# Question:solve equations issue (15equations with 16 varibles)

## Question:solve equations issue (15equations with 16 varibles)

Maple 2022

dear all,

I am trying to use the solve to get symbolic answer.

to be simple, here is issue:

I have 15equations with 16 varibles.

the 15 equation as follows:

first 4 equation set

```equList_Ya :=

[ Va1 Ya11 + Va2 Ya12 + Va3 Ya13 + Va4 Ya14 = Ia1,

Va1 Ya21 + Va2 Ya22 + Va3 Ya23 + Va4 Ya24 = Ia2,

Va1 Ya31 + Va2 Ya32 + Va3 Ya33 + Va4 Ya34 = Ia3,

Va1 Ya41 + Va2 Ya42 + Va3 Ya43 + Va4 Ya44 = Ia4]```

2nd 4 equation set

```equList_Yb :=

[ Vb1 Yb11 + Vb2 Yb12 + Vb3 Yb13 + Vb4 Yb14 = Ib1,

Vb1 Yb21 + Vb2 Yb22 + Vb3 Yb23 + Vb4 Yb24 = Ib2,

Vb1 Yb31 + Vb2 Yb32 + Vb3 Yb33 + Vb4 Yb34 = Ib3,

Vb1 Yb41 + Vb2 Yb42 + Vb3 Yb43 + Vb4 Yb44 = Ib4]```

the 3rd 4 equation set

```equList_ConnectCondition :=

[Ia3 = -Ib1, Ia4 = -Ib2, Va3 = Vb1,  Va4 = Vb2]```

the 4th 3 equation set

` equList_Y11Condition := [Va2 = 0, Vb3 = 0, Vb4 = 0]`

so total equation number is 4+4+4+3=15

```equList_Y11all := {Ia3 = -Ib1, Ia4 = -Ib2, Va2 = 0, Va3 = Vb1, Va4 = Vb2, Vb3 = 0,
Vb4 = 0, Va1*Ya11 + Va2*Ya12 + Va3*Ya13 + Va4*Ya14 = Ia1,
Va1*Ya21 + Va2*Ya22 + Va3*Ya23 + Va4*Ya24 = Ia2,
Va1*Ya31 + Va2*Ya32 + Va3*Ya33 + Va4*Ya34 = Ia3,
Va1*Ya41 + Va2*Ya42 + Va3*Ya43 + Va4*Ya44 = Ia4,
Vb1*Yb11 + Vb2*Yb12 + Vb3*Yb13 + Vb4*Yb14 = Ib1,
Vb1*Yb21 + Vb2*Yb22 + Vb3*Yb23 + Vb4*Yb24 = Ib2,
Vb1*Yb31 + Vb2*Yb32 + Vb3*Yb33 + Vb4*Yb34 = Ib3,
Vb1*Yb41 + Vb2*Yb42 + Vb3*Yb43 + Vb4*Yb44 = Ib4}```

the 16 varible is

```var_Y11 :=

[ Va1, Va2, Va3, Va4,

Ia1, Ia2, Ia3, Ia4,

Vb1, Vb2, Vb3, Vb4,

Ib1, Ib2, Ib3, Ib4]```

I hope to get Ia1=f(Va1) to calculate Y11(=Ia1/Va1)

but the solve give nothing:

`Y11_all := solve(equList_Y11all, {Ia1}, symbolic = true);                        `

Y11_all := NULL

Question1: why the above solve output nothing???

since not work,so I try another way:

```polys_Y11 := map(lhs - rhs = 0, equList_Y11all);
polys_Y11 := {Va2 = 0, Vb3 = 0, Vb4 = 0, Ia3 + Ib1 = 0,

Ia4 + Ib2 = 0, Va3 - Vb1 = 0, Va4 - Vb2 = 0,

Va1 Ya11 + Va2 Ya12 + Va3 Ya13 + Va4 Ya14 - Ia1 = 0,

Va1 Ya21 + Va2 Ya22 + Va3 Ya23 + Va4 Ya24 - Ia2 = 0,

Va1 Ya31 + Va2 Ya32 + Va3 Ya33 + Va4 Ya34 - Ia3 = 0,

Va1 Ya41 + Va2 Ya42 + Va3 Ya43 + Va4 Ya44 - Ia4 = 0,

Vb1 Yb11 + Vb2 Yb12 + Vb3 Yb13 + Vb4 Yb14 - Ib1 = 0,

Vb1 Yb21 + Vb2 Yb22 + Vb3 Yb23 + Vb4 Yb24 - Ib2 = 0,

Vb1 Yb31 + Vb2 Yb32 + Vb3 Yb33 + Vb4 Yb34 - Ib3 = 0,

Vb1 Yb41 + Vb2 Yb42 + Vb3 Yb43 + Vb4 Yb44 - Ib4 = 0}```

and solve it with

what I expected is Ia1=f(Va1) which Va1 as indepentent,but the above solution have no Va1
Question2: is the (22) give the right answer for Ia1 ? what is the indepent var for the above solution?

here is my full maple worksheet

CoupleLineSeriesConnect_Question.mw