If you are asking about the Examples section of the help topics, then maybe you are thinking about the triple question mark (???) syntax.

???topic opens the help page for "topic" with only the Examples section expanded. (The Description, See Also, and References sectios, if present, are all collapsed.)

From here the Copy Examples entry in the File menu is an easy way to copy all of the Examples to an active worksheet (or document).

There are a few help topics that do open a worksheet.  Within the help browser, most topics have an icon that contains a question mark (?); these are the typical help pages displayed in the help browser. Those with a D icon are entries in Maple's dictionary. And, those with a WS icon are actual Maple worksheets; click on one of these and a separate worksheet opens in a Maple window. To see all three, look at the help for applications: ?applications

If this is not what you were asking about, please ask again.

Wishing a Merry Christmas to one and all!

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

What others have done in response to your posts is to paste in an image taken from a screenshot of a Maple worksheet. This looks nice, but is not terribly functional. If you want to use something from that image, you have to retype it in your worksheet. I prefer to upload a file to MaplePrimes and insert a link to this file in my post. When you click on the link, you get the entire worksheet or image or whatever.

Here's how to upload a file to MaplePrimes and include it in a post.

1. Click on the green upward pointing arrow above the message composition window.
2. In the window that appears, click on Browse and locate the file you want to share; click on Upload.
3. To insert a link to this file in your current post, click OK, otherwise click Cancel.

The file will now appear in the Recent Files list on the lower right of the MaplePrimes window. Here's an example of what the link looks like. (You can also see the upload_demo.mw file in the Recent Files list.)

View 178_upload_demo.mw on MapleNet or Download 178_upload_demo.mw
View file details

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

What others have done in response to your posts is to paste in an image taken from a screenshot of a Maple worksheet. This looks nice, but is not terribly functional. If you want to use something from that image, you have to retype it in your worksheet. I prefer to upload a file to MaplePrimes and insert a link to this file in my post. When you click on the link, you get the entire worksheet or image or whatever.

Here's how to upload a file to MaplePrimes and include it in a post.

1. Click on the green upward pointing arrow above the message composition window.
2. In the window that appears, click on Browse and locate the file you want to share; click on Upload.
3. To insert a link to this file in your current post, click OK, otherwise click Cancel.

The file will now appear in the Recent Files list on the lower right of the MaplePrimes window. Here's an example of what the link looks like. (You can also see the upload_demo.mw file in the Recent Files list.)

View 178_upload_demo.mw on MapleNet or Download 178_upload_demo.mw
View file details

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

Here is what I see when I execute the commands from your last post:

piecewise(x<0,x^3+8,0<x<=3,x+3/x,x>3,3*x-5);
Error, unexpected relational operator
f(0);
                                    f(0)
f(2);
                                    f(2)

Maple's syntax does not allow writing inequalities like "0<x<=3". The correct syntax for the function you appear to be trying to define would be

f := x -> piecewise( x<0, x^3+8, x<=3, x+3/x, x>3, 3*x-5 );
              /        3                  3                \
x -> piecewise|x < 0, x  + 8, x <= 3, x + -, 3 < x, 3 x - 5|
              \                           x                /

But, when we try to evaluate this with x=0:

f(0);
Error, (in f) numeric exception: division by zero

Now the problem is that this function, when x=0, is trying to evaluate 0+3/0, which gives the error message.

I'll guess that you want 0 included in the first part of the definition. If so, you would have:

f := x -> piecewise( x<=0, x^3+8, x<=3, x+3/x, x>3, 3*x-5 );
              /         3                  3                \
x -> piecewise|x <= 0, x  + 8, x <= 3, x + -, 3 < x, 3 x - 5|
              \                            x                /
f(0);
                                      8
f(2);
                                      7
                                      -
                                      2

To explain these results:

• when x=0, the first boolean condition that evaluates to true is x<=0, so the value returned is 0^3+8 = 8
• when x=2, the first boolean condition that evaluates to true is x<=3, so the value returned is 2+3/2 = 7/2

I hope this is helpful,

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

Here is what I see when I execute the commands from your last post:

piecewise(x<0,x^3+8,0<x<=3,x+3/x,x>3,3*x-5);
Error, unexpected relational operator
f(0);
                                    f(0)
f(2);
                                    f(2)

Maple's syntax does not allow writing inequalities like "0<x<=3". The correct syntax for the function you appear to be trying to define would be

f := x -> piecewise( x<0, x^3+8, x<=3, x+3/x, x>3, 3*x-5 );
              /        3                  3                \
x -> piecewise|x < 0, x  + 8, x <= 3, x + -, 3 < x, 3 x - 5|
              \                           x                /

But, when we try to evaluate this with x=0:

f(0);
Error, (in f) numeric exception: division by zero

Now the problem is that this function, when x=0, is trying to evaluate 0+3/0, which gives the error message.

