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MaplePrimes Questions

Specify color for output variables...

Asked by: mohkam7 45
color
August 14 2017
3  12

Is there a way to specify different colors for different output variables? For example, if x,y, and z appear in the entire document as variables, I want x to be red, y to be blue, and z to be green whenever an output is displayed.

Thanks

how i can reduce the runtime of the program ?...

Asked by: torabi 90
performance programming
August 14 2017
1  6

hi..how i can rewrite section of this code as another form i,e ''for section''

I have a lot of line as this and runnig cise is time consuming.

is there another way to write this section in order to the runtime of the program is reduced??

thanks

for.mw
 

> 

restart;
> 

with(LinearAlgebra):
> 

with(VectorCalculus):
> 

#Digits:=5:
k:=6:
> 

l:=0:
> 

h:=1:
> 

m:=4:
> 

n:=4:
> 

l1:=2*h:
> 

l2:=2*h:
> 

N:=0.5:
> 

nu:=.3:
> 

E_m:=70e9:
> 

E_c:=380e9:
> 

rho_m:=2702:
> 

rho_c:=3800:
> 

lambda_m:=nu*E_m/((1+nu)*(1-2*nu)):
> 

lambda_c:=nu*E_c/((1+nu)*(1-2*nu)):
> 

mu_m:=E_m/(2*(1+nu)):
> 

mu_c:=E_c/(2*(1+nu)):
> 

with(orthopoly):
> 

for i from 0 to 5 do:
L(i):=sqrt((2*i+1)/2)*P(i,z):
end do:
> 

Z:=rho_m+(rho_c-rho_m)*((1/2)+(z/h))^N;

2702+1098*(1/2+z)^.5

 (1)
> 

U:=lambda_m+(lambda_c-lambda_m)*((1/2)+(z/h))^N;

0.4038461538e11+0.1788461538e12*(1/2+z)^.5

 (2)
> 

S:=mu_m+(mu_c-mu_m)*((1/2)+(z/h))^N;

0.2692307692e11+0.1192307692e12*(1/2+z)^.5

 (3)
> 

d:=Matrix([[0,0,0,0,0,0,0,0],[sqrt(3),0,0,0,0,0,0,0],[0,sqrt(15),0,0,0,0,0,0],[sqrt(7),0,sqrt(35),0,0,0,0,0],[0,sqrt(27),0,sqrt(63),0,0,0,0],[sqrt(11),0,sqrt(55),0,sqrt(99),0,0,0],[0,sqrt(39),0,sqrt(91),0,sqrt(143),0,0],[sqrt(15),0,sqrt(75),0,sqrt(135),0,sqrt(195),0]]);

d := Matrix(8, 8, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (2, 1) = 3^(1/2), (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (3, 1) = 0, (3, 2) = 15^(1/2), (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (4, 1) = 7^(1/2), (4, 2) = 0, (4, 3) = 35^(1/2), (4, 4) = 0, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0, (4, 8) = 0, (5, 1) = 0, (5, 2) = 3*3^(1/2), (5, 3) = 0, (5, 4) = 3*7^(1/2), (5, 5) = 0, (5, 6) = 0, (5, 7) = 0, (5, 8) = 0, (6, 1) = 11^(1/2), (6, 2) = 0, (6, 3) = 55^(1/2), (6, 4) = 0, (6, 5) = 3*11^(1/2), (6, 6) = 0, (6, 7) = 0, (6, 8) = 0, (7, 1) = 0, (7, 2) = 39^(1/2), (7, 3) = 0, (7, 4) = 91^(1/2), (7, 5) = 0, (7, 6) = 143^(1/2), (7, 7) = 0, (7, 8) = 0, (8, 1) = 15^(1/2), (8, 2) = 0, (8, 3) = 5*3^(1/2), (8, 4) = 0, (8, 5) = 3*15^(1/2), (8, 6) = 0, (8, 7) = 195^(1/2), (8, 8) = 0})

 (4)
> 

``

``

> 

e2 := 0;

0

  

-0.3192307692e12*W(1)+0.4396880662e12*W(3)-0.1474586301e12*W(5)-0.9235575669e11*W(2)+0.1979090105e12*W(4)

 (5)

``


 

Download for.mw

 

how I can dsolve this differential equation...

