I am wanting to write a procedure to take a square matrix and have it output a spiral matrix.

for example; M:=Matrix(3,[[1,1,1],[2,2,2],[3,3,3]]);

would turn into

S:=Matrix(3,[[1,1,1],[3,3,2],[3,2,2]]);

Starting in the top left corner and each row follows around clockwise until you reach the middle.

My first thought was I need to be able to call each element (m_i,j) from a matrix and tell it where to go. I could write a different procedure for each square matrix assigning where the elements in the matrix each should move to. Since I could not get it to work for n.

Here is what i have for a 3x3 matrix

Spiral := proc(a1,a2,a3,b1,b2,b3,c1,c2,c3)
local M,S;
M:=Matrix(3,[[a1,a2,a3],[b1,b2,b3],[c1,c2,c3]]);
S:=Matrix(3,[[a1,a2,a3],[c2,c3,b1],[c1,b3,b2]]);
print(M);
print(S);
end:
Spiral(1,2,3,4,5,6,7,8,9);

It is very difficult for me to find information about Matrices in Maple. Any hint on using Maple would be appreciated. Thank you.

Dear all

is it possible to solve bilevel optimization problems in maple?

            min F(x,y)

     s.t.    min G(x,y)

        s.t.   k(x,y)<=0

Hi,

I have a code which stores large amount of intermediate data.

Ones the data has been used i unassign the variables storing the data and perform garbage collection. But memory is not returned to the operating system for reallocation.

can somebody please tell me how to release memory back to os so that task manager shows memory release (without doing the maple server reset).

And i dont understand the purpose of stupid gc if it is not returning memory back to the windows?

I'm trying to plot the graph of a recursive function in Maple 17 but I keep getting the error Error, (in f) too many levels of recursion.

I need to plot a logarithmic graph in the range of x=1,...40. Here is the code:

with(plots); 
f:=x->(2.25*f(x-1)-0.5*f(x-2));
f(1):=1/3;
f(2):=1/12;
logplot(f(x),1..40);

How can I fix this problem? Maybe I need to write it in an iterative form, but I don't know how. Thank you very much for any help!

Hello everyone,

how exactly do i 3-d plot some data that i have to back-transform first. in 2-d it is so easy. why isnt it in 3d? all i end up with is an all black diagram

transformIT.mw

please see the file attached

Grateful for some hints

Goon

Hello every one,

I had a 3 equations with 3 unknown (X,Y,Z, conjugate(Y),conjugate(Z))

this is the code:

solve( {ao*x + a1*y + conjugate(a1)*conjugate(y)+a2*z+conjugate(a2)*conjugate(z) = 0.5, conjugate(a1)*x + bo*y + conjugate(a2)*conjugate(y)+a1*z = 0, 10*x + 10*y/4 + 10*z = 10}, {x, y, z});

where the coefficients are complex numbers

Is thee any simple way to solve it

thanks

Hi:

i will solve the five nonlinear coupled odes with maple in least time,can evey body help me?

eq1:= -3515.175096*Pi*q[1](T)*q[4](T)-3515.175096*Pi*q[1](T)*q[5](T)-2650.168890*Pi^2*q[3](T)*q[1](T)-9.871794877*10^7*q[2](T)*Pi+.5622514683*(diff(q[1](T), T, T))+1.893468706*q[1](T)^3*Pi^4+2.507772708*10^5*q[1](T)*Pi^2=0

eq2:= 496.9066665*q[2](T)*Pi^2-380.5288665*q[4](T)*Pi-62694.31768*Pi*q[1](T)+380.5288665*q[5](T)*Pi+0.3570776400e-3*(diff(q[2](T), T, T))+2.467948718*10^7*q[2](T)=0

eq3:= 2650.168888*q[1](T)^2*Pi^2+7.824250847*10^5*q[3](T)*Pi^2+1.037806000*10^6*q[5](T)*Pi+.5622514682*(diff(q[3](T), T, T))+1.037806000*10^6*q[4](T)*Pi=0

eq4:= 63661.97724-241.8620273*q[1](T)*(diff(q[1](T), T))-6.792272727*10^6*(diff(q[4](T), T))-5191.348749*q[4](T)-5191.348749*q[5](T)+71406.36133*(diff(q[3](T), T))-6.792272727*10^6*(diff(q[5](T), T))=0

eq5:= 70.02817496+2490.500000*(diff(q[5](T), T))-29887.90351*q[4](T)+29887.90351*q[5](T)-2490.500000*(diff(q[4](T), T))-45.34913011*(diff(q[2](T), T))=0

As I am trying to solve this integration:

restart; with(linalg); with(stats); with(plots); with(Statistics); with(LinearAlgebra); with(Optimization);
lambda0 := proc (t) options operator, arrow; gamma0+gamma1*t+gamma2*t^2 end proc;
lambda := lambda0(t)*exp(beta*s);
t1 := 145; t3 := 250; t2 := (t1+t3)*(1/2);
s := 1/(273.16+50); s1 := 1/(273.16+t1); s3 := 1/(273.16+t3); s2 := 1/(273.16+t2); gamma0 := 0.1e-3; gamma1 := .5; gamma2 := 0; beta := -3800;
c := 300; n := 200;
Theta := solve(1-exp(-(gamma0*tau1+(1/2)*gamma1*tau1^2+(1/3)*gamma2*tau1^3)*exp(beta*s1)) = 1-exp(-(gamma0*a+(1/2)*gamma1*a^2+(1/3)*gamma2*a^3)*exp(beta*s2)), a);

a := Theta[1];

