\section{Truss Design}

For the demonstration of the efficiency of the Solver finally the examples stated in the introduction \ref{TM}  and \ref{ET} are solved. In the following  the complete display of the outputs of the two program runs are reported. We use the following lexicon:

\begin{center}
\begin {tabular} {r r | l  }
{\sf LEXICON:} & {\it\color{black} German} & {\color{blue} English }  \\
\hline
   & Stabzweischlags & \color{blue} two-bar truss \\
     %\hline 
     &  Zweischlag &  \color{blue} two-bar \\
     &  Stababmessungen &  \color{blue} bar dimensions \\
     &  Zweischlagparameter &  \color{blue} two-bar parameters 
\end {tabular}
\end{center}



\begin{literatim}{|}
(COM1) Zweischlag :
[
  F*cos(gamma) - S1*cos(alpha) - S2*cos(beta) = 0,
  F*sin(gamma) - S1*sin(alpha) + S2*sin(beta) = 0,
  Delta_l1 = l1*S1/(E*A1),
  Delta_l2 = l2*S2/(E*A2),
  l1 = c/cos(alpha),
  l2 = c/cos(beta),
  a = Delta_l2/sin(alpha+beta),
  b = Delta_l1/sin(alpha+beta),
  u = a*sin(alpha) + b*sin(beta),
  w = -a*cos(alpha) + b*cos(beta),
  A1 = h1^2,
  A2 = h2^2
]$

(COM2) Stababmessungen : [h1, h2]$

(COM3) Zweischlagparameter : [alpha, beta, gamma, F, c, E, u, w]$

(COM4) SolverRepeatImmed : SolverRepeatLinear : FALSE$

(COM5) MsgLevel : 'DETAIL$

(COM6) Solver( Zweischlag, Stababmessungen, Zweischlagparameter );
The variables to be solved for are [H1, H2]
The parameters are [ALPHA, BETA, C, E, F, U, W, GAMMA]
Checking for inconsistencies...
... none found.
Searching for immediate assignments.
                   C
Assigning L1 = ----------
               COS(ALPHA)
                   C
Assigning L2 = ---------
               COS(BETA)
Checking for inconsistencies...
... none found.
Searching for linear equations...
  ...with respect to: [H1, H2, A, A1, A2, B, DELTA_L1, DELTA_L2, S1, S2]
Found 7 linear equations in 7 variables.
The variables to be solved for are [A, A1, B, DELTA_L1, DELTA_L2, S1, S2]
The equations are [F COS(GAMMA) - COS(BETA) S2 - COS(ALPHA) S1, 

F SIN(GAMMA) + SIN(BETA) S2 - SIN(ALPHA) S1, 

A SIN(BETA + ALPHA) - DELTA_L2, B SIN(BETA + ALPHA) - DELTA_L1, 

                                                                       2
U - B SIN(BETA) - A SIN(ALPHA), W - B COS(BETA) + A COS(ALPHA), A1 - H1 ]
Solving linear equations.
                                COS(BETA) U - SIN(BETA) W
The solutions are [A = -------------------------------------------, 
                       COS(ALPHA) SIN(BETA) + SIN(ALPHA) COS(BETA)

       2              SIN(ALPHA) W + COS(ALPHA) U
A1 = H1 , B = -------------------------------------------, 
              COS(ALPHA) SIN(BETA) + SIN(ALPHA) COS(BETA)

DELTA_L1 = (SIN(ALPHA) SIN(BETA + ALPHA) W

 + COS(ALPHA) SIN(BETA + ALPHA) U)/(COS(ALPHA) SIN(BETA)

 + SIN(ALPHA) COS(BETA)), DELTA_L2 = 

COS(BETA) SIN(BETA + ALPHA) U - SIN(BETA) SIN(BETA + ALPHA) W
-------------------------------------------------------------, 
         COS(ALPHA) SIN(BETA) + SIN(ALPHA) COS(BETA)

     COS(BETA) F SIN(GAMMA) + SIN(BETA) F COS(GAMMA)
S1 = -----------------------------------------------, 
       COS(ALPHA) SIN(BETA) + SIN(ALPHA) COS(BETA)

