}+ 4 \right)}\ {{p 2}^{2}}}\right)}\ q 2}+{{\left({8 \ p 1 \ p 2 \ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{3}}}+{{\left({{1
6}\ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 2}\right)}\ {{q 1}^{3}}}+{{\left(-{2 \ p 2 \ {{p 3}^{2}}}-{2 \ {{p 2}^{3}}}+{{\left(-{8 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{{\left({8 \ p 1 \ p 2 \ {{p 3}^{2}}}+{8 \ p 1 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 2}\right)}\ q 1}-{2 \ p 2 \ {{p 3}^{2}}}-{2 \ {{p 2}^{3}}}-{2 \ {{p 1}^{2}}\ p 2}\right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{{16}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{16}\ {{p 2}^{3}}}+{{\left(-{{16}\ {{p 1}^{2}}}-{16}\right)}\ p 2}\right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{5}}}+{{\left(-{4 \ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{3}}}+{{\left(-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 3}^{4}}}+{{\left({{\left(-{{32}\ {{p 2}^{2}}\ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 2}^{4}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{24}\right)}\ {{p 2}^{2}}}\right)}\ p 3}\right)}\ q 2}+{{\left(-{{32}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 1}+{8 \ p 2 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{{16}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{44}\ {{p 2}^{3}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{20}\right)}\ p 2}\right)}\ {{p 3}^{2}}}-{{16}\ {{p 2}^{5}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{20}\right)}\ {{p 2}^{3}}}+{{\left(-{4 \ {{p 1}^{4}}}-{8 \ {{p 1}^{2}}}- 4 \right)}\ p 2}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{48}\ p 1 \ {{p 2}^{2}}\ {{p 3}^{2}}}-{{24}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{2
4}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ {{p 2}^{2}}}\right)}\ q 1}+{{12}\ {{p 2}^{2}}\ {{p 3}^{2}}}+{6 \ {{p 2}^{4}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ {{p 2}^{2}}}\right)}\ q 2}+{{\left(-{{16}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{20}\ {{p 2}^{3}}}+{{\left(-{{44}\ {{p 1}^{2}}}-{20}\right)}\ p 2}\right)}\ {{p 3}^{2}}}-{4 \ {{p 2}^{5}}}+{{\left(-{{20}\ {{p 1}^{2}}}- 8 \right)}\ {{p 2}^{3}}}+{{\left(-{{16}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}- 4 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{{\left({{12}\ p 1 \ p 2 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 2}\right)}\ q 1}-{{16}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{20}\ {{p 2}^{3}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{16}\right)}\ p 2}\right)}\ {{p 3}^{2}}}-{4 \ {{p 2}^{5}}}+{{\left(-{8 \ {{p 1}^{2}}}- 6 \right)}\ {{p 2}^{3}}}+{{\left(-{4 \ {{p 1}^{4}}}-{6 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 3}^{2}}}+{{\left({{\left(-{{24}\ {{p 2}^{2}}\ {{p 3}^{3}}}+{{\left(-{{32}\ {{p 2}^{4}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{24}\right)}\ {{p 2}^{2}}}\right)}\ p 3}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{48}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 1}+{6 \ p 2 \ {{p 3}^{3}}}+{{\left({{1
2}\ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ {{p 2}^{2}}\ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 2}^{4}}}+{{\left(-{{48}\ {{p 1}^{2}}}-{24}\right)}\ {{p 2}^{2}}}\right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{12}\ p 1 \ {{p 2}^{2}}\ p 3 \ q 1}-{{24}\ {{p 2}^{2}}\ {{p 3}^{3}}}+{{\left(-{{24}\ {{p 2}^{4}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{20}\right)}\ {{p 2}^{2}}}\right)}\ p 3}\right)}\ q 2}+{{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{32}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{3}}}+{{\left({6 \ p 2 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{3}}}+{{\left({{12}\ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 