Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I am using DirectSearch package for optimization. I am using GlobalOptima function. I want to see the settings and results such as initial points, number of iterations, residuals etc. I tried using infolevel[Directsearch] but couldn't see any results. Let me know if there is any other command to get this information.

Hello here is a description of my issue:

1. I created a new code edit region

2. i put some code in the code edit region 

3. In the context Panel I unchecked the 'visible' setting for the code edit box

When I evaluate the worksheet the code in the code edit region still runs, but I can't figure out how to edit the code in that region. There is not an icon to open the code edit region as there would be had I toggled the 'expand' setting. Furthermore, I can't select the invisible code edit region in order to toggle the 'visible setting'.

How can I make the code edit region visible again?

 

Thanks for you help

This is my original question, but I can't ask, so I put it here.

I have a system of pde, and it's hard to solve.

But I want to find the type of solutions which are polynomials of degree n of the several independent variables.

Is it possible using 'pdsolve'? Or there are some other commands in Maple to do that?

Thanks!

I computed A and B matrices, now I want to write it in state space reperentation.

diff(x(t), t) = A*x(t)+B*u

where

diff(x(t), t) = (Vector(6, {(1) = diff(alpha(t), t), (2) = diff(alpha(t), t, t), (3) = diff(y(t), t), (4) = diff(y(t), t, t), (5) = diff(theta(t), t), (6) = diff(theta(t), t, t)}))

So I calculated A*x(t)+B*u and got this:

(Vector(6, {(1) = diff(alpha(t), t), (2) = diff(alpha(t), t, t), (3) = diff(y(t), t), (4) = diff(y(t), t, t), (5) = diff(theta(t), t), (6) = diff(theta(t), t, t)})) = (Vector(6, {(1) = 0, (2) = k/(J*R), (3) = 0, (4) = k/(M*R*r), (5) = 0, (6) = -k/(M*R*r*l)})).e+(Vector(6, {(1) = diff(alpha(t), t), (2) = -k^2*(diff(alpha(t), t))/(J*R), (3) = diff(y(t), t), (4) = -k^2*(diff(y(t), t))/(M*R*r^2)-m*g*theta(t)/M, (5) = diff(theta(t), t), (6) = k^2*(diff(y(t), t))/(M*R*r^2*l)+(M+m)*g*theta(t)/(M*l)}))

where u=e but the formation is not A*x(t)+B*u anymore. How can I enforce Maple to output the result in the form of A*x(t)+B*u?

I have been trying to solve this equation by obtaining solutions for x and I actually handed in for an assignment what Maple gave me as an output. Then it turns out that Maple was wrong. This is in fact not a solution for the equation. What am I doing wrong here?
Solve_error.mw

For any symbolic expression like

y = s + (a/b)*log((a+c/b)); 

I want to extract all possible sub-expressions which have one operator operating on exact two operands.
    

subExpression1 = a/b; # any operatoin(+,-,*,/ involving exact two variables)
subExpression2 = c/b;

 

Note: I need an sub-expression which is part of main expression. Above expression is an example. I have quite complex expressions where I need to extract these sub-expressions.  I need to scan my expression at all operators and see on what operands its working on
 

a+c/b # here + is acting on a and c/b clearly it is out of my interest

Maple users frequently solve differential equations. If you want to use the results later in Maple, you need to deconstruct the solution, and then assign the functions -- something that isn't done automatically in Maple. We wrote a multi-purpose routine to help you out. For instance, suppose you solve a simple linear system of equations:

restart;

eqs := { x + y = 3, x - y = 1 };
soln := solve( eqs ); # { x = 2, y = 1 }
x, y; # plain x and y

To assign the values from the solution to the corresponding variables:

assign( soln );
x, y; # 2, 1

This won't work for solutions of differential equations:

restart;

sys := { D(x)(t) = y(t), D(y)(t) = -x(t), x(0) = 1, y(0) = 0 };
soln := dsolve( sys ); # { x(t) = cos(t), y(t) = -sin(t) }
assign( soln );
x(s), y(s); # plain x(s) and y(s)

