For example,

collect(W,mu[4],distributed,factor);

  cos(mu[1] Pi) sin(mu[4] Pi) (mu[3] cos(mu[2] Pi) sin(mu[3] Pi)

                                                   3        3
         - cos(mu[3] Pi) sin(mu[2] Pi) mu[2]) mu[4]  + mu[3]

        sin(mu[3] Pi) cos(mu[4] Pi) (

        mu[1] sin(mu[1] Pi) cos(mu[2] Pi)

         - sin(mu[2] Pi) cos(mu[1] Pi) mu[2])

patmatch(%,mu[4]^3*cos(mu[1]*Pi)*sin(mu[4]*Pi)*W1::algebraic+
    mu[3]^3*sin(mu[3]*Pi)*cos(mu[4]*Pi)*W2::algebraic,p);

                                 true

p;

  [W1 = mu[3] cos(mu[2] Pi) sin(mu[3] Pi)

         - cos(mu[3] Pi) sin(mu[2] Pi) mu[2], W2 =

        mu[1] sin(mu[1] Pi) cos(mu[2] Pi)

         - sin(mu[2] Pi) cos(mu[1] Pi) mu[2]]

Alec

That depends on what kind of beverages they produce. Personally, I, probably, could sample 2 bottles of some beverages per minute (Edit: not easily, I should say, after few experiments), but 120 per hour seem like too high a goal to achieve. That would require a lot of training. Looks like a nice job though. Do they hire?

Alec

There might be some bugs (which may be fixed or not in other Maple versions) - it is hard to tell without seeing an example. It would be easier if you just posted some code that could be tried, and expected results.

Alec

And USERPROFILE combines them.

Alec

That can be done using DynamicSystems[Square] and DynamicSystems[Triangle].

Alec

There are quite a few LaTeX editors with a lot of buttons and palettes, allowing entering symbols by clicking there. However, as far as I can tell, they are in use mostly by novice users. It is much easier (and faster) to use keyboard instead. Some of editors (I think, Textures on Mac, in particular) display symbols parallel with typing. Others (LyX and TeXmacs) do even better job displaying LaTeX in WySiWyw (what you see is what you want) manner.

SAGE uses jsMath for math display in the notebook, and matplotlib for plots, with extensive LaTeX capabilities. Formulas entered in the notebook in usual SAGE format looks very nice in the 2D-output. See some screenshots done by a high school student. 1D-input and 2D-output as in SAGE (and in less developed form, but still, in Classic Maple), has many advantages compared to 2D-input in Standard Maple. One of the most significant is reproducibility. Also, it is much better for copying and pasting. However, I know that some people (mostly from Maplesoft) use 2D-input for their work, so it is theoretically possible (but they still have to rewrite it in LaTeX if they want to publish their work.)

Another possibility, not mentioned above, is Scientific WorkPlace. It combines LaTeX and CAS (MuPad, which is similar to Maple, more lightweight, but with good graphics including png and svg formats, and with very good combinatorial package - people who developed it, switched to development for SAGE now.)

Alec

-9*x^3 is O(x^3), so Maple is correct. And you are right, changing 3 to 4 at the end of your series commands would display cubic terms.

Alec

You can convert a series to polynomial form, see ?convert,polynom, and then use unapply to make it a function, if necessary.

Alec

A:=Matrix([[1,1,3],[1,5,1],[3,1,1]]);
                               [1    1    3]
                               [           ]
                          A := [1    5    1]
                               [           ]
                               [3    1    1]

LinearAlgebra:-Eigenvectors(A);

                        [-2]  [-1     1    1]
                        [  ]  [             ]
                        [ 3], [ 0    -1    2]
                        [  ]  [             ]
                        [ 6]  [ 1     1    1]

Alec

For example,

dsol := dsolve({diff(p(x),x) = p(x)*cos(x), p(-1) = 1},
    numeric, output=listprocedure);
 
p:=eval(p(x),dsol);

                     p := proc(x)  ...  end proc

fdiff(p,[1,1,1],0);

                             1.330000000

s:=p(0)+add(fdiff(p,[1$i],0)/i!*x^i,i=1..6);

                                                          2
  s := 2.31977948777296472 + 2.319769614 x + 1.159608000 x

                         3                4                  9  5
         + 0.2216666667 x  + 16583.33333 x  - 0.4433333333 10  x

                          14  6
         - 0.1968055556 10   x

It seems as if fdiff has a bug related to workprec though (or something is wrong with the numerical solution). In particular,

s:=p(0)+add(fdiff(p,[1$i],0,workprec=3)/i!*x^i,i=1..6);
                                                            44  4
  s := 2.31977948777296472 + 2.220000000 x - 0.3666666667 10   x

                          59  5                  73  6
         + 0.1108333333 10   x  + 0.7347222222 10   x

s:=p(0)+add(fdiff(p,[1$i],0,workprec=4)/i!*x^i,i=1..6);
                           s := 2.319779488

The symbolic solution gives the following series,

series(exp(sin(x))*exp(sin(1.)),x=0,7);
                                             2                 4
  2.319776825 + 2.319776825 x + 1.159888412 x  - 0.2899721031 x  -

                      5                   6      7
        0.1546517883 x  - 0.009665736771 x  + O(x )

Perhaps, it is better to use original ode(s) to find the derivatives, or use output=piecewise?!

Alec

I think, I already answered to that in your previous thread. For Z3 specifically,

with(group):
Z3:=permgroup(3,{[[1,2,3]]}):
elements(Z3);

                    {[], [[1, 2, 3]], [[1, 3, 2]]}

Personally, I wouldn't use Maple for such things.

I would use Group Explorer and SAGE.

Alec

Is it l or 1 in b?

Alec

There is also Tools:-DGsimplify. It doesn't work on single 0s, but eliminates them in other cases.

0 would be a wrong answer in the examples you gave, but if you would like to see it, it can be done in various ways. For example,

a:=evalDG(e[1] &wedge e[1]);

                            a := 0 dx ^ dy
op([1,2,1,2],a);
                                  0

or even more simple,

0*a;
                                  0

and

evalDG(0*a);
                                  0

which seems to be a bug, but gives what you wanted.

Alec

The usual way would be as in the following example,

M:=matrix([[a1,a2],[a3,a4]]);

                                [a1    a2]
                           M := [        ]
                                [a3    a4]

M(x,y);
                        [a1(x, y)    a2(x, y)]
                        [                    ]
                        [a3(x, y)    a4(x, y)]

However, that doesn't work for Matrices. It is possible to do the folowing,

M:=Matrix([[a1,a2],[a3,a4]]);

                                [a1    a2]
                           M := [        ]
                                [a3    a4]

convert(convert(M,matrix)(x,y),Matrix);

                        [a1(x, y)    a2(x, y)]
                        [                    ]
                        [a3(x, y)    a4(x, y)]

or

Matrix(convert(M,matrix)(x,y));

                        [a1(x, y)    a2(x, y)]
                        [                    ]
                        [a3(x, y)    a4(x, y)]

but there might be more simple ways.

map(a->a(x,y),M);

                        [a1(x, y)    a2(x, y)]
                        [                    ]
                        [a3(x, y)    a4(x, y)]

also works.

Alec

evalDG(%);
                               2
                              A  dx ^ dy

Alec