## Eigenvalues of Symmetrix matrix...

i am new user in maple .i want to calculate eigenvalues of a symmetrix matrix to find max or min value but i usually face a error code ' (in simpl/max) complex argument to max/min'

i know that a symmetrix matrix have real eigenvalues.

for example:
restart:with(LinearAlgebra):with(GraphTheory):interface(rtablesize=infinity):
SeidelMatrix:=proc(G::Graph) local J,B,A,S;
J:=Matrix(1..NumberOfVertices(G),1..NumberOfVertices(G),shape=constant[1]):
B:=IdentityMatrix(NumberOfVertices(G)):
S:=J-B-MatrixScalarMultiply(A,2):
convert(S,Matrix,shape=symmetric,datatype=float):
return S:
end proc:
E:=sort(eval(Eigenvalues(SeidelMatrix(CycleGraph(7)),output='list'))):
(min,max)(E);
Error, (in simpl/min) complex argument to max/min: (1/3)*(-28+(84*I)*3^(1/2))^(1/3)+(28/3)/(-28+(84*I)*3^(1/2))^(1/3)-1/3

## Evaluate min and max in Excel...

Hello,

a=number      b=number

=maple("Qm:=x->(diff(KelvinBei(0,x),x)*psi2(x)-(diff(KelvinBer(0,x),x)*psi1(x)))/&1";B11)

=maple("Qv:=x->(&1*psi2(x)-(&2*psi1(x)))/(&3*&4)";B6;B7;B2;B11)

=maple("Fm:=x->(Qv(x)+(&1*Qm(x)))/2";B3)

I need abs(max(Fm(x))) and abs(min(Fm(x))) values of function Fm(x), locals, for a<x<b in excel.

Now I use a vector to do this, but I need an exact values not an approximation of a fuction evaluated with n values of x.

what I do:

=maple("seq(i,i=&1..&2,&3)";N2;N3;N4)

=maple("A:=&1";N5)

=maple("G:=map(g->evalf(eval(Fm(x),x=g)),[A])")

=maple("max(abs~(G))")

Someone can help me??

## Bounds in several variables...

Hello! Hope everything fine with you. Please share the command to find the max and min values of the attached function, I had tried but I was only for one variable. I am waiting your quick response.

Examples.pdf

Mob #: 0086-13001903838

## How to plot parametric maximum?...

Suppose I have a function like this: f=cos(2t/m)+cos(2(t+5)/m).

Now for each fixed m, we get the maximum value of f. Then I want to build a plot where x-axis is m and y-axis is f, how could I do that? Please help!

## What logic is followed in this plot?...

plots[implicitplot3d](max(-x+y+z, x-y+z, x+y-z) = 1.0, x = 0 .. 1, y = 0 .. 1, z = 0 .. 1);

The help page for max does not explain or show an example of max(sequence of expressions)= a constant.

## How to extract data from graph...

Hello,

I would like to know how to do the following. If I received a plot of a graph, but I did not know it function, how could I get an accurate value for its maximum and minum points? Any help is greatly appreciated! Thank you in advance!

Kind regards,

Gambia Man

## Maximum point of plot...

hi all

i have a plot in maple. how can i print the maximum point of my plote?

## "max"/"min" Command in Maple...

Hi all,

min/max command in Maple can return the minimum/maximum of a sequence or array.

In my case, I want to find not only the minimum/maximum, but also where are them. How can I do?

For example, there is a squence [1,2,3,7,6,5,4].

Through max([1,2,3,7,6,5,4]), we can get 7.

But I still want to get "4" which is the index value of "7".

Thank you.

## evaluating derivatives of max(x^2,sqrt(abs(x)))...

I've plotted the graph for this max function. Is there any way I can find the points of discontinuity in general and then use that to compute the derivatives at points where it exists?

## Simplifying a procedure's result...

Hi all,

I'm having some trouble trying to make it so the answer Max(3,1,x,4) turns into Max(x,4), that is, only the greates number and the non numerical values are returned. I've tried a bunch of different things, but have gone out of ideas.

This is the link to the Maple file :6-1.mw and this is the code:

 > #Improve the general Max procedure on page 224 so that Max(3,x,1,4)returns Max(x,4). That is, the procedure returns the maximum numerical value along with all nonnumerical values.
 > Max:=proc() local m, i; m:=-infinity; for i in (args) do   if not type(i, numeric) then     return 'procname'(args):   end if;   if i>m then     m:=i   end if; end do; m; end proc;
 (1)
 > Max(3,1,x,4);
 (2)
 >

Would really appreaciate your help with this

## the maximize of equation...

I want to solve maximize of equation,but the maximize failed to solve it,who can help me.thanks.

 (1)

 (2)

 (3)

 (4)

 (5)

 (6)

Iwant to maximize the equation (5)and (6),under the conditon of x,y,z are negative or positive at the same time.

## maximum number of equations for MapleSim...

Dear Community,

Does anybody know, if there is a limit for the maximum number of equations for MapleSim? I tried with a system of 4456 equations, and I got the error message "(in DSN/RunSimulation ) system is inconsistent" When I took away most of the components (subsystems) it worked. So I suppose there must be some limit for the number of equations.