Asked by: torabi 90
parameter dsolve
August 14 2017
0  12

hi...

how I can dsolve this differential equations. parameter p is unkown.

I want to gain w(x) and u(x) and psi(x) and p.

thanks

sade.mw
 

> 

restart; eq1 := (diff(psi(x), x))^2+(diff(u(x), x)+(8*(1/2))*(diff(w(x), x))^2)((diff(psi(x), x))^2)+3*(diff(w(x), x, x))+5*(diff(w(x), x, x))*(diff(psi(x), x))-7*(diff(u(x), x, x, x)+(8*(1/2))*(diff(w(x), x, x))^2+(3/2)*(diff(w(x), x, x, x))*(diff(w(x), x)))+3 = p

(diff(psi(x), x))^2+(diff(u(x), x))((diff(psi(x), x))^2)+4*(diff(w(x), x))((diff(psi(x), x))^2)^2+3*(diff(diff(w(x), x), x))+5*(diff(diff(w(x), x), x))*(diff(psi(x), x))-7*(diff(diff(diff(u(x), x), x), x))-28*(diff(diff(w(x), x), x))^2-(21/2)*(diff(diff(diff(w(x), x), x), x))*(diff(w(x), x))+3 = p

 (1)
> 

eq2 := (51-31)(diff(psi(x), x, x))+(52-2)(diff(w(x), x, x, x))+8*(diff(psi(x), x, x, x, x))-7*(diff(w(x), x)-psi(x)) = 0

70+8*(diff(diff(diff(diff(psi(x), x), x), x), x))-7*(diff(w(x), x))+7*psi(x) = 0

 (2)
> 

eq3 := 4*(diff(w(x), x, x)-(diff(psi(x), x)))+(23+11)(diff(psi(x), x, x, x))+(14+12)*(diff(w(x), x, x, x, x)) = 0

4*(diff(diff(w(x), x), x))-4*(diff(psi(x), x))+34+26*(diff(diff(diff(diff(w(x), x), x), x), x)) = 0

 (3)
> 

dsys3 := {eq1, eq2, eq3, psi(0) = 0, psi(1) = 0, u(0) = 0, u(1) = 0, w(0) = 0, w(1) = 0, ((D@@1)(psi))(0) = 0, ((D@@1)(psi))(1) = 0, ((D@@1)(w))(0) = 0, ((D@@1)(w))(1) = 0}; dsol5 := dsolve(dsys3, 'maxmesh' = 1200, numeric, abserr = .1, output = array([.5]))

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 12, got 10

  
> 

dsolve({eq2, eq3}, {psi(x), w(x)}):
> 

with(PDEtools, casesplit, declare);

[casesplit, declare]

 (4)
> 

 


 

Download sade.mw

 

how i can dsolve this differential equations........

Asked by: 9009134 110
dsolve
August 14 2017
0  5

hi...

how i can dsolve this differential equations and obtain w(x) and U(x) and phi(x) analytical or numerically?

thanks

zah.mw
 

``

restart; L := 100; h := 1; eq1 := 1130*(diff(U(x), x, x))+1130*(diff(W(x), x))*(diff(W(x), x, x))+1130*(diff(U(x), x, x, x, x))

1130*(diff(diff(U(x), x), x))+1130*(diff(W(x), x))*(diff(diff(W(x), x), x))+1130*(diff(diff(diff(diff(U(x), x), x), x), x))

 (1)

eq2 := 1130*(diff(W(x), x))*(diff(U(x), x, x)+(diff(W(x), x))*(diff(W(x), x, x)))+(diff(W(x), x, x))*(1130*(diff(U(x), x))+565*(diff(W(x), x))^2-2.2*(int(diff(varphi(z), z), z = -5/2 .. 5/2)))+(14125/6)*(diff(W(x), x, x, x, x, x, x))+(10405/6)*(diff(W(x), x, x, x, x))+10

