expr:=cos(x)^2;
expr=combine[trig](expr);
(x->x=combine[trig])(expr);

Update:
Same outcome with

expr=`combine/trig`(expr);
(x->x=`combine/trig`)(expr);
                          2   1            1
                    cos(x)  = - cos(2 x) + -
                              2            2

                           2               
                     cos(x)  = combine/trig

Hi everyone ...

How can I define the below Matrix with for command: (A[n] is n*n and n=1...i)

Tnx...

It seems like there exists a bug when taking the following limit in Maple (I tried Maple 2021):

If I run this command:
> evalf(limit(CylinderU(0,CylinderU(0,x)),x=0));
1.2722774800
the result is 1.2722774800, which seems to be incorrect.
;

However, when I run this command:
> evalf(CylinderU(0,limit(CylinderU(0,x),x=0)));
0.5456799403
the result is 0.5456799403, which seems to be correct.

Finally, when I run this command:
> evalf(CylinderU(0,CylinderU(0,0)));
0.5456799403
the result is 0.5456799403 which is also correct.

My expectation is that all three commands must return the same result, thus I consider this a bug.
I also run the following command in WolframAlpha
> limit ParabolicCylinderU(0,ParabolicCylinderU(0,x)) as x->0.0
and obtained the correct result 0.54568, confirming that in Maple this is evaluated incorrectly.

Would appreciate if anybody can confirm that this is a bug.

How such Maple bug should be reported?

Is this a valid behvior by int?   

int(A,x,method=_RETURNVERBOSE) hangs.

But  int(simplify(A),x,method=_RETURNVERBOSE) returns in few seconds with "default" result same as int(A,x)

Should this have happen? I try to avoid calling simplify unless neccessary because it can add csgn's and signums and so on to the result. 

But the question is: Should one really need to simplify the integrand to get the result in this example? Does this mean one should call simplify on the integrand to avoid the hang that can show up? 

This only happens when using method=_RETURNVERBOSE 

Just trying to find out if this is normal behavior and can be expected sometimes.

Download why_int_hang_unless_simplify_june_15_2024.mw

How do you substitute into a contravariant index of a tensor say

T[~mu, nu]     ?

Nothing seems to work, I tried to subs(~mu=~1,T[~mu, nu]), subs(mu=1,T[~mu, nu]), and all permutations.

Substituting values into the covariant index works fine but not contravariant.

Surely it must be possible ?

When executing the attached work sheet, the output

changes to

Why is that (local seetings maybe?) and how to reproduce the former, more compact output?

Download Output_formated_with_rational_factor_.mw

Hi everyone...

I want to know how can I convert python code & c+ code into maple, is there any command or algorithm for these converts? 

Tnx...

restart;
with(combinat);
F := unapply(rsolve({F(1) = 1, F(2) = 1, F(n + 1) = F(n) + F(n - 1)}, F(n)), n);
combine(expand(F(n + 1)*F(n + 2) - F(n)*F(n + 3)));
F := n -> fibonacci(n);
combine(expand(F(n + 1)^2 - F(n)*F(n + 3) + (-1)^n));
is(F(n + 1)^2 = F(n)*F(n + 2) + (-1)^n);#should be true
G := n -> arctan(1/F(n));
is(G(4) = G(5) + G(6));
is(G(4) = G(5) + G(6));
is(G(2*n) = G(2*n + 1) + G(2*n + 2));#should be true
How to establish these formulas ? Thank you.

odetest should be made more robust.

Here is an example where the same exact solution and same exact IC, but when solution is just writtent in a  little different form, odetest no longer verifies it.

Do you consider this a bug? How is the user supposed to know their solution is correct or not now, since it depends on how it is written? What can a user then do to help odetest in this case verify the solution?

Download same_solution_not_verified_june_13_2024.mw

How can I get Prof. Wilhelm Werner's  FourierSeries  package? (See also "Fourier and Other Orthogonal Function Expansions in Maple" by Dr. Robert Lopez):

How to get logarithm expression using Maple command?

For example, enter log[2](x^2-3x+5)+x^3-1-log[3](x-1)

Output [x^2-3x+5,x-1]

Thank you very much for your help.

Hallo every body 

How to add vector fields to the figure of this example of a three-dimensional differential system.

in maple 18

Porgram_of_corollary_1_in_Maple.mw

Download Porgram_of_corollary_1_in_Maple.mw

Hi,

I am trying to produce two statistical tables representing a weighted series in a horizontal manner (Tab1) and in a vertical manner (Tab0). The xi and ni in Tab1 do not display well... Perhaps, there is a simpler way to do this?S5S4BoxPlotPondération.mw

Hello, 

do you have an idea how could be filtered several values from dataframe? 
I have a dataframe called "TestData". I need to select rows from data frame which are equal to the list called "SelectionList". 

Thank you for a comment. 
 

Data:=<"LC1", "LC2", "LC3", "LC4", "LC5", "LC6", "LC7", "LC8", "LC9", "LC10", "LC11", "LC12", "LC13", "LC14", "LC15", "LC16", "LC17", "LC18", "LC19", "LC20">;
LoadValue2:=<10,15,100,82,18,89,25,84,46,18,79,12,0,28,147,15,86,444,18,65>;

TestData:=DataFrame(<Data|LoadValue2>,columns=[Case,Load]);

SelectionList:={"LC3", "LC4", "LC5", "LC6", "LC7", "LC8", "LC9"};

I want to place a grid on this drawing 16x7=112 small squares. Thank you.
with(plots);
with(geometry);
_EnvHorizontalName := 'x';
_EnvVerticalName := 'y';
unprotect(D);
point(A, 0, 0);
point(B, 8, 0);
point(C, 8, 1);
point(D, 16, 2);
point(E, 15, 5);
line(AD, [A, D]);
line(AE, [A, E]);
line(DE, [D, E]);
line(AB, [A, B]);
segment(s1, B, C);
segment(s2, B, A);
triangle(Tr, [A, D, E]);
alpha := FindAngle(AB, AD);
beta := FindAngle(AD, AE);
is(alpha + beta = arctan(1/3));
pl := plot(gridlines = true, title = "Dessin pour montrer que arctan(1/3)=arctan(1/5)+arctan(1/8)", titlefont = ["ROMAN", 20]);
display(textplot([[coordinates(A)[], "A"], [coordinates(B)[], "B"], [coordinates(C)[], "C"], [coordinates(D)[], "D"], [coordinates(E)[], "E"]], align = {"above", 'right'}), draw([A(color = black, symbol = solidcircle, symbolsize = 16), D(color = black, symbol = solidcircle, symbolsize = 16), E(color = black, symbol = solidcircle, symbolsize = 16), s1(color = blue), s2(color = blue), Tr(color = orange, filled = true, transparency = 0.9), Tr(color = blue)]), pl, gridlines = true, axes = none);