Hi Everyone,

    I just upgraded a Linux 64-bit computer from Maple 17 to Maple 18.01.  Code that worked on Maple 17 no longer works on Maple 18.01.  The code uses BLAS matrix operations in in the LinearAlgebra package.  When the first such operation is called, I obtain the following fatal error:

MKL FATAL ERROR on loading the function mkl_blas_avx_xdcopy.

Maple 18.01 is unable to load any of the MKL routines even though the MKL shared libraries are in the Linux bin directory.  If I load my own MKL library (provided by Intel), Maple 18 will run these operatrions, but they ultimately lose precision which causes the program (which works fine in 17) to crash.  Any ideas about how to activate the version of MKL provided by Maple?  Will this version not loose floating-point precision?  Any help is greatly appreciated.

Best wishes.

David

University of Chicago

mode_shapes_and_critical_load(changed_model).mw

This is my code for finding mode shapes and critical load for a bimaterial strut under buckling. 

Although everything else is working fine but I have a problem while solving for critical load.

h_new := convert(series(h, P, 3), polynom):

h_new := convert(series(h, P, 3), polynom):

without converting to polynomial, the code is unable to solve for P. Even on conversion, for differnet S values, I need to change the truncation order of conversion (like for S=0.5, it would work with 3 but for other S values I have to change truncation (convert(series(h, P, 6), polynom)), which also causes the number of solutions of equation to change which causes problem with plotting of graphs of critical load that I need (basically I need lowest two plots), thereby restricts me from automating the code with a for loop. I need to test it for various S values and then later in code I need to put teh critical load back and check mode shapes for different a values.

Is there a better way to solve two variable equation to get one variable in terms of another(the equation is quite complicated, contains trigonometric expressions). 

and also if I try to automate the analysis for different S and a values, teh process needs to put teh value back in P which changes everything and teh next time loop operates it just ruins everything. Also there are varied number of solutions of P_crit for differnet S values which makes it difficult to store those solutions during automation?

Hi,

  I have an expression as p in the following. I would like to extract the coeffient with x^n*y^m and x^(n+2)*y^(m+2), however, coeff comand does not work...

***

p:=3*x^n*y^m+4*x^(n+2)*y^(m+2)+k*x^(n+2)*y^(m+2);
coeff(p,x,n);

***  

gives me

***

n m (n + 2) (m + 2) (n + 2) (m + 2)
3 x y + 4 x y + k x y
/ n m (n + 2) (m + 2) (n + 2) (m + 2) \
coeff\3 x y + 4 x y + k x y , x, n/

***

What is the correct command to get the coefficients? Thank you very much

Hi,

I would like to format the solution given by maple.
I have the answer given by a paper and I would like to reproduce the same formula.

I have the expression :

(a1/2+a2/2)*ln(a1/2+a2/2+sqrt((a1/2+a2/2)^2+(b1/2-b2/2)^2+d^2))+(a1/2-a2/)*ln(a1/2-a2/2+sqrt((a1/2-a2/2)^2+(b1/2-b2/2)^2+d^2))

I would like to assume deltaa = a1-a2 and sigmaa = a1+a2.

The issue is that algsubs(deltaa = a1-a2, expr), my a1+a2 is replaced by deltaa+2*a2 and same for algsubs(sigmaa = a1+a2, expr), so i can't have sigmaa*ln(...) + deltaa*ln(...).

And all my squares are developed, for example I have : sqrt(1/4*a1^2+1/4*a2^2+1/2*a1*a2+...)

I can't put them in canonical form (1/2*a1+1/2*a2)^2 to get (1/2*sigmaa)^2.

Sorry for my english,
If you know how to do, i would be really grateful !

Mathieu

Hi. I am trying to identify mode shapes (phi(x)) and natural frequencies  of non-uniform euler-bernoulli beam. There are number of numerical methods to solve ODE with certain boundary conditions (i.e. Runge Kutta method). Problem is that I am newbie here. I am interested in particularly first vibration mode and its frequency. Is there anyone acquainted with it and would be able to help me?  Non-unif.mw

I am writing a big numerical code in maple. I need to write the results in each step in a file. I mean in the first step of loop it writes the results in the first line of a text file, in the second step writes in the second line and to the end. when I use writedata command, it needs to write a complete array or matrix and it is not what i need. In  other words I want to save data for each steps of iteration during the calculation and when it goes to ther next step it writes the result in the next line.

Can you help me to perform it?

Thanks

hi,

I want to solve this to data table , i can plot but i need data in table 

sol1 := dsolve([diff(u(theta),theta) = 427.2461*u(theta)+385620.123/u(theta)-25671.3871, u(0) = .6], numeric);

plots[odeplot](sol1, 0..0.18, color = red);

thanks.

