Maple 2018 Questions and Posts

These are Posts and Questions associated with the product, Maple 2018

In attempting to store procedures in a table to create an extensible module, I used the following procedure to test whether a procedure could be queried from the table and executed.

proc() print("Metric is default") end proc;

The result was proc () print("Metric is default") end proc

I have checked the statement with mint in the code editor, but it reports no errors. I get the same result when I use an eval statement around the procedure.  I would be very interested in understanding what is wrong with the procedure as defined.

 


 

I can't figure out why this pattern is failing

restart;
r:= y=3;
patmatch(r,y=z::integer,'la');
patmatch(r,identical(y)=z::integer,'la');
patmatch(r,y::anything=z::anything,'la');

What Am I doing wrong?

 

 

Last week, in the first of a series of three articles, I demonstrated the new color syntax highlighting in the command line (TTY) interface of Maple 2018.1. This week, we'll look at a new facility for manipulating the command line history, the history meta-commands.

For the series of screen shots in this article, assume that the .maple_history file in your home directory initially contains the following:

    p1 := plot(sin,color="DeepPink"):
    p2 := plot(cos,color="DodgerBlue"):
    plots[display](p1,p2);

Now we'll start cmaple and execute a series of commands:

    |\^/|     Maple 2018.1 (X86 64 LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2018
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> y := 1/(x^4+1);
                                     1
                              y := ------
                                    4
                                   x  + 1

> int(y,x);
     1/2           1/2             1/2           1/2
1/4 2    arctan(x 2    + 1) + 1/4 2    arctan(x 2    - 1)

                    2      1/2
            1/2    x  + x 2    + 1
     + 1/8 2    ln(---------------)
                    2      1/2
                   x  - x 2    + 1

> diff(%,x);
          1                       1              1/2
--------------------- + --------------------- + 2
       1/2     2               1/2     2
2 ((x 2    + 1)  + 1)   2 ((x 2    - 1)  + 1)

    /         1/2        2      1/2              1/2 \
    |  2 x + 2         (x  + x 2    + 1) (2 x - 2   )|
    |--------------- - ------------------------------|
    | 2      1/2               2      1/2     2      |
    \x  - x 2    + 1         (x  - x 2    + 1)       /

      2      1/2        /      2      1/2
    (x  - x 2    + 1)  /  (8 (x  + x 2    + 1))
                      /

> simplify(%);
memory used=5.2MB, alloc=41.3MB, time=0.11
                                 4
                                x  + 1
                 -------------------------------------
                   2      1/2     2     1/2    2     2
                 (x  + x 2    + 1)  (x 2    - x  - 1)

> normal(%,expanded);
                                   1
                                 ------
                                  4
                                 x  + 1

There are two parts to the history:

  1. Session history consists of the commands you've entered in the current session.
  2. Command history consists of all commands from previous sessions, together with the session history (up to a maxium specified by interface(historysize), which is 1000 lines by default).

History meta-commands all begin with two exclamation marks at the beginning of the line. The !!= meta-command lists the session history:

> !!=
<< y := 1/(x^4+1);
<< int(y,x);
<< diff(%,x);
<< simplify(%);
<< normal(%,expanded);

Notice that each displayed line of the history is preceeded by << to differentiate it from Maple input and other Maple output. Each meta-command also has a long form. The long form for !!= is !!list:

> !!list
<< y := 1/(x^4+1);
<< int(y,x);
<< diff(%,x);
<< simplify(%);
<< normal(%,expanded);

Most meta-commands can take an argument specifying the amount of history to be affected. For example, a numeric argument refers to the last lines of the command history. Here, !!=8 includes the 3 lines from the previous history, as well as the 5 lines of session history:

> !!=8
<< p1 := plot(sin,color="DeepPink"):
<< p2 := plot(cos,color="DodgerBlue"):
<< plots[display](p1,p2);
<< y := 1/(x^4+1);
<< int(y,x);
<< diff(%,x);
<< simplify(%);
<< normal(%,expanded);

An argument beginning with a forward slash ("/") refers to all history lines beginning with the most recent one that contains the text entered after the slash (if the text to be searched for does not begin with a space or a digit, the slash can be omitted):

> !!=/diff
<< diff(%,x);
<< simplify(%);
<< normal(%,expanded);

We'll quit Maple and start a new session to illustrate another aspect of the history meta-commands.