1130*(diff(W(x), x))*(diff(diff(U(x), x), x)+(diff(W(x), x))*(diff(diff(W(x), x), x)))+(diff(diff(W(x), x), x))*(1130*(diff(U(x), x))+565*(diff(W(x), x))^2-2.2*(int(diff(varphi(z), z), z = -5/2 .. 5/2)))+(14125/6)*(diff(diff(diff(diff(diff(diff(W(x), x), x), x), x), x), x))+(10405/6)*(diff(diff(diff(diff(W(x), x), x), x), x))+10

 (2)

eq3 := diff(varphi(z), z, z)-.35*(diff(W(x), x, x))

diff(diff(varphi(z), z), z)-.35*(diff(diff(W(x), x), x))

 (3)

dsys3 := {eq1, eq2, eq3, U(0) = 0, U(L) = 0, W(0) = 0, W(L) = 0, `ϕ`(-(1/2)*h) = 0, `ϕ`(-(1/2)*h) = 2, ((D@@1)(W))(0) = 0, ((D@@1)(W))(L) = 0, ((D@@2)(W))(0) = 0, ((D@@2)(W))(L) = 0}; dsol5 := dsolve(dsys3, 'maxmesh' = 1200, numeric, abserr = .1, output = array([.5]))

Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {x, z}

  

``


 

Download zah.mw

 

fix error and identify any other wrong and explain...

Asked by: bashar27 55
August 14 2017
0  1

> {w = -4*mu, a[-1] = -12*mu/(a+b), a[0] = a[0], a[1] = 0, b[-1] = 0, b[0] = 0, b[1] = 0};
  /                     12 mu                                              
 { w = -4 mu, a[-1] = - -----, a[0] = a[0], a[1] = 0, b[-1] = 0, b[0] = 0,
  \                     a + b                                              

           \
   b[1] = 0 }
           /
> restart;
>
> w := -4*mu;
                                    -4 mu
> a[-1] := -12*mu/(a+b);
                                     12 mu
                                   - -----
                                     a + b
> a[0] := a[0];
                                    a[0]
> a[1] := 0;
                                      0
> b[-1] := 0;
                                      0
> b[0] := 0;
                                      0
> b[1] := 0;
                                      0
> xi := x+w*t;
                                 x - 4 mu t
> P := sqrt(mu)*tan(A-sqrt(mu)*xi);
                      (1/2)    /      (1/2)             \
                    mu      tan\A - mu      (x - 4 mu t)/
> u := a[0]+a[1]*P/(1+lambda*P)+a[-1]*(1+lambda*P)/P+b[0]*sqrt(sigma*(1+P^2/mu))/P+b[1]*sqrt(sigma*(1+P^2/mu))+b[-1]*sqrt(sigma*(1+P^2/mu))/P^2;
                (1/2) /             (1/2)    /      (1/2)             \\
           12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//
    a[0] - -------------------------------------------------------------
                                  /      (1/2)             \            
                       (a + b) tan\A - mu      (x - 4 mu t)/            
> Diff(u, x, t)+a*(Diff(u, x))*(Diff(u, x, y))+b*(Diff(u, `$`(x, 2)))*(Diff(u, y))+Diff(u, `$`(x, 3), y);
/   2   /            (1/2) /             (1/2)    /      (1/2)             \\\
|  d    |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|
|------ |a[0] - -------------------------------------------------------------|
| dt dx |                              /      (1/2)             \            |
\       \                   (a + b) tan\A - mu      (x - 4 mu t)/            /

  \     /    /    
  |     | d  |    
  | + a |--- |a[0]
  |     | dx |    
  /     \    \    

          (1/2) /             (1/2)    /      (1/2)             \\\\ /   2   /
     12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|| |  d    |
   - -------------------------------------------------------------|| |------ |
                            /      (1/2)             \            || | dy dx |
                 (a + b) tan\A - mu      (x - 4 mu t)/            // \       \

              (1/2) /             (1/2)    /      (1/2)             \\\\     /
         12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//||     |
  a[0] - -------------------------------------------------------------|| + b |
                                /      (1/2)             \            ||     |
                     (a + b) tan\A - mu      (x - 4 mu t)/            //     \

   2 /            (1/2) /             (1/2)    /      (1/2)             \\\\ /
  d  |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|| |
  -- |a[0] - -------------------------------------------------------------|| |
     |                              /      (1/2)             \            || |
     \                   (a + b) tan\A - mu      (x - 4 mu t)/            // \