Delta := solve(1-exp(-(gamma0*(a+tau2-tau1)+(1/2)*gamma1*(a+tau2-tau1)^2+(1/3)*gamma2*(a+tau2-tau1)^3)*exp(beta*s2)) = 1-exp(-(gamma0*b+(1/2)*gamma1*b^2+(1/3)*gamma2*b^3)*exp(beta*s3)), b);

b := Delta[1];

A1 := `assuming`([unapply(int(exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1))/(gamma0+gamma1*t+gamma2*t^`2`), t = N .. M), N, M)], [N > 0, M > 0]);
A2 := unapply(int(exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2))/(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2), t = N .. M), N, M);
A3 := unapply(int(exp(beta*s3)*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2+(1/3)*gamma2*(b+t-tau2)^3)*exp(beta*s3))/(gamma0+gamma1*(b+t-tau2)+gamma2*(b+t-tau2)^2), t = N .. M), N, M);
B1 := `assuming`([unapply(int(t^2*exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1))/(gamma2*t^2+gamma1*t+gamma0), t = N .. M), N, M)], [N > 0, M > 0]);
B2 := unapply(int((a+t-tau1)^2*exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2))/(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2), t = N .. M), N, M);
B3 := unapply(int((b+t-tau2)^2*exp(beta*s3)*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2+(1/3)*gamma2*(b+t-tau2)^3)*exp(beta*s3))/(gamma0+gamma1*(b+t-tau2)+gamma2*(b+t-tau2)^2), t = N .. M), N, M);

F0 := A1(0, tau1)+A2(tau1, tau2)+A3(tau2, c);
F1 := B1(0, tau1)+B2(tau1, tau2)+B3(tau2, c);

NLPSolve(1/(n^3*(F0*F1-F1)), tau1 = 115 .. 201, tau2 = 237 .. 273);

I need to have tau1 tau2 as varibles to get there optimal values ..

But this error keeps coming :

Error, (in Optimization:-NLPSolve) integration range or variable must be specified in the second argument, got HFloat(1.0) = HFloat(158.0) .. HFloat(255.0)

Please Help ..

Please help me to solve two equations in uploaded find and find two expressions for ‘T’ and ‘n’ as a function of other parameters.

maple.mw

I am a problem with solve differential equation, please help me: THANKS 

g := (y^2-1)^2; I4 := int(g^4, y = -1 .. 1); I5 := 2*(int(g^3*(diff(g, y, y)), y = -1 .. 1)); I6 := int(g^3*(diff(g, y, y, y, y)), y = -1 .. 1); with(Student[Calculus1]); I10 := ApproximateInt(6/(1-f(x)*g)^2, y = -1 .. 1, method = simpson);

dsys3 := {I4*f(x)^2*(diff(f(x), x, x, x, x))+I5*f(x)^2*(diff(f(x), x, x))+I6*f(x)^3 = I10, f(-1) = 0, f(1) = 0, ((D@@1)(f))(-1) = 0, ((D@@1)(f))(1) = 0};

dsol5 := dsolve(dsys3, numeric, output = array([0.]));

              Error, (in dsolve/numeric/bvp) system is singular at left endpoint, use midpoint method instead

****************FORMAT TWO ********************************************************

g := (y^2-1)^2; I4 := int(g^4, y = -1 .. 1); I5 := 2*(int(g^3*(diff(g, y, y)), y = -1 .. 1)); I6 := int(g^3*(diff(g, y, y, y, y)), y = -1 .. 1); with(Student[Calculus1]); I10 := ApproximateInt(6/(1-f(x)*g)^2, y = -1 .. 1, method = simpson);
dsys3 := {I4*f(x)^2*(diff(f(x), x, x, x, x))+I5*f(x)^2*(diff(f(x), x, x))+I6*f(x)^3 = I10, f(-1) = 0, f(1) = 0, ((D@@1)(f))(-1) = 0, ((D@@1)(f))(1) = 0};

dsol5 := dsolve(dsys3, method = bvp[midrich], output = array([0.]));
%;
                                   Error, (in dsolve) too many levels of recursion

I DONT KNOW ABOUT THIS ERROR

PLEASE HELP ME

THANKS A LOT

what conditions are necessary that a group G has stabilisers?

i have a work on Magic Squares , and i need to rotate or flip them to all 8 possible directions .
but i am confused to find such special commands in maple for doing my purpose !

may you guide me how can i do this programmaticaly ?

Download magicsquare4.mw

Good morning.

I request your kind suggestion to my query posted.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

Good morning

I request your kind suggestion to my query cited above.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

Hi all.

I'm a student learning Algebra.

I've been searching everywhere and cannot work out how to plot and analyze a function graphically in Maple.

For example, you can see in this video, There is a point for the Vertex of a parabola on the example

http://www.maplesoft.com/TeacherResource/topic.aspx?m=1&c=1&cha=3&sec=9&top=31

I would like to put things like this on my graph (Vertex, or X-Intercepts, or the intersection of 2 lines)

I can certainly find this information by using Algebra (vertex form, etc) but it would help my understanding to also visualize the functions graphically.