Maple bugs: maximize -> tan(z)^2
Vladimir Bondarenko
Let us quote Maplesoft's ambitions,
Maplesoft> Maplesoft is a world leader in mathematical and analytical
Maplesoft> software.
C. James Cooper P.Eng., President and C.E.O., Maplesoft
JC> Having earned the reputation as developers of the best general
JC> platform for math computing, we will be working hard to deliver
JC> additional components that will make it easier for anyone to
JC> access the full potential of our products - whether you are a
JC> teacher, a student, a researcher or an engineer in industry.
1 fact of about 10,000 we cataloguized up to now at Cyber Tester:
At least since 1994, none of Maple versions can drive the following
simple nail home.
maximize(tan(z)^2, z= 0..Pi/2);
--------------------Maple 9.5.1------------------------------------
Error, (in maximize) cannot minimize over a complex valued function
--------------------Maple 9.5--------------------------------------
Error, (in maximize) cannot minimize over a complex valued function
--------------------Maple 9----------------------------------------
Error, (in maximize) complex argument to max/min
--------------------Maple 8----------------------------------------
Error, (in maximize) complex argument to max/min
--------------------Maple 7----------------------------------------
Error, (in maximize) complex argument to max/min
--------------------Maple 6----------------------------------------
Error, (in maximize) complex argument to max/min
--------------------Maple V Rel 5----------------------------------
Error, (in maximize) minimize expects its 3rd argument, ranges, to
be of type {identical(infinite), {numeric, identical(-infinity)} ..
{numeric, identical(infinity)}, set(name = {numeric, identical(
-infinity)} .. {numeric, identical(infinity)})}, but received {z =
0 .. 1/2*Pi}
--------------------Maple V Rel 4----------------------------------
Error, (in maximize) minimize expects its 3rd argument, ranges, to
be of type {identical(infinite), {numeric, identical(-infinity)} ..
{numeric, identical(infinity)}, set(name = {numeric, identical(
-infinity)} .. {numeric, identical(infinity)})}, but received {z =
0 .. 1/2*Pi}
--------------------Maple V Rel 3----------------------------------
Error, (in maximize) minimize expects its 3rd argument, ranges, to
be of type {identical(infinite), {numeric, identical(-infinity)} ..
{numeric, identical(infinity)}, set(name = {numeric, identical(
-infinity)} .. {numeric, identical(infinity)})}, but received {z =
0 .. 1/2*Pi}
-------------------------------------------------------------------
For Maple V Release 5 and the earlier versions, use the syntax
maximize(tan(z)^2, z, {z= 0..Pi/2});
Compare with Mathematica:
In[1] := $Version
Out[1] = 5.1 for Microsoft Windows (October 25, 2004)
In[2] := Maximize[Tan[z]^2, 0 <= z <= Pi/2, z]
Out[2] = {Infinity, {z -> Pi/2}}
Best wishes,
Vladimir Bondarenko
http://www.cybertester.com/
http://maple.bug-list.org/
http://www.CAS-testing.org/
harald...@c2i.net
"At least since 1994, none of Maple versions can drive the following
simple nail home."
Here is the result from
Maple 9.5 Classic:
>with(Optimization):>Maximize(tan(z)^2, z= 0..Pi/2);
29
[0.820314804798495427 10 , [z = 1.57079632679490012]]
harald...@c2i.net
"At least since 1994, none of Maple versions can drive the following
simple nail home."
Here is the result from
Maple 9.5 Classic:
>with(Optimization):>Maximize(tan(z)^2, z= 0..Pi/2);
29
[0.820314804798495427 10 , [z = 1.57079632679490012]]
Harald Pleym
www.hpleym.no
Vladimir Bondarenko
Why millions persons use computer algebra systems?
Well, there are many reasons for it, but most probably it's because,
in contrast to piles of numbers showering from THOUSANDS amateurish
and professional numerical packages, a computer algebra system can
supply you with the highest math aesthetics, one of the biggest math
diamonds, with a - be in awful fear, the numerical folks! - with Her
Majesty FORMULA, all hues of the rainbow over Her.
Not with a rank-and-file private, a pack of digits.
Thus, my message is about the full palsy in the symbolic mode with
maximize. Numeric calculation is trivial here, and it is at the case
neither here not there.
Let us imagine such a comparison.
You go to a shop (Maplesoft), and you see at the showcase a yummy
almond cake with custard and dusted with caster sugar, the cat's
whiskers (Maple, Help, ?maximize).
Then you enter the shop and ask the salesgirl the blonde job about
selling you this dainty bit, this very moment!
She agrees, and you hand her money (- Gotcha! - she adds beneath her
breath), and get the money payment receipt, and a nice colorful
parcel. Life *is* good! Purr-purr-purr...
Broiling with impatience, you order a cup of tea on the spot, and
are going to relish this wonder of higher cooking!!
You tear up the shrink-wrapper, and... and see... large dented pieces
of lump sugar fit to hammer nails in absence of a hammer??!!
Strike me dead! - give you a cry - this is a piece of bamboozle! Where
on earth my pet yummy almond little cake with custard and dusted with
caster sugar?!
However, the belle gives you a chirp, Oh no, this sweet stuff at our
showcase is just a DEMO, this is why we put it into the showcase
(Maple Help, ?maximize). Actually, it does not work. What we can offer
you is the pack of lump sugar you already got.
- Okay, - say you hastily, - I want the refund.
Now the salesgirl sneers disdainfully.
Go to junior school, - she says between her teeth, - and learn the
ABC. Then, read our license agreement, carefully.
THERE IS NO REFUND. WE ARE NOT LIABLE FOR ANYTHING.
Take a load of this at last:
Maplesoft's guys are real programers.
1. Real programmers don't write specs.
2. Real programmers don't read manuals.
3. Reliance on a reference is a hallmark of the novice and the coward.
4. Users should be grateful for whatever they get.
5. They are lucky to get any program at all.
Thanks for the purchase, don't let me keep you!
---------------------------------------------------------------------
He that hath ears to hear, let him hear.
Best wishes,
Vladimir Bondarenko
P.S.
You ARE clever. You can beat this girl's trade show,
but this is another story to be told later.
Fred
>
> a computer algebra system can
> supply you with the highest math aesthetics, one of the biggest math
> diamonds, with a - be in awful fear, the numerical folks! - with Her
> Majesty FORMULA, all hues of the rainbow over Her.
>
Some say that a picture is worth a thousand words, we say
that a formula is worth a thousand numbers :)
Vladimir Bondarenko
When you have a table of numbers, you know the value of the
function in a finite set of points.
In contrast, when you have an analytic expression, you know
the value of the function in continuum of points (that is so
to say you have infinitely much more info than if you would
know the value of the function in all integer points). Thus
we can say that a formula is worth a continuum of numbers :)