     SIN(ALPHA) F COS(GAMMA) - COS(ALPHA) F SIN(GAMMA)
S2 = -------------------------------------------------]
        COS(ALPHA) SIN(BETA) + SIN(ALPHA) COS(BETA)
Checking for inconsistencies...
... none found.
Checking for remaining equations.
3 equation(s) and 2 variable(s) left.
The variables to be solved for are [H1, H2]
Applying valuation strategy.
Trying to solve equation 3 for H2
Valuation: 10
                       2
The equation is A2 - H2  = 0
Checking if equation was solved correctly.
The solutions are [H2 = - SQRT(A2), H2 = SQRT(A2)]
Solution is correct.
The solution is not unique. Tracing paths separately.
Solution 1 for H2
Checking for inconsistencies...
... none found.
Solution 2 for H2
Checking for inconsistencies...
... none found.
Consistent solutions for H2 : [H2 = - SQRT(A2), H2 = SQRT(A2)]
Checking for remaining equations.
2 equation(s) and 2 variable(s) left.
The variables to be solved for are [A2, H1]
Applying valuation strategy.
Trying to solve equation 2 for A2
Valuation: 8
The equation is COS(ALPHA) C F SIN(GAMMA) - SIN(ALPHA) C F COS(GAMMA)

 - A2 COS(BETA) SIN(BETA) SIN(BETA + ALPHA) E W

         2
 + A2 COS (BETA) SIN(BETA + ALPHA) E U = 0
Checking if equation was solved correctly.
The solutions are [A2 = (COS(ALPHA) C F SIN(GAMMA)

 - SIN(ALPHA) C F COS(GAMMA))/(COS(BETA) SIN(BETA) SIN(BETA + ALPHA) E W

      2
 - COS (BETA) SIN(BETA + ALPHA) E U)]
Solution is correct.
Solution 1 for A2
Checking for inconsistencies...
... none found.
Consistent solutions for A2 : [A2 = (COS(ALPHA) C F SIN(GAMMA)

 - SIN(ALPHA) C F COS(GAMMA))/(COS(BETA) SIN(BETA) SIN(BETA + ALPHA) E W

      2
 - COS (BETA) SIN(BETA + ALPHA) E U)]
Checking for remaining equations.
1 equation(s) and 1 variable(s) left.
The variables to be solved for are [H1]
Trying to solve equation 1 for H1
Valuation: (irrelevant)
The equation is - COS(BETA) C F SIN(GAMMA) - SIN(BETA) C F COS(GAMMA)

                                               2
 + COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E H1  W

      2                                     2
 + COS (ALPHA) SIN(BETA + ALPHA) E H1  U = 0
Checking if equation was solved correctly.
The solutions are [H1 = - SQRT(COS(BETA) C F SIN(GAMMA)

/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U)

 + SIN(BETA) C F COS(GAMMA)/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U)), 

H1 = SQRT(COS(BETA) C F SIN(GAMMA)/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA)

          2
 E W + COS (ALPHA) SIN(BETA + ALPHA) E U)

 + SIN(BETA) C F COS(GAMMA)/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U))]
Solution is correct.
The solution is not unique. Tracing paths separately.
Solution 1 for H1
Checking for inconsistencies...
... none found.
Solution 2 for H1
Checking for inconsistencies...
... none found.
Consistent solutions for H1 : [H1 = - SQRT(COS(BETA) C F SIN(GAMMA)

/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U)

 + SIN(BETA) C F COS(GAMMA)/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U)), 

H1 = SQRT(COS(BETA) C F SIN(GAMMA)/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA)

          2
 E W + COS (ALPHA) SIN(BETA + ALPHA) E U)

 + SIN(BETA) C F COS(GAMMA)/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U))]
Checking for remaining equations.
All variables solved for. No equations left.
Checking for remaining equations.
All variables solved for. No equations left.
Checking for remaining equations.
2 equation(s) and 2 variable(s) left.
The variables to be solved for are [A2, H1]
Applying valuation strategy.
Trying to solve equation 2 for A2
Valuation: 8
The equation is COS(ALPHA) C F SIN(GAMMA) - SIN(ALPHA) C F COS(GAMMA)