> quit
memory used=6.4MB, alloc=41.3MB, time=0.14

In the new session, the meta-command !!=/x^4 will list everyting from the previous session starting from the most recent matching line:

    |\^/|     Maple 2018.1 (X86 64 LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2018
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> !!=/x^4
<< y := 1/(x^4+1);
<< int(y,x);
<< diff(%,x);
<< simplify(%);
<< normal(%,expanded);

If a !!= meta-command with a numeric or search argument is executed as the first command in a fresh session, not only is the specified amount of command history listed, but that part of the history is then considered to be session history. Executing just !!= with no argument shows that this is the case:

> !!=
<< y := 1/(x^4+1);
<< int(y,x);
<< diff(%,x);
<< simplify(%);
<< normal(%,expanded);

The !!! meta-command (long form !!play) re-executes the entire session history:

> !!!
>> y := 1/(x^4+1);
                                     1
                              y := ------
                                    4
                                   x  + 1

>> int(y,x);
     1/2           1/2             1/2           1/2
1/4 2    arctan(x 2    + 1) + 1/4 2    arctan(x 2    - 1)

                    2      1/2
            1/2    x  + x 2    + 1
     + 1/8 2    ln(---------------)
                    2      1/2
                   x  - x 2    + 1

>> diff(%,x);
          1                       1              1/2
--------------------- + --------------------- + 2
       1/2     2               1/2     2
2 ((x 2    + 1)  + 1)   2 ((x 2    - 1)  + 1)

    /         1/2        2      1/2              1/2 \
    |  2 x + 2         (x  + x 2    + 1) (2 x - 2   )|
    |--------------- - ------------------------------|
    | 2      1/2               2      1/2     2      |
    \x  - x 2    + 1         (x  - x 2    + 1)       /

      2      1/2        /      2      1/2
    (x  - x 2    + 1)  /  (8 (x  + x 2    + 1))
                      /

>> simplify(%);
memory used=5.2MB, alloc=41.3MB, time=0.10
                                 4
                                x  + 1
                 -------------------------------------
                   2      1/2     2     1/2    2     2
                 (x  + x 2    + 1)  (x 2    - x  - 1)

>> normal(%,expanded);
                                   1
                                 ------
                                  4
                                 x  + 1

Notice that each command is displayed with a >> prompt. This prompt is used whenever a command in the history is being played back.

History commands can be played back one step at a time using the !!. (or !!step) meta-command. Each command is displayed with the >> prompt, and you are given the opportunity to edit it before pressing Enter to execute it. Here, we've changed the exponent of from 4 to 3 before pressing Enter, and then pressed Enter four more times to re-execute the remaining commands:

> !!.
>> y := 1/(x^3+1);
                                     1
                              y := ------
                                    3
                                   x  + 1

>> int(y,x);
                                                                  1/2
                          2                 1/2        (2 x - 1) 3
  1/3 ln(x + 1) - 1/6 ln(x  - x + 1) + 1/3 3    arctan(--------------)
                                                             3

>> diff(%,x);
                1          2 x - 1               2
            --------- - -------------- + ------------------
            3 (x + 1)       2              /         2    \
                        6 (x  - x + 1)     |(2 x - 1)     |
                                         3 |---------- + 1|
                                           \    3         /

>> simplify(%);
                                   1
                          --------------------
                                    2
                          (x + 1) (x  - x + 1)

>> normal(%,expanded);
                                   1
                                 ------
                                  3
                                 x  + 1

When editing a command prefixed with the >> prompt, the command is edited in-place in the history. In other words, the history is permanently modified. History meta-commands are not played back (or infinite loops could result), and lines containing only comments are displayed but not offered for editing.

Still in the same session, let's use !!. with a search pattern to generate and display the plots from the older history, pressing Enter after each command:

> !!./p1 :=
>> p1 := plot(sin,color="DeepPink"):
>> p2 := plot(cos,color="DodgerBlue"):
>> plots[display](p1,p2);

