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Floor function

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  • Joshua Zucker
    I m running 3.2d8 on my mac, and loving it of course. I will be going to OS X soon so I d love to see that version... Anyway, right now my issue is that I m
    Message 1 of 6 , Oct 25, 2001
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      I'm running 3.2d8 on my mac, and loving it of course.

      I will be going to OS X soon so I'd love to see that version...

      Anyway, right now my issue is that I'm trying to do some tricky
      arithmetic with floor functions. It graphs things like x - floor(x)
      beautifully, except for drawing in the vertical lines where a human
      would draw open or closed circles, but that's OK.

      It has HUGE problems with things like floor(x-floor(x)) when x is
      near an integer ... it can't tell whether the answer is 1 or -1, so it
      graphs funny vertical lines.

      This really makes it hard to tell whether my function is doing
      what I want it to do, because those points are exactly the ones
      I'm interested in.

      I can see why it would have trouble there (a tiny change in one of
      the two x's in my function could easily cause the function to flip
      from 1 to 0 to -1) ... is there any chance this behavior will improve
      in later versions, or is this just part of the way the graphing
      engine deals with things?

      Thanks,
      --Joshua Zucker
    • Ron Avitzur
      ... Hi Josh, This artifact is due to a bug/design-flaw in the underlying interval arithmetic which does not handle discontinuous functions well. GrafEq from
      Message 2 of 6 , Oct 25, 2001
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        At 4:40 PM +0000 10/25/01, Joshua Zucker wrote:
        >Anyway, right now my issue is that I'm trying to do some tricky
        >arithmetic with floor functions. It graphs things like x - floor(x)
        >beautifully, except for drawing in the vertical lines where a human
        >would draw open or closed circles, but that's OK.
        >
        >It has HUGE problems with things like floor(x-floor(x)) when x is
        >near an integer ... it can't tell whether the answer is 1 or -1, so it
        >graphs funny vertical lines.
        >
        >This really makes it hard to tell whether my function is doing
        >what I want it to do, because those points are exactly the ones
        >I'm interested in.

        Hi Josh,

        This artifact is due to a bug/design-flaw in the underlying interval
        arithmetic which does not handle discontinuous functions well.

        GrafEq from www.peda.com does a much better job drawing functions like this.

        In Graphing Calculator, you can switch an equation to "simple plotting" mode
        which does not use the interval arithmetic and will just compute the
        value at each point and connect the dots. This should handle these cases
        better. (However, cases where the function varies rapidly such as sin(e^x)
        will break down.)

        To switch mode, select the equation you want to affect, then:

        Command-option-s (simple plotting)
        Command-option-b (the version 3 default mode using interval arithmetic)
        Command-option-h (the version 1 Honest Plotting mode using interval
        arithmetic)

        >I can see why it would have trouble there (a tiny change in one of
        >the two x's in my function could easily cause the function to flip
        >from 1 to 0 to -1) ... is there any chance this behavior will improve
        >in later versions, or is this just part of the way the graphing
        >engine deals with things?

        I'll put this on the list of problems to be addressed in a future release.

        Best regards,

        Ron
      • ted spencer
        From the nimble fingers of Ron Avitzur (avitzur@veriomail.com) (25/10/2001 12:59 PM) came... ... How s that again? In 3.0, the above don t seem to have any
        Message 3 of 6 , Oct 26, 2001
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          From the nimble fingers of Ron Avitzur (avitzur@...) (25/10/2001
          12:59 PM) came...

          > To switch mode, select the equation you want to affect, then:
          >
          > Command-option-s (simple plotting)
          > Command-option-b (the version 3 default mode using interval arithmetic)
          > Command-option-h (the version 1 Honest Plotting mode using interval
          > arithmetic)

          How's that again? In 3.0, the above don't seem to have any effect.

          I've dragged through the whole equation so it's highlighted, and then
          administered the "puppyfoot"-option-(s,b,h). The effect was underwhelming!?
          --
          Ted Spencer; ted@...
          --
          Nature, you see, is very difficult to rehearse, and nature has
          a bad trick of missing its cues.
          (Robertson Davies)
        • Ron Avitzur
          ... Try the equation y = sin(e^x) In either Version 3, or Version 1 Honest mode, the area on the right will appear solid for x 6 where the function varies
          Message 4 of 6 , Oct 26, 2001
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            >From the nimble fingers of Ron Avitzur (avitzur@...) (25/10/2001
            >12:59 PM) came...
            >
            >> To switch mode, select the equation you want to affect, then:
            >>
            >> Command-option-s (simple plotting)
            >> Command-option-b (the version 3 default mode using interval arithmetic)
            >> Command-option-h (the version 1 Honest Plotting mode using interval
            >> arithmetic)
            >
            >How's that again? In 3.0, the above don't seem to have any effect.

