You asked Maple to solve the equality, while you asked Mma about the inequality.
As I previously mentioned, Maple doesn't produce a result for the inequality that you had previously supplied (whether using the extra inequalities x>-infinity,x
I suspect that I got confused (not the first time) about assuming. I believe that `int`, `simplify`, `dsolve`, `is`, and things-which-primarily-use-`is` can make good use of the assuming facility. But `solve` may not properly be in that collection, which is a pity.
It's a documentation bug, that there is no clear indication about precisely what supports `assume` and `assuming`.
So, instead of using `assuming`, one could try this,
solve({x^2+y^2 = 1,x>-infinity,x
-infinity,y-infinity,x
What does this mean?
Reduce[x^2+y^2<1,{x,y}] which returns -1
I guess that that was an instance of chopped output.
Do you realize that, in the absence of "assuming" qualification, by default Maple's `solve` treats the variables as if they might be complex-valued? And do you know that, also by default, Mma's Reduce treats the variables as if their were from the purely real domain?
So, I suppose that you could compare these two,
Mma% Reduce[x^2+y^2<1,{x,y}, Complexes]
Maple> solve(x^2+y^2<1,{x,y});
or these two,
Mma% Reduce[x^2+y^2<1,{x,y}]
Maple> solve(x^2+y^2<1,{x,y}) assuming x::real, y::real;
Maple's solve is not very strong at inequalities, however. It's been getting stronger, I believe, but it's functionality is not yet mature.
Can anyone explain this example to me, in Maple 11?
> solve(x^2+y^2 = -1, {x, y}) assuming x::real, y::real;
{y = y, x = (-y^2-1)^(1/2)}, {y = y, x = -(-y^2-1)^(1/2)}
acer
Within the procedure, right after where you have it call NLPSolve, could you simply assign the return value and/or arguments of the NLPSolve call into an Array declared as a global?
acer
What makes you think that this has a closed form solution? That is, what makes you think that the solution can be written down as an explicit formula?
Even when no formulaic, closed form solution might be forthcoming, Maple can still proceed with some sorts of computations with the RootOf, while keeping it as an exact representation. Don't you consider that useful?
acer
Could you upload a small example worksheet that illustrates this?
Are you saying that some of the (usually correctly displayed) content shows as question marks, or that the question marks appear where nothing was before then?
acer
Have a look at this,
showstat(`convert/binary/integer`);
You may notice that it uses 32 to take integer remainders. So this next table below could also be useful, in understanding that is going on in that procedure.
interface(rtablesize=50);
`convert/binary/table`;
It that procedure seems confusing, then read the help for routine irem(). You could also try this,
trace(`convert/binary/integer`);
convert(32^4+32^2+32,binary);
You could try writing a procedure that is similar, which takes integer remainders by division by 16, say, or divide by 2 (in the latter case of which case a table isn't really needed).
acer
What version of Maple, and on what platform, does that not produce the result like one gets from matrix(2,2,[1,2,3,-5]) ?
It works for me, on Linux with Maple 9.5.1, 10.02, or 11.
acer
Is this similar to what you are after?
eqns:= {a(s,y,z,t)+2*b(s,y,z,t)=0,3*a(s,y,z,t)-5*b(s,y,z,t)=0}:
linalg[genmatrix](eqns,[a(s,y,z,t),b(s,y,z,t)]);
If not then you might have to explain what you mean by "the matrix associated to the system."
acer
The labelled RootOf refers to an unspecified root. So in your case it may be meant to represent either root, rather than a particular root.
If you would rather see the solution explicitly in terms of particular roots, then try it after,
_EnvExplicit:=true:
I would say that the section explaining _EnvExplicit within the help-page ?solve,details is not clear about its behaviour for systems of equations. It's not even adequately clear that the section -- describing behaviour governed by _EnvExplicit -- refers only to the case of a single equation.
Also, the label in the solution to your example may seem confusing because it doesn't actually serve to distinguish between sets of unspecified roots -- which is what the help-pages suggest is its purpose. So why it it labelled? Why not just have it return the general unlabelled form in the solution to your problem, to specify "any" root? Why add in a label when the solution is meant to represent any root without qualification?
While I'm at it, I don't really see where in that ?solve,details help-page is an explanation of why solve(x^8-3) returns all eight explicit solutions by default. Instead it hints that it might do the opposite, by claiming this: "The solve command returns explicit solutions for low degree polynomial equations (by default, degree less than 4). For higher degree equations, implicit solutions are given in terms of RootOf."
acer
