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Determine using determinants the range of values of a (if any) such that
f(x,y,z)=4x^2+y^2+2z^2+2axy-4xz+2yz
has a minimum at (0,0,0).

From the theory, I understand that if the matrix corresponding to the coefficients of the function is positive definite, the function has a local min at the point. But, how do I get the range of values of a such that f is a min? Is this equivalent to finding a such that det(A) > 0?

 

2.

Now modify the function to also involve a parameter b: g(x,y,z)=bx^2+2axy+by^2+4xz-2a^2yz+2bz^2. We determine conditions on a and b such that g has a minimum at (0,0,0).
By plotting each determinant (using implicitplot perhaps, we can identify the region in the (a,b) plane where g has a local minimum.

Which region corresponds to a local minimum?

Now determine region(s) in the (a,b) plane where g has a local maximum.

I don't understand this part at all..

Hi,

 

I want to compute the determinant of a matrix A with this formula:

 Can someone help me to do it.  Of course, here I am using Einstein's convention.

Thank you in advance.

--------------------------------------
Mario Lemelin
Maple 18 Ubuntu 14.04 LTS - 64 bits
Maple 18 Win 7 Pro - 64 bits messagerie : mario.lemelin@cgocable.ca téléphone :  (819) 376-0987

I have following expression

f:=t->((1/8)*s^2*sinh(4*t)+t+(1/2)*s^2*t+s*sinh(2*t))/(1+s*cosh(2*t))

which is 1 solution of the ODE

ode2 := -(diff(y(t), t, t))+(4-12/(1+s*cosh(2*t))+(8*(-s^2+1))/(1+s*cosh(2*t))^2)*y(t) = 0

Now I wanted to construct 2 linear independent solutions via:

f1:=f(t_b-t)

f2:=f(t-t_a)

and calculate the Wronskian:

with(LinearAlgebra); with(VectorCalculus)

Determinant(Wronskian([f(t_b-t), f(t-t_a)], t))

Since I know these functions are solutions of the second order ODE which does not contain any first order derivative the Wronskian should be a constant. Unfortunately Maple has a hard time to simplify it since the epxression is a little big. Is it my fault or has anyone an idea what to do?

Dear users,

I have a Maple file to evaluate the shape functions on hexahedrons and to save the results in a .cpp file. However, the execution time is very long and when I do not loose the connection with the server, I ran out of memory (I have 32GB!!). So, I very keen to hear some tips on how to optimize it! I am sure this computation is simple enough for the Maple powerful and I quite sure there are some tricks to optimize it! The code is below.

Thanks in advance!

I have a matrix of order 14 with whose entries being variables about u_1 to u_12. I want to get its determinant, but it return no results. It explains that it is too big for maple to deal with. So I wonder how to deal with such kind of this problem?

Thank you very much for kind attention!

Hello,

I have the following problem:

My function is defined by the determinant of 2 Heun functions

If I plot the phase I get something which looks quite what I'm looking for.

To get a better result I thought I would manually carry out the Wronskian as far as possible...

Doing some manipulations I get another form of the Wronskian which in fact should give the same result...

the problem is it doesnt :-(

I've added the spreadsheet....

Hello everyone, new member here. I've been working with Maple 16/Mathematica 8/Matlab to find the determinants of some symbolic nxn matrices (a1,1 a1,2 etc). Matlab is able to do them quite easily but when they start getting too large it starts truncating them down to 25000 terms. Mathematica works like a charm but I want to beable to verify the results with Maple. Maple does great up to 7x7  but at 8x8 it seems to also truncate results like Matlab and past that...

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