            Try the equation

            y = sin(e^x)

            In either Version 3, or Version 1 Honest mode, the area on the right
            will appear solid for x > 6 where the function varies faster than the
            pixels. In simplie-plotting mode, you will see a noisy aliasing
            artifact.

            Try also
            y = sin(x) / x
            which looks the same in simple & version 3 mode, but fails in a
            difficult-to-explain way in the version-1 honest-plotting mode.

            (These hidden keys may not work on non-U.S. keyboards and some
            3rd party extensions may intercept these keys.)

            Best regards,

            Ron
          • George & Mary Dorner
            Ron: I think that the review I wrote for the American Assn. of Two Year Colleges Journal will appear this month. I also wrote a book review and I _know_ that
            Message 5 of 6 , Oct 26, 2001
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              Ron:

              I think that the review I wrote for the American Assn. of Two Year Colleges Journal will appear this month. I also wrote a book review and I _know_ that at least one of the two reviews will appear.

              I ordered a copy, I think of 3.0 but maybe 2.0, and one of NuCalc for my college math department. It turns out that we received approval to purchase more copies last year, but things got fouled up by our IT department, not an isolated instance. When I purchased them, I turned them over to IT, since they are supposed to install everything on college computers. Now, because they swapped my computer for a new one, Graphing Calculator doesn't work on my machine. NuCalc works on a fairly slow Toshiba laptop and doesn't do the software justice. Our chairman would like a live demo for the department so we can justify the purchase of multiple copies.

              I would like to put the demo on a Mac laptop at school so the demo could be done without moving my machine (the licensed, not working one) or cramming all into my office.

              Whatever you can do to help out here will certainly be repaid in order(s). I will finesse the loading on the Mac(s) (IT doesn't pay much attention to them. They have their hands full with the NT network which they are sorely understaffed for.) If the license of GC is only for 2.0, I will upgrade it myself to avoid IT involvement.  (Burn this message.)

              If we buy NuCalc 2.0, what is the upgrade policy when 3.0 comes out?

              All correspondence about this should be to gdorner@.... Our chair is dmagno@..., Dom Magno. The Mac guru and future contact for this in our department is skoswatt@..., Dr. Sunil Koswatta. You may see us all at www.harpercollege.com/mathdept  Dom and I are retiring this year. I hope I can get our computer facilities up to speed before I go and Graphing Calculator and NuCalc are currently part of that plan. We also have Maple and Derive on our network.

              Thanks.

              geo dorner

              gdorner@...

              Ron Avitzur wrote:

              >From the nimble fingers of Ron Avitzur (avitzur@...) (25/10/2001
              >12:59 PM) came...
              >
              >> To switch mode, select the equation you want to affect, then:
              >>
              >> Command-option-s  (simple plotting)
              >> Command-option-b  (the version 3 default mode using interval arithmetic)
              >> Command-option-h  (the version 1 Honest Plotting mode using interval
              >> arithmetic)
              >
              >How's that again? In 3.0, the above don't seem to have any effect.

              Try the equation

                 y = sin(e^x)

              In either Version 3, or Version 1 Honest mode, the area on the right
              will appear solid for x > 6 where the function varies faster than the
              pixels. In simplie-plotting mode, you will see a noisy aliasing
              artifact.

              Try also
                y = sin(x) / x
              which looks the same in simple & version 3 mode, but fails in a
              difficult-to-explain way in the version-1 honest-plotting mode.

              (These hidden keys may not work on non-U.S. keyboards and some
              3rd party extensions may intercept these keys.)

              Best regards,

              Ron


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            • Simon Hayman
              ... They work on Australian keyboards
              Message 6 of 6 , Oct 28, 2001
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                >>From the nimble fingers of Ron Avitzur (avitzur@...) (25/10/2001
                >>12:59 PM) came...
                >>
                >>> To switch mode, select the equation you want to affect, then:
                >>>
                >>> Command-option-s (simple plotting)
                >>> Command-option-b (the version 3 default mode using interval arithmetic)
                >>> Command-option-h (the version 1 Honest Plotting mode using interval
                >>> arithmetic)
                >>

                >
                >(These hidden keys may not work on non-U.S. keyboards and some
                >3rd party extensions may intercept these keys.)
                >
                They work on Australian keyboards
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