                                                                        
                                    |                                   
 -*\    /*-*                      1-+*     *-*\                     /*- 
   \   //  \\                    // |\\   /   \                     /   
    \  /    \\                   /  | \  //    \                   /    
    \ /      *                  *   |  * *     \\                  /    
     **      ||                 |   |  |*       *                 *     
     *|       |                |    |   *       ||               ||     
     ||       ||               |    |  |*        |               |      
    |||        |              |     |  | |       |               |      
    | ||       |              |     | || |        |             ||      
    |  |       ||            || 0.5 | |  |        |             |       
   |   |        |            |      | |   |       |             |       
   |   ||       |            |      |||   |        |           ||       
   |    |       ||           |      ||    |        |           |        
  |     |        |          |       ||     |       |           |        
  |     ||       |          |       ||     |        |         ||        
  |      |       ||         |       |      |        |         |         
 ||      |        |        |        |       |       |         |         
 |       ||       |        |        |       |       ||       ||         
 +--------+-------++-------+-------++-------+--------+-------+--------+ 
  -6      |  -4    |    -2|       0||        |2      |   4   |      6|| 
          ||       |      |        ||        |       ||     ||       |  
           |       |      |       | |        |        |     |        |  
           |        |    ||       | |        ||       |     |       ||  
           |        |    |        | |         |       ||    |       |   
            |       |    |       || |         |        |   |        |   
            |        |  ||       |  |         ||       |   |        |   
            |        |  |      -0.5 |          |       ||  |       |    
             |       |  |       ||  |          |        | |        |    
             |        |||       |   |          ||       | |       ||    
             ||       ||        |   |           |       |*|       |     
              |       **       |    |           |        *        |     
              |*      |*       |    |            |      **|      *      
               \     /*\\     *     |            *\     / *      /      
               \\    /  \    //     |             \    // \\    /       
                \\  //   \   /      |             \\   /   \\  //       
                 *-*/    \*-*    -1 |              \*-*     *-*/        
                                    |                                   
                                                                        

>> !! y := 1/(x^3+1);
> _

On the last line above, we typed !! followed by a space (long form !!stop) to tell Maple to stop playing back commands and give a fresh prompt. If we now issue !!=, we see that the session history still contains only the five commands it contained originally. The played back commands were not appended to the history:

> !!=
<< y := 1/(x^3+1);
<< int(y,x);
<< diff(%,x);
<< simplify(%);
<< normal(%,expanded);

Issuing a new command at the regular > prompt adds it to the end of the session history:

> cos(Pi) + 1;
                                   2

> !!=
<< y := 1/(x^3+1);
<< int(y,x);
<< diff(%,x);
<< simplify(%);
<< normal(%,expanded);
<< sin(Pi) + 1;

The !!- (or !!drop) meta-command deletes one or more commands from the history:

> !!-
> !!=
<< y := 1/(x^3+1);
<< int(y,x);
<< diff(%,x);
<< simplify(%);
<< normal(%,expanded);
> !!-/simpl
> !!=
<< y := 1/(x^3+1);
<< int(y,x);
<< diff(%,x);

In addition to the meta-commands described above for manipulating the history within a session, there are three meta-commands to copy history to and from files:

  • !!> (or !!save ) writes the session history to the specified file.
  • !!< (or !!read ) replaces the session history with the contents of the specified file.
  • !!+ (or !!append ) appends the contents of the specified file to the session history.

Used together, these meta-commands let you save important sessions for later examination or reuse without relying on the .maple_history file, or let you make large changes to the current session history using your favorite text editor.

The !!? (or !!help) meta-command displays a short summary of all the meta-commands:

> !!?

The sequence "!!" at the beginning of a line introduces a history meta-command.
Each has a short or long form (shown below in parentheses). The long form name
may be used instead of the single character appearing after "!!".

!!=specifier    - list session history or specified lines (list)
!!!specifier    - play back session history or specified lines (play)
!!.specifier    - step through session history or specified lines (step)
!!-specifier    - drop one or specified lines from history (drop)
!!<filename     - read file into session history (read)
!!+filename     - append file to session history (append)
!!>filename     - save session history to file (save)
!!?             - help for history meta-commands (help)
!!              - stop the single-step playback in progress (stop)

The 'specifier' is optional. If present, it can be an integer, N, referring to
the N most recent command lines, or a string beginning with a "/" character,
referring to the lines from the most recent one containing that string. The "/"
may be omitted if the search string does not begin with a space or digit.

Detailed information can be found in the ?edit_history help page.

 

Does Maple have a function which finds the domain of its variables such that the function is real valued?

I am only interested in a function of two variables, x and y.  I'd like to know what is the range of x and y, where f(x,y) is real valued.

