Isn't A[[v]] a shortcut for LinearAlgebra:-SubVector(A,v)? Why use LinearAlgebra:-Subvector(A,v) if A[[v]] does exactly the same, and much shorter?

Alec

Try pasting in Notepad.

Alec

Also, `randpoly/monomials/dense` can be used directly,

mon:=`randpoly/monomials/dense`([x,y,z],7):
add(cat(a,i)*mon[i],i=1..nops(mon));

       3  3                 5            4  2          4    2
  a32 x  z  + a77 x y + a6 x  y z + a12 x  y  z + a14 x  y z

                4            3  3          3  2  2        3  2
         + a15 x  y z + a22 x  y  z + a24 x  y  z  + a25 x  y  z

                3    3        3    2        3            2  4
         + a27 x  y z  + a28 x  y z  + a29 x  y z + a37 x  y  z

                2  3  2        2  3          2  2  3        2  2  2
         + a39 x  y  z  + a40 x  y  z + a42 x  y  z  + a43 x  y  z

                2  2          2    4        2    3        2    2
         + a44 x  y  z + a46 x  y z  + a47 x  y z  + a48 x  y z

                2              5            4  2          4
         + a49 x  y z + a58 x y  z + a60 x y  z  + a61 x y  z

                  3  3          3  2          3            2  4
         + a63 x y  z  + a64 x y  z  + a65 x y  z + a67 x y  z

                  2  3          2  2          2              5
         + a68 x y  z  + a69 x y  z  + a70 x y  z + a72 x y z

                    4            3            2
         + a73 x y z  + a74 x y z  + a75 x y z  + a76 x y z + a83 x z

                5  2        3  2        4  2        3  2          3
         + a88 y  z  + a26 x  y  + a13 x  y  + a33 x  z  + a66 x y

                3          2  2        2  3          3          2
         + a30 x  y + a45 x  y  + a41 x  y  + a81 x z  + a71 x y

                  4        3  4       5  2       6         6
         + a62 x y  + a31 x  z  + a5 x  y  + a3 x  z + a2 x  y

               5         5  2       5          4  3        4
         + a7 x  y + a8 x  z  + a9 x  z + a11 x  y  + a16 x  y

                4  3        4  2        4          3  4        3  3
         + a17 x  z  + a18 x  z  + a19 x  z + a21 x  y  + a23 x  y

                3          2  5        2  4        2          2  5
         + a34 x  z + a36 x  y  + a38 x  y  + a50 x  y + a51 x  z

                2  4        2  3        2  2        2            6
         + a52 x  z  + a53 x  z  + a54 x  z  + a55 x  z + a57 x y

                  5          6          5          4          2
         + a59 x y  + a78 x z  + a79 x z  + a80 x z  + a82 x z

                6          5          4  3        4  2        4
         + a86 y  z + a89 y  z + a91 y  z  + a92 y  z  + a93 y  z

                3  4        3  3        3  2        3           2  5
         + a95 y  z  + a96 y  z  + a97 y  z  + a98 y  z + a100 y  z

                 2  4         2  3         2  2         2
         + a101 y  z  + a102 y  z  + a103 y  z  + a104 y  z

                   6           5           4           3           2
         + a106 y z  + a107 y z  + a108 y z  + a109 y z  + a110 y z

                          7       6        5        4        3
         + a111 y z + a1 x  + a4 x  + a10 x  + a20 x  + a35 x

                2                7        6        5        4
         + a56 x  + a84 x + a85 y  + a87 y  + a90 y  + a94 y

                3         2                  7         6         5
         + a99 y  + a105 y  + a112 y + a113 z  + a114 z  + a115 z

                 4         3         2
         + a116 z  + a117 z  + a118 z  + a119 z + a120

Alec

It is described in the help page for addtable,

inttrans[addtable](fourier, t^m, 
    -I*Pi*(-I*omega)^(-m-1)*signum(omega)/GAMMA(-m), 
    t, omega, {m}, m::Range(-infinity,infinity));

inttrans[fourier](1/t^4.3,t,w);

                                        /33\
                                        |--|
                                        \10/
               -0.3547680227 I (-1. I w)     signum(w)

Alec

It is described in the help page for addtable,

inttrans[addtable](fourier, t^m, 
    -I*Pi*(-I*omega)^(-m-1)*signum(omega)/GAMMA(-m), 
    t, omega, {m}, m::Range(-infinity,infinity));

inttrans[fourier](1/t^4.3,t,w);

