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.

hi 

i want clear ss variable but i can not do it please help me.

my code:

restart;

a := Matrix([1, 2, 3, 4, 5]); S := {}; ss := {};

for k to 5 do

S := `union`(S, {op(DirectSearch:-SolveEquations([a(1, k)*x+2+y = 0, x+y = 0])[3])});

ss := map(proc (c) options operator, arrow; rhs(c) end proc, S);

aaa := op(ss[[1]]); bbb := op(ss[[2]]);

"i want clear ss and then make ss as ss:={} in loop"

"for example if clear command clear ss variable"

"clear(ss)"

"ss:={}"

end do

Does there exist a Frobenius Group which is not  neither a Dihedralgroup nor  Symm(3) ?

Best regards

Kurt Ewald

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

very slow cause my computer have sound and overheat, still can not 

calculated result

%c := Old_Asso_eigenvector1, a := Old_Asso_eigenvector3,

%b := Old_Asso_eigenvector2

% b <= c, a <= c,

% a ^ c = a, a V c = c

% b ^ c = b, b V c = c

restart;
with(ExcelTools):
with(ListTools):
with(DynamicSystems):
filename := "1207.HK";
open3 := Import(cat(cat("C://Temp//HK//Coal//",filename),".xls"), filename, "B2:B100");
high3 := Import(cat(cat("C://Temp//HK//Coal//",filename),".xls"), filename, "C2:C100");
low3 := Import(cat(cat("C://Temp//HK//Coal//",filename),".xls"), filename, "D2:D100");
close3 := Import(cat(cat("C://Temp//HK//Coal//",filename),".xls"), filename, "E2:E100");
with(CurveFitting):
n := 31;
f := Vector(n);
f2 := Vector(n);
open2 := Vector(n);high2 := Vector(n);gain2 := Vector(n);algebra2 := Vector(n);creative2 := Vector(n);creative3 := Vector(n);
upper2 := Vector(n);lower2 := Vector(n);upperloweratio := Vector(n);
deltaopen2 := Vector(n); deltahigh2 := Vector(n); deltalow2 := Vector(n); deltaclose2 := Vector(n);
logn := Vector(n);
for i from 0 to n-4 do
open2[i+1] := PolynomialInterpolation([[0,open3[n-i][1]],[1,open3[n-(i+1)][1]],[2,open3[n-(i+2)][1]],[4,open3[n-(i+3)][1]]],t):
high2[i+1] := PolynomialInterpolation([[0,high3[n-i][1]],[1,high3[n-(i+1)][1]],[2,high3[n-(i+2)][1]],[4,high3[n-(i+3)][1]]],t):
low2[i+1] := PolynomialInterpolation([[0,low3[n-i][1]],[1,low3[n-(i+1)][1]],[2,low3[n-(i+2)][1]],[4,low3[n-(i+3)][1]]],t):
if (close3[i+1][1]/close3[i+2][1]-1) < 0 then
gain2[i+1] := -1*round(100*abs(close3[i+1][1]/close3[i+2][1]-1)):
else
gain2[i+1] := round(abs(100*(close3[i+1][1]/close3[i+2][1]-1))):
end if;
deltaclose2[i+1] := close3[i+1][1] - close3[i+2][1];
deltahigh2[i+1] := high3[i+1][1] - high3[i+2][1];
deltaopen2[i+1] := open3[i+1][1] - open3[i+2][1];
logn[i+1] := ln(close3[i+1][1]/close3[i+2][1]);
f[i+1] := (high2[i+1] - open2[i+1])/4*1.8:
f2[i+1] := (open2[i+1] - low2[i+1])/4*1.8:
creative2[i+1] := simplify(((((close3[i+1][1]-close3[i+2][1]) + x)^2 -(close3[i+1][1]-close3[i+2][1])^2))/x)-x;
creative3[i+1] := simplify(((((close3[i+1][1]-close3[i+2][1]) + x)^3 -(close3[i+1][1]-close3[i+2][1])^3))/x);
upper2[i+1] := high3[i+1]-close3[i+1];
lower2[i+1] := close3[i+1]-low3[i+1];
upperloweratio[i+1] := round((lower2[i+1]/upper2[i+1])[1]);
od;
with(LinearAlgebra):
HilbertConj := proc(Px,Py)
return MatrixMatrixMultiply(Px,Py);
end proc:
HilbertDisj := proc(Px,Py)
return Px+Py- MatrixMatrixMultiply(Px,Py);
end proc:

t:=1;
i := 0;
InputMatrix3 := Matrix([[xxx, close3(t+1+i) , close3(t+2+i)],
[close3(t+1+i) , close3(t+2+i),0],
[close3(t+2+i),0 , 0]]):
InputMatrix3b := Matrix([[close3(t+1+i), close3(t+2+i) , close3(t+3+i)],
[close3(t+2+i) , close3(t+3+i),0],
[close3(t+3+i),0 , 0]]):
InputMatrix3c := Matrix([[close3(t+2+i), close3(t+3+i) , close3(t+4+i)],
[close3(t+3+i) , close3(t+4+i),0],
[close3(t+4+i),0 , 0]]):
m := MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3);
eigenvalues1 := Eigenvalues(m);
sys1 := MatrixMatrixMultiply(m-Matrix([[eigenvalues1[1],0,0],[0,eigenvalues1[1],0],[0,0,eigenvalues1[1]]]), Matrix([[x],[y],[z]]));
%solve([sys1[1][1],sys1[2][1],sys1[3][1]], [x,y,z]);
sol1 := solve([sys1[1][1],sys1[2][1]], [x,y,z]);

sys2 := MatrixMatrixMultiply(m-Matrix([[eigenvalues1[2],0,0],[0,eigenvalues1[2],0],[0,0,eigenvalues1[2]]]), Matrix([[x],[y],[z]]));
%solve([sys2[1][1],sys2[2][1],sys2[3][1]], [x,y,z]);
sol2 := solve([sys2[1][1],sys2[2][1]], [x,y,z]);

sys3 := MatrixMatrixMultiply(m-Matrix([[eigenvalues1[3],0,0],[0,eigenvalues1[3],0],[0,0,eigenvalues1[3]]]), Matrix([[x],[y],[z]]));
%solve([sys3[1][1],sys3[2][1],sys3[3][1]], [x,y,z]);
sol3 := solve([sys3[1][1],sys3[2][1]], [x,y,z]);

Old_Asso_eigenvector1 := Matrix([[rhs(sol1[1][1]),rhs(sol2[1][1]),rhs(sol3[1][1])],[rhs(sol1[1][2]),rhs(sol2[1][2]),rhs(sol3[1][2])],[rhs(sol1[1][3]),rhs(sol2[1][3]),rhs(sol3[1][3])]]);
Old_Asso_eigenvector2 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3b), InputMatrix3b)):
Old_Asso_eigenvector3 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3c), InputMatrix3c)):

% b <= c, a <= c, c := Old_Asso_eigenvector1, a := Old_Asso_eigenvector3, b := Old_Asso_eigenvector2
testa := HilbertConj(Old_Asso_eigenvector3[2], Old_Asso_eigenvector1);
testb := HilbertDisj(Old_Asso_eigenvector3[2], Old_Asso_eigenvector1);
testc := HilbertConj(Old_Asso_eigenvector2[2], Old_Asso_eigenvector1);
testd := HilbertDisj(Old_Asso_eigenvector2[2], Old_Asso_eigenvector1);

sysa := testa[1][1] = Old_Asso_eigenvector3[2][1][1];
sysb := testb[1][1] = Old_Asso_eigenvector1[2][1][1];
sysc := testc[1][1] = Old_Asso_eigenvector2[2][1][1];
sysd := testd[1][1] = Old_Asso_eigenvector1[2][1][1];

solve(sysa, xxx);

Hi all,

I'm trying to plot the regions of a cube that are defined by an inequality. At the moment I am able to plot only the surface defined by the corresponding equality. 

That's the code: 

with(plots)

implicitplot3d(x^2*y = z, z = 0 .. 1, y = 0 .. 1, x = 0 .. 1);

Now I would like to plot the two regions defined by the corresponding inequality. 

Have you got any idea on how to do this?

Bests

Manuele

Hi My main problem is that the new installer is ridiculously small that I cannot even press the buttons acuratley. I am running windows 8.1 on a Surface Pro 2. I had no problems installing maple 17.

I also ran into errors using the Bitrock installer 3 times, I am not even sure if it is installed correctly now.

is there anyway to get maple 18 without using the Bitrock installer?

Hello guys ...

I used a numerically method to solve couple differential equation that it has some boundary conditions. My problem is that some range of answers has 50% error . Do you know things for improving our answers in maple ?

my problem is :

a*Φ''''(x)+b*Φ''(x)+c*Φ(x)+d*Ψ''(x)+e*Ψ(x):=0

d*Φ''(x)+e*Φ(x)+j*Ψ''(x)+h*Ψ(x):=0

suggestion method by preben Alsholm:

a,b,c,d,e,j,h are constants.suppose some numbers for these constants . I used this code:


VR22:=0.1178*diff(phi(x),x,x,x,x)-0.2167*diff(phi(x),x,x)+0.0156*diff(psi(x),x,x)+0.2852*phi(x)+0.0804*psi(x);
VS22:=0.3668*diff(psi(x),x,x)-0.0156*diff(phi(x),x,x)-0.8043*psi(x)-0.80400*phi(x);
bok:=evalf(dsolve({VR22=0,VS22=0}));

PHI,PSI:=op(subs(bok,[phi(x),psi(x)]));
Eqs:={eval(PHI,x=1.366)=1,eval(diff(PHI,x),x=1.366)=0,eval(PHI,x=-1.366)=1,eval(diff(PHI,x),x=-1.366)=0,
eval(PSI,x=1.366)=1,eval(PSI,x=1.366)=1};
C:=fsolve(Eqs,indets(%,name));
eval(bok,C);
SOL:=fnormal(evalc(%));


I used digits for my code at the first of writting.

please help me ... what should i do?