      /            (1/2) /             (1/2)    /      (1/2)             \\\\
   d  |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//||
  --- |a[0] - -------------------------------------------------------------||
   dy |                              /      (1/2)             \            ||
      \                   (a + b) tan\A - mu      (x - 4 mu t)/            //

     / 4 /            (1/2) /             (1/2)    /      (1/2)             \\
     |d  |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//
   + |-- |a[0] - -------------------------------------------------------------
     |   |                              /      (1/2)             \            
     \   \                   (a + b) tan\A - mu      (x - 4 mu t)/            

  \\
  ||
  ||
  ||
  //
> value(%);
                       /                                 2\
              3        |       /      (1/2)             \ |
         96 mu  lambda \1 + tan\A - mu      (x - 4 mu t)/ /
         --------------------------------------------------
                               a + b                       

                                                                2   
                            /                                 2\    
                   3        |       /      (1/2)             \ |    
              96 mu  lambda \1 + tan\A - mu      (x - 4 mu t)/ /    
            - --------------------------------------------------- +
                                                         2          
                               /      (1/2)             \           
                    (a + b) tan\A - mu      (x - 4 mu t)/           

                                                  /             
                                                  |             
                             1                    |     (5/2) /
           -------------------------------------- \96 mu      \1
                                                3               
                      /      (1/2)             \                
           (a + b) tan\A - mu      (x - 4 mu t)/                

                       (1/2)    /      (1/2)             \\
            + lambda mu      tan\A - mu      (x - 4 mu t)//

                                               2\   
           /                                 2\ |   
           |       /      (1/2)             \ | |   
           \1 + tan\A - mu      (x - 4 mu t)/ / / -

                                                 /             
                             1                   |     (5/2) /
           ------------------------------------- \96 mu      \1
                      /      (1/2)             \               
           (a + b) tan\A - mu      (x - 4 mu t)/               

                                                            /
                       (1/2)    /      (1/2)             \\ |
            + lambda mu      tan\A - mu      (x - 4 mu t)// \1

                                           2\\
                 /      (1/2)             \ ||
            + tan\A - mu      (x - 4 mu t)/ //
> simplify(%);
Error, (in simplify/tools/_zn) too many levels of recursion
>

 

plot an indefinite integral ...

Asked by: mehdi jafari 774
plot integral integration
August 14 2017
0  7

hi every one, i want to plot an indefinite integral  , it is some what complex and maple can not compute the answer, ( but numeric integration can be computed) , but we want to plot the output, what should we do ? tnx for help in advance

corrected.mw

weighted norm of an expression...

Asked by: mehdi jafari 774
August 14 2017
0  3

how can we compute wighted norm of a matrix or a vector in maple? 

How can I convert a result to a trigonometric iden...

Asked by: Gillee 237
trigonometric-identities convert tanh
August 13 2017
1  5

``

How can I convert the result (2) to equal to the trigonometric identity (kw/s^2)*tanh(a*s/2)?

``

> 

g := kw*piecewise(t < a, t, t < 2*a, 2*a-t)

kw*piecewise(t < a, t, t < 2*a, 2*a-t)

 (1)
> 

simplify((int(exp(-s*t)*g, t = 0 .. a)+int(exp(-s*t)*g, t = a .. 2*a))/(1-exp(-2*a*s)))

-(exp(-a*s)-1)*kw/((exp(-a*s)+1)*s^2)

 (2)
> 

``

Download trigonometric_id.mw

 

how to dsolve for this equation?...

Asked by: LeeHoYeung 535
August 13 2017
0  5

this equation is complicated

how to dsolve for this equation for function f ?

f(t,x,diff(x,t)) - f(t,x,p) - (diff(x,t)-p)*diff(f(t,x,p), p) = tan(t)
 

how to find the contour of time series data? and c...

Asked by: LeeHoYeung 535
curvature contour
August 12 2017
0  1

how to find the contour of time series data? and how to find curvature function of this contour?

search value plot maximize...