To make this work, we wrote this multi-purpose routine:

restart;

# Type for a variable expression, e.g. x=5.
TypeTools:-AddType( 'varexpr', u -> type( u, 'And'('name','Non'('constant'))='algebraic' ) ):

# Type for a function expression, e.g. f(x)=x^2.
TypeTools:-AddType( 'funcexpr', u -> type( u, 'function'('And'('name','Non'('constant')))='algebraic' ) ):

# Procedure to assign variable and function expressions.
my_assign := proc( u :: {
        varexpr, 'list'(varexpr), 'rtable'(varexpr), 'set'(varexpr),
        funcexpr, 'list'(funcexpr), 'rtable'(funcexpr), 'set'(funcexpr)
}, $ )

        local F, L, R, V:       

        # Map the procedure if input is a data container, or apply regular assign(), where applicable.
        if not u :: {'varexpr','funcexpr'} then
               map( procname, u ):
               return NULL:
        elif u :: 'varexpr' then
               assign( u ):
               return NULL:
        end if:       

        L, R := lhs(u), rhs(u):
        F := op(0,L): 
        V := [ indets( L, 'And'( 'name', 'Non'('constant') ) )[] ]:    

        map( assign, F, unapply( R, V ) ):
        return NULL:

end proc:

# Example 1.

eqs := { x + y = 3, x - y = 1 };
my_assign( solve( eqs ) );
'x' = x, 'y' = y; # x=1, y=2

# Example 2.

unassign( 'x', 'y' ):
E := [ f(x,y) = x + y, g(x,y) = x - y ];
my_assign( E );
'f(u,v)' = f(u,v), 'g(u,v)' = g(u,v); # f(u,v)=u+v, g(u,v)=u-v

# Example 3.

sys := { D(x)(t) = y(t), D(y)(t) = -x(t), x(0) = 1, y(0) = 0 };
soln := dsolve( sys );
my_assign( soln ):
'x(s)' = x(s); # x(s)=cos(s)
'y(s)' = y(s); # y(s)=-sin(s)

With Maple 18.02 and 2017.2 on OSX 10.13.6: 

restart: 
int( exp(a*exp(I*x)) ,x=-Pi..Pi); 
                               0 

but we get the correct answer for numerical a, e.g. 

restart: 
int( exp(1*exp(I*x)) ,x=-Pi..Pi); 
                              2 Pi 

Is this fixed in version 2018.1? 
 

‏‏‏‏I want to solve partial differential equation by adomian decomposition method, I have a mistake  in define the nonlinear term, then  the calculations of integral does not display , can anyone help me please

‏‏ADM_1.mw


 

restart

" S3:=proc(psi) [[[cos(psi),-sin(psi),0],[sin(psi),cos(psi),0],[0,0,1]]]:  end  proc ;   S1:=proc(`ϕ`)  [[[1,0,0],[0,cos(`ϕ`),-sin(`ϕ`)],[0,sin(`ϕ`),cos(`ϕ`)]]]:   end proc;"

proc (psi) Matrix(3, 3, {(1, 1) = cos(psi), (1, 2) = -sin(psi), (1, 3) = 0, (2, 1) = sin(psi), (2, 2) = cos(psi), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1}) end proc

 

proc (`ϕ`) Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = cos(psi), (2, 3) = -sin(psi), (3, 1) = 0, (3, 2) = sin(psi), (3, 3) = cos(psi)}) end proc

(1)

``

S3(uu)

Matrix([[cos(uu), -sin(uu), 0], [sin(uu), cos(uu), 0], [0, 0, 1]])

(2)

S1(uu)

Matrix([[1, 0, 0], [0, cos(psi), -sin(psi)], [0, sin(psi), cos(psi)]])

(3)

``


 

Download test3.mw

Way i get the wrong output with procedure S1(uu)
 

How can I get the vlaue of matric c?

