#178 derivatives of acsc, ...

closed
nobody
Lisp Core (471)
5
2006-07-01
2002-11-07
No

Maxima's formulae for the derivatives of acsc, asec,
acsch,
and asech are incorrect in the left half plane. To
illustrate, we should have asin(1/x) - acsc(x) = 0
for all x # 0; however,

(C2) ratsimp(diff(asin(1/x) - acsc(x),x));
(D2) -SQRT(x^2-1)*(ABS(x)-x)/(x^4-x^2)

This only vanishes for x > 0. I've attached
a diff file for comm.lisp that fixes these
problems. And I attached an rtest file
that tests the derivatives of the inverse
trig functions.

Barton

Discussion

  • Barton Willis

    Barton Willis - 2002-11-07

    diff file for comm.lisp

     
  • Robert Dodier

    Robert Dodier - 2006-07-01

    Logged In: YES
    user_id=501686

    Problem shown here is OK now (5.9.3cvs):

    ratsimp(diff(asin(1/x) - acsc(x),x)); => 0

    Patch was applied to src/comm.lisp and committed as r1.12.

    Test cases found their way into the cvs as
    tests/rtest_diff_invtrig.mac and 5.9.3cvs passes all tests.

    Closing this report as fixed.

     
  • Robert Dodier

    Robert Dodier - 2006-07-01
    • status: open --> closed
    • labels: --> Lisp Core
     

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