Re: [Maxima-discuss] [Maxima-commits] [git] Maxima CAS branch, master, updated. branch-5_36-base-102-g2b1366c

[Raymond T. <toy...@gm...>]

>>>>> "Kris" == Kris Katterjohn <kat...@gm...> writes:

    Kris> [moved to maxima-discuss from the old maxima list]
    Kris> On 05/18/2015 01:16 AM, Raymond Toy wrote:
    >>
    >>
    >> On Sat, May 16, 2015 at 9:10 PM, Kris Katterjohn
    >> <kj...@us... <mailto:kj...@us...>> wrote:
    >>
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    >> commit 2b1366c1ffb07f117f3a4256aff2efe718141122 Author: Kris
    >> Katterjohn <kat...@gm... <mailto:kat...@gm...>>
    >> Date: Sat May 16 22:53:02 2015 -0500
    >>
    >> Fix issues with gamma_incomplete's GRAD and psi's INTEGRAL
    >> properties
    >>
    >> Part of the GRAD property for gamma_incomplete and the INTEGRAL
    >> property for psi are implemented with Lisp lambda expressions.
    >> The parameters in the lambda lists should have been used to
    >> construct the return values, but this was not done correctly
    >> (symbols matching the parameters' names were used in quoted
    >> lists instead of using the parameters' values).
    >>
    >> The parameter names in the lambda lists match the dummy
    >> variable names in the CARs of the GRAD and INTEGRAL properties,
    >> so the intended functionality still happened to work.  If the
    >> dummy variables were consistently renamed then this would cease
    >> to work.
    >>
    >>
    >> ​Is there a test case for this?  I think that would be a useful
    >> addition.
    >>

    Kris> I think that maybe I wasn't explicit enough in describing my
    Kris> use of the phrase "dummy variables" in the commit message,
    Kris> so I'll give a more in-depth description here (so hopefully
    Kris> the commit message will make more sense).  I'm assuming that
    Kris> this caused confusion.

    Kris> The dummy variables I mentioned in the commit message are
    Kris> not the "dummy variables" we use in calling diff, integrate,
    Kris> etc.  So prior to this commit using different variable names
    Kris> would work as expected:


    Kris> (%i1) assume(a>0, b>0)$

    Kris> (%i2) diff(gamma_incomplete(a,z), a); (%o2)
    Kris> (-(gamma(a)-gamma_incomplete(a,z))*log(z))
    Kris>  +gamma(a)^2*hypergeometric_regularized([a,a],[a+1,a+1],-z)*z^a
    Kris>  +(psi[0])(a)*gamma(a)

    Kris> (%i3) diff(gamma_incomplete(b,x), b); (%o3)
    Kris> (-(gamma(b)-gamma_incomplete(b,x))*log(x))
    Kris>  +gamma(b)^2*hypergeometric_regularized([b,b],[b+1,b+1],-x)*x^b
    Kris>  +(psi[0])(b)*gamma(b)

    Kris> In this example, the dummy variables I mentioned are the
    Kris> ones stored in the symbol plist for gamma_incomplete:

    Kris> (%i1) :lisp (get '%gamma_incomplete 'grad) ((A Z)
    Kris>  #<Anonymous Function #x300001F1B84F>
    Kris>  ((MTIMES) -1 ((MEXPT) $%E ((MTIMES) -1 Z)) ((MEXPT) Z
    Kris>  ((MPLUS) -1 A))))

    Kris> (%i1) diff(gamma_incomplete(f,s),s); (%o1) -s^(f-1)*%e^-s

    Kris> So these A and Z are the dummy variables (as seen being used
    Kris> in the expression for the derivative wrt the second
    Kris> argument).

    Kris> Consistently renaming the (visible) dummy variables from A,
    Kris> Z to Q, R still gives a working derivative wrt the second
    Kris> arg:

    Kris> (%i2) :lisp (get '%gamma_incomplete 'grad) ((Q R)
    Kris>  #<Anonymous Function #x30200077556F>
    Kris>  ((MTIMES) -1 ((MEXPT) $%E ((MTIMES) -1 R)) ((MEXPT) R
    Kris>  ((MPLUS) -1 Q))))

    Kris> (%i2) diff(gamma_incomplete(f,s),s); (%o2) -s^(f-1)*%e^-s

    Kris> However, prior to this commit, the derivative wrt the first
    Kris> arg would then give the wrong variables in the result (the
    Kris> bare Lisp symbols ?a and ?z instead of f and s):

    Kris> (%i3) lispdisp:true$ (%i4) assume(f>0)$

    Kris> (%i5) diff(gamma_incomplete(f,s),f); (%o5)
    Kris> (-gamma_incomplete_generalized(?a,0,?z)*log(?z))
    Kris>  +gamma(?a)^2*hypergeometric_regularized([?a,?a],[?a+1,?a+1],-?z)*?z^?a
    Kris>  +(psi[0])(?a)*gamma(?a)

    Kris> After this commit it works correctly.

    Kris> So the problem would occur only when changing the dummy
    Kris> variables in the plist (which should be a valid thing to do,
    Kris> since they're supposed to be dummy variables...).  It
    Kris> doesn't make sense to me for the lambda expression
    Kris> (anonymous function) to depend on its parameters and also
    Kris> the dummy variables in the plist if its parameters are all
    Kris> that it needs.

    Kris> So I'm not sure of a good test for this.  Or perhaps I
    Kris> misunderstood your suggestion?

Thanks for the clarification.  Isn't your example in %i5 a good test
case?  The original version would have ?a and ?z in the answer but
your fix would replace them with f and s appropriately.

--
Ray