Visualise 3 simultaneous cubic equationsI have three equations of the form: i 1 3 P 1 + i 1 ( Z 1 + Z 2 ) + ( i 2 + i 3 ) Z 2 − U 1 = 0 i 2 3 P 2 + i 2 ( Z 1 + Z 2 ) + ( i 1 + i 3 ) Z 2 − U 2 = 0 i 3 3 P 3 + i 3 ( Z 1 + Z 2 ) + ( i 1 + i 2 ) Z 2 − U 3 = 0where P 1 , P 2 , P 3 , K , U 1 , U 2 , U 3 , Z 1 and Z 2 are all known constant complex numbers.Can anyone recommend a way of visualising these three functions?

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Visualise 3 simultaneous cubic equationsI have three equations of the form:            i      1      3              P      1        +      i    1    (      Z    1    +      Z    2    )  +  (      i    2    +      i    3    )      Z    2    −      U    1    =  0            i      2      3              P      2        +      i    2    (      Z    1    +      Z    2    )  +  (      i    1    +      i    3    )      Z    2    −      U    2    =  0            i      3      3              P      3        +      i    3    (      Z    1    +      Z    2    )  +  (      i    1    +      i    2    )      Z    2    −      U    3    =  0where       P    1    ,      P    2    ,      P    3    ,  K  ,      U    1    ,      U    2    ,      U    3    ,      Z    1   and       Z    2   are all known constant complex numbers.Can anyone recommend a way of visualising these three functions?

coquinarq1 · Accepted Answer

Let me try to raise a quite unconventional method, since your question was on a way of visualisation. Your equations are quite symmetric and I cannot resist the temptation to suggest this. However, having an elegant analytical approach for a visualisation will be a calculation challenge and you would need to dig into the theory required for this.Your equations:      i    1    3    /      P    1    +      i    1    (      Z    1    +      Z    2    )  +  (      i    2    +      i    3    )      Z    2    −      U    1    =  0      i    2    3    /      P    2    +      i    2    (      Z    1    +      Z    2    )  +  (      i    1    +      i    3    )      Z    2    −      U    2    =  0      i    3    3    /      P    3    +      i    3    (      Z    1    +      Z    2    )  +  (      i    1    +      i    2    )      Z    2    −      U    3    =  0can easily be reformed to the right hand side of a system of non-linear differential equations, to which your equations seek the roots/zeros:            d              q        1                    d      t        =      a    1          q    1    3    +  b        q    1    +  c        q    2    +  c        q    3    +      d    1              d              q        2                    d      t        =      a    2          q    2    3    +  c        q    1    +  b        q    2    +  c        q    3    +      d    2              d              q        3                    d      t        =      a    3          q    3    3    +  c        q    1    +  c        q    2    +  b        q    3    +      d    3  I changed your variable   i with   q so it fits directly into the next reference. The parameters are just collecting your parameters and easily extractable.

realburitv4 · Accepted Answer

Great expert answer!

Visualise 3 simultaneous cubic equations I have three equations of the form: <msubsup>

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