Items tagged with multivariate

what do i call a homogenous  differential equation that is the linear sum of "N" differential of unique classification? ie, the implicit construction of a third homogenous differential by the summation of two known, is it the span of the solution sets of the first two or union? i prefer span because well that leaves the door open for multivariate differential basis definitions, non commutative groups like sets of square matrices and all of the other extra arousing subject content.

A new Maple e-book, Multivariate Calculus Study Guide, is now available. Part of the Clickable Calculus collection of interactive Maple e-books, this guide takes full advantage of Maple’s Clickable Math approach. It has over 600 worked examples, the vast majority of which are solved using interactive, Clickable Math techniques. 

Deisgned to help students taking this course, instructors may also find this e-book useful as a guide to using Clickable Math to teach Multivariate Calculus.

See Multivariate Calculus Study Guide for more information.





  I think similar question has been asked by several people, but I did not find a suitable thread. My question is, suppose I have a probablity distirubtion function like

  p(x,y) = exp(-alpha (x+y) ) x^2 y^2 / |x-y|  , alpha>0

 x,y goes from - \infty to + \infty. This function is normalizable but unbounded, which makes the rejection algorithm a bit difficult(?).


  How to generate samping points from this type of probability distribution function?


Thank you very much!




I'm writing to ask how to equalize the coefficients of two multivariate polynomials. In particluar, I have two polynomials whose arguments are ln(E),ln(K),ln(L) (their levels, squared levels and interaction terms). The first one is:


the second one is:


I would like to know if it is possible to equalize the coefficients of the two polynomials and find the following system:

v*a*b = x_1, -v*(a-1) x_3, -v*a*(-1+b) = x_2, a*b*v*(b*rho*a-b*rho+g*(-1+b)) = x_11, v*rho*a*(a-1) = x_33, v*a*(rho*(-1+b)*a-rho*(-1+b)+b*g)*(-1+b) = x_22, -a*v*rho*(a-1)*b = x_13, -a*v*(a*rho-rho*u+g)*b*(-1+b) = x_12, a*v*u*rho*(a-1)*(-1+b) = x_23

I tried using "coeffs" and creating a sequence of values for x but then I don't know how to equalize them.

Thank you very much in advance for your time,



I have a problem with MAPLE. I would like to solve a system of 18 inequalities with 4 variables. The variables shall be rational numbers. I should also mention that I am not sure if the system has a solution. Here is my MAPLE code: 

LinearMultivariateSystem({0 < (1/20)*b11, 0 < (1/20)*b1818, 0 < (1/20)*b22, 0 < (1/20)*b33, 0 < -653385574770525739/313841848320000+(1001/20)*b33+(3003/5)*b22+4004*b11-(91/5)*b1818, 0 < -476383516463665673/69742632960000+(3003/20)*b33-(1001/10)*b1818+(27027/2)*b11+(3861/2)*b22, 0 < -372810037848242383/52306974720000+(72072/5)*b11+(3003/20)*b33-(858/5)*b1818+2002*b22, 0 < -302968656462848461/125536739328000+(1001/20)*b33-(1001/10)*b1818+5005*b11+(1365/2)*b22, 0 < -94060277895192911/627683696640000+(91/20)*b33+273*b11-(7/10)*b1818+(91/2)*b22, 0 < -3219528868317343/14944849920000+468*b11+(91/20)*b33-(91/5)*b1818+63*b22, 0 < -1167616840098623/627683696640000+(7/10)*b22+(1/20)*b33+(21/4)*b11-(7/10)*b1818, 0 < 6620337745005653/9510359040000+(91/20)*b1818-(91/5)*b33-(6552/5)*b11-(819/4)*b22, 0 < 10321214321183681/627683696640000-(21/4)*b22-(7/10)*b33-28*b11+(1/20)*b1818, 0 < 19939504442621873/627683696640000-(7/10)*b33-(39/4)*b22-(364/5)*b11+(91/20)*b1818, 0 < 21128314477665001/24141680640000-(91/5)*b33-1848*b11+(1001/20)*b1818-(1001/4)*b22, 0 < 30458564958023749/6340239360000-(1001/10)*b33+(3003/20)*b1818-9828*b11-(27027/20)*b22, 0 < 78768022311702133/17933819904000-(1001/10)*b33-8580*b11+(1001/20)*b1818-(5005/4)*b22, 0 < 418747163878248241/52306974720000-(858/5)*b33+(3003/20)*b1818-16016*b11-(9009/4)*b22}, [b11, b22, b33, b1818])

I am sorry for the writing style but I do not know how to write the command in MAPLE-style in this forum:-)

The first 4 inequalities shall ensure that all four variables b11, b22, b33, b1818 are positive. When entering the command i get the following error:

Can anybody help me please?:-)

Best regards,


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.




Determine using determinants the range of values of a (if any) such that
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?



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..

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.



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



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?


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 (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.

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.




In a related question to this answer ( 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 ...

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