CAS.numer; denom; lcoeff; degree... ??!! [It's OK NOW ! :o)]

[dg1969]

I need these functions in a home program because i'd like to compute symbolicaly the phase \(\varphi\) of a transfer functions \(\dfrac{P(s)}{Q(s)}\cdot e^{-k\cdot s}\) initially placed in F0 to F9 var in term of 'X' in a FUNCTION APP like

"froot" from CAS give me all roots of numerator and denom with multiplicity so :

\(F(s)=K\cdot\dfrac{(s-r1)...(s-r_n)}{(s-p_1)...(s-p_m)}\cdot e^{-k\cdot s}\) with \(n \leq m\)

\(\varphi=arg(F(i\cdot \omega) \)

lcoeff(numer)/lcoeff(denom) give me \(K\) so first term of \(\varphi\) is known

I can easily compute the major terms of the sum of \( \varphi\) : \(+/-m_i\cdot atan \dfrac{\beta_i-\omega}{\alpha_i}\) where \(\omega \) is the pulsation ; \(\alpha_i; \beta_i ;m_i \) are resp the real part the imaginary part and multiplicity of roots and poles of \(F(s)\)
I need to test if an exp term is there to add the last term in the phase sum... Don't know how to parse yet...

At the end I want to place these phase functions in F_i var's in term of 'X' for plot...

I try these way to plot bode phase without +/- pi discontinuity... At the end I want to keep benefits of the function app plot facility (max, zero etc...)