Hi guys. I am new to the Maple environment.

Was trying to do some GR calculations when the following problem arose.

restart; with(Physics);
Setup(coordinates = (X = [t, r, theta, phi]), metric = -A(r)^2*(dt^2)+B(r)^2*(dr^2)+r^2*(dtheta^2)+r^2*(sin(theta)^2)*(dphi^2));
Setup(math = true);
g_[line_element]; g_[];
Christoffel[nonzero]; Christoffel[`~mu`, alpha, beta, nonzero];
D_[mu](g_[`~alpha`, `~beta`]);
expand(D_[2](g_[`~2`, `~beta`]));
D_[2](g_[`~2`, `~2`]);

The output for the last 3 lines are:

1. 0

2. Expansion in terms of Christoffel symbols (which does equal zero on substituting various values)

3. Non-zero value.

Obviously the answer must be zero for all cases (covariant derivative of metric). So what have I missed/misunderstood here?

Regards

BuddT

What is the Maple command to simplify  -x^(a)+x^n  to zero under the assumption that a=n?

I have attempted the following command

simplify(-x^(a)+x^n) assuming a=n;

However, it did not produce zero. The following command however produces zero

subs(a=n,-x^(a)+x^n);

 How to do this operation using assumptions. How to inform Maple to assume that a=n.

Hi MaplePrimes,

I try again to ask about a procedure I wrote.  Maybee someone can spot my error.

collatz_conjecture_2.mw

Here is the broken procedure - 

cs := proc (n::integer)::integer;
local count;
description "Find the number of steps for a Collatz sequence to reach 1";
count := 1;
while 1 < n do
if `mod`(n, 2) = 0 then n := (1/2)*n else n := 3*n+1 end if;
count := count+1
end do;
return count
end proc

Regards,

Matt

im a huge fan of using the is boolean function maple has in my studies, and in as much as the CAS is a million times smarter than me, i just wanted to show an example of a situation where i am reluctant to use this feature. (see the uploaded worksheet)

perhaps someone with more  programming ability/experience than me can explain how it works, as so i can have a means of knowing whether or not it is appropriate to use in each situation.IS_function_problem_example.mw

how are iterated functions represented in maple? as in f(f(f(x))) is (x)  in conventional notation where by the reader knows it is refering to the iteration conducted 3 times on the argument x, but what does maple use to differentiate between iteration ,exponentiation and differentiation?

Hello 

can I get values from combobox?

for exemple: if I select "X" in combobox, it returns me "a:=1".

But, I'd like to put this comand inside the combobox and dont in the worksheet..

thanks a lot

Can Maple determine the value of DthetaZero such that the solution to the ODE, for some specific value of t, simultaneously provides the two values theta(t)=Pi and diff(theta(t),t)=0?

sol:=dsolve({4*sin(theta(t))*cos(theta(t))-9.8100*sin(theta(t))-(diff(theta(t), t, t)) = 0, theta(0) = 2*Pi*(1/3), D(theta)(0) = DthetaZero}, numeric)

odeplot(sol,[t,theta(t),diff(theta(t),t)],t=0..5) for trial values of DthetaZero shows that the desired value is

1.0340*Pi <DthetaZero<1.0345*Pi.

Hi 

how can I find equilibria points of nonlineay system?

Like 

x'=sin(x)+y

y'=y^2-x

I modelled a telecamera and line follower sensors in Maple in order to calculate the "error" for my PID controller. Know i would like to share this information with the PID in MapleSim but I have no idea how to do it. Is there a way to import maple libraries into MapleSim?

Thanks!

Hi,

I'm trying to export a plot using the open maple api but it looks like open maple API doesnt support certain specific features.

Eg. "Export(\"images\\\result1.gif\", plot(sin(x), title = \"The sine function\", thickness = 3, gridlines=true));"

Above works fine when executing in actual maple application (i.e. correctly exports with gridlines) however doing the same via open maple api it does export the chart but not the specified gridlines.

Had the same issue when setting axis options to show log instead of linear. 

Did anyone else get this? Is this a known issue with open maple api? Is there workaround available?

Thanks,

Bidur

I know that whattype() is used to find the basic data type of an expression. Unfortunately that information is rarely useful. How can I dig down deeper and get Maple to tell me more about the expression?

I read somewhere that there is a properties() procedure that does that but I cannot find that procedure.

Thanks.

Quite accidentally I discovered incorrect calculation of the simple definite integral:

int(1/(x^4+4), x=0..1);  

evalf(%);

                            1/8*ln(2)-1/16*ln(5)+1/32*Pi+1/8*arctan(1/3)   # This is incorrect result

                                                   0.1244471178

Is this a known bug?

If  first we calculate corresponding indefinite integral, and then by the formula of Newton - Leibniz, that everything is correct:

F:=int(1/(x^4+4), x):

eval(F, x=1)-eval(F, x=0);

evalf(%);

                                             1/16*ln(5)+1/8*arctan(2)

                                                     0.2389834593

In a recent blog post, I found a single rotation that was equivalent to a sequence of Givens rotations, the underlying message being that teaching, learning, and doing mathematics is more effective and efficient when implemented with a tool like Maple. This post has the same message, but the medium is now the Householder reflection.

Given the vector x = , the Householder matrix H = I - 2 uu^T reflects x to y = Hx, where I is the appropriate identity matrix, u = (x - y) / ||x - y|| is a unit normal for the plane (or hyperplane) across which x is reflected, and y necessarily has the same norm as x. The matrix H is orthogonal but its determinant is -1, making it a reflection instead of a rotation.

Starting with x and u, H can be constructed and the reflection y calculated. Starting with x and y, u and H can be determined. But what does any of this look like? Besides, when the Householder matrix is introduced as a tool for upper triangularizing a matrix, or for putting it into upper Hessenberg form, a recipe such as the one stated in Table 1 is the starting point.

In other words, the recipe in Table 1 reflects x to a vector y in which all entries below the kth are zero. Again, can any of this be visualized and rendered more concrete? (The chair who hired me into my first job averred that there are students who can learn from the general to the particular. Maybe some of my classmates in graduate school could, but in 40 years of teaching, I've never met one such student. Could that be because all things are known through the eyes of the beholder?)

In the attached worksheet, Householder matrices that reflect x = <5, -2, 1> to vectors y along the coordinate axes are constructed. These vectors and the reflecting planes are drawn, along with the appropriate normals u. In addition, the recipe in Table 1 is implemented, and the recipe itself examined. If you look at the worksheet, I believe you will agree that without Maple, the explorations shown would have been exceedingly difficult to carry out by hand.

Attached: RHR.mw