On Fri, Sep 4, 2015 at 4:16 AM, Francesco Bonazzi
<franz.bona...@gmail.com> wrote:
> You may assume variables to be positive/negative, for now.
>
> Sage uses a lot of backends. In case of assume(zeta > 1), I believe it
> relies on Maxima, which can handle that kind of assumptions.
>
> SymPy's aim, on the other hand, is to implement all the algorithms on its
> own.
>
> Assumptions with inequalities look like they are not yet supported, but I
> suppose they will be supported by a syntax similar to this one, as soon as
> the algorithm handling them will be finished:
>
> from sympy.assumptions.assume import global_assumptions
> global_assumptions.add(Q.positive(zeta - 1))
>
> (Note: this code doesn't currently work as expected)
>
>
> On Thursday, 3 September 2015 18:19:38 UTC+2, Carl Sandrock wrote:
>>
>> I am trying to build a workbook to illustrate the effect of various
>> parameters of second order transfer functions. The full workbook is on
>> GitHub, but here is a minimal example of the problem:
>>
>> import sympy
>>
>> tau, zeta, t, w, K = sympy.symbols('tau, zeta, t, w, K', real=True,
>> positive=True)
>> s = sympy.Symbol('s')
>>
>>
>> G = K/(tau**2*s**2 + 2*tau*zeta*s + 1)
>>
>>
>> The impulse response of the second order system is simply the inverse
>> Laplace of G. However, the nature of the inverse depends on the parameter ζ.
>> TAttempting directly to calculate the inverse results in
>>
>>
>> TypeError: cannot determine truth value of
This error usually indicates a bug in library code. Can you open an
issue with a full reproducing example and a full traceback?
Aaron Meurer
>>
>> -zeta/tau - sqrt(zeta + 1)*cos(atan2(0, zeta - 1)/2)*sqrt(Abs(zeta -
>> 1))/tau < oo
>>
>>
>> There are three cases of interest, ζ>1, ζ=1 and 0<ζ<1
>>
>> In Sage, I would be able to use assume(zeta > 1) before calculating the
>> inverse to obtain the correct version of the inverse, but I have not found a
>> way to impose such constraints in SymPy. So, first question is whether I can
>> find nice solutions for these cases to the inverse.
>>
>>
>> Failing that, I want at least to be able to calculate the inverse with
>> known values of all the parameters so that I can animate the response using
>> IPython notebook widgets. Here I have also been out of luck, as some cases
>> result in special values which are not cleanly evaluated to
>>
>>
>> knownbadvalues = [{K: 5.05, tau: 5., zeta: 1.},
>> {K: 5.05, tau: 5.05, zeta: 1.05}
>> ]
>> for values in knownbadvalues:
>> print sympy.inverse_laplace_transform(G.subs(values), s, t,
>> noconds=True)
>>
>> (0.202*t - 0.404*EulerGamma - 0.404*polygamma(0, 1.0))*exp(-0.2*t)
>> 0.198019801980198*meijerg(((0.728681938243239, 0.855476477598345), ()),
>> ((), (-0.271318061756761, -0.144523522401655)), exp(t))
>>
>> ts = numpy.linspace(0, tmax, 100)
>>
>> sympy.lambdify(t, invL(G.subs(values)), ['numpy', 'sympy'])(ts).n()
>>
>>
>> fails with "ValueError: sequence too large; must be smaller than 32"
>> Any advice on getting either getting the closed forms or just finding a
>> version which can be evaluated cleanly?
>
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