LinearSolve returns a message if the system is inconsistant. OTOH, solve may return a null sequence or an empty list, depending on how one writes its arguments. For instance,

> solve([x+y = 2, 2*x+2*y = 3], {x, y});

> solve([x+y = 2, 2*x+2*y = 3], [x, y]);

                                     []

> LinearSolve(Matrix([[1, 1], [2, 2]]), Vector([[2, 3]]));

Error, (in LinearAlgebra:-LA_Main:-LinearSolve) inconsistent system

The documentation for solve (?solve) is more or less illuminating on the subject: If the solve command does not find any solutions, then if the second argument is a name, then the empty sequence (NULL) is returned and if the second argument is a list, then empty list is returned. This means that there are no solutions, or the solve command cannot find the solutions. In the latter case, a warning is issued and the global variable _SolutionsMayBeLost is set to true. Regards, --Jean-Marc

It might be platform, version, or interface dependent or you might have change something in the Maple environment. It works fine on my system (standard interface, document mode).

> kernelopts(version);

        Maple 12.02, APPLE UNIVERSAL OSX, Dec 10 2008 Build ID 377066

For the second question, what command did you use (LinearSolve)? Regards, --Jean-Marc

Maybe it is just me or because it is late night (local time), but I could not make sense of the above. Could you, please, explain in words what the above is supposed to mean? (You could also use correct Maple syntax to describe things such as functions of two variables, which, I believe, p and q are, and partial differential operator for partial differentiation.) Regards, --Jean-Marc

I shall answer only the first question to help you started and to leave some work for you to do! (Note that it is not clear whether your questions are related to the mathematics or to Maple syntax and functions. It is always a good idea to show your working.) Two things to keep in mind: in Euclidean geometry the sum of the angles X, Y, and Z of a triangle is Pi, i.e. X + Y + Z = Pi, and for an arbitrary angle alpha we have sin(Pi - alpha) = sin(alpha). So the idea is to express Z in terms of X and Y (and Pi) only and substitute it in the given expression, then convert it to a function of two variables. For the second part, you may want to differentiate f(X, Y) or perhaps use some of the optimization functions available in Maple (that mostly depends on what class you are taking).

> eq1 := X+Y+Z = Pi;

                            eq1 := X + Y + Z = Pi

> eq2 := sin(X)*sin(Y)*sin(Z);

                         eq2 := sin(X) sin(Y) sin(Z)

> solve(eq1, Z);

                                 -X - Y + Pi

> subs(Z = %, eq2);

                       sin(X) sin(Y) sin(-X - Y + Pi)

> f := unapply(%, X, Y);

                   f := (X, Y) -> sin(X) sin(Y) sin(X + Y)

> evalb(sin(Pi-alpha) = sin(alpha));

                                    true

> eliminate({eq1, eq2}, {Z});

               [{Z = -X - Y + Pi}, {sin(X) sin(Y) sin(X + Y)}]

Regards, --Jean-Marc

with(plots); 
implicitplot(y-x^2, x = -1 .. 1, y = 0 .. 1, coloring = [white, red], 
filledregions = true)

Regards, --Jean-Marc

The following thread might be of some help: Solve numerically a system of PDEs. [edited] Note that you made a typo in the last equation of the IC: change the "O" by "0", thus D[2,2](u)(x,0)=0 rather than D[2,2](u)(x,O)=0. HTH, --Jean-Marc

OK. Something was wrong in the way you installed Maple. For most of the file, owner should be root and the x permission (execute) should be set for the owner, the owner group, and everybody else. Permissions can be changed via the command chmod, but I would not change them manually for the overall installation seems to be really messed up in term of security. So, you could reinstall Maple 12 or also ask Maplesoft technical support for more advice, possibly a shell script that would repair the all hierarchy. Regards, --Jean-Marc

Are you using Maple from the same account with which you did the installation? Also, you could check the permissions, owner, and group with the ls command. For instance,

