Equation library - Hewlett Packard

This is a discussion on Equation library - Hewlett Packard ; The equation library included in the hp 50g is really useful and helpful. However, I'm encountering some problems with the equation concerning the "thin lenses" (or the one concerning "spherical reflecion", which is the same). When I solve the equation ...

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Thread: Equation library

  1. Equation library

    The equation library included in the hp 50g is really useful and
    helpful. However, I'm encountering some problems with the equation
    concerning the "thin lenses" (or the one concerning "spherical
    reflecion", which is the same). When I solve the equation using the
    numeric solver, and i choose negative values for some vars (for
    example, negative value of the focal length), the calculation results
    in two possible errors:
    1) a message is displayed, saying that no solution could be found;
    2) (more frequently) the solution is the biggest number the calculator
    can disaply (9.999e499).
    As the equation is not so difficult to solve, I wonder why the numeric
    solver doesn't manage to solve it.

    Giovanni


  2. Re: Equation library

    Because it was ported rather hastily ?

    You might want to consider the use of an alternative EQNLIB, some are
    available on hpcalc.org or give my TreeBrowser a try. A demo version
    (in English and German) is available on my website http://www.software49g.gmxhome.de.
    It is
    also possible to create your own libraries of equations with it
    easily.

    Greetings
    Andreas

    On 6 Apr., 21:29, "Giovanni" wrote:
    > The equation library included in the hp 50g is really useful and
    > helpful. However, I'm encountering some problems with the equation
    > concerning the "thin lenses" (or the one concerning "spherical
    > reflecion", which is the same). When I solve the equation using the
    > numeric solver, and i choose negative values for some vars (for
    > example, negative value of the focal length), the calculation results
    > in two possible errors:
    > 1) a message is displayed, saying that no solution could be found;
    > 2) (more frequently) the solution is the biggest number the calculator
    > can disaply (9.999e499).
    > As the equation is not so difficult to solve, I wonder why the numeric
    > solver doesn't manage to solve it.
    >
    > Giovanni




  3. Re: Equation library

    On Fri, 06 Apr 2007 14:29:26 -0500, Giovanni wrote:

    > The equation library included in the hp 50g is really useful and
    > helpful. However, I'm encountering some problems with the equation
    > concerning the "thin lenses" (or the one concerning "spherical
    > reflecion", which is the same). When I solve the equation using the
    > numeric solver, and i choose negative values for some vars (for
    > example, negative value of the focal length), the calculation results
    > in two possible errors:
    > 1) a message is displayed, saying that no solution could be found;
    > 2) (more frequently) the solution is the biggest number the calculator
    > can disaply (9.999e499).
    > As the equation is not so difficult to solve, I wonder why the numeric
    > solver doesn't manage to solve it.


    The *numeric* solver does not "solve" equations;
    it merely tries existing numeric guesses for the variable
    to be calculated, then heads in whatever direction
    seems to reduce the difference between the value of
    left and right sides of the equation.

    To obtain a useful answer therefore requires:

    o Existence of a solution.

    o Supplying feasible initial guess(es).

    Example: 'INV(X)=-1' STEQ 0 'X' STO 30 MENU

    If you try solving for X without supplying another guess,
    it will head toward +infinity and stop at 9.99999999999E499

    If you first store -5 into 'X' and try again,
    the solution X=-1 will promptly be found.

    Although this equation is rather trivial to solve
    *algebraically*, the *numeric* solver does not use algebra;
    it is therefore able to get numerical answers even for equations
    that are algebraically intractible, but there is a small price
    to pay for "blind searching" via only "closer" vs. "farther"
    as clues, which is that you have to put the target within reach
    to begin with, and start searching in the right general direction.

    [r->] [OFF]

  4. Re: Equation library

    On 6 Apr, 22:48, "John H Meyers" wrote:
    > On Fri, 06 Apr 2007 14:29:26 -0500, Giovanni wrote:
    > > The equation library included in the hp 50g is really useful and
    > > helpful. However, I'm encountering some problems with the equation
    > > concerning the "thin lenses" (or the one concerning "spherical
    > > reflecion", which is the same). When I solve the equation using the
    > > numeric solver, and i choose negative values for some vars (for
    > > example, negative value of the focal length), the calculation results
    > > in two possible errors:
    > > 1) a message is displayed, saying that no solution could be found;
    > > 2) (more frequently) the solution is the biggest number the calculator
    > > can disaply (9.999e499).
    > > As the equation is not so difficult to solve, I wonder why the numeric
    > > solver doesn't manage to solve it.

    >
    > The *numeric* solver does not "solve" equations;
    > it merely tries existing numeric guesses for the variable
    > to be calculated, then heads in whatever direction
    > seems to reduce the difference between the value of
    > left and right sides of the equation.
    >
    > To obtain a useful answer therefore requires:
    >
    > o Existence of a solution.
    >
    > o Supplying feasible initial guess(es).
    >
    > Example: 'INV(X)=-1' STEQ 0 'X' STO 30 MENU
    >
    > If you try solving for X without supplying another guess,
    > it will head toward +infinity and stop at 9.99999999999E499
    >
    > If you first store -5 into 'X' and try again,
    > the solution X=-1 will promptly be found.
    >
    > Although this equation is rather trivial to solve
    > *algebraically*, the *numeric* solver does not use algebra;
    > it is therefore able to get numerical answers even for equations
    > that are algebraically intractible, but there is a small price
    > to pay for "blind searching" via only "closer" vs. "farther"
    > as clues, which is that you have to put the target within reach
    > to begin with, and start searching in the right general direction.
    >
    > [r->] [OFF]


    So, the numeric solver is the same as the one which can be found on
    the HP 33s, I see...
    Thnak you so much for helping me!

    Giovanni


  5. Re: Equation library

    Giovanni wrote:
    > The equation library included in the hp 50g is really useful and
    > helpful. However, I'm encountering some problems with the equation
    > concerning the "thin lenses" (or the one concerning "spherical
    > reflecion", which is the same). When I solve the equation using the
    > numeric solver, and i choose negative values for some vars (for
    > example, negative value of the focal length), the calculation results
    > in two possible errors:
    > 1) a message is displayed, saying that no solution could be found;
    > 2) (more frequently) the solution is the biggest number the calculator
    > can disaply (9.999e499).
    > As the equation is not so difficult to solve, I wonder why the numeric
    > solver doesn't manage to solve it.


    Try starting the Equation Library while being in approximate mode, see
    how it goes.

    JY

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