Andras

## Spacial Matrix Prodution...

Hi all

I have a mathematical problem and I asked it in various sites but the answers till yet are not correct.

Assume that we have:

T[m]:=t->t^m:
b[n,m]:=unapply(piecewise(t>=(n-1)*tj/N and t<n*tj/N, T[m](N*t-(n-1)*tj), 0), t):

where n,N,tj are known constants. furthermore assume that we want to comute the following integral:

for following approximations:

I have written the following code but it seems to be incorrect:

V1:=Vector([seq(seq(b[n,m](t),m=0..1),n=1..3)]);
V:=evalf(V1.Transpose(V1));

the original program is :

taaylor.mws

I will be so grateful if any one can help me to solve it by maple

Ph.D Candidate

Applied Mathematics Department

## How do I compare solutions from numeric dsolve?...

Hello,

This is probably a silly question, but I am trying to compare the difference between two variables in the numerical solution of a system of ODEs. Ideally, I would like a method to find the maximal difference that occurs between two variables.

The following is a highly simplified example of what I'm talking about. In this case I'd like some means to find the timepoint and magnitude of the maximal difference between y2(t) and y3(t) for t>0, which from the plot can be seen to occur at about 1.75 seconds. Note: I realise this particular case admits an analytic solution of y3(t) which could be exploited, but in the general case I'm interested in that won't be true.

 (1)

 (2)

## Error, (in ysol) cannot evaluate the solution furt...

Hello everybody, I need help please

 > restart:with(plots):
 > mb:=765; mp:=587;Ib:=76.3*10^3;Ip:=7.3*10^3; l:=0.92; d:=10; F:=-1.2; omega:=0.43;g:=9.81;ly:=3;k:=0.02001014429;
 (1)
 > A:=168913.8672;
 (2)
 > s:=0.0666666666667;
 (3)
 > n:=49.97465213;
 (4)
 > eq1:=(mp+mb)*diff(x(t),t\$2)+mp*(d*cos(theta(t))+l*cos(alpha(t)+theta(t)))*diff(theta(t),t\$2)+mp*l*cos(alpha(t)+theta(t))*diff(alpha(t),t\$2)+mp*(d*diff(theta(t),t)^2*sin(theta(t))+l*(diff(theta(t),t)+diff(alpha(t),t))^2*sin(alpha(t)+theta(t)))+A*2*(s*sinh(k*ly+k*ly)*sin(omega*t-k*x(t)))=0;
 (5)
 > eq2:=(mp+mb)*diff(z(t),t\$2)-mp*d*(sin(theta(t)+alpha(t))+sin(theta(t)))*diff(theta(t),t\$2)-mp*l*sin(alpha(t)+theta(t))*diff(alpha(t),t\$2)+mp*(d*diff(theta(t),t)^2*cos(theta(t))+l*(diff(theta(t),t)+diff(alpha(t),t))^2*cos(alpha(t)+theta(t)))+9.81*(mp+mb)+1000*g*z(t)*15.3*30+A*cosh(k*ly+k*z(t))*n*(cos(omega*t-k*15)-cos(omega*t+k*15))=0;
 (6)
 > eq3:=mp*(d*cos(theta(t))+l*cos(alpha(t)+theta(t)))*diff(x(t),t\$2)-mp*(l*sin(theta(t)+alpha(t))+d*sin(theta(t)))*diff(z(t),t\$2)+(Ip+Ib+mp*(d^2+l^2)+2*mp*d*l*cos(alpha(t)))*diff(theta(t),t\$2)+(Ip+mp*l^2+mp*d*l*cos(alpha(t)))*diff(alpha(t),t\$2)-mp*sin(alpha(t))*(l*d*diff(alpha(t),t)^2-l*d*(diff(alpha(t),t)+diff(theta(t),t))^2)+mp*9.81*l*sin(alpha(t)+theta(t))+mp*9.81*d*sin(theta(t))=0;
 (7)
 > eq4:=mp*l*cos(alpha(t)+theta(t))*diff(x(t),t\$2)-mp*l*sin(alpha(t)+theta(t))*diff(z(t),t\$2)+(Ip+mp*l^2+mp*d*l*cos(alpha(t)))*diff(theta(t),t\$2)+(Ip+mp*l^2)*diff(alpha(t),t\$2)-mp*9.81*l*sin(alpha(t)+theta(t))+l*d*mp*diff(theta(t),t\$1)^2*sin(alpha(t))=0;
 (8)
 > CI:= x(0)=0,z(0)=0,theta(0)=0,alpha(0)=0,D(x)(0)=0,D(alpha)(0)=0,D(z)(0)=0,D(theta)(0)=0;
 (9)
 > solution:=dsolve([eq1,eq2,eq3,eq4,CI],numeric,maxfun=100000);
 (10)

 > odeplot(solution,[[t,x(t)],[t,alpha(t)],[t,z(t)],[t,theta(t)]], t=0..1000, thickness=2);
 > odeplot(solution,[[t,x(t)]], t=0..1000, thickness=2);
 > odeplot(solution,[[t,z(t)]], t=0..1000, thickness=2);
 > odeplot(solution,[[t,alpha(t)]], t=0..1000, thickness=2);
 > odeplot(solution,[[t,theta(t)]], t=0..1000, thickness=2);

thank you

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