 - A2 COS(BETA) SIN(BETA) SIN(BETA + ALPHA) E W

         2
 + A2 COS (BETA) SIN(BETA + ALPHA) E U = 0
Checking if equation was solved correctly.
The solutions are [A2 = (COS(ALPHA) C F SIN(GAMMA)

 - SIN(ALPHA) C F COS(GAMMA))/(COS(BETA) SIN(BETA) SIN(BETA + ALPHA) E W

      2
 - COS (BETA) SIN(BETA + ALPHA) E U)]
Solution is correct.
Solution 1 for A2
Checking for inconsistencies...
... none found.
Consistent solutions for A2 : [A2 = (COS(ALPHA) C F SIN(GAMMA)

 - SIN(ALPHA) C F COS(GAMMA))/(COS(BETA) SIN(BETA) SIN(BETA + ALPHA) E W

      2
 - COS (BETA) SIN(BETA + ALPHA) E U)]
Checking for remaining equations.
1 equation(s) and 1 variable(s) left.
The variables to be solved for are [H1]
Trying to solve equation 1 for H1
Valuation: (irrelevant)
The equation is - COS(BETA) C F SIN(GAMMA) - SIN(BETA) C F COS(GAMMA)

                                               2
 + COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E H1  W

      2                                     2
 + COS (ALPHA) SIN(BETA + ALPHA) E H1  U = 0
Checking if equation was solved correctly.
The solutions are [H1 = - SQRT(COS(BETA) C F SIN(GAMMA)

/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U)

 + SIN(BETA) C F COS(GAMMA)/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U)), 

H1 = SQRT(COS(BETA) C F SIN(GAMMA)/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA)

          2
 E W + COS (ALPHA) SIN(BETA + ALPHA) E U)

 + SIN(BETA) C F COS(GAMMA)/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U))]
Solution is correct.
The solution is not unique. Tracing paths separately.
Solution 1 for H1
Checking for inconsistencies...
... none found.
Solution 2 for H1
Checking for inconsistencies...
... none found.
Consistent solutions for H1 : [H1 = - SQRT(COS(BETA) C F SIN(GAMMA)

/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U)

 + SIN(BETA) C F COS(GAMMA)/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U)), 

H1 = SQRT(COS(BETA) C F SIN(GAMMA)/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA)

          2
 E W + COS (ALPHA) SIN(BETA + ALPHA) E U)

 + SIN(BETA) C F COS(GAMMA)/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U))]
Checking for remaining equations.
All variables solved for. No equations left.
Checking for remaining equations.
All variables solved for. No equations left.
Postprocessing results.

(D6) [[H1 = - SQRT((COS(BETA) C F SIN(GAMMA) + SIN(BETA) C F COS(GAMMA))

/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U)), 

H2 = - SQRT((SIN(ALPHA) C F COS(GAMMA) - COS(ALPHA) C F SIN(GAMMA))

     2
/(COS (BETA) SIN(BETA + ALPHA) E U - COS(BETA) SIN(BETA) SIN(BETA + ALPHA)

 E W))], [H1 = SQRT((COS(BETA) C F SIN(GAMMA) + SIN(BETA) C F COS(GAMMA))

/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U)), 

H2 = - SQRT((SIN(ALPHA) C F COS(GAMMA) - COS(ALPHA) C F SIN(GAMMA))

     2
/(COS (BETA) SIN(BETA + ALPHA) E U - COS(BETA) SIN(BETA) SIN(BETA + ALPHA)

 E W))], [H1 = - SQRT((COS(BETA) C F SIN(GAMMA) + SIN(BETA) C F COS(GAMMA))

/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U)), 

H2 = SQRT((SIN(ALPHA) C F COS(GAMMA) - COS(ALPHA) C F SIN(GAMMA))

     2
/(COS (BETA) SIN(BETA + ALPHA) E U - COS(BETA) SIN(BETA) SIN(BETA + ALPHA)

 E W))], [H1 = SQRT((COS(BETA) C F SIN(GAMMA) + SIN(BETA) C F COS(GAMMA))

/(COS(ALPHA) SIN(ALPHA) SIN(BETA + ALPHA) E W

      2
 + COS (ALPHA) SIN(BETA + ALPHA) E U)), 

H2 = SQRT((SIN(ALPHA) C F COS(GAMMA) - COS(ALPHA) C F SIN(GAMMA))

