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  • integrals involving floor(x)

    From nobody@nowhere.invalid@21:1/5 to All on Sun Jan 22 14:33:52 2023
    Maple and Sage (per GIAC, I assume) get certain integrals involving
    FLOOR(x) wrong, whereas Derive 6.10 does not:

    INT(FLOOR(x)^2, x) = - 2*FLOOR(x)^3/3 + (x - 1/2)*FLOOR(x)^2 +
    FLOOR(x)/6

    INT(2*FLOOR(x), x) = (2*x - 1)*FLOOR(x) - FLOOR(x)^2

    The integrands are from a complaint on sage-devel at Google Groups.

    Martin.

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  • From nobody@nowhere.invalid@21:1/5 to clicliclic@freenet.de on Sun Jan 22 18:03:55 2023
    "clicliclic@freenet.de" schrieb:

    Maple and Sage (per GIAC, I assume) get certain integrals involving
    FLOOR(x) wrong, whereas Derive 6.10 does not:

    INT(FLOOR(x)^2, x) = - 2*FLOOR(x)^3/3 + (x - 1/2)*FLOOR(x)^2 +
    FLOOR(x)/6

    INT(2*FLOOR(x), x) = (2*x - 1)*FLOOR(x) - FLOOR(x)^2

    The integrands are from a complaint on sage-devel at Google Groups.


    Oops, the second integral should have been:

    INT(2^FLOOR(x), x) = 2^FLOOR(x)*(x + 1) - 2^FLOOR(x)*FLOOR(x)

    Martin.

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  • From Albert Rich@21:1/5 to All on Sun Jan 22 19:28:46 2023
    Mathematica 13 returns Integrate[Floor[x], x] unevaluated, even when assuming x is real.

    Derive 6.10 is 20 years old and its mathematical engine was implemented by two people. Wonder how many people worked on Maple and Mathematica over the past 20 years.

    Albert

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  • From Peter Luschny@21:1/5 to All on Wed Apr 19 04:56:58 2023
    Albert Rich:

    Mathematica 13 returns Integrate[Floor[x], x] unevaluated, even when assuming x is real.

    Derive 6.10 is 20 years old and its mathematical engine was implemented by two people. Wonder how many people worked on Maple and Mathematica over the past 20 years.

    That may not have been meant as an explanation, but maybe it is the explanation.

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  • From nobody@nowhere.invalid@21:1/5 to Peter Luschny on Thu Apr 20 11:09:57 2023
    Peter Luschny schrieb:

    Albert Rich:

    Mathematica 13 returns Integrate[Floor[x], x] unevaluated, even
    when assuming x is real.

    Derive 6.10 is 20 years old and its mathematical engine was
    implemented by two people. Wonder how many people worked on Maple
    and Mathematica over the past 20 years.

    That may not have been meant as an explanation, but maybe it is the explanation.

    Your remark seems to require an explanation.

    Martin.

    PS: The integrals involving floor(x) were discussed on sage-devel at
    Google Groups, the initial post is archived under:

    <https://www.mail-archive.com/sage-devel@googlegroups.com/msg105858.html>

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  • From Peter Luschny@21:1/5 to All on Thu Apr 20 08:10:23 2023
    Derive 6.10 is 20 years old and its mathematical engine was
    implemented by two people. Wonder how many people worked on Maple
    and Mathematica over the past 20 years.

    That may not have been meant as an explanation, but maybe it is the explanation.

    Your remark seems to require an explanation.

    Well, if you insist. But I wanted to know if at least ChatGPT understands me.

    Here is its answer:

    "Generally speaking, as complexity increases, so does the potential
    for error rate. This is because complexity introduces more potential
    points of failure or sources of error.

    "In other words, the more complex a system, process, or task is,
    the more difficult it may be to manage, monitor, and control,
    and the greater the likelihood that mistakes will be made.

    "For example, if a software program has many lines of code,
    there are more opportunities for bugs or errors to be introduced.

    "Similarly, if a manufacturing process involves many different
    components or steps, there are more chances for something to
    go wrong. On the other hand, a simpler system or process may
    have fewer potential sources of error and may therefore be more reliable."

    As I am writing this I read the news: "Maiden flight of
    SpaceX's Starship rocket ends in explosion."

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