Maple Questions and Posts

Double integration and summation. How to speed up?...

Asked by: Vortex 65

July 04 2018

3 3

Hello.

Regarding to my previous question I'd like to speed up calculations of the expression.

restart;
tt := -0.689609e-3; T_c := .242731; mu := .365908; k := 1;
R1 := a*tanh((a^2-mu)/(2*T_c))*ln((2*a^2+2*a*q+q^2-2*mu-(I*2)*Pi*N)/(2*a^2-2*a*q+q^2-2*mu-(I*2)*Pi*N))/q-2;
R2 := Int(R1, a = 0 .. 10000);
R3 := q*ln((-q^2-k^2+mu+I*(2*N*Pi*T_c-(2*m+1)*Pi*T_c)+k*q)/(-q^2-k^2+mu+I*(2*N*Pi*T_c-(2*m+1)*Pi*T_c)-k*q))/(k*(tt+R2));
R4 := Sum(R3, N = -100 .. 100);
m := 1;
R5 := Int(R4, q = 0.1e-2 .. 10000);
R6 := evalf(R5);

Here I have integration procedure inside the expression R3, then the summation over the integer parameter N and then finally the integration again.

Is it possible to speed up calculations of this cumbersome expression? Or actually was I correct to write this simple code?

Thank you in a advance.

how we can substitute the c1, c2,c3,c4,c5 in expre...

Asked by: hitecwaseem 15

July 04 2018

0 1

K := simplify(C, 'size');
5 4
lambda + (-a__11 - a__33 - a__44 - a__55 - a__22) lambda +

((a__44 + a__33 + a__22 + a__11) a__55

+ a__44 (a__33 + a__22 + a__11) + (a__33 + a__22) a__11

3
+ a__33 a__22 - a__32 a__23) lambda + (((-a__33 - a__22

- a__11) a__44 + (-a__33 - a__22) a__11 - a__33 a__22

+ a__32 a__23) a__55

+ ((-a__33 - a__22) a__11 - a__33 a__22 + a__32 a__23) a__44

+ (-a__22 a__33 + a__23 a__32) a__11

2
- a__32 (a__13 a__21 + a__24 a__43)) lambda + ((((a__33

+ a__22) a__11 + a__33 a__22 - a__32 a__23) a__44

+ (a__22 a__33 - a__23 a__32) a__11

+ a__32 (a__13 a__21 + a__24 a__43)) a__55

+ ((a__22 a__33 - a__23 a__32) a__11 + a__13 a__21 a__32) a__44

+ a__32 (a__11 a__43 a__24 - a__21 (a__14 a__43 + a__15 a__53)

)) lambda + (((-a__22 a__33 + a__23 a__32) a__11

- a__13 a__21 a__32) a__44

- a__43 a__32 (a__11 a__24 - a__14 a__21)) a__55

- a__15 a__21 a__32 (a__43 a__54 - a__44 a__53)

u := [coeffs(K, [lambda], 'l')];
[(((-a__22 a__33 + a__23 a__32) a__11 - a__13 a__21 a__32) a__44

- a__43 a__32 (a__11 a__24 - a__14 a__21)) a__55

- a__15 a__21 a__32 (a__43 a__54 - a__44 a__53), 1,

-a__11 - a__33 - a__44 - a__55 - a__22, (a__44 + a__33 + a__22

+ a__11) a__55 + a__44 (a__33 + a__22 + a__11)

+ (a__33 + a__22) a__11 + a__33 a__22 - a__32 a__23, ((-a__33

- a__22 - a__11) a__44 + (-a__33 - a__22) a__11 - a__33 a__22

+ a__32 a__23) a__55

+ ((-a__33 - a__22) a__11 - a__33 a__22 + a__32 a__23) a__44

+ (-a__22 a__33 + a__23 a__32) a__11

- a__32 (a__13 a__21 + a__24 a__43), (((a__33 + a__22) a__11

+ a__33 a__22 - a__32 a__23) a__44

+ (a__22 a__33 - a__23 a__32) a__11

+ a__32 (a__13 a__21 + a__24 a__43)) a__55

+ ((a__22 a__33 - a__23 a__32) a__11 + a__13 a__21 a__32) a__44

+ a__32 (a__11 a__43 a__24 - a__21 (a__14 a__43 + a__15 a__53)

