jakubi

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It may depend on whether the source of the potential is bounded. For a matter source that extends to infinity, the gravitational potential does not vanish at infinity.

The point was an answer to Axel's question.

The point was an answer to Axel's question.

After the output of showstat(Typesetting[delayDotProduct]), it seems related to the VectorCalculus package.
 

After the output of showstat(Typesetting[delayDotProduct]), it seems related to the VectorCalculus package.
 

Basically I have added a shell script entry named "Maple" to the "Tools" menu for running Maple 13 console UI on the editor document, for which I am using termination "mpl". 

So, in Edit > Preferences > Tools:

Files: *.mpl
Options:
Command type: Shell command
Input: Whole document
Output: Output pane
Filter: default

And my /usr/local/bin script name for executing Maple 13 console UI in the script box. I have associated also a hot key to this "Maple" entry  (by Edit > Configure Shortcuts).

On Windows it does not work so nice, but I have been able to launch Maple 13 console UI on a cmd box, or Classic and Standard GUI, with the editor content within the worksheet, by more or less similar methods.

 

 

 

Basically I have added a shell script entry named "Maple" to the "Tools" menu for running Maple 13 console UI on the editor document, for which I am using termination "mpl". 

So, in Edit > Preferences > Tools:

Files: *.mpl
Options:
Command type: Shell command
Input: Whole document
Output: Output pane
Filter: default

And my /usr/local/bin script name for executing Maple 13 console UI in the script box. I have associated also a hot key to this "Maple" entry  (by Edit > Configure Shortcuts).

On Windows it does not work so nice, but I have been able to launch Maple 13 console UI on a cmd box, or Classic and Standard GUI, with the editor content within the worksheet, by more or less similar methods.

 

 

 

The installation order is largely irrelevant. An issue is with with Maple version you wish .mws and .mw files be associated. Using defaults, it will be with the last one. But you can choose otherwise, or change it later. Just be careful to install different versions in different directories.

I was talking about possibly bounding the region where real zeroes lay. Finding all of them within that region is another story. And I am thinking about mixed symbolic-numeric techniques for a class of good enough functions (which may cover most cases in practice). E.g. those for which is provable that are larger than a constant A>0 for x>x0 say, and then using x0 as a right bound. For functions that diverge or have a nonzero limit for x->infinity, it sounds to me as something possible.

I was talking about possibly bounding the region where real zeroes lay. Finding all of them within that region is another story. And I am thinking about mixed symbolic-numeric techniques for a class of good enough functions (which may cover most cases in practice). E.g. those for which is provable that are larger than a constant A>0 for x>x0 say, and then using x0 as a right bound. For functions that diverge or have a nonzero limit for x->infinity, it sounds to me as something possible.

But I wonder whether such bound estimates could be automated. I.e. algorithmically implemented, beyond simple cases like this one (linear in 'cos'), for writing a reliable procedure. Sounds to me that some automated proving capabilities would be needed. And Maple is rather weak in this field. 

But I wonder whether such bound estimates could be automated. I.e. algorithmically implemented, beyond simple cases like this one (linear in 'cos'), for writing a reliable procedure. Sounds to me that some automated proving capabilities would be needed. And Maple is rather weak in this field. 

I get a fast failure:

r1 := fsolve(x^2/20-10*x-15*cos(x+15),x);

                          r1 := 1.274092075

RootFinding:-NextZero(x->x^2/20-10*x-15*cos(x+15),r1);

                                 FAIL

There is an option to make it work:

RootFinding:-NextZero(x->x^2/20-10*x-15*cos(x+15),r1,maxdistance=200);

                             200.1193789

But then you need some additional bound information.

I get a fast failure:

r1 := fsolve(x^2/20-10*x-15*cos(x+15),x);

                          r1 := 1.274092075

RootFinding:-NextZero(x->x^2/20-10*x-15*cos(x+15),r1);

                                 FAIL

There is an option to make it work:

RootFinding:-NextZero(x->x^2/20-10*x-15*cos(x+15),r1,maxdistance=200);

                             200.1193789

But then you need some additional bound information.

May be because of how grey is generated on screen. May be also an issue of pixels and screen resolution. The fact is that even thickness values, like 2 or 4, produce blurred borders, while for odd ones, like 3 or 5, the borders look sharper.

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