The question, as it formulated in the subject, was why 2 equal inputs, one in a fraction form, and another one - in a decimal (float) form, produce 2 different answers. There is no such a problem with 1/3, because it doesn't have a finite decimal representation equal to it, in which case getting different answers is not surprising - different inputs produce different outputs.

Increasing digits over the hardware limit is not for achieving a better precision - it is for disabling of the usage of hardware floats. The default setting of UseHardwareFloats is deduced which means using them if the Digits setting is less than 16, and not using them otherwise.

Advising not using RREF in this situation is certainly correct - not using RREF won't produce different answers for equal inputs in this example. That may be a good template for other answers in similar situations. Even better one would be not to use Maple if you get something wrong - not using it won't produce an error.

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Alec Mihailovs
Maplesoft Member

Why was the blue color chosen? Traditionally, the Maple's color was red.

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Alec Mihailovs
Maplesoft Member

What is the purpose of the limits?

Maple immediately calculates both

tan(x+Pi/2);

and

simplify(tan(x)*tan(x+Pi/2));

A simple way to show that the product of slopes of 2 perpendicular lines is -1, is noticing that the slope of a line parallel to the vector <a, b> is b/a, and the vector <-b, a> is perpendicular to <a, b>,

<a | b>.<-b, a>;

so the product of the slopes of perpendicular lines parallel to these vectors is

b/a * a/(-b);

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Alec Mihailovs
Maplesoft Member

Is it possible using one handle to vote up for the posts created by the same user with another handle?

I didn't realize that using several different handles by the same user is allowed on this site. What is the purpose of that?

I understand that anonimity (i.e. not using your own name) may be convenient for some purposes, but wouldn't one handle be enough for that?

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Alec Mihailovs
Maplesoft Member

While we could adjust to new posting habits since now on, but many valuable old discussions, not adjusted to that, might be hard to read. Perhaps, it would be possible to provide access to the site in its old format from a slightly different URL - something like old.mapleprimes.com?

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Alec Mihailovs
Maplesoft Member

Well, what I wrote, was mostly a kind of a joke.

That would work, certainly, but for compatibility reasons, I would, probably, stick with what you had originally in your procedures. 

It may seem like a kind of an overhead to retype the same global variables again and again, but in a big scheme of things, with maintainability and reusability in mind, that may be be the right thing to go with.

Alec

Well, what I wrote, was mostly a kind of a joke.

That would work, certainly, but for compatibility reasons, I would, probably, stick with what you had originally in your procedures. 

It may seem like a kind of an overhead to retype the same global variables again and again, but in a big scheme of things, with maintainability and reusability in mind, that may be be the right thing to go with.

Alec

Sorry - I was just being quite busy playing at 16 (poker) tables - it wasn't easy to post even a 3-letter post in the middle of that - the problem is that when a table gets active, the focus is switching to it - so when I start typing a word here, the first letter of it gets to the first table, the second letter gets to the second table etc.:)

Alec

Sorry - I was just being quite busy playing at 16 (poker) tables - it wasn't easy to post even a 3-letter post in the middle of that - the problem is that when a table gets active, the focus is switching to it - so when I start typing a word here, the first letter of it gets to the first table, the second letter gets to the second table etc.:)

Alec

Thanks again!

Alec

Mediocrity knows nothing higher than itself, but talent instantly recognizes genius. - Arthur Conan Doyle

As being an acknowledged true genius, I am starting to give just general directions since now on.

Alec

As being an acknowledged true genius, I am starting to give just general directions since now on.

Alec

Yes, I just looked there and would like to change it to

mysort:=l->[{map(x->[evalhf(-x),x],l)[]}[]][..,2]:

That saves some time.

I think I posted a similar thing earlier, just with sort instead of using sets, which in this situation would look as

mysort:=l->sort(map(x->[evalhf(-x),x],l))[..,2]:

Alec

Yes, I just looked there and would like to change it to

mysort:=l->[{map(x->[evalhf(-x),x],l)[]}[]][..,2]:

That saves some time.

I think I posted a similar thing earlier, just with sort instead of using sets, which in this situation would look as

mysort:=l->sort(map(x->[evalhf(-x),x],l))[..,2]:

Alec

That certainly looks nice. Also, 1/~S[1..3] is about ten times faster than Vector...,

time(seq(1/~S[1..3],i=1..100000));

                                0.405

time(seq(Vector(3,i->evalhf(1/S[i])),i=1..100000));

                                5.569

Alec