I learned about this problem from Aser's post   See  page of tasks still without  Maple implementation. 

The procedure  game24  solves the problem. In the procedure Acer's  procedure  MyHandler is  used, which prevents the program to stop in case of 0 in the denominator.

game24:=proc(a,b,c,d)

local MyHandler,It, K, M, i, P;

uses StringTools, combinat;

 MyHandler := proc(operator,operands,default_value)

      NumericStatus( division_by_zero = false );

      return infinity;

   end proc;

   NumericEventHandler(division_by_zero=MyHandler); 

It:=proc(L1,L2)

local i, j, L;

L:=[];

for i in L1 do

for j in L2 do

L:=[op(L), op([Substitute(Substitute("( i + j )","i",convert(i,string)),"j",convert(j,string)),Substitute(Substitute("( i - j )","i",convert(i,string)),"j",convert(j,string)),Substitute(Substitute("( i * j )","i",convert(i,string)),"j",convert(j,string)),Substitute(Substitute("( i / j )","i",convert(i,string)),"j",convert(j,string))])];

od; od;

L;

end proc; 

P:=permute([a,b,c,d]); 

K:=[];

for i in P do

K:=[op(K),op(It(It(It([i[1]],[i[2]]),[i[3]]),[i[4]])), op(It(It([i[1]],It([i[2]],[i[3]])),[i[4]])), op(It([i[1]],It(It([i[2]],[i[3]]),[i[4]]))), op(It([i[1]],It([i[2]],It([i[3]],[i[4]])))), op(It(It([i[1]],[i[2]]),It([i[3]],[i[4]])))];

od;

M:=[];

for i in K do

if parse(i)=24 then M:=[op(M), i] fi;

od;

if nops(M)=0 then return `No solutions` else

for i in M do

print(SubString(i,2..length(i)-1));

od; fi; 

end proc:

Two examples:

game24(2,3,8,9);

game24(2,3,3,4);

        No solutions

24.mws

how i can trust in DirectSearch solution result.is there any creteria?

my variable is intensity.

this is my code:

ep0 := 1/(4*3.14); el := 8.54*10^(-2); hbar := 1; vf := 1/300; kb := 1; tem := 2.586*10^(-2); ci := 1; p := 1.458*10^16; beta := 2; ai := 7.1*10^(-4); bi := ai/sqrt(3); enph := .196; d := enph/(kb*tem); n0 := 1/(exp(enph/(kb*tem))-1); gama := hbar*vf; intensity := 10000001; w := 1.55; impurity := 7.2*10^3;

g := hbar*beta/(bi^2*sqrt(2*p*enph)); aa := g^2*(n0+1)/(2*Pi*hbar*gama^2); bb := g^2*n0/(2*Pi*hbar*gama^2); cc := 2/(Pi*gama^2); l := (1*hbar)*w/(2*kb*tem);u := el^2*intensity/(32*w*hbar^2);

