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Equations

A = {{-0.03333, 0, 0}, {0.0667, -0.6799, 0.6667}, {0,     0.3399, -0.3467}};
B = {0.0333, 0, 0};
CC = {1, 1, 1};
myInverse = Inverse[s*IdentityMatrix[3] - A];
P = CC*myInverse*B;
P = P[[1,1]];

Goal

Express the polynomial $P$ in the format $\frac{1}{1+\text{something}}$.

Trials

1. Trial: tried to play with denominator and numerator, FAIL, here.

2. Trial: tried Solve command but errs, the code here fires the error with a transfer function $G(s)$ and the picture here. I try to express the line 146 i.e. the equation $G(s)$ in the form $\frac{1}{1+C}$. How can I simplify this? Why do I get the error? How can I get the equation for the $G(s)$ in the requested form? Err report "Solve::ivar: ... is not a valid variable".

3. Trial: fixing the preserved-variable problem revealed by Artes's answer, I get very peculiar answer -- I get empty set!? Why? I should get some non-empty equation. Notice the line 336 in the picture here.

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  • $\begingroup$ @NasserM.Abbasi thank you for the notice, done. $\endgroup$
    – hhh
    Commented Dec 5, 2012 at 15:19

2 Answers 2

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You can't use Solve[ mySeries == 1/(1 + A), A] because A had been defined in your code. Moreover you can't use capital C because 

it is the default form for the i-th parameter or constant generated in representing
the results of various symbolic computations.

mySeries has been defined with mySeries = Series[ P[[1, 1]], {s, 0, 1}]; thus it has the value in terms of SeriesData : 

Head @ mySeries

SeriesData

therefore you should use Normal. Because of inexact coefficients Solve produces this message :

Solve::ratnz: Solve was unable to solve the system with inexact coefficients.
The answer was obtained by solving a corresponding exact system and numericizing
the result. >>

If you want to suppress the message use Quiet. Then you'll get the result :

Solve[ Normal[mySeries] == 1/(1 + x), x] // Quiet

{{x -> (0.333333 (-3.19716*10^7 - 1.06476*10^12 s))/(-1.18295*10^10 + 3.5492*10^11 s)}}

A bit more involved algebraic expression was P and you wanted to find P[[1,1]] in the form 1/(1 + x). You can use the MaxExtraConditions option in Solve to get all conditions for a general solution.

Solve[ 1/(1 + x) == P[[1, 1]], x, MaxExtraConditions -> All] // Quiet

or if you know that conditions are satisfied you may simply write

1/(1 + x) /. Solve[ 1/(1 + x) == P[[1, 1]], x] // Quiet

to get the result in the expected form.

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    $\begingroup$ @hhh You wanted mySeries == 1/(1+x) so write simply 1/(1 + x) /. Solve[ Normal[mySeries] == 1/(1 + x), x] // Quiet $\endgroup$
    – Artes
    Commented Dec 5, 2012 at 15:27
  • $\begingroup$ @hhh You are welcome. I recommend to edit your question once more and put your equations in a good order. Next you neednt use P = P[[1]][[1]]` because you set another value to P which was originally a matrix , moreover you can simply use P[[1,1]] instead of P[[1]][[1]]. $\endgroup$
    – Artes
    Commented Dec 5, 2012 at 15:59
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If you are only after "something" you could simply employ

something = Denominator[P]/Numerator[P] - 1 // Together

Note that system commands generally start with a capital letter. You can also apply this to Normal[ mySeries] (instead of P) if you wish/require. For target expressions more general than 1/(1+something) Artes answer can always be generalized.

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