Thanks for your help


restart;
with(Student[LinearAlgebra]);
a := Matrix(2, 2, [[1, 2], [3, 4]]);
                               [1  2]
                          a := [    ]
                               [3  4]
b := Matrix(2, 2, [[2, 4], [6, 2]]);
                               [2  4]
                          b := [    ]
                               [6  2]
c := multiply(a, b);
                              /[1  2]  [2  4]\
                 c := multiply|[    ], [    ]|
                              \[3  4]  [6  2]/
evalm(c);
           [        /   [2  4]\          /   [2  4]\]
           [multiply|1, [    ]|  multiply|2, [    ]|]
           [        \   [6  2]/          \   [6  2]/]
           [                                        ]
           [        /   [2  4]\          /   [2  4]\]
           [multiply|3, [    ]|  multiply|4, [    ]|]
           [        \   [6  2]/          \   [6  2]/]
 

This is my first problem with Maple but i am pretty confused as to why it would struggle with these steps.

Just using a standard worksheet, here is what i have:

> f:=(4^x)+1

>g:=x^4

> solve(g=f,x)

now, i would just expect this to come back with 3 answers, but instead i get 

Warning, solutions may have been lost
                     RootOf(-4^_Z - 1 + _Z^4)

if I do:

>fsolve(g=f,x)

It comes back with only one of the answers(2.094012853), instead of all three.

What am I doing wrong?

I mean, for example,

solve({4*x1+7*x2+6*x3 = 186, floor((1/2)*x1)+floor((1/5)*x2)+floor((1/3)*x3) = 18, 
floor((1/5)*x1)+floor((1/2)*x2)+floor((1/4)*x3) = 21});
Warning, solutions may have been lost

A finite number of the solutions can be found by DirectSearch

DirectSearch:-SolveEquations([floor((1/2)*x1)+floor((1/5)*x2)+floor((1/3)*x3) = 18, 
floor((1/5)*x1)+floor((1/2)*x2)+floor((1/4)*x3) = 21, 4*x1+7*x2+6*x3 = 186], 
{x1 >= -100, x2 >= -100, x3 >= -100, x1 <= 100, x2 <= 100, x3 <= 100}, 
AllSolutions, solutions = 3, number = 1000);

Matrix(3, 4, [[0., Vector[column](3, [0., 0., 0.]),
 [x1 = 74.18778903830886, x2 = 58.93905207777524, x3 = -87.22075344961036], 185], 
[0., Vector[column](3, [0., 0., 0.]),
 [x1 = 71.22714241634635, x2 = 56.43467122661542, x3 = -82.32521137528222], 164],
 [0., Vector[column](3, [0., 0., 0.]), 
[x1 = 73.6407870507502, x2 = 58.33738250527096, x3 = -86.15413762331626], 165]])

I don't see a way to obtain the MMA answer (in Maple notation)