)]
u[1] = C__5;
(((-a__22 a__33 + a__23 a__32) a__11 - a__13 a__21 a__32) a__44

- a__43 a__32 (a__11 a__24 - a__14 a__21)) a__55

- a__15 a__21 a__32 (a__43 a__54 - a__44 a__53) = C__5
C__1 = u[3];
C__1 = -a__11 - a__33 - a__44 - a__55 - a__22
C__2 = u[4];
C__2 = (a__44 + a__33 + a__22 + a__11) a__55

+ a__44 (a__33 + a__22 + a__11) + (a__33 + a__22) a__11

+ a__33 a__22 - a__32 a__23
C__3 = u[5];
C__3 = ((-a__33 - a__22 - a__11) a__44 + (-a__33 - a__22) a__11

- a__33 a__22 + a__32 a__23) a__55

+ ((-a__33 - a__22) a__11 - a__33 a__22 + a__32 a__23) a__44

+ (-a__22 a__33 + a__23 a__32) a__11

- a__32 (a__13 a__21 + a__24 a__43)
C__4 = u[6];
C__4 = (((a__33 + a__22) a__11 + a__33 a__22 - a__32 a__23) a__44

+ (a__22 a__33 - a__23 a__32) a__11

+ a__32 (a__13 a__21 + a__24 a__43)) a__55

+ ((a__22 a__33 - a__23 a__32) a__11 + a__13 a__21 a__32) a__44

+ a__32 (a__11 a__43 a__24 - a__21 (a__14 a__43 + a__15 a__53)

)

Latest Physics update makes a pdsolve hangs on one...

Asked by: nm 11378

July 03 2018

3 3

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, Now in Color

by: stefanv 357 Product: Maple 2018

July 03 2018

12 9

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:

Color syntax highlighting on input and output
Extended command history manipulation
Image display support on text terminals

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.

From Mathematica's "Conditioned" to Maple's .......

Asked by: BigBugBuzz 20

July 03 2018

3 21

I am attempting to make the transition from Mathematica to Maple. I that regard, I would like to know how I would implement something like Mathematica's "Conditioned" in Maple. For example, how would I implement the example given in the diagram shown below involving the Poisson Distribution?

How do we solve a diffusion equation with an integ...

Asked by: ibndirac 5

July 03 2018

1 8

I am trying to solve a diffusion equation with a potential term that has an integral in it. The equation has the following form:

PDE := diff(g(x, t), t) = diff((beta(x, t)+diff(g(x, t), x)), x),

with the function beta:

beta := proc (x, t) options operator, arrow; int(exp(-abs(x-y))*g(y, t), y = -infinity .. +infinity) end proc

The boundary conditions for the function g(x,t) are simply assumed to be a zero-centered Gaussian in space (i.e. in x). So it is unity for x=0 and zero for the outer boundary that we can set as x=L.

The problem is easily solved if the function beta is not an integral, but in the current form I get the following error:
*******
Error, (in pdsolve/numeric/process_PDEs) inconsistent dependencies in PDEs: g(x, t) v.s. g(y, t)

*******

So it does not like the dummy variable in the function g.

I can not write an additional PDE for beta because my Kernel is an exponential so the integral never goes away. Anyone with a way to solve this?