     2
/(COS (BETA) SIN(BETA + ALPHA) E U - COS(BETA) SIN(BETA) SIN(BETA + ALPHA)

 E W))]]
\end{literatim}

For the system of equations, which describe the 
 'Truss' the 
Solver gives four distinct analytical solutions, which are different only in their signs. 
Due to the physical boundary condition, that the lengths
$h_1$ and $h_2$ cannot have negative values, only the last solutionis  meaningful
\begin{eqnarray}
h_1 &=& \sqrt{
  \frac{
    \cos \beta \, c \, F \, \sin \gamma + \sin \beta \, c \, F \, 
    \cos \gamma
  }{
    \cos \alpha \, \sin \alpha \, \sin \left( \beta + \alpha \right) \, 
    E \, w + \cos^2 \alpha \, \sin \left( \beta + \alpha \right) \, E \, 
    u
  }
} \\
h_2 &=& \sqrt{
  \frac{
    \sin \alpha \, c \, F \, \cos \gamma - \cos \alpha \, c \, F \, 
    \sin \gamma
  }{
    \cos^2 \beta \, \sin \left( \beta + \alpha \right) \, E \, u
    - \cos \beta \, \sin \beta \, \sin \left( \beta + \alpha \right) \, 
    E \, w
  }
}
\end{eqnarray}

\clearpage
\section{Transistor Amplifier Design}

We use the following

\begin{center}
\begin {tabular} {r r | l  }
{\sf LEXICON:} & {\it\color{black} German} & {\color{blue} English }  \\
\hline
   & Verstaerker & \color{blue} amplifier \\
     &  Widerstaende &  \color{blue} resistances \\
          &  Designparameter &  \color{blue} design parameter 
\end {tabular}
\end{center}



\begin{literatim}{|}
(COM7) Verstaerker :
[
  -V_V1+V_R1+V_OC_1+V_FIX2_Q1 = 0,-V_V1+V_R2+V_OC_1+V_I1+V_FIX2_Q1 = 0,
  -V_V1+V_OC_1+V_I1+V_FIX2_Q2+V_FIX2_Q1-V_FIX1_Q2-V_FIX1_Q1 = 0,
  V_V1-V_R6+V_R3-V_OC_1-V_I1-V_FIX2_Q1+V_FIX1_Q1 = 0,
  -V_V1+V_R7+V_R4+V_OC_1+V_I1-V_FIX1_Q2 = 0,-V_V1+V_R7+V_R5+V_OC_1 = 0,
  V_OC_2-V_I1+V_FIX1_Q2 = 0,V_V_CC-V_V1+V_R6+V_OC_1+V_FIX2_Q1-V_FIX1_Q1 = 0,
  I_V1+I_OC_1 = 0,I_R7-I_OC_1+I_FIX2_Q1 = 0,I_R2+I_R1-I_FIX2_Q1-I_FIX1_Q1 = 0,
  I_R6+I_FIX2_Q2+I_FIX1_Q1 = 0,-I_R7+I_R5+I_R4 = 0,
  -I_R4+I_OC_2-I_FIX2_Q2-I_FIX1_Q2 = 0,I_R3-I_R2+I_I1+I_FIX1_Q2 = 0,
  I_V_CC-I_R6-I_R3 = 0,V_V1 = 0,I_I1 = 0,I_OC_1 = 0,V_FIX1_Q1 = 2.72,
  V_FIX2_Q1 = 0.607,I_R1*R1-V_R1 = 0,I_R7*R7-V_R7 = 0,I_R2*R2-V_R2 = 0,
  I_R6*R6-V_R6 = 0,V_FIX1_Q2 = 6.42,V_FIX2_Q2 = 0.698,I_R3*R3-V_R3 = 0,
  I_R4*R4-V_R4 = 0,I_R5*R5-V_R5 = 0,I_OC_2 = 0,V_V_CC = VCC,
  I_FIX1_Q1 = 1.11e-4,I_FIX2_Q1 = 5.75001e-7,I_FIX1_Q2 = 0.00401,
  I_FIX2_Q2 = 1.26e-5,
  A = 145303681853*R2/(145309663773*R1),
  ZIN = R7,
  ZOUT = (1675719398828125*R2*R7+394048139880824192*R1*R2)
         /(136552890630303121408*R1)
]$