For example, given f(x,y)= x * ln(y), then the domain is all of x, and for y>0.    So it is the upper half plane.  For f(x,y)=sin(x)*cos(y), then it is the whole plane (all x and all y) and so on. 

I looked at singular(), and this does part of what I want, but it only gives me the singular points. So for the above it gives y=0 and x=x, but I am looking for something a little more specific. I also looked at package called RealDomain, but I do not see how to use this for what I want to do. But I could have missed something.

I do not know what the function is beforehand, but it will always be a function of x and y, and I need an automated way to determine the range of x and y where this function is real valued. 

I can't do plots and look at them, since this is all automated and has to be done algorithmically only and non-interactive.

I could use singular, and try evaluating the function at different points and see if it produces real or complex values, but this is not practial to do and can fail.

Does Maple have support for such functionality?

 

I am still buffled by a Record in Maple.

I simply want to make one variable be a Record. Then make separate variable, by making a COPY of the content of the first variable, then change the second variable. Sounds easy, right?

When I do this, I find that the changes in the second variable are being made also to the first variable.

I used eval() to make a copy of all field of first variable to the second.  May be this is not the correct way, but do not know how else (other by explicit copying one field one at a time).

I looked at help, and see nothing there. It talks about making the Record packed. I tried that, but it is still not working. Not a single example in help of how to copy the "content" of one record to another.

I simply want to make a new instance of the first variable, a copy. and change the second instance without the first changing at same time. Why is this so hard in Maple?

restart;
c:=Record('a','b'):
c:-a:=0:
c:-b:=-1:

c1:=eval(c): #make a copy of c??
print("c1=",eval(c1)); #yes, made a copy

c1:-b:=99:  #change one field  in the second variable

print("c1=",eval(c1));
print("c=",eval(c)); #why did c change?

I tried using Record[packed]('a' , 'b'): since help says something about same Record sharing same memory but that make no difference.

How to make a copy of a record to another in Maple without them being the same? I know I could do this

restart;
c:=Record('a','b'):
c:-a:=0:
c:-b:=-1:

c1:=Record('a','b'):
c1:-a:=c:-a;
c1:-b:=c:-b;

c1:-b:=99:  #change one field  in the second variable

print("c1=",eval(c1));
print("c=",eval(c)); #Now it did not change.

But my actual record has many fields. and I do not want to do the above each time.

hi 

i cant comute the double integrate with infinity integral of my function and just evaluating

The calculation steps are too time consuming and will not be answered

 

Well I also come to think of it, disagree with calling the double factorial function the double factorial function, i would have thought bi-factorial to be better. or singular parity factorial function. 

 

But my interface (2016)  queries me everytime i enter "n!!" as to whether I am referring to the double factorial function or the application of the factorial twice in iteration, ie :  (n!)!

I just think this was a bad decision to make common place and the notation cabal need to review and change this. 

Hi,

I m trying to work some Maple Formulas in the Excel 2016 environnement, but i m always getting Error Mesages ( See attachments)

Thanks

I need to move a term in the denominator, inside the radical sign in the numerator.  After some struggle, I can do it for a simple expression. But once the expression gets little more complicate, the method does not work.

Given expr:=sqrt(x*y)/x;  I want to force the "x" in the denominator inside the sqrt so I can simplify things. I can do this like this

restart;
expr1  := sqrt(x*y)/x;
expr1  := simplify(expr1,symbolic);
combine(expr1,symbolic);
algsubs(y/x=u,%);

But for the following similar expression, it does not work. Given expr:=sqrt(x^2+y^2)/x, I want to change to sqrt( (x^2+y^2)/x^2) or sqrt(1+ y^2/x^2) or sqrt(1 + u^2).  So the first step is as above, to force the x in denomiantor to go inside the radical. But the same steps do not work on this now

expr1:=sqrt(x^2+y^2)/x;
expr1:=simplify(expr1,symbolic);
combine(expr1,symbolic);

 

I tried radsimp(expr1); simplify(expr1,radical,symbolic); radnormal, I tried adding assuming positive everywhere. Nothing is working.

I am trying to convert an expression to be   (y/x) and then replace (y/x) to u.  BUt the first step is to get the x inside the radical and I am not sure how to do it for the second example and why it is failing. It is always hard for me in Maple to figure the right method to manipulate an expression.

Any suggestions?

