apart_list() does not seem to support the « full=True » mode. So I guess I have to loop over the summed terms. Do you agree ? thanks again, Mike
Le lundi 10 août 2020 23:05:42 UTC+2, Aaron Meurer a écrit : > > Yes, that is what I mean by only getting the real roots. I don't think > it's possible now, though it shouldn't be hard to do it manually with > apart_list(). > > Aaron Meurer > > On Mon, Aug 10, 2020 at 3:03 PM Mikhael Myara <[email protected] > <javascript:>> wrote: > >> Thanks again Aaron, >> here is what I did : >> >> import sympy as sp >> >> sp.var('s t') >> >> >> Hstab = 1/(s**3+s**2+5*s+4) >> Hstab = sp.apart(Hstab,full=True).doit().evalf() >> display(Hstab) >> And I get : >> >> [image: Capture d’écran 2020-08-10 à 23.00.45.png] >> >> >> >> Which is great. However I would have liked the conjugate denominator >> fractions combined. Is this possible ou should I write some code for this ? >> Moreover : I am not sure I understood how is appart_list() interesting ? >> >> Thanks again, >> Mikhaël >> >> Le lundi 10 août 2020 21:58:23 UTC+2, Aaron Meurer a écrit : >>> >>> If you replace the coefficients with floating point numbers, you can use >>> full=True and get an answer with floats (although they aren't fully >>> simplified for some reason, so you may want to use apart_list() instead). >>> I'm not sure if it is possible to get an answer with just the real roots, >>> so that there are no complex numbers added. >>> >>> Aaron Meurer >>> >>> On Mon, Aug 10, 2020 at 1:53 PM Mikhael Myara <[email protected]> >>> wrote: >>> >>>> Thanks a lot Aaron. >>>> However : for my usage, an approximate root would be sufficient. Is >>>> there a way to allow this in Sympy ? >>>> Thanks again, >>>> Mikhaël >>>> >>>> Le lundi 10 août 2020 20:48:04 UTC+2, Aaron Meurer a écrit : >>>>> >>>>> The roots are the key difference. The second polynomial has a rational >>>>> root, -1, meaning it can be split out in a partial fraction >>>>> decomposition. >>>>> If you don't call evalf() on the roots you can also see that the roots of >>>>> the first polynomial are more complicated, because they are coming from >>>>> the >>>>> general cubic formula. You can also see the difference in the two if you >>>>> call factor(). >>>>> >>>>> >>> factor(s**3+s**2+5*s+4) >>>>> s**3 + s**2 + 5*s + 4 >>>>> >>> factor(s**3+2*s**2+5*s+4) >>>>> (s + 1)*(s**2 + s + 4) >>>>> >>>>> The first polynomial is irreducible over rationals, but the second >>>>> factors. So if you do a partial fraction decomposition, it will not split >>>>> because apart() only decomposes over rational numbers by default. If you >>>>> want a full decomposition over all the roots, you can use something like >>>>> apart(1/(s**3+s**2+5*s+4), full=True).doit(). >>>>> >>>>> Note that it's not uncommon for polynomials to work like this, where >>>>> if you change a coefficient it changes the behavior of it. That's because >>>>> it's easy for a polynomial to have a rational root with one coefficient >>>>> but >>>>> not with another close coefficient, like in this case. >>>>> >>>>> Aaron Meurer >>>>> >>>>> On Mon, Aug 10, 2020 at 2:29 AM Mikhael Myara < >>>>> [email protected]> wrote: >>>>> >>>>>> Dear all, >>>>>> >>>>>> I don't know if my problem is with the knowledge of fractionnal >>>>>> decomposition itself or with symPy's implementation. >>>>>> >>>>>> I start with the following code : >>>>>> >>>>>> import sympy as sp >>>>>> sp.var('s') >>>>>> >>>>>> >>>>>> Hstab = 1/(s**3+s**2+5*s+4) >>>>>> Hstab = sp.apart(Hstab) >>>>>> display(Hstab) >>>>>> >>>>>> >>>>>> The result is : >>>>>> >>>>>> [image: Capture d’écran 2020-08-10 à 10.18.18.png] >>>>>> Now I check another similar expression : >>>>>> >>>>>> Hstab2 = 1/(s**3 + 2*s**2 + 5*s + 4) >>>>>> Hstab2 = sp.apart(Hstab2,s) >>>>>> display(Hstab2) >>>>>> >>>>>> and I get : >>>>>> >>>>>> [image: Capture d’écran 2020-08-10 à 10.21.14.png] >>>>>> >>>>>> >>>>>> >>>>>> >>>>>> If now I check for the roots of the denominator for each case : >>>>>> >>>>>> >>>>>> print("\n\nFirst case :") >>>>>> P1=(1/Hstab).simplify() >>>>>> display(P1) >>>>>> for sol in sp.solve(P1,s): >>>>>> display(sol.evalf()) >>>>>> >>>>>> >>>>>> print("\n\nSecond case :") >>>>>> P2=(1/Hstab2).simplify() >>>>>> display(P2) >>>>>> for sol in sp.solve(P2,s): >>>>>> display(sol.evalf()) >>>>>> >>>>>> I get : >>>>>> >>>>>> [image: Capture d’écran 2020-08-10 à 10.26.18.png] >>>>>> Which is very similar except that the real root of the first case is >>>>>> not ass simple as the one of the second case. So I do not understand as >>>>>> I >>>>>> can't see any mathematical impossibility, the two cases are very close. >>>>>> Is there a way to reach the fractional decomposition for the first >>>>>> case ? >>>>>> >>>>>> Thanks a lot, >>>>>> Mike >>>>>> >>>>>> >>>>>> -- >>>>>> You received this message because you are subscribed to the Google >>>>>> Groups "sympy" group. >>>>>> To unsubscribe from this group and stop receiving emails from it, >>>>>> send an email to [email protected]. >>>>>> To view this discussion on the web visit >>>>>> https://groups.google.com/d/msgid/sympy/4ccc519f-8a28-4478-bc2e-adbc302a9647o%40googlegroups.com >>>>>> >>>>>> <https://groups.google.com/d/msgid/sympy/4ccc519f-8a28-4478-bc2e-adbc302a9647o%40googlegroups.com?utm_medium=email&utm_source=footer> >>>>>> . >>>>>> >>>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups "sympy" group. >>>> To unsubscribe from this group and stop receiving emails from it, send >>>> an email to [email protected]. >>>> To view this discussion on the web visit >>>> https://groups.google.com/d/msgid/sympy/b4c883c0-0840-4cd2-b964-cb32a27c8aaao%40googlegroups.com >>>> >>>> <https://groups.google.com/d/msgid/sympy/b4c883c0-0840-4cd2-b964-cb32a27c8aaao%40googlegroups.com?utm_medium=email&utm_source=footer> >>>> . >>>> >>> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected] <javascript:>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sympy/9a1d5c28-b8f7-4d66-b197-02d615c7af18o%40googlegroups.com >> >> <https://groups.google.com/d/msgid/sympy/9a1d5c28-b8f7-4d66-b197-02d615c7af18o%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> > -- You received this message because you are subscribed to the Google Groups "sympy" group. 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