1}+{6 \ p 2 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 4 \right)}\ p 2}\right)}\ p 3}\right)}\ q 3}+{{\left(-{2 \ p 2 \ {{p 3}^{4}}}+{{\left(-{{16}\ {{p 2}^{3}}}+{{\left(-{4 \ {{p 1}^{2}}}- 4 \right)}\ p 2}\right)}\ {{p 3}^{2}}}-{{16}\ {{p 2}^{5}}}+{{\left(-{{16}\ {{p 1}^{2}}}-{16}\right)}\ {{p 2}^{3}}}+{{\left(-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 2}^{4}}}+{{\left({{\left(-{{24}\ p 1 \ {{p 2}^{2}}\ {{p 3}^{2}}}-{{32}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ {{p 2}^{2}}}\right)}\ q 1}+{6 \ {{p 2}^{2}}\ {{p 3}^{2}}}+{8 \ {{p 2}^{4}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ {{p 2}^{2}}}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{4 \ p 2 \ {{p 3}^{4}}}+{{\left(-{{2
0}\ {{p 2}^{3}}}+{{\left(-{{20}\ {{p 1}^{2}}}- 8 \right)}\ p 2}\right)}\ {{p 3}^{2}}}-{{16}\ {{p 2}^{5}}}+{{\left(-{{44}\ {{p 1}^{2}}}-{20}\right)}\ {{p 2}^{3}}}+{{\left(-{{16}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}- 4 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{{\left({6 \ p 1 \ p 2 \ {{p 3}^{2}}}+{{12}\ p 1 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 2}\right)}\ q 1}-{4 \ p 2 \ {{p 3}^{4}}}+{{\left(-{{20}\ {{p 2}^{3}}}+{{\left(-{8 \ {{p 1}^{2}}}- 6 \right)}\ p 2}\right)}\ {{p 3}^{2}}}-{{1
6}\ {{p 2}^{5}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{16}\right)}\ {{p 2}^{3}}}+{{\left(-{4 \ {{p 1}^{4}}}-{6 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ p 1 \ {{p 2}^{2}}\ {{p 3}^{2}}}-{{24}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{3
2}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ {{p 2}^{2}}}\right)}\ {{q 1}^{3}}}+{{\left({6 \ {{p 2}^{2}}\ {{p 3}^{2}}}+{6 \ {{p 2}^{4}}}+{{\left({{12}\ {{p 1}^{2}}}+ 6 \right)}\ {{p 2}^{2}}}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{2}}\ {{p 3}^{2}}}-{{2
4}\ p 1 \ {{p 2}^{4}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ {{p 2}^{2}}}\right)}\ q 1}+{6 \ {{p 2}^{2}}\ {{p 3}^{2}}}+{6 \ {{p 2}^{4}}}+{{\left({6 \ {{p 1}^{2}}}+ 4 \right)}\ {{p 2}^{2}}}\right)}\ q 2}+{{\left(-{2 \ p 2 \ {{p 3}^{4}}}+{{\left(-{4 \ {{p 2}^{3}}}+{{\left(-{{16}\ {{p 1}^{2}}}- 4 \right)}\ p 2}\right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{5}}}+{{\left(-{{16}\ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{3}}}+{{\left(-{{16}\ {{p 1}^{4}}}-{{16}\ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 1}^{4}}}+{{\left({6 \ p 1 \ p 2 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 2}\right)}\ {{q 1}^{3}}}+{{\left(-{4 \ p 2 \ {{p 3}^{4}}}+{{\left(-{8 \ {{p 2}^{3}}}+{{\left(-{{20}\ {{p 1}^{2}}}- 6 \right)}\ p 2}\right)}\ {{p 3}^{2}}}-{4 \ {{p 2}^{5}}}+{{\left(-{{20}\ {{p 1}^{2}}}- 6 \right)}\ {{p 2}^{3}}}+{{\left(-{{16}\ {{p 1}^{4}}}-{{16}\ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{{\left({6 \ p 1 \ p 2 \ {{p 3}^{2}}}+{6 \ p 1 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 2}\right)}\ q 1}-{2 \ p 2 \ {{p 3}^{4}}}+{{\left(-{4 \ {{p 2}^{3}}}+{{\left(-{4 \ {{p 1}^{2}}}- 2 \right)}\ p 2}\right)}\ {{p 3}^{2}}}-{2 \ {{p 2}^{5}}}+{{\left(-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{p 2}^{3}}}+{{\left(-{2 \ {{p 1}^{4}}}-{2 \ {{p 1}^{2}}}\right)}\ p 2}}\over{{{\left({{\left({4 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({6 \ p 2 \ p 3 \ q 2}+{6 \ p 1 \ p 3 \ q 1}-{2 \ p 3}\right)}\ q 3}+{{\left({{p 3}^{2}}+{4 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({6 \ p 1 \ p 2 \ q 1}-{2 \ p 2}\right)}\ q 2}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{4 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}-{2 \ p 1 \ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{4 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{6 