DirectSearch:-SolveEquations([op([((enph*ln(1+exp(c+enph/(kb*tem)))/(kb*tem)-polylog(2, -exp(c))+polylog(2, -exp(c+enph/(kb*tem))))*enph*(kb*tem)^2-(enph^2*ln(1+exp(c+enph/(kb*tem)))/(kb^2*tem^2)+2*enph*polylog(2, -exp(c+enph/(kb*tem)))/(kb*tem)+2*polylog(3, -exp(c))-2*polylog(3, -exp(c+enph/(kb*tem))))*(kb*tem)^3+(-exp(b)*enph*ln(1+exp(c+enph/(kb*tem)))+exp(c+d)*enph*ln(1+exp(b-d+enph/(kb*tem)))+exp(b)*kb*tem*polylog(2, -exp(c))-exp(c+d)*kb*tem*polylog(2, -exp(b-d))-exp(b)*kb*tem*polylog(2, -exp(c+enph/(kb*tem)))+exp(c+d)*kb*tem*polylog(2, -exp(b-d+enph/(kb*tem))))*enph*(kb*tem)^2/((exp(b)-exp(c+d))*kb*tem)+(exp(b)*enph^2*ln(1+exp(c+enph/(kb*tem)))-exp(c+d)*enph^2*ln(1+exp(b-d+enph/(kb*tem)))+2*exp(b)*enph*kb*tem*polylog(2, -exp(c+enph/(kb*tem)))-2*exp(c+d)*enph*kb*tem*polylog(2, -exp(b-d+enph/(kb*tem)))+2*exp(b)*kb^2*tem^2*polylog(3, -exp(c))-2*exp(c+d)*kb^2*tem^2*polylog(3, -exp(b-d))-2*exp(b)*kb^2*tem^2*polylog(3, -exp(c+enph/(kb*tem)))+2*exp(c+d)*kb^2*tem^2*polylog(3, -exp(b-d+enph/(kb*tem))))*(kb*tem)^3/((exp(b)-exp(c+d))*kb^2*tem^2))*bb+u*(1/(1+exp(-l-c))-1/((1+exp(-l-c))*(1+exp(l-b))))-(((1*enph)*(enph-2*kb*tem*ln(1+exp(-b+enph/(kb*tem))))/(2*kb^2*tem^2)+2*kb^2*tem^2*(-polylog(2, -exp(-b+enph/(kb*tem)))+polylog(2, -cosh(b)+sinh(b))))*enph*(kb*tem)^2-(enph^2*(enph-3*kb*tem*ln(1+exp(-b+enph/(kb*tem))))-6*kb^2*tem^2*(enph*polylog(2, -exp(-b+enph/(kb*tem)))+kb*tem*(-polylog(3, -exp(-b+enph/(kb*tem)))+polylog(3, -cosh(b)+sinh(b)))))*(kb*tem)^3/(3*kb^3*tem^3)-(-exp(b)*enph^2+exp(c+d)*enph^2-2*exp(c+d)*enph*kb*tem*ln(1+exp(-b+enph/(kb*tem)))+2*exp(b)*enph*kb*tem*ln(1+exp(-c-d+enph/(kb*tem)))+2*exp(c+d)*kb^2*tem^2*polylog(2, -exp(-b))-2*exp(b)*kb^2*tem^2*polylog(2, -exp(-c-d))-2*exp(c+d)*kb^2*tem^2*polylog(2, -exp(-b+enph/(kb*tem)))+2*exp(b)*kb^2*tem^2*polylog(2, -exp(-c-d+enph/(kb*tem))))*enph*(kb*tem)^2/((2*(-exp(b)+exp(c+d)))*kb^2*tem^2)-(exp(b)*enph^3-exp(c+d)*enph^3+3*exp(c+d)*enph^2*kb*tem*ln(1+exp(-b+enph/(kb*tem)))-3*exp(b)*enph^2*kb*tem*ln(1+exp(-c-d+enph/(kb*tem)))+6*exp(c+d)*enph*kb^2*tem^2*polylog(2, -exp(-b+enph/(kb*tem)))-6*exp(b)*enph*kb^2*tem^2*polylog(2, -exp(-c-d+enph/(kb*tem)))+6*exp(c+d)*kb^3*tem^3*polylog(3, -exp(-b))-6*exp(b)*kb^3*tem^3*polylog(3, -exp(-c-d))-6*exp(c+d)*kb^3*tem^3*polylog(3, -exp(-b+enph/(kb*tem)))+6*exp(b)*kb^3*tem^3*polylog(3, -exp(-c-d+enph/(kb*tem))))*(kb*tem)^3/((3*(-exp(b)+exp(c+d)))*kb^3*tem^3))*aa-u*(1/(1+exp(l-b))-1/((1+exp(-l-c))*(1+exp(l-b)))) = 0, -cc*polylog(2, -exp(b))+cc*polylog(2, -exp(-c))-impurity = 0])], tolerances = 10^(-8), evaluationlimit = 20000)

Can someone please advise me how to solve the following for 'beta'. Solve function is not able to do that, or at least I dont know how.

-9999990000000000000000*cos(166*beta)*sinh(166*beta)*cosh(88*beta)^2-9999990000000000000000*cos(88*beta)^2*sin(166*beta)*cosh(166*beta)+9999990000000000000000*sinh(166*beta)*cos(88*beta)^2*cos(166*beta)+9999990000000000000000*cosh(88*beta)^2*cosh(166*beta)*sin(166*beta)+10000010000000000000000*cos(166*beta)*sinh(166*beta)+10000010000000000000000*sin(166*beta)*cosh(166*beta)+9999990000000000000000*sinh(88*beta)*cos(166*beta)*cosh(166*beta)*cosh(88*beta)-9999990000000000000000*sinh(88*beta)*sin(166*beta)*sinh(166*beta)*cosh(88*beta)+9999990000000000000000*sin(88*beta)*cos(88*beta)*sinh(166*beta)*sin(166*beta)+9999990000000000000000*cos(88*beta)*cos(166*beta)*sin(88*beta)*cosh(166*beta)-9980010000000000000000*cosh(88*beta)^2*sinh(166*beta)*cos(88*beta)^2*cos(166*beta)-9980010000000000000000*cosh(88*beta)^2*cosh(166*beta)*sin(166*beta)*cos(88*beta)^2+9980010000000000000000*sinh(88*beta)*cos(88*beta)^2*sin(166*beta)*sinh(166*beta)*cosh(88*beta)-9980010000000000000000*cos(88*beta)*cosh(88*beta)^2*sin(88*beta)*sin(166*beta)*sinh(166*beta)+9980010000000000000000*sinh(88*beta)*cosh(88*beta)*cosh(166*beta)*cos(88*beta)^2*cos(166*beta)+9980010000000000000000*cosh(88*beta)^2*cosh(166*beta)*cos(88*beta)*sin(88*beta)*cos(166*beta)-9980010000000000000000*cos(88*beta)*sinh(88*beta)*cos(166*beta)*sin(88*beta)*sinh(166*beta)*cosh(88*beta)+9980010000000000000000*cos(88*beta)*cosh(88*beta)*sin(88*beta)*sin(166*beta)*cosh(166*beta)*sinh(88*beta)=0