I need to know if an expression contain a radical in it. For example, expr:=1/x*sqrt(x*y)  or expr:=3*(x*y)^(2/3)+5; or expr := sqrt(5), etc.. all these will return true, but for expr:=3+sin(x) it will return false.

I need to find if the expression has radical, becuase then I want to do special simplify if that is the case.

I do not want to use pattern matching, since the expression can be complicated, and thought to ask if there might be a simpler way, one of those hidden Maple commands which can do it.

I looked at  "has", "hasfun". with(PolynomialIdeals) has function IsRadical but it is only for polynomials.

Is there a way other than using patmatch?  

is possible to solve these partial differential equations in maple via pdsolve?

Thanks

In an unrelated thread, I provided the OP with some 1-D code, which contained the Array definition

TC:= Array(0...1001, fill=0)

Note the existence of three '.' characters in the range specification. This was a typo on my part, or my '.' key bounced, or something. The code containing the above definition "worked" with no problem, which, presumably, was why I didn't notice.

The Maple help does state (my emphasis)

Note that more than two dots in succession are also parsed as the range (..) operator.

although I wasn't making use of this fact - I just screwed up when typing the original.

The OP preferred to use 2-D input, and used cut-and-paste to transfer the above code, resulting in 2-D input, which is where the fun started. It seems(?) that when using 2-D input, more than two dots in succession is only interpreted as a straightforward range, if the total number of dots is even.

If the total number of dots is odd, then it appears(?) as if the 'final' dot is associated with the second number in the range as a 'decimal point', (so producing .1001 in the above example). This is then 'coerced/rounded' to an integer - ie it becomes '0', and the above Array definition is interpreted as

TC:= Array(0..0, fill=0)

Consequences in the following code are left to your imagination

Worth an SCR?

 

 

 

Can anyone  produce these diagram?  Please Read the theory in:

   https://en.wikipedia.org/wiki/Logistic_map.

Wikipedia pages that explain bifurcation diagrams and attractors in more elementary contexts.

See the bifurcation diagram in the picture

   https://en.wikipedia.org/wiki/Logistic_map#/media/File:Logistic_Bifurcation_map_High_Resolution.png

 

For some reason, Maple now hangs on the following Schrodinger PDE with initial and boundary conditions.

In Physics version 60, it works OK. No solution is returned, but it does not hang.

But when I updated to latest version of Physics, it hangs. I am not sure which version makes it hangs, I just know Maple does not hang in version 60. So the problem could have happend in any version after 60. I have not attempted to try them all to find out.

PackageTools:-Install("5137472255164416", version = 60, overwrite);
restart;
PackageTools:-IsPackageInstalled("Physics Updates");

              60


x:='x'; t:='t'; y:='y'; hbar:='hbar';f:='f';
pde:=  I* diff(f(x,y,t),t) = -hBar^2/(2*m) * (diff(f(x,y,t),x$2) +  diff(f(x,y,t),y$2)):
ic := f(x, y, 0) = sqrt(2)*(sin(2*Pi*x)*sin(Pi*y) + sin(Pi*x)*sin(3*Pi*y)):
bc := f(0, y, t) = 0,f(1, y, t) = 0, f(x, 1, t) = 0, f(x, 0, t) = 0:
sol:=pdsolve({pde,ic,bc},f(x,y,t));

            ()   #after only few seconds. No hang. good

 

Now in latest version of Physics

PackageTools:-Install("5137472255164416",  overwrite);
restart;
PackageTools:-IsPackageInstalled("Physics Updates");

                                  "74"

pde:=  I* diff(f(x,y,t),t) = -hBar^2/(2*m) * (diff(f(x,y,t),x$2) +  diff(f(x,y,t),y$2)):
ic := f(x, y, 0) = sqrt(2)*(sin(2*Pi*x)*sin(Pi*y) + sin(Pi*x)*sin(3*Pi*y)):
bc := f(0, y, t) = 0,f(1, y, t) = 0, f(x, 1, t) = 0, f(x, 0, t) = 0:
sol:=pdsolve({pde,ic,bc},f(x,y,t));

#after waiting for long time, had to terminate it
Warning,  computation interrupted

 

Why does Maple hangs on this PDE now and it did not before?

