Maybe there's a problem displaying the output. I haven't looked hard at it. This "3rd party" package seems to have problems. Maybe you could contact the author.

acer

Maybe there's a problem displaying the output. I haven't looked hard at it. This "3rd party" package seems to have problems. Maybe you could contact the author.

acer

Are you sure that you regenerated the package, and also that there is no original problematic version in some .mla archive in your libname? You may be picking up an original saved version.

ps. It now appears that with(plots) might do better than with(plots,display). Before the module definition. After the restart. Or rewrite the whole package with uses.

acer

Are you sure that you regenerated the package, and also that there is no original problematic version in some .mla archive in your libname? You may be picking up an original saved version.

ps. It now appears that with(plots) might do better than with(plots,display). Before the module definition. After the restart. Or rewrite the whole package with uses.

acer

The intpakX package's export init does with(plots). That really shouldn't ever be done inside a procedure. I believe that it all worked in M9.5.1 because at that time the plots package was table-based rather than module-based.

Issuing with inside a proc was never guaranteed to work properly, as far as I know. If that's true, then it's not clear that this is a regression bug. (One should not rely on undocumented features...)

Now that the plots package is a module itself in modern Maple, the intpakX code should be rewritten to either use plots:-diplay explicitly, or to use use or uses.

There may well be other plots routines used by intpakX. If that's the case, then issuing only  with(plots,display) done up front, before the module definition, won't fix all those other routine calls. One could instead issue a quick and dirty with(plots) outside and before the module definition, or one could do it properly as outlined above (use, uses, or explicit plots's export calls).

acer

The intpakX package's export init does with(plots). That really shouldn't ever be done inside a procedure. I believe that it all worked in M9.5.1 because at that time the plots package was table-based rather than module-based.

Issuing with inside a proc was never guaranteed to work properly, as far as I know. If that's true, then it's not clear that this is a regression bug. (One should not rely on undocumented features...)

Now that the plots package is a module itself in modern Maple, the intpakX code should be rewritten to either use plots:-diplay explicitly, or to use use or uses.

There may well be other plots routines used by intpakX. If that's the case, then issuing only  with(plots,display) done up front, before the module definition, won't fix all those other routine calls. One could instead issue a quick and dirty with(plots) outside and before the module definition, or one could do it properly as outlined above (use, uses, or explicit plots's export calls).

acer

> y := (-Pi-1/2)*I:

> simplify( y ); evalf(%);

                               -1/2 I (2 Pi + 1)
 
                                -3.641592654 I
 
> simplify( ln(exp( y )) ); evalf(%);

                               1/2 I (2 Pi - 1)
 
                                 2.641592654 I
 
> simplify( ln(exp( x )) ) assuming x::real;
                                       x

acer

> y := (-Pi-1/2)*I:

> simplify( y ); evalf(%);

                               -1/2 I (2 Pi + 1)
 
                                -3.641592654 I
 
> simplify( ln(exp( y )) ); evalf(%);

                               1/2 I (2 Pi - 1)
 
                                 2.641592654 I
 
> simplify( ln(exp( x )) ) assuming x::real;
                                       x

acer

I wish that there were something for Standard that were as useful and as easy to use (without a mouse) as the X11_defaults/Maple file is for Classic.

ps. There's an anti-aliasing toggle under the Tools->Options-Display menutab. (Why is there an entry to that drop-down box labelled "Default", without indicating whether the default is to have anti-aliasing enabled or disabled?)

acer

Come up with another example yourself, and work through it. Otherwise you'll just be copying, and you won't really learn it.

If you want a third equation in two variables, then add a linear combination of the two that you already have. (In the example below, the third equation is just the first minus the second. But you could also do, say, 5 times the first plus 2 times the second.)

> with(LinearAlgebra):

> A,b := GenerateMatrix([2*x-2*y=-2,-x+2*y=3,3*x-4*y=-5],[x,y]):
 
> S := Matrix([A,b]); # augmented Matrix, represents system
                                  [ 2    -2    -2]
                                  [              ]
                             S := [-1     2     3]
                                  [              ]
                                  [ 3    -4    -5]
 
> RowOperation(S,[2,1]); # exchange 1st and 2nd rows
                               [-1     2     3]
                               [              ]
                               [ 2    -2    -2]
                               [              ]
                               [ 3    -4    -5]
 
> RowOperation(%,1,-1); # scale 1st row by -1
                                [1    -2    -3]
                                [             ]
                                [2    -2    -2]
                                [             ]
                                [3    -4    -5]
 
