Oh ... I was aware that the cookies may persist after simply leaving the page.

But it is the first forum for me, where one explicitely says "logout" with no effect. Perhaps a genious feature of the board software, Drupal.

I noticed it accidental, since usually for security reason after a 'login site' I always close my browser to clear everything.

Well, I search to find something. Easily. And not to find what to do if it does
not work easily. Especially if I am a newbe. Or about to buy Maple. Or not.

Such search functionality has the feeling of a last century - if I need to do
something 'advanced' to find 2 simple words ...

Also - for example - sorted by date, ignoring crazy orders :-)

Re *.wm: they are slow, and difficult to modify. They suffer from the UI (say
the annoying multiplication sign or blanks). And concurent versions need about
2 minutes to start at my PC. They are not what I want to work with.

@Markiyan Hirnyk 

You are welcome. As I said the documentation is poor:

I never heared the notion of dimension of an ideal in Algebra, they mean the
dimension of Ring modulo Ideal. And even providing indeterminates does not make
clear which polynomial algebra is meant - I am never sure, which is the ring
of coefficients for that: in the help they talk about Rationals and beyond.

But also about finite fields. However then they can only work over the integers.

"The HilbertDimension command computes the Hilbert dimension of an ideal" makes
not much sense: one should provide the algebra in an explicit way. It should say
"the Krull dimension of algebra/ideal, computed via Hilbert's dimension", so users
have a chance to look up literature or Wikipedia. And it should provide some
warnings: interpretation as solutions of equations usually only makes sense, if
done over a 'good' fields - and even then there may be components with smaller
dimensions (I guess that 'primary composition' can give them).

Or for short: an ideal lives in a ring, one should be able and forced to provide it
instead of guessing what may be meant.

@Markiyan Hirnyk 

You are welcome. As I said the documentation is poor:

I never heared the notion of dimension of an ideal in Algebra, they mean the
dimension of Ring modulo Ideal. And even providing indeterminates does not make
clear which polynomial algebra is meant - I am never sure, which is the ring
of coefficients for that: in the help they talk about Rationals and beyond.

But also about finite fields. However then they can only work over the integers.

"The HilbertDimension command computes the Hilbert dimension of an ideal" makes
not much sense: one should provide the algebra in an explicit way. It should say
"the Krull dimension of algebra/ideal, computed via Hilbert's dimension", so users
have a chance to look up literature or Wikipedia. And it should provide some
warnings: interpretation as solutions of equations usually only makes sense, if
done over a 'good' fields - and even then there may be components with smaller
dimensions (I guess that 'primary composition' can give them).

Or for short: an ideal lives in a ring, one should be able and forced to provide it
instead of guessing what may be meant.

@Markiyan Hirnyk 

HilbertDimension(theIdeal, 
  {C, V, alpha, beta, a[0], a[1], a[2], a[3], a[4]} ); # my notations

Then it works, returning (Hilbert-) Dimension = 4.
Which fits with those 5 equations in the solution,
they are the codimension.

PS: I do not like the documentation for that package

@Markiyan Hirnyk 

HilbertDimension(theIdeal, 
  {C, V, alpha, beta, a[0], a[1], a[2], a[3], a[4]} ); # my notations

Then it works, returning (Hilbert-) Dimension = 4.
Which fits with those 5 equations in the solution,
they are the codimension.

PS: I do not like the documentation for that package

It says, that the solutions (of those 16 equations) define a (4-dimensional) variety
which is actually given by those 5 equations in the space of the 9 parameters.

PS: I would avoid using 'gamma' (which is Euler's constant in Maple) and also would
avoid using a variable and indexing it in the same context. So I used a[0] etc and
delta instead of gamma.

It says, that the solutions (of those 16 equations) define a (4-dimensional) variety
which is actually given by those 5 equations in the space of the 9 parameters.

PS: I would avoid using 'gamma' (which is Euler's constant in Maple) and also would
avoid using a variable and indexing it in the same context. So I used a[0] etc and
delta instead of gamma.

I do not understand your explanation: what is a critical point of an intersection?

Anyway:

Ok, then m_i, s_i are real numbers and s_i are positive, I guess.

I used the expressions only (not the equations) and only considered numerators,
naming them gx,gy, and checked like the following
 
  normal(-fx): gx,Bx:= numer(%), denom(%): '-fx=gx/Bx'; is(%);

Now that only seemed to be more easy to solve, I stopped Maple after some time.


Doing it by hand I *would* isolate squares on one side (always starting with
pairs sqrt(...)*sqrt(...)) and square that, thus the very square vanishes, but
degree now is increases and the expressions become quite long.

I can imagine, that Maple does such or similar and the expressions become too
long or the degrees are too high to reply by a formal solution.

Even if there would be one it may so lengthy that it might be not useful for
applications.

Thus I have given up.

I do not understand your explanation: what is a critical point of an intersection?

Anyway:

Ok, then m_i, s_i are real numbers and s_i are positive, I guess.

I used the expressions only (not the equations) and only considered numerators,
naming them gx,gy, and checked like the following
 
  normal(-fx): gx,Bx:= numer(%), denom(%): '-fx=gx/Bx'; is(%);

Now that only seemed to be more easy to solve, I stopped Maple after some time.


Doing it by hand I *would* isolate squares on one side (always starting with
pairs sqrt(...)*sqrt(...)) and square that, thus the very square vanishes, but
degree now is increases and the expressions become quite long.

I can imagine, that Maple does such or similar and the expressions become too
long or the degrees are too high to reply by a formal solution.

Even if there would be one it may so lengthy that it might be not useful for
applications.

Thus I have given up.

Ok. But what is the background, the geometric reason?

It is a kind of (x,y) relating distance to 2 points in a 3-dim space and some shift. Or so. Not sure for the s1, s2,s3.

Note: without that you can not expect a 'reasonable' answer. Even for a linear problem it may be complicated. Why it should exist and be unique beyond it?

Ok. But what is the background, the geometric reason?

It is a kind of (x,y) relating distance to 2 points in a 3-dim space and some shift. Or so. Not sure for the s1, s2,s3.

Note: without that you can not expect a 'reasonable' answer. Even for a linear problem it may be complicated. Why it should exist and be unique beyond it?

indets({fx, fy}, symbol);

        {m1, m2, m3, s1, s2, s3, x, x1, x2, x3, y, y1, y2, y3}

PS: you need: s1,s2,s2 are not zero

PPS: what is the geometric reason for the question? It is one, no?

completesquare(fx,x): completesquare(%,y): simplify(%, size);
completesquare(fy,y): completesquare(%,x): simplify(%, size);

@Alejandro Jakubi 

I would appreciate such improvements.

While they still may be non-trivial, as they also have to check for
more than Zeros: for log or sqrt they will have to check for brunch
cuts as well (which is easy in the example knowing about No-Zeros
in  the interval)

@Alejandro Jakubi 

I would appreciate such improvements.

While they still may be non-trivial, as they also have to check for
more than Zeros: for log or sqrt they will have to check for brunch
cuts as well (which is easy in the example knowing about No-Zeros
in  the interval)