Using Maple 2018.1 on Linux

 

The Maple command line interface (cmaple), often referred to as the "TTY interface" for its original use on Teletype terminals, is still the tool of choice for many Maple developers and power users. Maple 2018.1 introduces several new capabilities to this long-lived interface:

This post, the first in a series of three, will address color syntax highlighting. We'll start with a very short sample session:

    |\^/|     Maple 2018.1 (X86 64 LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2018
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> piecewise(4 < x^2 and x < 8, f(x));
                            {                  2
                            { f(x)        4 < x  and x < 8
                            {
                            {  0             otherwise

> p := unapply(%,x);
                                               2
                      p := x -> piecewise(4 < x  and x < 8, f(x))

> 1/p(1);
Error, numeric exception: division by zero
> quit
memory used=5.3MB, alloc=41.3MB, time=0.07

In the above example, you can see that general keywords are in bold blue, variables in italics (not supported by all terminals), error messages in bold red, control flow interrupting keywords in bold magenta, and memory usage messages in normal blue.

Color syntax highlighting is turned on by default in cmaple for Linux and OS/X if the terminal you are using (as specified by the TERM environment variable) is known to support it. It is currently turned off by default under Windows. It can be explicitly turned on or off for 2D and message output using interface(ansi=) where is true or false (under Windows, you can put interface(ansi=true) in your maple.ini file to automatically turn it on). Likewise, interface(ansilprint=) controls highlighting for 1D output (such as that produced by lprint), and interface(ansiedit=) for input.

Not all terminals support all possible highlighting modes. The following two commands show what colors your terminal can display, and how they are used by Maple's syntax highlighting:

> interface(showtermcolors):

ANSI X3.64 Standard Attributes

Normal  Bold  Italic  Underlined  Reverse  

System Colors (0-15) Using ANSI Escape Sequences

Color00  Color01  Color02  Color03  Color04  Color05  Color06  Color07  
Color08  Color09  Color10  Color11  Color12  Color13  Color14  Color15  

System Colors (0-15) Using Extended Escape Sequences

  0    0    1    1    2    2    3    3    4    4    5    5    6    6    7    7  
  8    8    9    9   10   10   11   11   12   12   13   13   14   14   15   15  

Extended 6x6x6 Color Cube (16-231)

 16   16   17   17   18   18   19   19   20   20   21   21  
 22   22   23   23   24   24   25   25   26   26   27   27  
 28   28   29   29   30   30   31   31   32   32   33   33  
 34   34   35   35   36   36   37   37   38   38   39   39  
 40   40   41   41   42   42   43   43   44   44   45   45  
 46   46   47   47   48   48   49   49   50   50   51   51  

 52   52   53   53   54   54   55   55   56   56   57   57  
 58   58   59   59   60   60   61   61   62   62   63   63  
 64   64   65   65   66   66   67   67   68   68   69   69  
 70   70   71   71   72   72   73   73   74   74   75   75  
 76   76   77   77   78   78   79   79   80   80   81   81  
 82   82   83   83   84   84   85   85   86   86   87   87  

 88   88   89   89   90   90   91   91   92   92   93   93  
 94   94   95   95   96   96   97   97   98   98   99   99  
100  100  101  101  102  102  103  103  104  104  105  105  
106  106  107  107  108  108  109  109  110  110  111  111  
112  112  113  113  114  114  115  115  116  116  117  117  
118  118  119  119  120  120  121  121  122  122  123  123  

124  124  125  125  126  126  127  127  128  128  129  129  
130  130  131  131  132  132  133  133  134  134  135  135  
136  136  137  137  138  138  139  139  140  140  141  141  
142  142  143  143  144  144  145  145  146  146  147  147  
148  148  149  149  150  150  151  151  152  152  153  153  
154  154  155  155  156  156  157  157  158  158  159  159  

160  160  161  161  162  162  163  163  164  164  165  165  
166  166  167  167  168  168  169  169  170  170  171  171  
172  172  173  173  174  174  175  175  176  176  177  177  
178  178  179  179  180  180  181  181  182  182  183  183  
184  184  185  185  186  186  187  187  188  188  189  189  
190  190  191  191  192  192  193  193  194  194  195  195  

196  196  197  197  198  198  199  199  200  200  201  201  
202  202  203  203  204  204  205  205  206  206  207  207  
208  208  209  209  210  210  211  211  212  212  213  213  
214  214  215  215  216  216  217  217  218  218  219  219  
220  220  221  221  222  222  223  223  224  224  225  225  
226  226  227  227  228  228  229  229  230  230  231  231  

Extended 24-Level Grayscale (232-255)

232  232  233  233  234  234  235  235  236  236  237  237  238  238  239  239  
240  240  241  241  242  242  243  243  244  244  245  245  246  246  247  247  
248  248  249  249  250  250  251  251  252  252  253  253  254  254  255  255  

If your terminal does not support 256 color mode, then many of the colored blocks shown above will appear differently or not at all.

