grobner basis: hints for the variables elimination order ?
Subject: grobner basis: hints for the variables elimination order ?
From: depuis
Date: Tue, 19 Oct 2010 11:15:34 +0200
Hello,
I'm performing electrical circuits parameters extraction from measured
frequency response. For instance,
if the admittance is given by
Cp1 Rp1 s + 1
Y(s) = ------------------------
Cp1 Rp1 Rc s + Rc + Rp1
I identify a transfer function as
n1 s + n0
H(s) = -----------
d1 s + 1
>From there, I solve the system in Maxima as
grobner_basis([n1*(Rc+Rp1)-Cp1*Rp1, n0*(Rc+Rp1)-1,
d1*(Rc+Rp1)-Cp1*Rp1*Rc]);
[(- Cp1 Rc + d1) Rp1 + d1 Rc,
(- n1 + Cp1) Rp1 - d1,
- n0 Rp1 - n0 Rc + 1,
- n1 Rc + d1,
- Cp1 n0 Rc - n1 + Cp1,
2
- n1 + Cp1 n1 - Cp1 d1 n0]
>From the last line I get Cp1, from the previous Rc, and so on. The problem
is that n1, n0 and d1 are considered as variables, though there are just
coefficients extracted from data. Would it be possible, with grobner_basis,
to specify that there are three independant variables, namely Rc, Rp1 and
Rc1, which must be obtained mainly as functions of n1, n0 and d1 ? Or,
alternativelly, I tried
solve(grobner_basis([n1*(Rc+Rp1)-Cp1*Rp1, n0*(Rc+Rp1)-1,
d1*(Rc+Rp1)-Cp1*Rp1*Rc]), [Rc, Rp1, Cp1]);
But is seems that the output of grobner_basis is not compatible with solve
input. Any hint ?
Regards
Pascal Dupuis
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