how to decompose a matrix into time invariant and time variant 

is it possible to make time invariant and time variant template and then decompose into it

i mean decomposition can be 

 time invariant matrix + time variant matrix

or

 time invariant matrix * time variant matrix

 dsolve([Diff(f, t) = f, Diff(f,t) + g = h], f);

 dsolve([Diff(f, t) = f, Diff(f,t)*g = h], f);

where h is orthogonal matrix, f,g,h are matrix

would like to find g and f from h

can dsolve solve differential equation of matrix ? how?

dsolve([Diff(f(t), t) = f(t), Diff(f(t),t) + g(t) = h1(x)*h2(x), int(h1(x)*h2(x),x=-1..1) = 0], [f(t),g(t),h1(x),h2(x)]);

dsolve([Diff(f(t), t) = f(t), Diff(f(t),t)*g(t) = h1(x)*h2(x), int(h1(x)*h2(x),x=-1..1) = 0], [f(t),g(t),h1(x),h2(x)]);

assume x^2 + 1 is from interpolation of polynomial

pdsolve([Diff(f(t), t) = f(t), Diff(f(t),t) + g(t) = h1(x,t)*h2(x,t), h1(x,t)*h2(x,t)= x^2+1], [f(t),g(t),h1(x,t),h2(x,t)]);
pdsolve([Diff(f(t), t) = f(t), Diff(f(t),t)*g(t) = h1(x,t)*h2(x,t), h1(x,t)*h2(x,t) = x^2+1], [f(t),g(t),h1(x,t),h2(x,t)]);

these system can not be solved

hope no real number any more after decomposition and only have iinteger in I time invariant function

The matrix:

<3,-2,-1,2,0>;

<11,4,-8,2,7>;

<0,0,2,0,0>;

<3,3,-4,3,3>;

<-8,4,5,-4,-1>;

has eigenvector:

<2,0,-1,0,1>

Find its corresponding eigenvalue.

(Hint: you don't need to find all the eigenvalues and eigenvectors to answer this question.)

Steps and the solution will be greatly appreciated. thanks!

number10:=`466d06ece998b7a2fb1d464fed2ced7641ddaa3cc31c9941cf110abbf409ed39598005b3399ccfafb61d0315fca0a314be138a9f32503bedac8067f03adbf3575c3b8edc9ba7f537530541ab0f9f3cd04ff50d66f1d559ba520e89a2cb2a83`:

number8:=`315c4eeaa8b5f8bffd11155ea506b56041c6a00c8a08854dd21a4bbde54ce56801d943ba708b8a3574f40c00fff9e00fa1439fd0654327a3bfc860b92f89ee04132ecb9298f5fd2d5e4b45e40ecc3b9d59e9417df7c

I first define

f:=x->convert(x, decimal, hex):

with(Bits):
str1:=convert( `Xor(f(number8), f(number10))`, bytes);

now how can I get back the alphabets, since again use of convert with bytes return the inital argument.

Moreover, I would really appreciate if someone could explain the difference between 

convert(`expr`, bytes)

convert( [expr], bytes)

Many regards!!

if kernel is solve(A*x, x);

then , what is cokernel of a numeric matrix ?

I'd like to pay attention to an application "Periodicity of Sunspots " by Samir Khan, where a real data is analysed. That application can be used in teaching statistics.

PS. The code by Samir Khan works well for me.

Hi everyone

I am currently trying to make my own simple package including a few procedures. So far I have been able to write some "code" that actually works when I open the document and hit "enter". I would, however, like to save the package so it can be accessed during any Maple session using the command "with". I have unsuccesfully tried to comprehend the Maple help pages regarding this question but I definitely don't want to mess things up.

This is what I have written:

mat := module ()
description "useful procedures for mathematics, physics and chemistry";
export AtomicWeight;
option package;

   AtomicWeight := proc (x) description "returns the average atomic mass of the naturally ocurring element";
   Units:-AddSystem(NewSystem, Units:-GetSystem(SI), u);
   return evalf(ScientificConstants:-Element(x, atomicweight, system = NewSystem, units))
   end proc

end module;

What should I do to save it correctly?

