integrals involving floor(x)

[nob...@nowhere.invalid]

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.

[nob...@nowhere.invalid]

"clicl...@freenet.de" schrieb:

Oops, the second integral should have been:

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

Martin.

[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.

Albert

[Peter Luschny]

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.

[nob...@nowhere.invalid]

Peter Luschny schrieb:

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-...@googlegroups.com/msg105858.html>

[Peter Luschny]

> > > 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."

[Jean-Michel Collard]

Dear Albert and all,

In fact I did that Albert; even more than your 20 years ago and I am not a masochist :)
I began using Maple at the beginning of the '90 (Maple V.2) and Mathematica in 1990
(release 1.1.a).
And I still use them.
I am not a CS guy/geek at all , I am a retired mathematician and I do enjoy playing
with that 2 softwares.
Moreover the "Personal/Home" editions are pretty cheap.
Kind regards to all,
JMC (Jean-Michel)
PS: Don't take care of the so-called email you see regarding me, this is a fake.