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I would like to use Newton's Method (the multivariate one) in order to solve a system of equations. From what I understand, fsolve is essentially MAPLE's version of the multivariate Newton's Method. Is there a way to do the multivariate Newton's method any other way, other than fsolve? Also, is there a way to specify our own initial guess and tolerance for the Newton's Method and to get other details such as the number of iterations?

Hello maple users,

I have 2 functions and each functions has 8 variables. I run a matlab code and get outputs for different values of these variables. I assumed 3 of them as constant because the combinations are too many. Anyway, I plot the results and I can see that one function is much better than the other. But I need to compare these functions mathematically. I need to show some proofs. Has anyone any idea what should I do? I wrote the functions on maple and take derivative with respect to one variable and try to see the reaction of the functions to that variable. i am confused.

 

Thanks

 

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..

cubic4.mw

I have created a multivariate polynomial with variables P1,...,P6, and would like to factor the poly in terms of (Px-Py) where x,y are combinations of 1-6 (x not equal y). I am new to Maple and have only tried the "Factor" and "Simplify" dropdown menu commands, but neither of these seem to produce anything remotely close to what I need.

Thanks

Derek

I would like to attach a maple document to refer to but dont see how to attach a document to this question.

 

Edit:

Having Uploaded the intended file, I can direct your attention to eqn (14) which is factored into (15) nicely, but when things get a little more complicated as in (45), the factored form in (46) does not contain any of the (Px-Py) forms I am looking for. Is there a way to steer the factor function toward certain forms?

Edit2:

divide.mw

As seen in this form of the problem statement (using quadratics instead of cubics), the divide function does not seem to capture the factorability. From file divide.mw (attached), eqns (19) and (24) are equivalent since the subtraction of the two produces 0 as seen in (28), however both the factor command (23) and the divide command (29) produce nothing substantive.

Dear Maple experts,

I would like to generate population data that is the best possible approximation of a multivariate normal distribution with a specified covariance matrix and vector of means. I do not want to draw a sample from a multivariate distribution, but I want the population values itself which are approximately multivariate normal distributed. The size of the datamatrix should be limited, otherwise I could draw a huge sample from a multivariate normal distribution. For instance, I would like to generate a 200 by 6 data matrix that is the best (or at least good enough) approximation of a MVN distribution. For a bivariate normal distribution one could calculate the probalities of a grid by integrating the density, but for six variables that seems undoable. 

Before trying the invent the wheel again, I think I will ask this question to experts, because it is unlikely that there is no already existing algorithm that does the job pretty well.

Thanks in advance,

Harry Garst

I need to maximize two multivariate objective functions (f(x1,y1,z1,t1) and g(x2,y2,z2,t2)) with inequality and nonnegativity constraints (x1, x2>0 and y1, z1, t1, y2, z2, t2 >=0). I am looking for parametric not numerical solutions.


What is the best way to find the solution to such a problem using maple?

Say I have a polynomial x^5 + 4xy^4 + 2y^3 +  x*y^2 + x^2 + y + 3

Can I truncate it up to total degree 3 (for example), so 2y^3 +  x*y^2 + x^2 + y + 3

 

 

I have a multivariate polynomial P (written with the order "tdeg")in the (x_i)_i ; the coefficients are functions of the (a_i)_i. I'd want the set of the monomials that appear in the development of P. For instance P=a_1xy^2z^3+a_2x^4yz^2+a_3 is associated to {xy^2z^3,x^4yz^2,1}. Does there exist a command to do that ?

In a second time, I'd want the coefficients of {xy^2z^3,x^4yz^2,1} in the same order. Does there exist a command to do that ?

Thanks in advance.

In Maple 17, the Student MultivariateCalculus package has been augmented with fifteen new commands relevant for defining and manipulating lines and planes. There already exists a functionality for this in the geom3d package whose structures differ from those in the new Student packages. Students...

I have a multivariate polynomial equation, in that somehow I know the coeffcients, using this information, I want to extract the variables. This will be the opposite of coeffs function.

for e.g. I have 3*x3 + 5*x4

Given 3 and 5, I want to extract x3 and x4.

 

Thanks in advance.

 

Satya

 

In a related question to this answer (http://www.mapleprimes.com/questions/129140-Surface-Fitting#comment129195). How can we take partial derivatives of the multivariable fitting function (in the example above, the function B(a,b)?
It seems like the package CurveFitting only allows to numerically evaluate the fitted function when we use ArrayInterpolation, but I assume deep in the code there must be an analytic ...

I am trying to solve the so called Bethe ansatz equations in Mathematical Physics.

I have four multivariate polynomials equations with four unknown p_i(x[1],x[2],x[3],x[4]) i=1,2,3,4; which have integer coefficients. The equations are mixed; P_i is linear in x[j] for x[j]\ne x[i]; and x[i] is of order 10. Due to this structure,  I first eliminate x[4] from these equations. Then use resultant to eliminate x[3],  I got error messages (invalid series, in gcd...

Greetings All

I have several equations and each have their own individual frequencies and amplitudes. I would like to sum the equations together and adjust ONLY the individual phases, phase1,phase2, and phase3 to keep the total amplitude value of eq_total under a specific value like 0.8. I know I can normalize the signal or change the vertical offset, but for my purposes I need to have the amplitude controlled by changing/finding the values for just...

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