Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

What would be the IBC conditions for the 1D heat equation describing the temperature distribution along a circular rod with a heat source at its base?


I have 6 by 6 Hessian matrix H. I want to check whether it is a negative definite. The rule of negative definite is "if and only if its n leading principlal minors alternate in sign with the kth order leading principal minor should have same sign as (-1)^k".

In my Hessian H, some leading principal minor of H is zero while the nonzero ones follows above rule. So negative definite test fails and Now I have to check negative semidefinite test which state that "H is negative semidefinite if and only if every principal minor of odd order is <=0 and every principal minor of even orderis >=0". So I have to check sign of every principal minor ( instead of just leading principal minor) to check for negative semidefinite of H matrix.

Can anyone help me how can I compute sign of all principal minor of a 6 by 6 square Hessian matrix.

Thanks and Regards,





Hello people in mapleprimes,

I want to single out omega^epsilon from and modify the rhs of the following expression
to the expression where the  the part without omega^epsilon and  another part of  omega^epsilon
are multiplied.

Y = -L*epsilon^epsilon*(1-epsilon)^(1-epsilon)*(-omega^(-1+epsilon)*k*theta+(1-theta)*omega^epsilon)/(1-epsilon-theta)

I am glad if you teach me this.



I found this error extremely confusing when using the solve function:


Error, (in Engine:-Dispatch) cannot determine if this expression is true or false: 1000 < 5^(1/2)

Hi, i encountered this, error, and the link to the help page was broken.

Error, (in RootOf) expression independent of _S000100

when I enter a trig function as cos(pi/2) I get as a return the same input.  What I would like is the numeric answer displayed. also there are times when I don't want pi in the answer but a numeric value calculated based on pi * whatever.



I am trying to prove the equation of the least square estimator. For example, I have: 

X := Matrix(2,3,symbol=p)

Y:= Matrix(2,1,symbol=f)

b:= Matrix(2,1,symbol=n)

or Y=X.b

The known estimation of b results from the minimization of the objective function: 


We take the derivative of the above expression and set it equals with zero. 

Then the estimator is: b=MatrixInverse(Transpose(X).X).Transpose(X).Y

How can I get this expression using commands οn maple?

My final task is to change the objective function to see the different estimations. For example if I have the below objective function which is the results of estimation as equation:


where C:=Matrix(2,2,symbol=w)

Ofcorsse I know the answer, but I am not sure for more complicated objective functions.





Hello people in maple primes,

I have an expression,


, which I want to put in order as 


Isn't there any ways to do the modification above?

 I am very glad if you answer to my question.



Here below is the code I got problems:


Dens := proc(v)
local theta, r;
        , theta = 0. .. 2*Pi)
    , r = 0. .. v)
) assuming v>=0
end proc;


FitFinalDens := NonlinearFit(
, depth
, veloc
, [u]
, initialvalues = [a = 1.4, b = 0.13]
, parameternames = [a, b]
, output = [leastsquaresfunction, residuals, parametervector]
, parameterranges=[a=1.1..3.0,b=0.02..0.8]


Then, I obtain two sort of errors:

First error message:

Error, (in Statistics:-NonlinearFit) invalid input: no implementation of NonlinearFit matches the arguments in call, 'NonlinearFit(0.13*(1.+1.4*u)*(int(int(4*r/..........



Second error message:

Error, (in Statistics:-NonlinearFit) complex value encountered


So, really I don't known how to correct the code.

I tried a lot  of things such as using  "value" command,  "Re" command, etc.

Do you have a solution?

Sincerely yours.





invalid input: LinearAlgebra:-Basis expects its 1st argument, V, to be of type {Vector, set(Vector), list(Vector)


a := Int(exp(cos(x)), y = 0 .. sin(x), x = 0 .. (1/2)*Pi);
i get error 


Trying to solve:

solve (arctan((2*x^2-1)/(2*x^2+1)) = 0, x);

The answer I get is the original function:



This example is from the Maple book by Keck, and he shows the Maple V answer as

1/2 sqrt(2) -1/2 sqrt(2)     


Hi every body : 

I want to slove this below PDE with conditions 1&2, can every body help me, tnx.

PDE := diff(u(x, t), t)+6*u(x, t)*(diff(u(x, t), x))+diff(u(x, t), x, x, x) = 0;


2.assume t is step function(Heaviside).

with regards....

sol:=dsolve(diff(y(x),x)= x/(sqrt(x^2-16))*1/(2*y(x)),y(x));


But the solution can also be written as

I just do not know how to transform the first solution to the second simpler one. I tried:


Also tried simplify(sol,sqrt); simplify(sol,radical,symbolic); simplify(sol,size);

The simpler solution can be found as follows

sol:=dsolve(diff(y(x),x)= x/(sqrt(x^2-16))*1/(2*y(x)),y(x),'implicit');

But the term in the middle above is

Therefore the solution is really

eq:=y(x)^2-sqrt(x^2-16)-_C1 = 0;

Which gives

What command to simplify the long solution to the shorter one obtained from the implicit?


The solution by Maple below is correct, but non-the-less, a little strange.



Ofcourse 3*constant is still constant. But it is a little strange and have no reason for it to be there.  When I solve it by hand

What could made Maple put the 3 in there? Again, solution is 100% correct, but it could be simpler.

Maple 2017.1



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