                                        /33\
                                        |--|
                                        \10/
               -0.3547680227 I (-1. I w)     signum(w)

Alec

Traditionally it is done as

[$1..5];
                           [1, 2, 3, 4, 5]

Also, the seq in recent Maple versions allows the following construction,

[seq(1..5)];
                           [1, 2, 3, 4, 5]

Alec

Traditionally it is done as

[$1..5];
                           [1, 2, 3, 4, 5]

Also, the seq in recent Maple versions allows the following construction,

[seq(1..5)];
                           [1, 2, 3, 4, 5]

Alec

While that is true in general, in this particular example, there is only one local maximum. It is also global.

Alec

While that is true in general, in this particular example, there is only one local maximum. It is also global.

Alec

Besides much more convenient editing in Classic, copying, pasting, etc., it has a very convenient help feature - select a word (a Maple command), click F1, and you will get a help page for it. That doesn't work in Standard.

Alec

Besides much more convenient editing in Classic, copying, pasting, etc., it has a very convenient help feature - select a word (a Maple command), click F1, and you will get a help page for it. That doesn't work in Standard.

Alec

Wolfram Alpha is certainly very useful. As well as Wolfram MathWorld, the Wolfram Functions site, and other Wolfram products.

The algorithms in Maple came from different sources. Many of them are more than 20 years old. That doesn't make many of them bad though. The fact that they are written in Maple language and not in C (or other compilable language) does though.

Mathematica has much more algorithms (especially time consuming) written in C, which make them significantly faster. A good example can be found in the A110375 thread. While that bug was fixed in Maple 13 (at least for small enough values), the speed of calculations in Maple is not comparable to Mathematica or Sage.

Sage is faster than Mathematica in this and many other examples, not even talking about Maple. Besides, Sage covers much more mathematics than Mathematica (and Mathematica covers much more mathematics than Maple).

The most significant difference between Sage and Mathematica or Maple is that Sage is free (including being open source) and is actively developed. Every couple of weeks more and more new code is added. And if somebody is not happy with some of algorithms implemented in Sage, he or she can write a patch, submit it and enjoy it being included in a couple of weeks in Sage (in case if the review is positive.)

Alec

Wolfram Alpha is certainly very useful. As well as Wolfram MathWorld, the Wolfram Functions site, and other Wolfram products.

The algorithms in Maple came from different sources. Many of them are more than 20 years old. That doesn't make many of them bad though. The fact that they are written in Maple language and not in C (or other compilable language) does though.

Mathematica has much more algorithms (especially time consuming) written in C, which make them significantly faster. A good example can be found in the A110375 thread. While that bug was fixed in Maple 13 (at least for small enough values), the speed of calculations in Maple is not comparable to Mathematica or Sage.

Sage is faster than Mathematica in this and many other examples, not even talking about Maple. Besides, Sage covers much more mathematics than Mathematica (and Mathematica covers much more mathematics than Maple).

The most significant difference between Sage and Mathematica or Maple is that Sage is free (including being open source) and is actively developed. Every couple of weeks more and more new code is added. And if somebody is not happy with some of algorithms implemented in Sage, he or she can write a patch, submit it and enjoy it being included in a couple of weeks in Sage (in case if the review is positive.)

Alec

Thank you for your interest in my Maple usage.

Historically, I started using it at UPenn in 1996 when it was a requirement for the TA. Later, after getting a PhD, I used it in practically all of my classes for a while. Starting from Maple 9, that became more and more problematic, mostly because of the Standard interface issues. And at around Maple 9.5 and Maple 10 I stopped doing that.

For my own research and/or programming, Maple was never especially helpful. Partially because it is extremely slow, and partially because it has very limited mathematical capabilities.

Alec

Thank you for your interest in my Maple usage.

Historically, I started using it at UPenn in 1996 when it was a requirement for the TA. Later, after getting a PhD, I used it in practically all of my classes for a while. Starting from Maple 9, that became more and more problematic, mostly because of the Standard interface issues. And at around Maple 9.5 and Maple 10 I stopped doing that.

For my own research and/or programming, Maple was never especially helpful. Partially because it is extremely slow, and partially because it has very limited mathematical capabilities.

Alec