Though DirectSearch is very good you may wish to reduce such equations by exp(x) = X etc and search on X = 0 .. infinity.

Also be aware that numerical solvers may fail to find all solutions (even if the set are isolated points, though DirectSearch can do a lot)

I do not have the need for Email with Maple, but for me that recipe would be too technical. And too special.

Usually I have my credentials for my account in a different form and want to feed that. May be Samir Khan can suggest a version which does not assume a certain provider. That, of course, may depend on settings a provider may accept. This is part of a task which a Mail Client usually does.

Personally I never would sign up a provider for that use.

In his post http://www.mapleprimes.com/posts/201720-Sending-Emails-From-The-Maple-Command-Line he also refers to setting up an SMTP server (fine, but sigh ...)

At least in Math I am used to consider 2*x etc as monomial (for example https://www.encyclopediaofmath.org/index.php/Monomial), so the elements of the underlying ring are monomials of degree 0.

No idea why Maple seems to treat it different in that package, in the Help they write Warning: the notions of monomials and terms were interchanged; see Groebner[terminology] for details

Edited: I think that notion makes sense to have an algebra structure on the polynomial ring (usual "canonical ordering" [hm ... depends on ordering of variables ?], considered as module over the ring of coefficients). But I do not have some systematic treatment like Bourbaki at hand. I am not enough familiar with Groebner stuff to understand the situation there.

Hm ... you may wish to reduce your avatar from 7 MB to a reasonable size

Hmpf ... pi should be Pi in s.

And f misses a multiplication,
f:= h*(z1+3*z2)/z2-(z1+2*r) * (2*r)*(z1+3*z2)+2*z2;
#.........................  ^

Perhaps you want to scale, subs(c = x/10^13, c1 = x1/10^13, %);

And the relation defines a (rational) curve. You can try implicitplot,
but will have to work, cf Markiyan's remark

Be aware that you also differentiate the 'abs' function - not a good idea.

@asa12 

I do not want to insult you in any way - but my impression is: you are trying to learn Math by stumbling from topic to topic and ask how to feed Maple. That probably makes not much sense and will give you nothing. As others already have said: post your questions with care and as clear as possible (and in some cases: use your Mother's language if English is to difficult for you). And provide references.

But be aware: this forum is not to educate in Math.

Anyway:

'syz' indicates you want to learn about https://en.wikipedia.org/wiki/Syzygy_%28mathematics%29, or more generally https://en.wikipedia.org/wiki/Hilbert's_syzygy_theorem (so your former (?) question may be not about composition of polynomials, but about linear algebra over polynomial rings, describing relations / generators for ideals or varieties).

You mention 'SGA': these are several volumes (Seminaire Grothendieck), you only may have a chance to understand parts with a good teacher and a very sound education in Algebra and Geometry

That's all I have to say. Good luck.

Thx. This remembers me of "old" discussions in the newsnet group what a 'measure' should be used and price (in time) should be payed.

Though in your case the answer is clear ... sometimes I wish to have a FullSimplify and just wait some seconds (and even to have a list of answers

Example (u-1)*(u+1) = u^2 - 1: it is 3 operations on the LHS and 2 on the RHS. But having roots in mind then LHS is more simple. So what ...

@tomleslie Thx for making it clear. I convert my "answer" to a "comment"

I do not use Excel+Maple, but always install Maple in directories with names having no special characters like blanks or bracket etc. And I vaguely remember situations where MS was not able to find stuff in directories with special characters. Also I am sure about situations where Java versions / installations had difficulties with such namings in commercial systems

You may wish to append your worksheet, else it is difficult to guess the reason (and you can start your worksheet with the command "restart; interface(version);" )

If you *type in* the commands then you see what you have done, whether it is what you want to command and to correct it in case. 

This is odd (and just checked in Maple 18) ... it does not know the limit, but inserting the value gives it?

FunctionAdvisor(hypergeom([a],[b,c],z)) "shows" that asymptotics are not implemented for 1F2

Maple does not know how to integrate f(x)*polynomial, but seems to know the
answer for monomials. Your way can be modified slightly to get a symbolic
result (in general one would have to teach it Int(f(x)*x^k), else it works):

  # modify the last lines in the previous solution:
  'Int( exp(-xp^3)*H, xp=0..p)'; 
  Expand(%):     # reduce to 'monomials' 
  Val:=value(%): # symbolic answer, using Whittaker
  evalf[60](%):  # care for cancellations in sums 
  evalf[50](%);
                                                             -5
      0.25461203895942403099185602899627343417057152304579 10

After pondering I recognized Whittaker as an ugly way to write Gamma:

  # WhittakerM -> Gamma:
  convert(Val, hypergeom): convert(%, GAMMA):  
  # clean up for numerics:
  map(combine, %, exp): simplify(%): simplify(%, size):
    collect(%, [GAMMA, exp]): combine(%, exp):
  Result:=%; # see below

  evalf[50](Result);
                                                            -5
      0.25461203895942403099185602899627343417057152304467 10


# Result = 
251/979776*GAMMA(4/3,1)+6631/54432*GAMMA(4/3,8)+7505/81648*G\
AMMA(4/3,27)-1011449/11664*GAMMA(4/3,64)+41047847/38880*GAMM\
A(4/3,125)-59260889/11664*GAMMA(4/3,216)+142992923/11664*GAM\
MA(4/3,343)-856553465/54432*GAMMA(4/3,512)+10059318611/97977\
6*GAMMA(4/3,729)-6561251993/2449440*GAMMA(4/3,1000)+5/10368*\
GAMMA(5/3,1)-1/72*GAMMA(5/3,8)-619/96*GAMMA(5/3,27)+3941/27*\
GAMMA(5/3,64)-650825/576*GAMMA(5/3,125)+50225/12*GAMMA(5/3,2\
16)-7210483/864*GAMMA(5/3,343)+82726/9*GAMMA(5/3,512)-674539\
/128*GAMMA(5/3,729)+796075/648*GAMMA(5/3,1000)+(-3503/18144*\
exp(992)-3909307/1944*exp(936)-2100475163/4536*exp(488)-695/\
653184*exp(999)+2518049887/7776*exp(657)+119776733/5184*exp(\
875)+39761/672*exp(973)+899947939/2688*exp(271)-1929735/16*e\
xp(784)-15698834527/163296)*exp(-1000)+1/1574640*Pi*3^(1/2)/\
GAMMA(2/3);

I was tryong the idea of @Rouben Rostamian, considering a hyperplane. Let me keep it simple for typing and use dimension n = 4 (the following extends in an obvious way for any n)

I used the linear transform x[1] = -z[2]-z[3]-z[4]+z[1], x[2] = z[2], x[3] = z[3], x[4] = z[4], found by the 'solve' command (because LinearAlgebra is a mess for me to handle it in that case).

Maple does not like multi-dim IntegrationTools:-Change with the given bounds, so I used it without, which evaluates to Int(Int(Int(Int(exp(-z[1]^3), z[1]), z[2]), z[3]), z[4]).

Maple evaluates the inner integral through Whittaker functions.

Now one has to find the new bounds. These is the pre-image of the cube under the linear transform and I get 0 .. 10 in z1 and 0 .. 1 under the other variables.

The determinant of the transform is 1 (if I am correct).

But that is false due to the numerical results given here.

My question: where is my fault? I am too blind to find it :-(

@Carl Love  and vv:

Thank you, I used some compiled code off Maple, which is much slower here