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{6 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{2 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{6 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left(-{6 \ p 1 \ p 2 \ p 3 \ q 1}+{2 \ p 2 \ p 3}\right)}\ q 2}+{{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 3 \ q 1}-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ q 3}+{{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{4 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{6 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{2 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 2 \ q 1}-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{4 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ {{q 1}^{3}}}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{2 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}
\
{{{{\left({{\left({{16}\ {{p 3}^{4}}}+{{\left({8 \ {{p 2}^{2}}}+{8 \ {{p 1}^{2}}}+ 8 \right)}\ {{p 3}^{2}}}\right)}\ {{q 3}^{3}}}+{{\left({{\left({{32}\ p 2 \ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left({{32}\ p 1 \ {{p 3}^{3}}}+{{\left({8 \ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 3}\right)}\ q 1}-{8 \ {{p 3}^{3}}}+{{\left(-{2 \ {{p 2}^{2}}}-{2 \ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 3}^{2}}}+{{\left({{\left({8 \ {{p 3}^{4}}}+{{\left({{32}\ {{p 2}^{2}}}+{8 \ {{p 1}^{2}}}+ 8 \right)}\ {{p 3}^{2}}}\right)}\ {{q 2}^{2}}}+{{\left({{48}\ p 1 \ p 2 \ {{p 3}^{2}}\ q 1}-{{12}\ p 2 \ {{p 3}^{2}}}\right)}\ q 2}+{{\left({8 \ {{p 3}^{4}}}+{{\left({8 \ {{p 2}^{2}}}+{{32}\ {{p 1}^{2}}}+ 8 \right)}\ {{p 3}^{2}}}\right)}\ {{q 1}^{2}}}-{{12}\ p 1 \ {{p 3}^{2}}\ q 1}+{8 \ {{p 3}^{4}}}+{{\left({8 \ {{p 2}^{2}}}+{8 \ {{p 1}^{2}}}+ 4 \right)}\ {{p 3}^{2}}}\right)}\ q 3}+{{\left({8 \ p 2 \ {{p 3}^{3}}}+{{\left({{16}\ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 2}^{3}}}+{{\left({{\left({8 \ p 1 \ {{p 3}^{3}}}+{{\left({{3
2}\ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 3}\right)}\ q 1}-{2 \ {{p 3}^{3}}}+{{\left(-{8 \ {{p 2}^{2}}}-{2 \ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{\left({8 \ p 2 \ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{3}}}+{{\left({{32}\ {{p 1}^{2}}}+ 8 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{2}}}-{{12}\ p 1 \ p 2 \ p 3 \ q 1}+{8 \ p 2 \ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{3}}}+{{\left({8 \ {{p 1}^{2}}}+ 4 \right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left({8 \ p 1 \ {{p 3}^{3}}}+{{\left({8 \ p 1 \ {{p 2}^{2}}}+{{16}\ {{p 1}^{3}}}+{8 \ p 1}\right)}\ p 3}\right)}\ {{q 1}^{3}}}+{{\left(-{2 \ {{p 3}^{3}}}+{{\left(-{2 \ {{p 2}^{2}}}-{8 \ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left({8 \ p 1 \ {{p 3}^{3}}}+{{\left({8 \ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 3}\right)}\ q 1}-{2 \ {{p 3}^{3}}}+{{\left(-{2 \ {{p 2}^{2}}}-{2 \ {{p 1}^{2}}}\right)}\ p 3}\right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{{16}\ {{p 3}^{5}}}+{{\left(-{{16}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{2}}}-{16}\right)}\ {{p 3}^{3}}}+{{\left(-{2 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 3}^{4}}}+{{\left({{\left(-{{32}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{24}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{24}\right)}\ p 2}\right)}\ {{p 3}^{2}}}\right)}\ q 2}+{{\left(-{{32}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{2}}}-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ {{p 3}^{2}}}\right)}\ q 1}+{8 \ {{p 3}^{4}}}+{{\left({6 \ {{p 2}^{2}}}+{6 \ {{p 1}^{2}}}+ 6 \right)}\ {{p 3}^{2}}}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{{16}\ {{p 3}^{5}}}+{{\left(-{{44}\ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}-{20}\right)}\ {{p 