(155/2 < x1 and x1 < 78 and 744/7-4*x1*(1/7) < x2 and x2 < 62 or 72 <= x1 and x1 <= 73 and
 102-4*x1*(1/7) < x2 and x2 < 62 or 73 < x1 and x1 <= 147/2 and 102-4*x1*(1/7) < x2 and
 x2 <= 726/7-4*x1*(1/7) or 147/2 < x1 and x1 < 74 and 60 <= x2 and x2 <= 726/7-4*x1*(1/7) or
 74 <= x1 and x1 < 75 and 726/7-4*x1*(1/7) < x2 and x2 < 62 or 153/2 < x1 and x1 < 78 and
 726/7-4*x1*(1/7) < x2 and x2 < 60 or x1 = 72 and 58 <= x2 and x2 < 60 or 72 < x1 and x1 < 74 and
 58 <= x2 and x2 <= 708/7-4*x1*(1/7) or 75 <= x1 and x1 < 76 and 102-4*x1*(1/7) < x2 and x2 < 60 or
 x1 = 74 and 442/7 < x2 and x2 < 64 or 74 < x1 and x1 < 75 and 738/7-4*x1*(1/7) < x2 and 
x2 <= 744/7-4*x1*(1/7) or 74 <= x1 and x1 < 75 and 708/7-4*x1*(1/7) < x2 and x2 <= 102-4*x1*(1/7) or 
151/2 < x1 and x1 < 76 and 708/7-4*x1*(1/7) < x2 and x2 < 58 or 157/2 < x1 and x1 < 80 and
 762/7-4*x1*(1/7) < x2 and x2 < 64 or 68 <= x1 and x1 < 137/2 and 56 <= x2 and x2 <= 666/7-4*x1*(1/7) or
 x1 = 137/2 and x2 = 56 or x1 = 70 and 56 < x2 and x2 < 58 or 70 < x1 and x1 <= 71 and 56 <= x2 and
 x2 < 58 or 71 < x1 and x1 < 72 and 56 <= x2 and x2 <= 690/7-4*x1*(1/7) or 70 <= x1 and x1 <= 281/4 and
 54 <= x2 and x2 < 55 or 281/4 < x1 and x1 < 72 and 54 <= x2 and x2 <= 666/7-4*x1*(1/7)) and
 x3 = 31-2*x1*(1/3)-7*x2*(1/6)

PS. MMA_solution.pdf MMA_solution.mw

I have 2 same integrals, but there is difference between  them at the end.WHy?


 

``

restart

N := 8:

I__1 := add(int(zt*ro[i], zt = Z[i] .. Z[i+1]), i = 1 .. N)

(1/2)*ro[1]*(-Z[1]^2+Z[2]^2)+(1/2)*ro[2]*(-Z[2]^2+Z[3]^2)+(1/2)*ro[3]*(-Z[3]^2+Z[4]^2)+(1/2)*ro[4]*(-Z[4]^2+Z[5]^2)+(1/2)*ro[5]*(-Z[5]^2+Z[6]^2)+(1/2)*ro[6]*(-Z[6]^2+Z[7]^2)+(1/2)*ro[7]*(-Z[7]^2+Z[8]^2)+(1/2)*ro[8]*(-Z[8]^2+Z[9]^2)

(1)

ro := Vector(8, {(1) = 2051.904, (2) = 2051.904, (3) = 2051.904, (4) = 2051.904, (5) = 2051.904, (6) = 2051.904, (7) = 2051.904, (8) = 2051.904})

Z := Vector(9, {(1) = -0.4998720000e-6, (2) = -0.3749040000e-6, (3) = -0.2499360000e-6, (4) = -0.1249680000e-6, (5) = 0, (6) = 0.1249680000e-6, (7) = 0.2499360000e-6, (8) = 0.3749040000e-6, (9) = 0.4998720000e-6})

I__2 := add(int(zt*ro[i], zt = Z[i] .. Z[i+1]), i = 1 .. N)

0.1e-19

(2)

I__1-I__2

-0.1e-19

(3)

``

``

``

``

``

``

``


 

Download Ajib.mw

I am trying to solve a set of differential equations in maple. The maple code:

de1:=diff(u1(x,t),x)=-h*(u1(x,t))+i*exp(-i*t)*(u2(x,t));
              d
       de1 := -- u1(x, t) = -h u1(x, t) + i exp(-i t) u2(x, t)
              dx

> de2:=diff(u1(x,t),t)=(-h-i/2)*u1(x,t)-h*exp(-i*t)*u2(x,t);

         d
  de2 := -- u1(x, t) = (-h - 1/2 i) u1(x, t) - h exp(-i t) u2(x, t)
         dt

> dsolve({de1,de2},{u1(x,t),u1(x,t)});
 

However, when I execute it, maple show "Warning: system is consistent". How to remove it

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