Is it for classical interface as well?

Well, I believe you are not interested in an answer, if you are too lazy to correct it and post your question in a complete and readable manner.

Well, I believe you are not interested in an answer, if you are too lazy to correct it and post your question in a complete and readable manner.

Though I like all the given answers I want to say, that 1) Maple does not prove that
limit(s) exists and 2) that Adri uses the standard reasoning *assuming* the existence,
the most easy way.

If you want a mathematical proof you may use Maple like Kitonum did (and trust Maple).

Due to your own reasoning (formalize using Maple instead of fix point) you only need 2)

Here is my suggestion, somewhat late ... 

Consider the LHS as expression of algebraic numbers (similar as Kitonum did) and use
the resolvent to find a polynomial, which has it as root by construction. 

View at it as a polynomial in a cubic X = x^3 now try to solve for roots symbollically.

Amazingly Maple translates that to a polynomial over the integers - it simplifies the
trigonometric expression that way.

For the new polynomial it is easy to recognize RHS as root. And that both polynomials
are equal after norming them is 'proved' by the command 'is'.


It would be very nice to have that power of Maple not only hidden in 'RootOf' and 'is'.

trig_alg_resultan.mws
trig_alg_resultan.pdf

PS: I do not know, how to post that as 'answer' without a new thread ...

Though it is true I am still puzzled how to set it up for the *LHS*
to get radicals, i.e. to understand your setting x= ..., y= ... etc.

Working with resultants I failed to pass from trigs to radicals :-(

PS: and the compact form of the *RHS*, of course. Any "recipes"?

The usual notions for a function F: X -> Y are X = domain (where a function starts),
Y = co-domain or destination (=where the function ends), F(X) = image (= elements y
in Y where there is x, such that y = f(x)). If the function is a morphism between
groups, then kernel = {x in X | F(x) = 0}.

Wikipedia or a mathematical dictionary may help you to find it in your language.


I think you mean Q = field of Rationals and the usual (free) polynomial algebras.
By map you mean a morphism - respecting the algebra structures - yes? 


There is no morphism f: Q[x,y] -> Q[r,s,u,v] such that all of r,s,u,v are images under
that map. Otherwise it would be surjective - which is not possible for various reasons

The most simple 'argumentation' is: then it would be generated by 2 elements, not 4
and the 'uniqueness of coefficients' would not be valid.

The usual notions for a function F: X -> Y are X = domain (where a function starts),
Y = co-domain or destination (=where the function ends), F(X) = image (= elements y
in Y where there is x, such that y = f(x)). If the function is a morphism between
groups, then kernel = {x in X | F(x) = 0}.

Wikipedia or a mathematical dictionary may help you to find it in your language.


I think you mean Q = field of Rationals and the usual (free) polynomial algebras.
By map you mean a morphism - respecting the algebra structures - yes? 


There is no morphism f: Q[x,y] -> Q[r,s,u,v] such that all of r,s,u,v are images under
that map. Otherwise it would be surjective - which is not possible for various reasons

The most simple 'argumentation' is: then it would be generated by 2 elements, not 4
and the 'uniqueness of coefficients' would not be valid.

I do not understand what you want to say, it is very cryptic.

May be the French Wikipedia helps to state the question.

Using Prebens's 'input' I get 24 equations and 32 unknowns

S.R=~T;
convert(%,set);
% union {eq1,eq2}; nops(%);
indets(%%);
nops(%);

The setting is: equations of degree 2, so some normal form for quadrics
comes to mind, but 8 more variables is quite much - have not cared for
symmetries. May be a task for Groebner package (=complex input) ?

Using Prebens's 'input' I get 24 equations and 32 unknowns

S.R=~T;
convert(%,set);
% union {eq1,eq2}; nops(%);
indets(%%);
nops(%);

The setting is: equations of degree 2, so some normal form for quadrics
comes to mind, but 8 more variables is quite much - have not cared for
symmetries. May be a task for Groebner package (=complex input) ?

I am only interested in the classical interface: Is it forclassic or standard interface ?

Even if it is encouraging for advertising: I do NOT send mail to some xxx without knowing for what ...

@Carl Love 

Solving by radicals if possible for higher orders ...

Not within Maple, but with GAP, http://www.gap-system.org/Packages/radiroot.html (I do not have it).
the German Diploma thesis is at http://www.icm.tu-bs.de/ag_algebra/software/distler/Diplom.pdf

For a short discussion one may look at the following links

http://math.stackexchange.com/questions/97587/solution-of-a-polynomial-of-degree-n-with-soluble-galois-group
http://mathoverflow.net/questions/22923/computing-the-galois-group-of-a-polynomial

And, yes, unfortunately not within Maple ...

May be it is better to use mathematical notation to state what you want to have

p : R -> S = R / I the residual map (i.e. ring modulo an ideal),

Now A an ideal in R, then the image is (A+I) / I

Is that what you want?

Though I do not know, how Maple handles residual rings ...

@Kitonum

Yes, may be I just hate those questions considering them ...  (no, I do no want to say that). The polynomial solution always produces that. I wonder whether the original questioneer can specify what s/he wants beyond. It is not 'interpolation', it is a lame question.

Ok, I hate that ...