(COM8) Widerstaende : [R1, R2, R3, R4, R5, R6, R7]$

(COM9) Designparameter : [VCC, A, ZIN, ZOUT]$

(COM10) SolverRepeatImmed : SolverRepeatLinear : TRUE$

(COM11) Solver( Verstaerker, Widerstaende, Designparameter );
The variables to be solved for are [R1, R2, R3, R4, R5, R6, R7]
The parameters are [A, VCC, ZIN, ZOUT]
Checking for inconsistencies...
... none found.
Searching for immediate assignments.
Assigning V_V1 = 0
Assigning I_I1 = 0
Assigning I_OC_1 = 0
                      68
Assigning V_FIX1_Q1 = --
                      25
                      607
Assigning V_FIX2_Q1 = ----
                      1000
                      321
Assigning V_FIX1_Q2 = ---
                      50
                      349
Assigning V_FIX2_Q2 = ---
                      500
Assigning I_OC_2 = 0
Assigning V_V_CC = VCC
                        111
Assigning I_FIX1_Q1 = -------
                      1000000
                         5
Assigning I_FIX2_Q1 = -------
                      8695637
                       401
Assigning I_FIX1_Q2 = ------
                      100000
                        25
Assigning I_FIX2_Q2 = -------
                      1984127
Assigning R7 = ZIN
Checking for inconsistencies...
... none found.
Searching for immediate assignments.
Assigning I_V1 = 0
Checking for inconsistencies...
... none found.
Searching for immediate assignments.
No immediate assignments found.
Searching for linear equations...
  ...with respect to: [R1, R2, R3, R4, R5, R6, I_R1, I_R2, I_R3, I_R4, 

I_R5, I_R6, I_R7, I_V_CC, V_I1, V_OC_1, V_OC_2, V_R1, V_R2, V_R3, V_R4, 

V_R5, V_R6, V_R7]
Found 18 linear equations in 18 variables.
The variables to be solved for are [I_R1, I_R2, I_R3, I_R4, I_R5, I_R6, 

I_R7, I_V_CC, V_I1, V_OC_1, V_OC_2, V_R1, V_R2, V_R3, V_R4, V_R5, V_R6, 

V_R7]
The equations are [1000 V_R1 + 1000 V_OC_1 + 607, 

1000 V_R2 + 1000 V_OC_1 + 1000 V_I1 + 607, 200 V_OC_1 + 200 V_I1 - 1567, 

- 1000 V_R6 + 1000 V_R3 - 1000 V_OC_1 - 1000 V_I1 + 2113, 

50 V_R7 + 50 V_R4 + 50 V_OC_1 + 50 V_I1 - 321, V_R7 + V_R5 + V_OC_1, 

50 V_OC_2 - 50 V_I1 + 321, 1000 V_R6 + 1000 V_OC_1 + 1000 VCC - 2113, 

8695637 I_R7 + 5, 8695637000000 I_R2 + 8695637000000 I_R1 - 970215707, 

1984127000000 I_R6 + 245238097, - I_R7 + I_R5 + I_R4, 

- 198412700000 I_R4 - 798134927, 100000 I_R3 - 100000 I_R2 + 401, 

I_V_CC - I_R6 - I_R3, I_R7 ZIN - V_R7]
Solving linear equations.
                            8695637000000 I_R3 + 33899288663
The solutions are [I_R1 = - --------------------------------, 
                                     8695637000000

       100000 I_R3 + 401            798134927
I_R2 = -----------------, I_R4 = - ------------, 
            100000                 198412700000

        6939299538713499               245238097                5
I_R5 = -------------------, I_R6 = - -------------, I_R7 = - -------, 
       1725324815389900000             1984127000000         8695637

         1984127000000 I_R3 - 245238097           200 V_OC_1 - 1567
I_V_CC = ------------------------------, V_I1 = - -----------------, 
                 1984127000000                           200

           200 V_OC_1 - 283           1000 V_OC_1 + 607           4221
V_OC_2 = - ----------------, V_R1 = - -----------------, V_R2 = - ----, 
                 200                        1000                  500