3}^{3}}}+{{\left(-{{16}\ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{20}\right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{4}}}-{8 \ {{p 1}^{2}}}- 4 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{48}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 1}+{{12}\ p 2 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left(-{{16}\ {{p 3}^{5}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{{44}\ {{p 1}^{2}}}-{20}\right)}\ {{p 3}^{3}}}+{{\left(-{4 \ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{2}}}- 8 \right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}- 4 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left({{12}\ p 1 \ {{p 3}^{3}}}+{{\left({6 \ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 3}\right)}\ q 1}-{{16}\ {{p 3}^{5}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}-{16}\right)}\ {{p 3}^{3}}}+{{\left(-{4 \ {{p 2}^{4}}}+{{\left(-{8 \ {{p 1}^{2}}}- 6 \right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{4}}}-{6 \ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 3}^{2}}}+{{\left({{\left(-{{24}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{3
2}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{24}\right)}\ p 2}\right)}\ {{p 3}^{2}}}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{{24}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{48}\ p 1 \ {{p 2}^{2}}}-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ {{p 3}^{2}}}\right)}\ q 1}+{6 \ {{p 3}^{4}}}+{{\left({{12}\ {{p 2}^{2}}}+{6 \ {{p 1}^{2}}}+ 6 \right)}\ {{p 3}^{2}}}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{24}\ {{p 2}^{3}}}+{{\left(-{{48}\ {{p 1}^{2}}}-{24}\right)}\ p 2}\right)}\ {{p 3}^{2}}}\right)}\ {{q 1}^{2}}}+{{12}\ p 1 \ p 2 \ {{p 3}^{2}}\ q 1}-{{24}\ p 2 \ {{p 3}^{4}}}+{{\left(-{{24}\ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{2}}}-{20}\right)}\ p 2}\right)}\ {{p 3}^{2}}}\right)}\ q 2}+{{\left(-{{24}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{2}}}-{{32}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ {{p 3}^{2}}}\right)}\ {{q 1}^{3}}}+{{\left({6 \ {{p 3}^{4}}}+{{\left({6 \ {{p 2}^{2}}}+{{12}\ {{p 1}^{2}}}+ 6 \right)}\ {{p 3}^{2}}}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ p 1 \ {{p 3}^{4}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{2}}}-{{24}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ {{p 3}^{2}}}\right)}\ q 1}+{6 \ {{p 3}^{4}}}+{{\left({6 \ {{p 2}^{2}}}+{6 \ {{p 1}^{2}}}+ 4 \right)}\ {{p 3}^{2}}}\right)}\ q 3}+{{\left(-{2 \ {{p 3}^{5}}}+{{\left(-{{16}\ {{p 2}^{2}}}-{4 \ {{p 1}^{2}}}- 4 \right)}\ {{p 3}^{3}}}+{{\left(-{{16}\ {{p 2}^{4}}}+{{\left(-{{16}\ {{p 1}^{2}}}-{16}\right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 2}^{4}}}+{{\left({{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{32}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 1}+{6 \ p 2 \ {{p 3}^{3}}}+{{\left({8 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{4 \ {{p 3}^{5}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}- 8 \right)}\ {{p 3}^{3}}}+{{\left(-{{16}\ {{p 2}^{4}}}+{{\left(-{{44}\ {{p 1}^{2}}}-{20}\right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{20}\ {{p 1}^{2}}}- 4 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left({6 \ p 1 \ {{p 3}^{3}}}+{{\left({{12}\ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 3}\right)}\ q 1}-{4 \ {{p 3}^{5}}}+{{\left(-{{20}\ {{p 2}^{2}}}-{8 \ {{p 1}^{2}}}- 6 \right)}\ {{p 3}^{3}}}+{{\left(-{{16}\ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{2}}}-{16}\right)}\ {{p 2}^{2}}}-{4 \ {{p 1}^{4}}}-{6 \ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left({{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{32}\ {{p 1}^{3}}}-{{24}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{3}}}+{{\left({6 \ p 2 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{3}}}+{{\left({{12}\ {{p 1}^{2}}}+ 6 \right)}\ p 2}\right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left(-{{24}\ p 1 \ p 2 \ {{p 3}^{3}}}+{{\left(-{{24}\ p 1 \ {{p 2}^{3}}}+{{\left(-{{24}\ {{p 1}^{3}}}-{{20}\ p 1}\right)}\ p 2}\right)}\ p 3}\right)}\ q 1}+{6 \ p 2 \ {{p 3}^{3}}}+{{\left({6 \ {{p 2}^{3}}}+{{\left({6 \ {{p 1}^{2}}}+ 4 \right)}\ p 2}\right)}\ p 3}\right)}\ q 2}+{{\left(-{2 \ {{p 3}^{5}}}+{{\left(-{4 \ {{p 2}^{2}}}-{{16}\ {{p 1}^{2}}}- 4 \right)}\ {{p 3}^{3}}}+{{\left(-{2 \ {{p 2}^{4}}}+{{\left(-{{16}\ {{p 1}^{2}}}- 4 \right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{16}\ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 1}^{4}}}+{{\left({6 \ p 1 \ {{p 3}^{3}}}+{{\left({6 \ p 1 \ {{p 2}^{2}}}+{8 \ {{p 1}^{3}}}+{6 \ p 1}\right)}\ p 3}\right)}\ {{q 1}^{3}}}+{{\left(-{4 \ {{p 3}^{5}}}+{{\left(-{8 \ {{p 2}^{2}}}-{{20}\ {{p 1}^{2}}}- 6 \right)}\ {{p 3}^{3}}}+{{\left(-{4 \ {{p 2}^{4}}}+{{\left(-{{20}\ {{p 1}^{2}}}- 6 \right)}\ {{p 2}^{2}}}-{{16}\ {{p 1}^{4}}}-{{16}\ {{p 1}^{2}}}- 2 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{{\left({6 \ p 1 \ {{p 3}^{3}}}+{{\left({6 \ p 1 \ {{p 2}^{2}}}+{6 \ {{p 1}^{3}}}+{4 \ p 1}\right)}\ p 3}\right)}\ q 1}-{2 \ {{p 3}^{5}}}+{{\left(-{4 \ {{p 2}^{2}}}-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{p 3}^{3}}}+{{\left(-{2 \ {{p 2}^{4}}}+{{\left(-{4 \ {{p 1}^{2}}}- 2 \right)}\ {{p 2}^{2}}}-{2 \ {{p 1}^{4}}}-{2 \ {{p 1}^{2}}}\right)}\ p 3}}\over{{{\left({{\left({4 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({6 \ p 2 \ p 3 \ q 2}+{6 \ p 1 \ p 3 \ q 1}-{2 \ p 3}\right)}\ q 3}+{{\left({{p 3}^{2}}+{4 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({6 \ p 1 \ p 2 \ q 1}-{2 \ p 2}\right)}\ q 2}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{4 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}-{2 \ p 1 \ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {\sqrt{{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}\ {\sqrt{{{q 3}^{2}}+{{q 2}^{2}}+{{q 1}^{2}}+ 1}}}+{{\left(-{4 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 3}^{3}}}+{{\left({{\left(-{6 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{6 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{2 \ {{p 3}^{2}}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1 \right)}\ {{q 3}^{2}}}+{{\left({{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{6 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 2}^{2}}}+{{\left(-{6 \ p 1 \ p 2 \ p 3 \ q 1}+{2 \ p 2 \ p 3}\right)}\ q 2}+{{\left(-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 3 \ q 1}-{3 \ {{p 3}^{3}}}+{{\left(-{3 \ {{p 2}^{2}}}-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 3}\right)}\ q 3}+{{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{4 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 2}^{3}}}+{{\left({{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{6 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{2 \ {{p 2}^{2}}}+{{p 1}^{2}}+ 1 \right)}\ {{q 2}^{2}}}+{{\left({{\left(-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{6 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ {{q 1}^{2}}}+{2 \ p 1 \ p 2 \ q 1}-{3 \ p 2 \ {{p 3}^{2}}}-{3 \ {{p 2}^{3}}}+{{\left(-{3 \ {{p 1}^{2}}}- 3 \right)}\ p 2}\right)}\ q 2}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{4 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ {{q 1}^{3}}}+{{\left({{p 3}^{2}}+{{p 2}^{2}}+{2 \ {{p 1}^{2}}}+ 1 \right)}\ {{q 1}^{2}}}+{{\left(-{3 \ p 1 \ {{p 3}^{2}}}-{3 \ p 1 \ {{p 2}^{2}}}-{3 \ {{p 1}^{3}}}-{3 \ p 1}\right)}\ q 1}+{{p 3}^{2}}+{{p 2}^{2}}+{{p 1}^{2}}+ 1}}") | (15) |
Type: Matrix(Expression(Integer))