I'll guess that you want 0 included in the first part of the definition. If so, you would have:

f := x -> piecewise( x<=0, x^3+8, x<=3, x+3/x, x>3, 3*x-5 );
              /         3                  3                \
x -> piecewise|x <= 0, x  + 8, x <= 3, x + -, 3 < x, 3 x - 5|
              \                            x                /
f(0);
                                      8
f(2);
                                      7
                                      -
                                      2

To explain these results:

• when x=0, the first boolean condition that evaluates to true is x<=0, so the value returned is 0^3+8 = 8
• when x=2, the first boolean condition that evaluates to true is x<=3, so the value returned is 2+3/2 = 7/2

I hope this is helpful,

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

Aside from the specific names of the variables, Robert's solution should be pretty optimal, particularly if you are looking for a graphical representation of the inverse function.

Here is an alternate way to obtain this graph. Start by plotting the original function, then apply the transformation (x,y)->[y,x] to reflect the points across the line y=x. For example:

f := x -> int( sin(t*x)/(1+x^2), t=0..x );
P := plot( f, 0..1 ):
Inv := plottools:-transform( (x,y)->[y,x] ):
plots:-display( [P,Inv(P)] );
 

You mention that the function you are trying to invert is given as an integral. If your example is of the right form, you might be able to use the ideas for deriving formulas for the derivatives of inverse functions to actually obtain the inverse function. For example,

q1 := t(z)=tan(z);
                                t(z) = tan(z)
dq1 := diff(q1,z);
                            d                   2
                           --- t(z) = 1 + tan(z) 
                            dz                   
dq2 := diff(z(t),t)=1/rhs(dq1);
                            d              1     
                           --- z(t) = -----------
                            dt                  2
                                      1 + tan(z) 
dq3 := eval( dq2, rhs(q1)=lhs(q1) );
                             d             1    
                            --- z(t) = ---------
                             dt                2
                                       1 + t(z) 
map( int, eval(dq3,t(z)=t), t );
                              z(t) = arctan(t)

I hope something in here will be helpful for you,

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

Aside from the specific names of the variables, Robert's solution should be pretty optimal, particularly if you are looking for a graphical representation of the inverse function.

Here is an alternate way to obtain this graph. Start by plotting the original function, then apply the transformation (x,y)->[y,x] to reflect the points across the line y=x. For example:

f := x -> int( sin(t*x)/(1+x^2), t=0..x );
P := plot( f, 0..1 ):
Inv := plottools:-transform( (x,y)->[y,x] ):
plots:-display( [P,Inv(P)] );
 

You mention that the function you are trying to invert is given as an integral. If your example is of the right form, you might be able to use the ideas for deriving formulas for the derivatives of inverse functions to actually obtain the inverse function. For example,

q1 := t(z)=tan(z);
                                t(z) = tan(z)
dq1 := diff(q1,z);
                            d                   2
                           --- t(z) = 1 + tan(z) 
                            dz                   
dq2 := diff(z(t),t)=1/rhs(dq1);
                            d              1     
                           --- z(t) = -----------
                            dt                  2
                                      1 + tan(z) 
dq3 := eval( dq2, rhs(q1)=lhs(q1) );
                             d             1    
                            --- z(t) = ---------
                             dt                2
                                       1 + t(z) 
map( int, eval(dq3,t(z)=t), t );
                              z(t) = arctan(t)

I hope something in here will be helpful for you,

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

Aside from the specific names of the variables, Robert's solution should be pretty optimal, particularly if you are looking for a graphical representation of the inverse function.

Here is an alternate way to obtain this graph. Start by plotting the original function, then apply the transformation (x,y)->[y,x] to reflect the points across the line y=x. For example:

f := x -> int( sin(t*x)/(1+x^2), t=0..x );
P := plot( f, 0..1 ):
Inv := plottools:-transform( (x,y)->[y,x] ):
plots:-display( [P,Inv(P)] );
 

You mention that the function you are trying to invert is given as an integral. If your example is of the right form, you might be able to use the ideas for deriving formulas for the derivatives of inverse functions to actually obtain the inverse function. For example,

q1 := t(z)=tan(z);
                                t(z) = tan(z)
dq1 := diff(q1,z);
                            d                   2
                           --- t(z) = 1 + tan(z) 
                            dz                   
dq2 := diff(z(t),t)=1/rhs(dq1);
                            d              1     
                           --- z(t) = -----------
                            dt                  2
                                      1 + tan(z) 
dq3 := eval( dq2, rhs(q1)=lhs(q1) );
                             d             1    
                            --- z(t) = ---------
                             dt                2
                                       1 + t(z) 
map( int, eval(dq3,t(z)=t), t );
                              z(t) = arctan(t)

I hope something in here will be helpful for you,

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

Aside from the specific names of the variables, Robert's solution should be pretty optimal, particularly if you are looking for a graphical representation of the inverse function.