> interface(showcolors):

 1 Normal output:           evalf(1/2) = 0.5
 2 Italics (variables):     x, y, z
 3 Symbol text (not used):  symbol
 4 Bold (fallback):         Begin, be bold, and venture to be wise.
 5 Underlined (fallback):   Morality, like art, means drawing a line someplace.
 6 Reversed (not used):      The reverse side also has a reverse side. 
 7 Input prompts:           >  DBG>
 8 User input:              1/(x^4+1);
 9 Userinfo output:         message, x, y
10 Trace output:            {--> enter f, args = x, y
11 Warning messages:        Warning, x is implicitly declared local
12 Error messages:          Error, (in f) invalid subscript selector
13 Debugger output:         No breakpoints set
14 General Maple keywords:  for  from  to  while  do  until
15 Declaration keywords:    local  option  description
16 Flow interruptions:      break  return
17 Exception keywords:      error  try  catch
18 Subexpression labels:    %1  %2
19 Special & quoted names:  thisproc  `diff/sin`
20 String literals:         "Hello, world!"
21 Maple startup message:   Maple 2019
22 Output from printf:      x=1.234 y=5.678
23 Status messages:         memory used=1.7MB, alloc=8.3MB, time=0.03
24 System command output:   1466  4739  43140  myprog.mpl
25 Maple comments:          # Comments are free but facts are sacred.

The colors used for the different categories of output as listed by the command above are user selectable. The default is to use only the sixteen ANSI X3.64 standard colors (or Windows command prompt standard colors). These may appear differently than shown here depending on the color palette of your terminal window.

The color settings can be queried or set as follows:

> currentColors := interface(ansicolor);
currentColors := [-1, -1, -1, -1, -1, -1, 2, -1, 2, 3, 11, 9, 6, 12, 10, 13, 9, 14, 6,

    5, 2, 136, 4, 134, 3]

# Individual colours, as numbered in the output of interface(showcolors), can
# be changed. Let's make keywords bright yellow:
> myColors := subsop(14=226,currentColors);
myColors := [-1, -1, -1, -1, -1, -1, 2, -1, 2, 3, 11, 9, 6, 226, 10, 13, 9, 14, 6, 5,

    2, 136, 4, 134, 3]

> interface(ansicolor=myColors);
[-1, -1, -1, -1, -1, -1, 2, -1, 2, 3, 11, 9, 6, 12, 10, 13, 9, 14, 6, 5, 2, 136, 4,

    134, 3]

> piecewise(4 < x^2 and x < 8, f(x));
                            {                  2
                            { f(x)        4 < x  and x < 8
                            {
                            {  0             otherwise

There are several predefined color schemes that can be selected using interface(ansicolor=), where is an integer from 0 to 6. Scheme 0, the default, should work on any terminal. Of the remaining schemes, the odd numbered ones are designed to look good on light backgrounds, and the even numbered ones on dark backgrounds.

There is also a new character plot driver, selectable using interface(plotdevice=colorchar), which supports character plotting in color. Colors are mapped to the nearest color supported by the terminal:

> interface(plotdevice=colorchar):
> p1 := plot(sin(x),x=-Pi..Pi,thickness=1,color="DeepPink"):
> p2 := plot(sin(x)+sin(3*x)/3,x=-Pi..Pi,thickness=2,color="LawnGreen"):
> p3 := plot(sin(x)+sin(5*x)/5,x=-Pi..Pi,thickness=3,color="DodgerBlue"):
> plots[display](p1,p2,p3);