ls -lah /Library/Frameworks/Maple.framework/Versions/12/bin/

total 192
drwxrwxr-x  13 root      admin   442B Dec 21 11:39 .
drwxrwxr-x  16 root      admin   544B Sep 28 22:51 ..
-rwxr-xr-x   1 root      admin   1.0K Aug  8 19:05 Maple12.png
-rwxr-xr-x   1 root      admin   1.0K Aug  8 19:05 Maple12Classic.png
-rwxr-xr-x   1 root      admin   323B Aug  8 19:05 TestMaple
-rwxr-xr-x   1 root      admin   5.6K Aug  8 19:05 activation
-rwxr-xr-x   1 root      admin   2.7K Aug  8 19:05 linux_shlibs
-rwxrwxr-x   1 root      admin    18K Dec 21 11:39 maple
-rwxr-xr-x   1 root      admin   2.3K Aug  8 19:05 maple.system.type
-rwxr-xr-x   1 jeanmarc  admin    18K Oct 13 11:28 maple_Maple12.01_Upgrade_Backup
-rwxr-xr-x   1 root      admin    18K Sep 29 23:58 maple_Maple12.02_Upgrade_Backup
-rwxr-xr-x   1 root      admin   903B Aug  8 19:05 mint
-rwxr-xr-x   1 root      admin   417B Aug  8 19:05 xmaple

Regards, --Jean-Marc

Since the issue seems to be related to file and/or folder access privileges, I would suggest to run Disk Utility to check, and repair if needed, any access authorization inconsistencies on the system file. Start Disk Utility (located in /Applications/Utilities), select the hard drive where your system resides, in the tab First Aid select Verify Disk Permissions. Wait for the process to finish. If any error are reported, click on Repair Disk Permissions. The following documents might be worth reading: Using Disk Utility in Mac OS X 10.4.3 or later to verify or repair disks, and also Mac OS X - Using Disk Utility to Repair a Disk. HTH, --Jean-Marc

Cmd+R to switch to 2D-Math mode. --Jean-Marc

Note that the package student is deprecated; therefore, except if you have some compelling reason not to use it (say you have an old version of Maple), you should use RiemannSum from the Student[Calculus1] package. It has many more options and you can even get a plot or an animation of the sum. See > help("RightRiemannSum) for more info.

> restart;
> with(Student[Calculus1]); f := proc (n) options operator, arrow;
RiemannSum(x^6, x = 0 .. 4, method = right, partition = n) end proc;

> seq(evalf(f(n)), n = 1 .. 10);

 16384., 8320., 5948.283493, 4890., 4302.307328, 3931.361683, 3676.906828, 

   3491.906250, 3351.513991, 3241.418752
> f := proc (n) options operator, arrow; RiemannSum(x^6, x = 0 .. 4,
method = right, partition = n, output = plot) end proc;
> f(20);

Regards, --Jean-Marc

> with(student);
> f := proc (n) options operator, arrow; rightsum(x^6, x = 0 .. 4, n) end
proc; seq(evalf(f(n)), n = 1 .. 10);

                                      / 6               \
                    f := n -> rightsum\x , x = 0 .. 4, n/
 16384., 8320., 5948.283492, 4890., 4302.307328, 3931.361683, 3676.906828, 

   3491.906250, 3351.513990, 3241.418752
> limit(f(n), n = infinity);

                                    16384
                                    -----
                                      7  
> evalf(%);

                                 2340.571429

> int(x^6, x = 0 .. 4);

                                    16384
                                    -----
                                      7  

Regards, --Jean-Marc

between Pi and the left parenthesis (otherwise, the expression is evaluated as a function call).

> 2*(int(Pi*(r^2-y^2), y = 0 .. r));

                                   4     3
                                   - Pi r 
                                   3      

Regards, --Jean-Marc

The package called "powseries" should be a good start for formal power series manipulatons. See help("powseries") and/or help("powseries,quotient") for more info. Regards, --Jean-Marc

Well, I am not sure what kind of differences you expect since the commands differs only by the way you pass the first argument to them. On my system ---Maple 12.0.2 64-bit Intel Mac OS X Leopard 10.5.6--- the plots differ by the colors assigned to each curve (see below), which is consistent with the way lists and sets work, and, IFAIK, this is the only difference that one can expect in the resulting plots for the given commands. A set {func1, func2, ...}, denoted by curly brackets, does not guarantee that the order of the function will be preserved when evaluated. OTOH, a list [func1, func2, ...], denoted by square brackets, will preserve the order of its arguments; consequently, the functions will always be evaluated from left to right. Here is an extract from the online help (see help("plot,details") for the full page) Generating Multiple Curves Multiple curves can be plotted by replacing the first argument with a list or set of items, in every calling sequence except the last. Options such as color or thickness can be specified for each curve by using a list of values as the right-hand-side of the option equation. In this situation, the first argument to the plot command must also be a list; if it is a set, the order of the plots might not be preserved. Here is what I get on my system.

plot({x^2, 2-x^2}, x = -1 .. 1)

plot(plot([2-x^2, x^2], x = -1 .. 1)

Regards, --Jean-Marc