> RowOperation(%,[2,1],-2); # add -2 times 1st row to 2nd row
                                [1    -2    -3]
                                [             ]
                                [0     2     4]
                                [             ]
                                [3    -4    -5]
 
> RowOperation(%,[3,1],-3);
                                [1    -2    -3]
                                [             ]
                                [0     2     4]
                                [             ]
                                [0     2     4]
 
> RowOperation(%,2,1/2);
                                [1    -2    -3]
                                [             ]
                                [0     1     2]
                                [             ]
                                [0     2     4]
 
> RowOperation(%,[3,2],-2);
                                [1    -2    -3]
                                [             ]
                                [0     1     2]
                                [             ]
                                [0     0     0]
 
> RowOperation(%,[1,2],2);
                                 [1    0    1]
                                 [           ]
                                 [0    1    2]
                                 [           ]
                                 [0    0    0]
 
> %[1..2,3];
                                      [1]
                                      [ ]
                                      [2]
 
> LinearSolve(A,b);
                                      [1]
                                      [ ]
                                      [2]

acer

Come up with another example yourself, and work through it. Otherwise you'll just be copying, and you won't really learn it.

If you want a third equation in two variables, then add a linear combination of the two that you already have. (In the example below, the third equation is just the first minus the second. But you could also do, say, 5 times the first plus 2 times the second.)

> with(LinearAlgebra):

> A,b := GenerateMatrix([2*x-2*y=-2,-x+2*y=3,3*x-4*y=-5],[x,y]):
 
> S := Matrix([A,b]); # augmented Matrix, represents system
                                  [ 2    -2    -2]
                                  [              ]
                             S := [-1     2     3]
                                  [              ]
                                  [ 3    -4    -5]
 
> RowOperation(S,[2,1]); # exchange 1st and 2nd rows
                               [-1     2     3]
                               [              ]
                               [ 2    -2    -2]
                               [              ]
                               [ 3    -4    -5]
 
> RowOperation(%,1,-1); # scale 1st row by -1
                                [1    -2    -3]
                                [             ]
                                [2    -2    -2]
                                [             ]
                                [3    -4    -5]
 
> RowOperation(%,[2,1],-2); # add -2 times 1st row to 2nd row
                                [1    -2    -3]
                                [             ]
                                [0     2     4]
                                [             ]
                                [3    -4    -5]
 
> RowOperation(%,[3,1],-3);
                                [1    -2    -3]
                                [             ]
                                [0     2     4]
                                [             ]
                                [0     2     4]
 
> RowOperation(%,2,1/2);
                                [1    -2    -3]
                                [             ]
                                [0     1     2]
                                [             ]
                                [0     2     4]
 
> RowOperation(%,[3,2],-2);
                                [1    -2    -3]
                                [             ]
                                [0     1     2]
                                [             ]
                                [0     0     0]
 
> RowOperation(%,[1,2],2);
                                 [1    0    1]
                                 [           ]
                                 [0    1    2]
                                 [           ]
                                 [0    0    0]
 
> %[1..2,3];
                                      [1]
                                      [ ]
                                      [2]
 
> LinearSolve(A,b);
                                      [1]
                                      [ ]
                                      [2]

acer

> simplify(M1-N1);
                                       0

For the substitution, you could try something like this,

eval(M1,[s1=sqrt(mu1*epsilon1*kappa^2+v^2+u^2),
         s2=sqrt(mu2*epsilon2*kappa^2+v^2+u^2)]);

acer

p1:=plots:-pointplot(<<1,2,3,4,5>|<1,3,5,7,9>>):
p2:=plots:-pointplot(<<1,2,3,4,5>|<1,4,9,16,25>>):
plots:-display([p1,p2]);

acer

p1:=plots:-pointplot(<<1,2,3,4,5>|<1,3,5,7,9>>):
p2:=plots:-pointplot(<<1,2,3,4,5>|<1,4,9,16,25>>):
plots:-display([p1,p2]);

acer

The expressions assigned to M1 and N1 are not equal.

That's the central problem. Assign M1 and N1 those long expressions without the attempt to subs for s1^2 and s2^2. Then, it is easy to find a set of values for which they are not equal.

> eval(M1-N1,[s1=sqrt(3),s2=sqrt(3),xp=1,mu1=1,mu2=1,
>             epsilon1=1,epsilon2=1,kappa=1,v=1,u=1,w=1,a=1]);

The other problem is trying to substitute s1^2=... and expecting it to replace all instances of s1. Maybe you could consider substituting s1=sqrt(...), etc, using eval instead of subs, and simplify with assumptions on the range/realness of the variables? That might be a means to show the equality, given the the bigger problem were fixed and they were actually equal.

acer