ADDENDUM: I have now copied the scriptPDE_DIFFUSION_INTEGRAL.mw

>

L := 20; betaz := proc (x, t) options operator, arrow; int(exp(-abs(x-y))*g(y, t), y = 0 .. L) end proc

proc (x, t) options operator, arrow; int(exp(-abs(x-y))*g(y, t), y = 0 .. L) end proc

(1)

>

diff(g(x, t), t) = -(int(-abs(1, x-y)*exp(-abs(x-y))*g(y, t), y = 0 .. 20))+diff(diff(g(x, t), x), x)

(2)

>	$v__t := 1; v__d := 0; IBC := {g(0, t) = exp(-(0.-v__d)^2/v__t), g(L, t) = 0*exp(-(L-v__d)^2/v__t), g(x, 0) = exp(-(x-v__d)^2/v__t)}$

${g(0, t) = 1., g(20, t) = 0, g(x, 0) = exp(-x^2)}$

(3)

>

Error, (in pdsolve/numeric/process_PDEs) inconsistent dependencies in PDEs: g(x, t) v.s. g(y, t)

>

Download PDE_DIFFUSION_INTEGRAL.mw

below.

Behaviour of forget: Maple 2015 vs Maple 2018...

Asked by: sand15 882

July 03 2018

0 2

Hi everybody,

Maybe it's more a warning than a true question ?

I have written a rather heavy-duty code in Maple 2015. A few years ago I faced strong problems of increases in memory. After some investigations I found there came from a procedure P in which a loop realizes a few tenth of calls to fsolve.
This same procedure P was itself called a large number of times.

To try to fix them I inserted a forget(fsolve, initialize=true) command after the fsolve command.
At the end this didn't prove to be very efficient and I decided to rewrite some part of the code in a more efficient way. Basically the procedure P is now called only a few times but its inner loop is executed about 200 hundred times.
This new version of the code no longer presents memory size problems, while being more efficient from a computational time point of view.

Today procedure P still contains the forget(fsolve, initialize=true) command (I had forgotten to remove it)

Now I keep developping this same code under Maple 2018.
The Maple 2015 and Maple 2018 versions both return the same results, but the procedure P runs in about 20 times the time it runs in Maple 2015 (40 seconds instead of 2)
This comes from the 200 forget(fsolve, initialize=true) calls which consumme about 38 seconds.

With Maple 2015 these same 200 calls to forget(fsolve, initialize=true) only consumme 0.5 second:

As a cure I remove the forget(fsolve, initialize=true) command, plain and simple.

But maybe this misadventure could reveal an unseen behaviour of Maple 2018 ?

Calculating dimensionality of a solution space usi...

Asked by: Annonymouse 160

July 03 2018

0 8

Hi

I'm using solve,and i want to quantify the dimensions of the solution spaces of the output. For example

solve([a+b, c+b])

produces a singular 1 dimensional object

solve([a+b, -b^2+d^2])

produces 2 objects with dimension 2

EDIT:
my intuition is that the simplest way of doing this is to create a counter for equations of the form
variable=variable
and to run it on each of the lists that solve might produce- so far this kind of thing is beyond me

Maple's solution does not reflect its plot...

Asked by: BigBugBuzz 20

July 03 2018

1 6

I am trying to solve an equation with respect to the variable w. However, although there seems to be a solution (see plot indicating a root), Maple produces the wron solution (0, when P = 1/2 and d = 1/10):

>

equations := S-P*S*((ln(-2*d*w+P+d)-ln(P-d))*(P-d)/(-1+w)+(P+d)*(ln(-P-d)-ln(d*(2*w-1)-P))/w)/(2*d^2) = 0

S-(1/2)*P*S*((ln(-2*d*w+P+d)-ln(P-d))*(P-d)/(-1+w)+(P+d)*(ln(-P-d)-ln(d*(2*w-1)-P))/w)/d^2 = 0

(1)

>

(2)

>

(1/2)*(P+d-exp(RootOf(-P^2*exp(_Z)*ln(1/(P+d))-P*d*exp(_Z)*ln(1/(P+d))+P^3*ln(1/(P+d))-P*d^2*ln(1/(P+d))-ln(P-d)*P^2*exp(_Z)+ln(P-d)*P*d*exp(_Z)-2*P*d*exp(_Z)*_Z+ln(P-d)*P^3-ln(P-d)*P*d^2+d*(exp(_Z))^2-2*P*d*exp(_Z)+P^2*d-d^3)))/d

(3)