         200 V_OC_1 + 200 VCC - 1567         1000 ZIN - 2460865271
V_R3 = - ---------------------------, V_R4 = ---------------------, 
                     200                          1739127400

         8695637 V_OC_1 - 5 ZIN           1000 V_OC_1 + 1000 VCC - 2113
V_R5 = - ----------------------, V_R6 = - -----------------------------, 
                8695637                               1000

          5 ZIN
V_R7 = - -------]
         8695637
Checking for inconsistencies...
... none found.
Searching for linear equations...
  ...with respect to: [I_R3, R1, R2, R3, R4, R5, R6, V_OC_1]
Found 6 linear equations in 5 variables.
The variables to be solved for are [R2, R4, R5, R6, V_OC_1]
The equations are [8695637000000 V_OC_1 - 8695637000000 I_R3 R1

 - 33899288663 R1 + 5278251659000, 1984127000000 V_OC_1 + 1984127000000 VCC

 - 245238097 R6 - 4192460351000, 200 V_OC_1 + 200 VCC + 200 I_R3 R3

 - 1567, - 992063500000 ZIN - 6940291602213499 R4 + 2441334613776708500, 

- 992063500000 ZIN + 1725324815389900000 V_OC_1 + 6939299538713499 R5, 

145309663773 A R1 - 145303681853 R2]
Solving linear equations.
Checking for inconsistencies...
... none found.
                        145309663773 A R1
The solutions are [R2 = -----------------, 
                          145303681853

       992063500000 ZIN - 2441334613776708500
R4 = - --------------------------------------, 
                  6940291602213499

R5 = - (- 9920635000000 ZIN + (17253248153899000000 I_R3

 + 67260493917052201) R1 - 10472721629416693000)/69392995387134990, 

R6 = (17253248153899000000 VCC + (17253248153899000000 I_R3

 + 67260493917052201) R1 - 46928834978605280000)/2132501470082789, 

         (8695637000000 I_R3 + 33899288663) R1 - 5278251659000
V_OC_1 = -----------------------------------------------------]
                             8695637000000
Checking for inconsistencies...
... none found.
Searching for linear equations...
  ...with respect to: [I_R3, R1, R3]
No linear equations found.
Checking for remaining equations.
3 equation(s) and 3 variable(s) left.
The variables to be solved for are [I_R3, R1, R3]
Applying valuation strategy.
Trying to solve equation 1 for I_R3
Valuation: 4
The equation is 14530966377300000 A I_R3 R1 + 58269175172973 A R1

                                                   + 122665368220302600 = 0
Checking if equation was solved correctly.
                            6474352796997 A R1 + 13629485357811400
The solutions are [I_R3 = - --------------------------------------]
                                    1614551819700000 A R1
Solution is correct.
Solution 1 for I_R3
Checking for inconsistencies...
... none found.
Consistent solutions for I_R3 : [I_R3 = 

                                    6474352796997 A R1 + 13629485357811400
                                  - --------------------------------------]
                                            1614551819700000 A R1
Checking for remaining equations.
2 equation(s) and 2 variable(s) left.
The variables to be solved for are [R1, R3]
Applying valuation strategy.
Trying to solve equation 1 for R3
Valuation: 20
The equation is - R1 (- 16062755182397110876073408478539448677201569671148#

116383372395290156600000000 A VCC + 64411648281412414613054367998943189195#

578294381303946697323305113527966000 A R3 + 135601779249796410015811714375#

830025732935651163832398508429761039502017200000 A + 135596196971410595846#

324806740533400875556129557784494104259093864172929200000) - 1355961969714#

10595846324806740533400875556129557784494104259093864172929200000 R3 - 179#

2201925592952751292050414582157181324535016813917972727234536207382600 A

   2
 R1  = 0
Checking if equation was solved correctly.
The solutions are [R3 = (140395565418006489000000 A R1 VCC

                            2
 - 15664635352383720279 A R1  + (- 1185219363258810780138000 A

 - 1185170571683430488618000) R1)/(562986217326206020890 A R1

 + 1185170571683430488618000)]
Solution is correct.
Solution 1 for R3
Checking for inconsistencies...
... none found.
Consistent solutions for R3 : [R3 = (140395565418006489000000 A R1 VCC

