Featured Post

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.

Featured Post

11110

Recently I looked through an interesting book D. Wells "The Penquin book of Curious and Interesting Geometry" and came across this result, which I did not know about before: starting with a given quadrilateral , construct a square on each side. Van Aubel's theorem states that the two line segments between the centers of opposite squares are of equal lengths and are at right angles to one another. See the picture below:

                                  

It is interesting that this is true not only for a convex quadrilateral, but for arbitrary one and even self-intersecting one. This post is devoted to proving this result in Maple. The proof was very short and simple. Note that the coordinates of points are given not by lists, but by vectors. This is convenient when using  LinearAlgebra:-DotProduct  and  LinearAlgebra:-Norm  commands.

The code of the proof (the notation of the points on the picture coincide with their names in the code):

restart;
with(LinearAlgebra):
assign(seq(P||i=<x[i],y[i]>, i=1..4)):
P||5:=P||1:
assign(seq(Q||i=(P||i+P||(i+1))/2+<0,1; -1,0>.(P||(i+1)-P||i)/2, i=1..4)):
expand(DotProduct((Q||3-Q||1),(Q||4-Q||2), conjugate=false));
is(Norm(Q||3-Q||1, 2)=Norm(Q||4-Q||2, 2));

The output:

                                                      0
                                                    true

 

VA.mw



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