Thank in advance,
Mads

Following my previous question

http://www.mapleprimes.com/questions/200627-Lssolve-Midpoint

I wrote the following code

restart:
Phiavg:=0.06;
lambda:=0.05;
Ha:=0;
NBT:=0.5;
Nr:=500;
#N[bt]:=cc*NBT+(1-cc)*4; ## cc between 0 and 1
N[bt]:=cc*NBT+(1-cc^2)*0.75;


                              0.06
                              0.05
                               0
                              0.5
                              500
                                           2
                    0.5 cc + 0.75 - 0.75 cc
eq1:=diff(u(eta),eta,eta)+1/(mu(eta)/mu1[w])*(sigma-Nr*(phi(eta)-phi1[w])-(1-phi(eta))*T(eta)-Ha^2*u(eta))+((1/mu(eta)*(mu_phi*diff(phi(eta),eta)))*diff(u(eta),eta));
eq2:=diff(T(eta),eta)-1/(k(eta)/k1[w]);
eq3:=diff(phi(eta),eta)-phi(eta)/(N[bt]*(1-gama1*T(eta))^2)*diff(T(eta),eta);
 /  d   /  d         \\      1                                 
 |----- |----- u(eta)|| + ------- (mu1[w] (sigma - 500 phi(eta)
 \ deta \ deta       //   mu(eta)                              

    + 500 phi1[w] - (1 - phi(eta)) T(eta)))

             /  d           \ /  d         \
      mu_phi |----- phi(eta)| |----- u(eta)|
             \ deta         / \ deta       /
    + --------------------------------------
                     mu(eta)                
                    /  d         \   k1[w]
                    |----- T(eta)| - ------
                    \ deta       /   k(eta)
                                       /  d         \            
                              phi(eta) |----- T(eta)|            
/  d           \                       \ deta       /            
|----- phi(eta)| - ----------------------------------------------
\ deta         /   /                       2\                   2
                   \0.5 cc + 0.75 - 0.75 cc / (1 - gama1 T(eta))
mu:=unapply(mu1[bf]*(1+a[mu1]*phi(eta)+b[mu1]*phi(eta)^2),eta):
k:=unapply(k1[bf]*(1+a[k1]*phi(eta)+b[k1]*phi(eta)^2),eta):
rhop:=3880:
rhobf:=998.2:
cp:=773:
cbf:=4182:
rho:=unapply(  phi(eta)*rhop+(1-phi(eta))*rhobf ,eta):
c:=unapply(  (phi(eta)*rhop*cp+(1-phi(eta))*rhobf*cbf )/rho(eta) ,eta):
mu_phi:=mu1[bf]*(a[mu1]+2*b[mu1]*phi(eta)):
gama1:=0.00:
a[mu1]:=39.11:
b[mu1]:=533.9:
mu1[bf]:=9.93/10000:
a[k1]:=7.47:
b[k1]:=0:
k1[bf]:=0.597:
zet:=1:
phi1[w]:=phi0:
mu1[w]:=mu(0):
k1[w]:=k(0):

eq1:=subs(phi(0)=phi0,eq1);
eq2:=subs(phi(0)=phi0,eq2);
eq3:=subs(phi(0)=phi0,eq3);
/  d   /  d         \\   //                                    
|----- |----- u(eta)|| + \\0.0009930000000 + 0.03883623000 phi0
\ deta \ deta       //                                         

                      2\                                 
   + 0.5301627000 phi0 / (sigma - 500 phi(eta) + 500 phi0

                           \//               
   - (1 - phi(eta)) T(eta))/ \0.0009930000000

                                                   2\   
   + 0.03883623000 phi(eta) + 0.5301627000 phi(eta) / +

  /                                       /  d           \ /  d  
  |(0.03883623000 + 1.060325400 phi(eta)) |----- phi(eta)| |-----
  \                                       \ deta         / \ deta

         \\//                                        
   u(eta)|| \0.0009930000000 + 0.03883623000 phi(eta)
         //                                          