Asked by: lucaud 45
August 12 2017
0  1

In this fuction the maximize is about at t=46 and x=46 but in the plot I look other max at other value, why?because is discontinus fuction?I need not the local max (it is potential energy but I think don't matter)optimization2enerpot.mws

how to solve this system?...

Asked by: LeeHoYeung 535
solve groebner
August 12 2017
0  0
updated:
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));
 
restart:
with(Groebner):
p1 := vector([a*cos(q1), a*sin(q1)]);
p2 := evalm(p1 + b*vector([cos(q1+q2), sin(q1+q2)]));
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));
Pe := map(expand, P);
A := {cos(q1) = c1, sin(q1) =s1, cos(q2)=c2, sin(q2)=s2, cos(q3)=c3, sin(q3)=s3};
P := subs(A, op(Pe));
F1 := [x - P[1], y - P[2], s1^2+c1^2-1, s2^2+c2^2-1, s3^2+c3^2-1 ];
F2 := subs({a=1, b=1, c=1}, F1);
 
g2 := Basis(F2, plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[1], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[2], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[3], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[4], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[5], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[6], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[7], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[8], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[9], plex(c3, s3, c2, s2, c1, s1));
 
                                   1, c1
                               2       2    2   2
                           16 y  + 16 x , s1  s2
                                           2
                                 8 x, c1 s2
                                2      2    2  
                             2 y  + 2 x , s1  c2
                                 2 x, c1 c2
                            3            2        
                         2 x  - 2 x + 2 y  x, s2 c2
                                        2
                                   1, c2
                                   2 x, s3
                                    2, c3
originally i think
g2[1], g2[7], g2[9] have single variables c1, c2, c3 respectively
can be used to solve system
 
but without x and y, these equations can not be used
if choose leading term has x and y , but there is no single variable s1 or c1.
 
originally expect solve as follows
g2spec := subs({x=1, y=1/2}, [g2[3],g2[5],g2[6]]);
S1 := [solve([g2spec[1]])];
q1a := evalf(arccos(S1[1]));
q1b := evalf(arccos(S1[2]));
S2 := [solve(subs(s1=S1[1], g2spec[2])), solve(subs(s1=S1[2], g2spec[2])) ];
q2a := evalf(arccos(S2[1]));
q2b := evalf(arccos(S2[2]));
S3 := [solve(subs(s1=S2[1], g2spec[2])), solve(subs(s1=S2[2], g2spec[2])) ];
q2a := evalf(arccos(S3[1]));
q2b := evalf(arccos(S3[2]));
 

contours from an array of points using surfdata in...

Asked by: mikemeson 25
contour plotting surfdata
August 11 2017
2  5

I found from this forum that to plot a 2D array of points use can be made of the Maple procedure surfdata.
 

Does anyone have suggestions on how to plot contours in (preferrably) Maple 16 or Maple 17?

I tried the following

Output := Array(-10 .. 10, -10 .. 10, proc (i, j) options operator, arrow; i^2+j^2 end proc):
F := proc (x, y) -> x^2+y^2 end proc:
surfdata(Output, color = F, dimension = 2);

but "the option dimension = 2" is a Maple 18 addition.

Ideally, I would like also to be able to plot contours with options found in the procedure
contourplot

Is there a way to numerically solve a set of PDEs ...

Asked by: Dmitrii 15
numeric pdsolve
August 11 2017
1  8

Please illustrate the answer on the example of a simple wave equation, for instance.

Inverse Poisson Distribution...

Asked by: Teep 200
quantile probability poisson-distribution
August 11 2017
1  10

I'm wondering if there is an available command that can evaluate the number of terms required to produce a desired outcome.

Specifically, I am interested in determining the probability of a Poisson distribution, given the parameter (mean) value and the probability outcome. I can obtain the desired result using trial and error / brute force, but I am curious to know if there is a more efficient way. 

Suppose that, lambda = 2.6 and the cumulative sum of the probabilities is 95%. I know that I must add the first 6 terms for P(x) in the series (x=0,1, ..,5) to sum to 0.95. Each term ...  P(x=0)= 0.07, P(x=1)=0.19, and so on.

However, how can we know that desired 95% outcome can be determined from the first 5 terms without trial & error?

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