                                                                                       
                                           |                                           
                                           |                  @@@@@                    
                                           |                 @@   @@                   
                                           |                 @     @                   
                                         1 |                *.......*                  
                                           |       *******.*@       @*..******         
                                           |      **    .**@         @**.    **        
                                           |     **   ..  ***       ***  ..   **       
                                           |    **   ..  @@ **** **** @@  ..   **      
                                           |    *   ..  @@     ***     @@  ..   *      
                                           |   *@@@**@@@                 @@@**@@@*     
                                       0.5 |  **@ ..                         .. @**    
                                           |  *@ ..                           .. @*    
                                           | ** .                               . **   
                                           | * .                                 . *   
                                           |**..                                 ..**  
                                           |*..                                   ..*  
                                           |*.                                     .*  
                                           *.                                       .* 
 **---------------------------------------**-----------------------------------------* 
  -3           -2            -1          0*|            1             2            3   
  *..                                   ..*|                                           
  **..                                 ..**|                                           
   * .                                 . * |                                           
   ** ..                              . ** |                                           
    *@ ..                           .. @*  |                                           
    **@ ..                         .. -0.5 |                                           
     *@@@**@@@                 @@@**@@@*   |                                           
      *   ..  @@     ***     @@  ..   *    |                                           
      **   ..  @@ **** **** @@  ..   **    |                                           
       **   ..  @**       **@  ..   **     |                                           
        **    .**@         @**.    **      |                                           
         *******.*@       @*.*******       |                                           
                  *.......*             -1 |                                           
                   @     @                 |                                           
                   @@   @@                 |                                           
                    @@@@@                  |                                           
                                           |                                           
                                                                                       

> plot3d([1,x,y],x=0..2*Pi,y=0..2*Pi,coords=toroidal(10));

                                                                                       
                                  -------------------                                  
                             --------\\\-|-|-|-///--------                             
                          ---------\\\-\-|-|-|-/-///---------                          
                        ----------\\\-\-||-|-||-/-///----------                        
                      /-/-/-/-----\\\\\-|||||-|-/////------------                      
                     -//-/-/-/---\-\\-\||-|||-||/-//-/---\-\-\-\--                     
                   --//-|||-/-/--\\\\\\|||||||-|//////--\-\-|||\|\-\                   
                  /---||-||||-|--\\-\\\|||||||||///-//--|-||||--|---\                  
                 /--|--\-\-\-\\--\\/\\|||||||||||//-//-|-///-/-/--|--\                 
                //-//--\\-\-----\-\\\\|||||||||||////-///////-//--\\-\\                
                |//\/\------------\\\|||||||||||||////-------//--/\\\\|                
               /// / / -- /--- -----\|||||||||||||/---------\ --/\ \\\\\               
               //\/ /-//-/-//-//-/--/-/--/-|-\--\-\--\-\\-\\-\-\\/\ \/\\               
               ///\/ /--/ //-// /--/--/-|--|--|-\--\--\ \\-\\ \--\ \/\\\               
               /||/-// /--/  /--/-//-|  |  |  |  |-\\-\--\  \\-\ \\/\||\               
               || |-/ /  /--/  /  | -|--|--|--|--|- |  \ -\--\  \ \/| |||              
              |||| | -/ /  ||--/-||- |  |  |  |  | -||--\  | \\-\- | |/|               
               |||-| | -/--|  |  |  -|--|--|--|---|  |  |  |--\  | |/|||               
               |\| |-|  | ||--|- |  |   |  |  |   |  | -|--|| |  |-- |/|               
               |\||  |-|  |  |  -|--|---|--|---|--|--|-  |  |  |-|  ||/|               
               \|-| |  |--|- |   |  |  |   |   |  |  |   | -|--| |  |/|/               
                \||-|- |  |--|--|-  |  |   |   |  |  -|--|--|  | -|-||/                
                \|-|||-|- |  |  | --|--|---|---|--|-- |  |  |  |-|||/|/                
                 \\|-| |--|--|  |   |  |   |   |  |   |  |--|--| |-|//                 
                  \\ |-|  |  |--|---|  |   |   |  |---|--|  |  |-| //                  
                   -\| |--|  |  |   |--|---|---|--|   |  |  |--| |//                   
                     \|-| |--|--|   |  |   |   |  |   |--|--| |-|/                     
                      \\|\|| |  |---|--|---|---|--|---|  | ||-|//                      
                        -\----|--|  |  |   |   |  |  |--|----/-                        
                          --\-\\ |--|--||--|---|--|--|  /-/--                          
                             ----\\-||--|--|--|---|--///--                             
                                  \--\--|--|--|--/--/                                  
                                                                                       

For more details, please refer to the help page, ?ansicolor.

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