> printf("name\t%d\t%d\t=\t%g\n", 13,17,19.3457);
name    13      17      =       19.3457

See Maple's backslash help-page.

acer

The ?sum help-page mentions that add is capable of such finite addition. And, indeed, it is usually preferred.

But the question may still be asked, why doesn't it work as follows for sum,

> sum(sum(1/k!/j!/m!,k=2-m-j..2-m-j),j=0..2-m);
                                    (2 - m)
                                   2
                                  -----------
                                  (2 - m)! m!

> sum(%,m=0..2);
                                      9/2

Also, note that you invoked limit(%%,N=2-m), but the previous line produced an error. So it looks as if limit was being applied to 0 the penultimate result and not to the expression containing hypergeom. Hence it is not clear why this produces 0 in Maple 12.02,

> sum(sum(1/k!/j!/m!,k=2-m-j..2-m-j),j=0..2-m);
                                       0

Indeed,

maple9.03> sum(sum(1/k!/j!/m!,k=2-m-j..2-m-j),j=0..2-m);
                                      4
                                --------------
                                             m
                                (2 - m)! m! 2

maple9.03> sum(%,m=0..2);
                                      9/2

while,

maple9.50> sum(sum(1/k!/j!/m!,k=2-m-j..2-m-j),j=0..2-m);

                                       0

acer

The ?sum help-page mentions that add is capable of such finite addition. And, indeed, it is usually preferred.

But the question may still be asked, why doesn't it work as follows for sum,

> sum(sum(1/k!/j!/m!,k=2-m-j..2-m-j),j=0..2-m);
                                    (2 - m)
                                   2
                                  -----------
                                  (2 - m)! m!

> sum(%,m=0..2);
                                      9/2

Also, note that you invoked limit(%%,N=2-m), but the previous line produced an error. So it looks as if limit was being applied to 0 the penultimate result and not to the expression containing hypergeom. Hence it is not clear why this produces 0 in Maple 12.02,

> sum(sum(1/k!/j!/m!,k=2-m-j..2-m-j),j=0..2-m);
                                       0

Indeed,

maple9.03> sum(sum(1/k!/j!/m!,k=2-m-j..2-m-j),j=0..2-m);
                                      4
                                --------------
                                             m
                                (2 - m)! m! 2

maple9.03> sum(%,m=0..2);
                                      9/2

while,

maple9.50> sum(sum(1/k!/j!/m!,k=2-m-j..2-m-j),j=0..2-m);

                                       0

acer

The apparent "powers" in the derivatives' output are simply artefacts of the notation -- it's just how they get printed but not how they are represented in the underlying structure.

You can use eval in the usual way, to evaluate after substitution,

> expr := sin(x)*diff(f(x),x,x)/sqrt(diff(f(x),x));
                                          / 2      \
                                          |d       |
                                   sin(x) |--- f(x)|
                                          |  2     |
                                          \dx      /
                           expr := -----------------
                                     /d      \1/2
                                     |-- f(x)|
                                     \dx     /

> lprint(expr);
sin(x)*diff(diff(f(x),x),x)/diff(f(x),x)^(1/2)
 
> eval(expr, [diff(f(x),x)=4.0, diff(f(x),x,x)=-17.0]);
                              -8.500000000 sin(x)

acer

Yes, similarity is necessary, and so I tried be phrase it carefully. You had asked about efficient means, and since the problem is hard it seemed to me that a test of some necessary conditions (at a cost like that of, say, eigenvalue computation) might be of some use in practice. It might be used as a (reasonably low complexity) rejection filter.

acer

Yes, similarity is necessary, and so I tried be phrase it carefully. You had asked about efficient means, and since the problem is hard it seemed to me that a test of some necessary conditions (at a cost like that of, say, eigenvalue computation) might be of some use in practice. It might be used as a (reasonably low complexity) rejection filter.

acer

If Matrices A and B are not similar then there is no invertible Matrix C such that C.A=B.C, and hence no P=C^(-1) with the same property. See IsSimilar. For floating-point Matrices, you might consider looking at eigenvalues.