>

${3-5*exp(RootOf(-25*(exp(_Z))^2+75*exp(_Z)*ln(5/3)+50*ln(2/5)*exp(_Z)+25*exp(_Z)*_Z+25*exp(_Z)-30*ln(5/3)-30*ln(2/5)-6))}$

(4)

>

(5)

>	$plot(eval(S(-P(-2dw+P+d)ln(-2dw+P+d)+Pw(P-d)ln(P-d)-(-1+w)(P(P+d)ln(P+d)-2d^2w))/(2d^2(-1+w)w), {P = 1/2, S = 1, d = 1/10}), w = 0 .. 1)$

>

Download MaplePrimes_03072018.mw

an error in pdsolve after upgrading to 2018.1...

Asked by: nm 11378

July 03 2018

3 5

This pde used to be solved in 2018 as far as I know. Now it gives a strange new error

restart;
interface(showassumed=0);
pde :=  diff(u(x,t),t)+k*diff(u(x,t),x$2)+sin(2*Pi*x/L);
ic  :=  u(x,0)=f(x);
bc  :=  D[1](u)(0,t)=0, D[1](u)(L,t)=0;
sol :=  pdsolve({pde,ic,bc},u(x,t)) assuming L>0,t>0,k>0;

Error, (in assuming) when calling 'dsolve'. Received: 'found differentiated functions with same name but depending on different arguments in the given DE system: {F0_0(L), F0_0(x)}'

I am using Physics:-Version(); MapleCloud version: 72

Do others get this erorr? Why does it show up now when it worked OK before?

update

Iam running on Linux. Here is screen shot

Find the minimum of a function of two variables...

Asked by: jnjn0291 25

July 02 2018

2 6

Hello, can someone help me please?

I have to find the minimum (x,y) over the domain [0;2Pi] of the following function

f(x,y):=1+8 cos(1/2 x-1/2 y) cos(1/2 x) cos(1/2 y) which i plotted to have an idea where its minimum is located.

plot3d(f(x,y),x=0..2Pi,y=0..2Pi)

I tried to use the command ' minimize(f(x,y)) '

Thank you in advance,

best regards.

Ps: the function normaly attains its minimum at (2Pi/3,-2Pi/3) and (-2Pi/3,2Pi/3).

Need roots of cubic equation...

Asked by: Muhammad Usman 245

July 02 2018

0 1

Hello dear users!

Hope you would be fine. I want to fine the roots of the following cubic equation

u^3+u*d[1]+d[0];

when the discriment is zero, positive and negative. I am waiting your positive response. Thanks

@acer @Carl Love @Kitonum @Preben Alsholm

Integration in a region?...

Asked by: Mariusz Iwaniuk 1586

July 02 2018

0 2

I want to calculate and reproduce this question in Maple.

with(Optimization):

f := (x, y) -> op(1, NLPSolve(sin(a*x*y), a = 1 .. 5));

int(`if`(f(x, y) > 0, 1, 0), [x = 0 .. 1, y = 0 .. 1], numeric);

# 0

,but I FAIL.

It should give me: 0.922105

Thanks.

How do I construct a 3-D plot using imported data ...

Asked by: Teep 200

July 02 2018

0 4

I have three columns of data (real numbers) in Excel that have about one thousand rows and I wish to plot their relationships in Maple. The source data simply comprises three columns of numbers and so, are not ordered in triples, [x,y,z]. Does anyone know of a simple routine available that allows me to import the raw data and output a 3-D wire / solid plot in Maple?

Thank you!

Collect as dot product...

Asked by: MarcoFerro 25

July 02 2018

1 2

I have an explicit mathematical expresssion in the form

m = f[1](x,y)*A + f[2](x,y)*B + f[3](x,y)*C

I wonder if it is possible to use the collect function on the vector z = [A,B,C]^T and write the resulting expression as the dot product

m = f^T.z

Basically, I am interested in obtaining the vector f = [f[1](x,y),f[2](x,y),f[3](x,y)] ^T as a Maple variable in closed-form.

Thank you in advance for your help.

Marco

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