That's what I guess too. I used the symbolic math toolbox of Matlab in a
recent past and I did not notice this behavior. But perhaps I do not
remember very well, I am not sure.
Thanks for your answer Aaron.
Le vendredi 31 juillet 2020 21:51:58 UTC+2, Aaron Meurer a écrit :
>
> If you compare H.factor() and H1.factor(), you will see that there are
> factors in the numerator and denominator that should cancel out. The
> issue is that SymPy has issues doing polynomial division with floating
> point coefficients. Due to their inexact nature, SymPy has to guess if
> a polynomial expression should cancel or not when they are present,
> and the logic for doing this isn't as good as it should be. With
> rational coefficients, this problem doesn't exist because the
> arithmetic is all exact.
>
> To be clear, I do think SymPy should be able to do a better job here,
> but this isn't an easy problem to solve.
>
> Aaron Meurer
>
> On Fri, Jul 31, 2020 at 12:46 PM Oscar Benjamin
> <oscar.j...@gmail.com <javascript:>> wrote:
> >
> > On Fri, 31 Jul 2020 at 17:26, Mikhael Myara
> > <mikhae...@umontpellier.fr <javascript:>> wrote:
> > >
> > > Thanks for your answer.
> > >
> > > I don’t do it « for sport » ;-) My example is a reduced example coming
> from a practical situation I encountered.
> >
> > I understand that you have reduced this but it is a lot better if the
> > reduction is self-contained so that others can literally copy-paste
> > the code to test what is happening with an expression that
> > demonstrates the issue. I could probably tell you exactly what the
> > problem is in a given example if you provided minimal code for that
> > example.
> >
> > > Here it is :
> > > I developed a small software that solves the voltages and currents of
> an electronic circuit described by means of a standard format (« netlist
> »). This file is parsed, equations are solved. In this netlist file, the
> values of the components are given.
> >
> > How exactly are they given in the file (e.g. to how many digits)?
> >
> > If the file has something like 0.12 then you can read that in directly
> > as Rational('0.12') rather than converting the string to a float. Then
> > you will have an object that represents the value from the file
> > exactly with no rounding error. Alternatively you can use nsimplify to
> > convert the floats to an approximate rational representation (direct
> > string to Rational is better though).
> >
> > > I imagined that I could mix symbolic and numerical values in the
> description of the circuit (for example we want to study de variations of a
> single component, not of all), and it seems to be a bad idea because mixed
> expressions seem to be really difficult to handle for Sympy.
> >
> > Generally speaking simplification will work better with numbers rather
> > than symbols. However this is only true if you give numbers in exact
> > form. When you pass a float to sympy it will be treated as an
> > inherently imprecise object. As a result many simplifications will be
> > refused and also any arithmetic will be computed in floating point.
> > The kind of simplification needed here is most likely factorisation
> > and cancellation of polynomials which is poorly conditioned in
> > floating point.
> >
> > > So I will have to make 100% symbolic treatment and then only replace
> the values of the components. It was to explore the possibilities for my ?
> students : this kind of question will help me giving to them good
> orientations during classroom work.
> >
> > If the class work involves using sympy then good orientation would be
> > to avoid the use of floats in symbolic computation.
> >
> > --
> > Oscar
> >
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>
>
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