acer

If Matrices A and B are not similar then there is no invertible Matrix C such that C.A=B.C, and hence no P=C^(-1) with the same property. See IsSimilar. For floating-point Matrices, you might consider looking at eigenvalues.

acer

> M := Matrix(2,2,symbol=m);
                                [m[1, 1]    m[1, 2]]
                           M := [                  ]
                                [m[2, 1]    m[2, 2]]
 
> M^(-1) ;
                           [ m[2, 2]       m[1, 2]]
                           [ -------     - -------]
                           [   %1            %1   ]
                           [                      ]
                           [  m[2, 1]     m[1, 1] ]
                           [- -------     ------- ]
                           [    %1          %1    ]
 
                    %1 := m[1, 1] m[2, 2] - m[1, 2] m[2, 1]

There are the formulae for each entry of the inverse of a general 2x2 Matrix. Just code those up in a procedure that accepts argument m (a 2x2 Matrix).

acer

> M := Matrix(2,2,symbol=m);
                                [m[1, 1]    m[1, 2]]
                           M := [                  ]
                                [m[2, 1]    m[2, 2]]
 
> M^(-1) ;
                           [ m[2, 2]       m[1, 2]]
                           [ -------     - -------]
                           [   %1            %1   ]
                           [                      ]
                           [  m[2, 1]     m[1, 1] ]
                           [- -------     ------- ]
                           [    %1          %1    ]
 
                    %1 := m[1, 1] m[2, 2] - m[1, 2] m[2, 1]

There are the formulae for each entry of the inverse of a general 2x2 Matrix. Just code those up in a procedure that accepts argument m (a 2x2 Matrix).

acer

The user can create a initialization file to correct a bad default value for currentdir. The user can also adjust the Properties of the desktop launcher to correct a bad default value for currentdir.

The user can fix the bad default currentdir value, if told how. That is not at issue.

My point is that users (and especially new users) will have little or no idea how to do these things, or even be aware that they could/should be done. It should be fixed in the product.

acer

The user can create a initialization file to correct a bad default value for currentdir. The user can also adjust the Properties of the desktop launcher to correct a bad default value for currentdir.

The user can fix the bad default currentdir value, if told how. That is not at issue.

My point is that users (and especially new users) will have little or no idea how to do these things, or even be aware that they could/should be done. It should be fixed in the product.

acer

When Maple gets installed, can its installer set the Properties of the desktop launcher? If it could, then it could explicitly set it to a better default.

acer

When Maple gets installed, can its installer set the Properties of the desktop launcher? If it could, then it could explicitly set it to a better default.

acer

It is great to see Maple's help online.

The feedback mechanism on each page looks useful.

As first-versions go, it is very good. (It's very hard to make the first version of anything near perfect.) And since it is online it can be adjusted or improved independently of Maple patch releases.

I have a few suggestions for improvements:

• When a search would return only one item, then display it immediately (that is how Maple's own Help works). Right now it shows a page with just the link to the single result.
• Provide the alternate text in the properties on any 2D Math output. (Mapleprimes does this.)
• Have the subsections of a help-page be url targets, so that one can link to the offset Examples, See Also, Description, CallingSequence, etc.
• Provide a way to get all the Examples as 1D Maple Notation. Maple's own Help has a toggle for this, but the Online Help might provide 1D with its own mechanism.
• Have a better way to deal with hidden code in the Applications worksheets. I realize this could be difficult, but otherwise application pages like the one for Image Processing appear obscure.
• Make the site faster.
• The information for titles for individual pages is certainly availaible (it gets used nicely in the table-of-contents in the left-bar). But it doesn't get properly used in the summaries on the right. For example, going to this summary page shows titles like Student/plot_options while the table-of-contents shows the much nicer Plot Options. It could be set out more nicely on the right as Student / Plot Options. There are many more unreadable examples, such as on the Error Message Guide summary here. Again, the table-of-contents demonstrates that the nicer name is available.

acer