                            2
 - 15664635352383720279 A R1  + (- 1185219363258810780138000 A

 - 1185170571683430488618000) R1)/(562986217326206020890 A R1

 + 1185170571683430488618000)]
Checking for remaining equations.
1 equation(s) and 1 variable(s) left.
The variables to be solved for are [R1]
Trying to solve equation 1 for R1
Valuation: (irrelevant)
The equation is R1 (19841637776253069394020865409024 ZOUT

 - 243498222421608533966015625 A ZIN)

                                     2
 - 57259002716458635629644396416 A R1  = 0
Checking if equation was solved correctly.
The solutions are [R1 = 

19841637776253069394020865409024 ZOUT - 243498222421608533966015625 A ZIN
-------------------------------------------------------------------------, 
                     57259002716458635629644396416 A

R1 = 0]
Solution is correct.
The solution is not unique. Tracing paths separately.
Solution 1 for R1
Checking for inconsistencies...
... none found.
Solution 2 for R1
Checking for inconsistencies...
... none found.
Consistent solutions for R1 : [R1 = 

19841637776253069394020865409024 ZOUT - 243498222421608533966015625 A ZIN
-------------------------------------------------------------------------, 
                     57259002716458635629644396416 A

R1 = 0]
Checking for remaining equations.
All variables solved for. No equations left.
Checking for remaining equations.
All variables solved for. No equations left.
Postprocessing results.

(D11) [[R1 = - (243498222421608533966015625 A ZIN

 - 19841637776253069394020865409024 ZOUT)

/(57259002716458635629644396416 A), R2 = 

  1493854125285941926171875 A ZIN - 121727839118116990147367272448 ZOUT
- ---------------------------------------------------------------------, 
                       351267764122759016747201152

R3 = (334763184724568105702258732451550460395708593115792893559436793085952

     2
 ZOUT  + VCC

                                                                      2
 (106256457337115768692100530787195899963103895496024350000000000000 A  ZIN

 - 8658388208766832396126274743883820688291739892383476917089599488000000 A

 ZOUT) + A

 (73094113258409599088098011387867214250558868171501312134070398877696000

 ZOUT + ZIN

 (- 8216483067762383568115091483320660991714242249851965644800000000 ZOUT

 - 896980085605567678321894471091892803815897329518698154700000000000))

 + 73091104214643137701992515955008538217110816411520639295650692857856000

         2
 ZOUT + A  (50416680420198682402077210492446131565566605185394287109375

    2
 ZIN  - 897017012839931319298712680905507787488523085777437562700000000000

 ZIN))/(A

 (- 34720136717154997908466361722974120960049876968457742437529293946880

 ZOUT

 - 210926324831111746833250971831897544037167089192987941918299029504000)

                                                                    2
 + 426088393921834232455323128456655558852046620939057643500000000 A

              992063500000 ZIN - 2441334613776708500
 ZIN), R4 = - --------------------------------------, 
                         6940291602213499

R5 = (38195771383195691504052086845016246794667687936 ZOUT

 + A (99303995957664108704965549227744192421875 ZIN

 + 599657596227485533261336202180916694139772288000)

 + 8339540409811836894068029655629814665587863808000)

/(3973373711375163964000922192169533030064195840 A), 

R6 = (- 38195771383195691504052086845016246794667687936 ZOUT

 + A (468741670456330507974731687410699967578125 ZIN

 - 2687098289520198765190831087202789799110676480000)

 + 987903782911837781320158487942202132025984000000 A VCC

 - 8339540409811836894068029655629814665587863808000)

/(122104907468322449250303944919525361454884224 A), R7 = ZIN], 

                                992063500000 ZIN - 2441334613776708500
[R1 = 0, R2 = 0, R3 = 0, R4 = - --------------------------------------, 
                                           6940291602213499

     992063500000 ZIN + 1047272162941669300
R5 = --------------------------------------, 
                6939299538713499

     1984127000000 VCC - 5396825440000
R6 = ---------------------------------, R7 = ZIN]]
                 245238097
\end{literatim}
Here we have more than one solution of the system ,too, but only first one is
physically meaningful result.
