On Tuesday, September 19, 2017 at 10:45:06 PM UTC-7, Yann Cargouet wrote:
>
> Hi Simon,
>
> Thank you for your answer, I will try the Ansatz and comparison of
> coefficients.
> To find coefficients a, b, and c I tried to solve a system of three
> equations but unfortunately it doesn't work. The system is depicted below:
> eq1 = a + b == Rl*Rs*Cc*gm + Rc*Cc + Rl*Cc + Rl*Cl + Rs*Cc + Rs*Cin
> eq2 = c + a*b == Rc*Rl*Cc*Cl + Rc*Rs*Cc*Cin + Rs*Rl*Cc*Cin + Rs*Rl*Cc*Cl +
> Rs*Rl*Cin*Cl
> eq3 = a*c == Rc*Rl*Rs*Cc*Cin*Cl
> solve([eq1,eq2,eq3],a,b,c)
> Here is the result given by SAGE:
> sage: []
> Why this systen doesn't work ?
>
Why do you think the polynomial factors into lower degree factors. It
doesn't in QQ[Rl,...Cc,s] (as a simple call to "factor" verifies) and one
would expect the same to be true in CC[...].
You can already see it from your system above: eq3 gives only finitely many
combinations for a,c (up to scalars), so given those choices you get a
bunch of overdetermined systems in b. One would expect none of those are
solvable. The solve command might have verified that, but I don't think
"solve" gives any guarantees that it tries anything exhaustive.
>
> Regards,
> Yann
>
> Le mardi 19 septembre 2017 10:23:07 UTC+2, Yann Cargouet a écrit :
>>
>> Hi everybody,
>>
>> I would like to factorize a polynomial function of third degree in order
>> to obtain the following form:
>> (1 + a*s + b*s^2)*(1 + c*s).
>>
>> Here my test case:
>>
>> When I use the factor() function there is no change on the expression.
>> Which function I have to use to obtain the wanted simplication ?
>>
>> all my variables are defined with the command var('Cc, Cin,...)
>>
>> Thanks in advance for your answers
>> Yann
>>
>
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