                          2\
   + 0.5301627000 phi(eta) /
           /  d         \     0.597 + 4.45959 phi0  
           |----- T(eta)| - ------------------------
           \ deta       /   0.597 + 4.45959 phi(eta)
                                        /  d         \
                            1. phi(eta) |----- T(eta)|
         /  d           \               \ deta       /
         |----- phi(eta)| - --------------------------
         \ deta         /                           2
                             0.5 cc + 0.75 - 0.75 cc  
Q:=proc(pp2,fi0) option remember; local res,F0,F1,F2,a,INT0,INT10,B;
print(pp2,fi0);
if not type([pp2,fi0],list(numeric)) then return 'procname(_passed)' end if;
res := dsolve(subs(sigma=pp2,phi0=fi0,{eq1=0,eq2=0,eq3=0,u(1)=-lambda*D(u)(1),u(0)=lambda*D(u)(0),phi(0)=phi0,T(0)=0}), numeric,output=listprocedure,initmesh=10, continuation=cc);
F0,F1,F2:=op(subs(res,[u(eta),phi(eta),T(eta)]));
INT0:=evalf(Int((abs(F0(eta)),eta=0..1)));
INT10:=evalf(Int(abs(F0(eta))*F1(eta),eta=0..1));
a[1]:=evalf(Int(F0(eta)*(F1(eta)*rhop+(1-F1(eta))*rhobf),eta=0..1));
#a[1]:=evalf(Int((F0(eta),eta=0..1)));
a[2]:=(INT10/INT0-Phiavg)/Phiavg; #relative
[a[1],a[2]]
end proc:
Q1:=proc(pp2,fi0) Q(_passed)[1] end proc;
Q2:=proc(pp2,fi0) Q(_passed)[2] end proc;
proc(pp2, fi0)  ...  end;
proc(pp2, fi0)  ...  end;
#Q(116,0.0041);
#tempe:=Optimization:-LSSolve([Q1,Q2],initialpoint=[130,0.01]);
#tempe:=Optimization:-LSSolve([Q1,Q2],initialpoint=[43.55,0.39]);
tempe:=Optimization:-LSSolve([Q1,Q2],initialpoint=[5.65,0.00036]);
#tempe:=Optimization:-LSSolve([Q1,Q2],initialpoint=[12,0.003]); # khoob ba 1
#tempe:=Optimization:-LSSolve([Q1,Q2],initialpoint=[5,0.01]);
                  HFloat(5.65), HFloat(3.6e-4)
           HFloat(5.650000070103341), HFloat(3.6e-4)
           HFloat(5.65), HFloat(3.600105456508193e-4)
     HFloat(29.63242379055208), HFloat(0.0205927592420527)
    HFloat(12.803902258015825), HFloat(0.006395385884750864)
    HFloat(12.803902403534572), HFloat(0.006395385884750864)
    HFloat(12.803902258015825), HFloat(0.00639539649402585)
   HFloat(12.804004931505949), HFloat(0.0063954867657199386)
    HFloat(12.804107604996073), HFloat(0.006395587646689013)
    HFloat(12.80400483062498), HFloat(0.006498160255844027)
    HFloat(12.803902157134855), HFloat(0.006498059374874952)
   HFloat(-1.0206939292143726), HFloat(-3.32764179807047e-4)
   HFloat(-1.0206939079125088), HFloat(-3.32764179807047e-4)
   HFloat(-1.0206939292143726), HFloat(-3.327536344433438e-4)
    HFloat(18.749500943683863), HFloat(0.01993840615828979)
    HFloat(3.9953780262640484), HFloat(0.00481041471606933)
     HFloat(6.166152606930136), HFloat(0.00703619658484674)
    HFloat(7.3193201827812295), HFloat(0.008218585352824569)
Error, (in Optimization:-LSSolve) complex value encountered
sigma:=tempe[2](1);
                          tempe[2](1)
phi0:=tempe[2](2);
                          tempe[2](2)
with(plots):

res2 := dsolve({eq1=0,eq2=0,eq3=0,u(1)=-lambda*D(u)(1),u(0)=lambda*D(u)(0),phi(0)=phi0,T(0)=0}, numeric,output=listprocedure,continuation=cc);
Error, (in dsolve/numeric/process_input) boundary conditions specified at too many points: {0, 1, 2}, can only solve two-point boundary value problems
G0,G1,G2:=op(subs(res2,[u(eta),phi(eta),T(eta)])):
ruu:=evalf((Int(abs(G0(eta))*(G1(eta)*rhop+(1-G1(eta))*rhobf ),eta=0..zet)))/(Phiavg*rhop+(1-Phiavg)*rhobf);
phb:=evalf((Int(abs(G0(eta))*G1(eta),eta=0..1))) / evalf((Int(abs(G0(eta)),eta=0..1))) ;
TTb:=evalf(Int(abs(G0(eta))*G2(eta)*(G1(eta)*rhop*cp+(1-G1(eta))*rhobf*cbf ),eta=0..1))/evalf(Int(abs(G0(eta))*(G1(eta)*rhop*cp+(1-G1(eta))*rhobf*cbf ),eta=0..1));
Error, invalid input: subs received res2, which is not valid for its 1st argument
                /  /1.                                        \
                | |                                           |
0.0008538922115 | |    |G0(eta)| (2881.8 G1(eta) + 998.2) deta|
                | |                                           |
                \/0.                                          /
                    /1.                       
                   |                          
                   |    |G0(eta)| G1(eta) deta
                   |                          
                  /0.                         
                  ----------------------------
                        /1.                   
                       |                      
                       |                      
                       |    |G0(eta)| deta    
                      /                       
                       0.                     
                                                              /Int(
                              1                               |     
------------------------------------------------------------- |     
  /1.                                                         |     
 |                                                            \     
 |              /             6                       6\            
 |    |G0(eta)| \-1.1752324 10  G1(eta) + 4.1744724 10 / deta       
/                                                                   
 0.                                                                 

                    /             6                       6\ , eta = 0. .. 1.)
  |G0(eta)| G2(eta) \-1.1752324 10  G1(eta) + 4.1744724 10 /                  

  \
  |
  |
  |
  /
#rhouu:=evalf((Int((G1(eta)*rhop+(1-G1(eta))*rhobf)*G0(eta),eta=0..1)));

odeplot(res2,[[eta,u(eta)/ruu],[eta,phi(eta)/phb],[eta,T(eta)/TTb]],0..1);
#odeplot(res2,[[eta,u(eta)],[eta,phi(eta)],[eta,T(eta)]],0..1);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
rhou:=evalf((Int(abs(G0(eta))*(G1(eta)*rhop+(1-G1(eta))*rhobf ),eta=0..zet))):

Nub:=(1/G2(1))*(((1+a[k1]*abs(G1(0))+b[k1]*abs(G1(0))^2)/(1+a[k1]*Phiavg+b[k1]*Phiavg^2)));
                0.6905123602 (1 + 7.47 |G1(0)|)
                -------------------------------
                             G2(1)             
(rhs(res2(0.0000000000001)[3])-rhs(res2(0)[3]))/0.0000000000001;
Error, invalid input: rhs received res2(0.1e-12)[3], which is not valid for its 1st argument, expr
sigma;
                          tempe[2](1)
NBT;
                              0.5
>

the above code has been worked for NBT=0.6 and higher, whereas as NBT decreases, the code doesnt converge easily.

How can I fix this problem?

Thanks for your attention in advance

Amir

Good afternoon sir.

I request your kind suggestion to the above cited question.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

This is a Windows specific question. If I currently have the worksheet named "myworksheet.mw" in the directory "C:\projects" open in Maple, is there a command I can execute to retreive the path "C:/projects" as a string? 

assume f:= x^2*y^3/z^7

would like to get [x^2, y^3, z^(-7)]

Voting is open for the next individual prize to be awarded as part of the Möbius App Challenge.  The winner will receive a DSLR Camera Prize Pack! 

Here are the finalist Apps:

• Interactive Beam Analysis
• Heat Equation
• Ellipse
• Solving Systems of Equations

If you do not have the latest version of Java installed, released last week, you may have problems viewing these apps, as older versions of Java seem to be quietly disabling themselves.  I’ve attached a zip file of the finalist Apps in case it is helpful. finalists.zip

Note that, if you ever have any problems viewing Apps in your browser, or simply want to work offline, you can always download a Möbius App and view it in Maple or the free Maple Player. To download a Möbius App, follow the link to the App and then click on the Download button near the top left of the page.

You can vote for your favorite through our Facebook page or, if you’re not on Facebook, send an email with your vote to Mobius-Project@maplesoft.com.

And remember, we are now accepting entries for the next quarterly prize. You could win an Xbox One!  See the Möbuis App Challenge for details.

Voting closes Jan. 30.

eithne

Voting is open for the next individual prize to be awarded as part of the Möbius App Challenge.  The winner will receive a DSLR Camera Prize Pack! 

Here are the finalist Apps:

• Interactive Beam Analysis
• Heat Equation
• Ellipse
• Solving Systems of Equations

If you do not have the latest version of Java installed, released last week, you may have problems viewing these apps, as older versions of Java seem to be quietly disabling themselves.  I’ve attached a zip file of the finalist Apps in case it is helpful. finalists.zip

Note that, if you ever have any problems viewing Apps in your browser, or simply want to work offline, you can always download a Möbius App and view it in Maple or the free Maple Player. To download a Möbius App, follow the link to the App and then click on the Download button near the top left of the page.

You can vote for your favorite through our Facebook page or, if you’re not on Facebook, send an email with your vote to Mobius-Project@maplesoft.com.

And remember, we are now accepting entries for the next quarterly prize. You could win an Xbox One!  See the Möbuis App Challenge for details.

Voting closes Jan. 30.

eithne

compute the squarefree decomposition of the following polynomials in Q[x] and inF_3[x].
(1)  f=x^6-x^5-4x^4+2x^3+5x^2-x-2
(2)  g=x^6-5x^5+12x^4-6x^3-9x^2+12x-4
            

I am trying to solve a fixed-point equation.

However, no solutions are returned, and I get the warning message "Warning, solutions may have been lost."  How can I be sure that the full set of solutions has been returned?  (I should also say that, based on other cases of the same problem, I expect that there are two or three solutions.)

I received an unexpected error message when trying to minimize a function: evaluating

returns the error message

Error, (in @) too many levels of recursion

Why am I getting this message?  It's hard for me to see how minimizing a function involves recursion, unless Maple is trying to iteratively approximate a solution.