Is it within the Physics environment possible to specify two sets, A and B, say, of quantities for which the following holds?

1.) any two elements of A anticommute,

2.) any two elements of B anticommute (as well), but

3.) any quantity from A commutes (not anticommutes) with any quantity from B.

Hello those in Mapleprimes,

What I want to know is whether this is possible or not, and if possible, how should I write a code?

The following code works properly:

U:=(x,y)->(x^theta+y^theta+X)^(1/theta);

diff(U(x,y),x)/diff(U(x,y),y)=p/q;simplify(%);

But, what I want to ask is this. As for the part of simplify(%), I want to do it with a way which has me 

feel more being from the former to latter.

That is, if ,for example, "diff(U(x,y),x)/diff(U(x,y),y)=p/q;@simplify;" works, it is better to me, though this does not work.

As the second part, @simplify, receives the result of the first part"diff(U(x,y),x)/diff(U(x,y),y)", it seems more 

natural to me than to write simplify(%).

Can't I do this, in a meaning, reversal of operator to argument?

taro

Hello,
I have a system of first order diff. equations which I would like to solve symbolically. Unfortunately, Maple does not solve the system. Do anybody have suggestions how can I solve this system (please see below):

diff(S(t), t) = -eta*(C[max]*w*N-alpha*Q(t))*K(t)*S(t)/(w*N*(S(t)+K(t))),

diff(K(t), t) = S(t)*((z*eta*alpha*(C[max]*w*N-alpha*Q(t))*S(t)-upsilon*(eta*alpha^2*Q(t)^2-2*C[max]*w*N*eta*alpha*Q(t)+((-N*w+z)*alpha+N*C[max]^2*w*eta)*N*w))*K(t)^2+(2*((1/2)*z*eta*(C[max]*w*N-alpha*Q(t))*S(t)+N*w*upsilon*(N*w-z)))*S(t)*alpha*K(t)+N*S(t)^2*w*alpha*upsilon*(N*w-z))/((K(t)^2*alpha*z+3*S(t)*K(t)*alpha*z+S(t)*(2*S(t)*z*alpha+upsilon*(C[max]*w*N-alpha*Q(t))))*(S(t)+K(t))*N*w),

diff(Q(t), t) = (-alpha*z*(z*eta*(C[max]*w*N-alpha*Q(t))*K(t)+N*w*upsilon*(N*w-z))*S(t)^2+(-z^2*eta*alpha*(C[max]*w*N-alpha*Q(t))*K(t)^2-(eta*alpha^2*Q(t)^2-2*C[max]*w*N*eta*alpha*Q(t)+N*w*((2*N*w-2*z)*alpha+N*C[max]^2*w*eta))*z*upsilon*K(t)-N*w*upsilon^2*(N*w-z)*(C[max]*w*N-alpha*Q(t)))*S(t)-N*w*z*alpha*upsilon*K(t)^2*(N*w-z))/((2*S(t)^2*alpha*z+(3*z*alpha*K(t)+upsilon*(C[max]*w*N-alpha*Q(t)))*S(t)+K(t)^2*alpha*z)*N*w*upsilon)

where initials conditions are:

S(0) = S0, K(0) = K0, Q(0) = Q0

Thanks,

Dmitry

Hello those in Mapleprimes,

I want to know whether there is a good way to modify the first expression to the second one below.

first expression: 

> p+p^(-1/(theta-1))*sum(q[i]^(theta/(theta-1)), i = (1 .. n));

second expression:

> p^(-1/(theta-1))*(p^(theta/(theta-1))+sum(q[i]^(theta/(theta-1)),i=1..n));

First and Second are the same. But, I want to know how I can modify from the former to the latter.

Thank you in advance.

taro

Let us consider the expression

restart;
f := log[x](1+(x^a-1)*(x^b-1)/(x-1));
Does it define a convex function on the interval 0..1 and on the interval 1..infinity if the parameters a>0, a< 1, b >0, b <1?

My try is

and

.

At the same time I have got problems in the general case. For example,

Error, (in @) too many levels of recursion

and

That's all right if

convex.mw