X belongto A, eigenvector(X) = 0

from this statement , 

using linearalgebra package eigenvectors function

the eigenvector matrix [3][1],[3][2],[3][3] are 1 , contradict 1=0

so, need to find another kind of eigenvector in terms of algebra 

using original basic calculation solve, however got error

m := Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]]);
eigenvector1 := Eigenvectors(m);
solve(
[eigenvector1[2][1][1]=0, eigenvector1[2][1][2]=0, eigenvector1[2][1][3]=0,
eigenvector1[2][2][1]=0, eigenvector1[2][2][2]=0, eigenvector1[2][2][3]=0,
eigenvector1[2][3][1]=0, eigenvector1[2][3][2]=0, eigenvector1[2][3][3]=0]
);

solve(
[eigenvector1[2][1][1]=0, eigenvector1[2][1][2]=0, eigenvector1[2][1][3]=0,
eigenvector1[2][2][1]=0, eigenvector1[2][2][2]=0, eigenvector1[2][2][3]=0]
);

eigenvalue1 :=
(1/6)*(36*a7*a1*a3+108*a7*a2*a6+108*a8*a4*a3+36*a8*a5*a6

...

eigenvalue2 :=
-(1/12)*(36*a7*a1*a3+108*a7*a2*a6+108*a8*a4*a3+36*a8*a5*a6

...

eigenvalue3 :=
-(1/12)*(36*a7*a1*a3+108*a7*a2*a6+

...

solve(MatrixMatrixMultiply(Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]])-Matrix([[eigenvalue1,0,0],[0,eigenvalue1,0],[0,0,eigenvalue1]]), Matrix([[x],[y],[z]])),[x,y,z]);
solve(MatrixMatrixMultiply(Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]])-Matrix([[eigenvalue2,0,0],[0,eigenvalue2,0],[0,0,eigenvalue2]]), Matrix([[x],[y],[z]])),[x,y,z]);
solve(MatrixMatrixMultiply(Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]])-Matrix([[eigenvalue3,0,0],[0,eigenvalue3,0],[0,0,eigenvalue3]]), Matrix([[x],[y],[z]])),[x,y,z]);

got error when using solve

> solve(MatrixMatrixMultiply(Matrix([[a1, a2, a3], [a4, a5, a6], [a7, a8, a9]])-Matrix([[eigenvalue1, 0, 0], [0, eigenvalue1, 0], [0, 0, eigenvalue1]]), Matrix([[x], [y], [z]])), [x, y, z]);
Error, invalid input: solve expects its 1st argument, eqs, to be of type {`and`, `not`, `or`, algebraic, relation(algebraic), ({set, list})({`and`, `not`, `or`, algebraic, relation(algebraic)})}, but received Matrix(3, 1, {(1, 1) = ((2/3)*a1-(1/6)*(36*a7*a1*a3+108*a7*a2*a6+108*a8*a4*a3+36*a8*a6*a5-72*a7*a3*a5-72*a8*a6*a1-72*a9*a4*a2+48*a9*a5*a1-12*a9*a1^2-12*a5*a1^2+8*a1^3-12*a9^2*a1-12*a5^2*a1-12*a9^2*a5-12*a9*a5^2+36*a8*a6*a9+36*a7*a3*a9+36*a4*a2*a1+36*a4*a2*a5+8*a9^3+8*a5^3+12*(54*a7*a2^2*a6*a4*a1+114*a8*a6*a9*a1*a4*a2+6*a8*a6*a9*a1*a7*a3+54*a8*a4*a3^2*a7*a9-60*a9*a1^2*a8*a6*a5-60*a8*a6*a7*a3*a5^2-60*a8*a6*a4*a2*a9^2-24*a9*a1*a4^2*a2^2+6*...

MatrixOperation := module() option package;  export `+`, LinearAlgebra;
    `+` := proc(a::float, b::float) option overload;
 :-`+`(map(x->x^2,a),map(x->x^2,b));
    end proc;
end module;

with(MatrixOperation);
with(LinearAlgebra):
m := Matrix([[1,2],[3,4]]);
L := MatrixMatrixMultiply(m,m);

1 2  1 2
3 4  3 4

1*1+2*3 = 1 + 6 = 1 after overload + with a+b-a*b
1*2+2*4 = 2 + 8 = -6

L should be Matrix([[1, -6],[....]])

 http://en.wikibooks.org/wiki/Linear_Algebra/

Representing_Linear_Maps_with_Matrices

how to calculate the first step

(2,0) -> (1,1,1) and (1,4) -> (1,2,0)

how to use maple command to get (1,1,1) and (1,2,0)