Here is an alternate way to obtain this graph. Start by plotting the original function, then apply the transformation (x,y)->[y,x] to reflect the points across the line y=x. For example:

f := x -> int( sin(t*x)/(1+x^2), t=0..x );
P := plot( f, 0..1 ):
Inv := plottools:-transform( (x,y)->[y,x] ):
plots:-display( [P,Inv(P)] );
 

You mention that the function you are trying to invert is given as an integral. If your example is of the right form, you might be able to use the ideas for deriving formulas for the derivatives of inverse functions to actually obtain the inverse function. For example,

q1 := t(z)=tan(z);
                                t(z) = tan(z)
dq1 := diff(q1,z);
                            d                   2
                           --- t(z) = 1 + tan(z) 
                            dz                   
dq2 := diff(z(t),t)=1/rhs(dq1);
                            d              1     
                           --- z(t) = -----------
                            dt                  2
                                      1 + tan(z) 
dq3 := eval( dq2, rhs(q1)=lhs(q1) );
                             d             1    
                            --- z(t) = ---------
                             dt                2
                                       1 + t(z) 
map( int, eval(dq3,t(z)=t), t );
                              z(t) = arctan(t)

I hope something in here will be helpful for you,

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

I find it very difficult that someone would give an assignment that *requires* the use of Maple 12 without giving you any instruction on how to use this software.

They may not show you exactly how to answer these questions, but might show you how to use Maple to get the information you need.

While we cannot guess at the exact formulation you are using to find the "derived function", it will certainly involve a limit. If you ask to see Maple's help page for limit (type ?limit in an input region, or type limit in the help browser that can be started via the Help menu).

I agree. The point of your exercise is for you to learn about this, not for you to find someone else who knows how to do the work for you.

I am glad to help, but am not willing to do your work for you.

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

I find it very difficult that someone would give an assignment that *requires* the use of Maple 12 without giving you any instruction on how to use this software.

They may not show you exactly how to answer these questions, but might show you how to use Maple to get the information you need.

While we cannot guess at the exact formulation you are using to find the "derived function", it will certainly involve a limit. If you ask to see Maple's help page for limit (type ?limit in an input region, or type limit in the help browser that can be started via the Help menu).

I agree. The point of your exercise is for you to learn about this, not for you to find someone else who knows how to do the work for you.

I am glad to help, but am not willing to do your work for you.

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

Patrick,

To remove a post, you just "flag" it. The moderators will then remove the post before too long.

I'll let you decide exactly which posts you want to flag. (You can flag this one, too, if you wish.)

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

There is a MaplePrimes FAQ (search for FAQ). But, shouldn't this be easier to find? Possibly a permanent item?

There is an entry about how to ENTER math in a post, but I do not believe this information is still 100% accurate. And, there is nothing about how to extract the Maple code from a maple tag.

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

Thanks Robert.

I agree that it's best to use plain text for Maple code, but it is not too hard to access the code in the Maple tag: in my browser (Firefox) I right-click on the image, choose Properties, and the code is in the "Alternate text" field, and can be copied from there.
the image

I think I remember seeing this, but I did not remember it today. This is very useful. Something that should be in a FAQ for (new) members of MaplePrimes. Is there such a list? I don't see one that is readily available. (It's different from the Quick Reference Guide and Top Ten Errors book entries.)

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed

This remnds me of two of my longstanding requests for improvements in Maple:

1. multivariate limits
2. discrete limits (sequences)

Mathematically, there is only one limit, but we have different techniques and tools depending on the specific domain and range: interval, integers, or multi-dimensional.

This is not an area where I can claim any expertise, so I ask:

1. Is there any work being done in this area?
2. What are thefundamental issues that make this difficult to implement?

In my mind, it appears that if this functionality existed (efficiently) it could be possible to greatly expand Maple's reliability. It might even make it easier to make Maple "smarter" about what it does in a "student" environment.

I look forward to any insights others can provide.

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed