Under piecewise in ?updates,Maple2024,AdvancedMath I find

{simplify,combine}(piecewise(x <= 0, 2*ln(1 - x), 0 < x, ln((x - 1)^2))) assuming (x, real);
                         /  /       2\\ 
                        { ln\(x - 1) / }
                         \            / 

Same result without simplify

{combine}(piecewise(x <= 0, 2*ln(1 - x), 0 < x, ln((x - 1)^2))) assuming (x, real);
                         /  /       2\\ 
                        { ln\(x - 1) / }
                         \            / 

What I do not understand is the grouping of simplify and combine in a set. This looks like a function composition which is normally done with the composition operator

(simplify@combine)(expr)

Asking differently: What is

{simplify,combine}(expr)

supposed to do in the examples?

Why sorting these 4 vectors wrt L(+oo) norm returns a correct result bur sorting them wrt L2 norm doesn't (unless if I evaluate the norms as floats)?
 

Download SortingVectors.mw

TIA

trouverTripletsDecroissants := proc(tripletInitial) local m, n, a, b, c, triplets, dernierTriplet; triplets := []; dernierTriplet := tripletInitial; m := dernierTriplet[3]; do m := m - 1; for n to m - 1 do if igcd(m, n) = 1 and (m - n) mod 2 = 1 then a := m^2 - n^2; b := 2*m*n; c := m^2 + n^2; if a^2 + b^2 = c^2 and a < dernierTriplet[1] and b < dernierTriplet[2] and c < dernierTriplet[3] then dernierTriplet := [a, b, c]; triplets := [op(triplets), dernierTriplet]; break; end if; end if; end do; break; if 0 < nops(triplets); end do; return triplets; end proc;
tripletInitial := [275, 252, 373];
tripletsDecroissants := trouverTripletsDecroissants(tripletInitial);
print(tripletsDecroissants);
               tripletInitial := [275, 252, 373]

           tripletsDecroissants := [[273, 136, 305]]

                       [[273, 136, 305]]

;
trouverTripletsDecroissants(275, 252, 373);
Error, (in trouverTripletsDecroissants) final value in for loop must be numeric or character
How to correct this error. Thank you.

I want to rescale a projective vector. Have been using gcd on the numerators and denominators. This works in simple situations. It doesn;t work well here, admitadely the points have been just made up for the question.  Square roots seem to make it mal-preform. I run into a lot of squate roots in symbolic situations. What would be a better way? I have been wondering if frontend would help?

Download 2024-05-09_Q_Rescale_projective_vector.mw

Hi everyone,

I'm having trouble in maple to do the following:
Plot the curve x^3-4xy+2y^3=0 , as x variesbetween -3 and 3 with the aid of the implicitplot command

find dy/dx at all points (x,y) on the curve for which x=1. and find the equations of the lines tangent to the curve at the points

plot the curve and tangent lines on the same set of axes

Any help would be appreciated , thank you.

I'm new to Mapple 2024, and probably miss something.
lie, e[i] i=1..4, and G are previously defined objects. Then whe I define:

cf:=(k,l,m,t,x,y,z)->seq(lie(p,e[k](t,x,y,z),e[l](t,x,y,z))*G(t,x,y,z)[p,m],p=1..4);
cf(2,4,2,t,x,y,z);

I get:

0, 0, 0, -6*(-6*z^3*(7*z - 4)*(z - 1)^2*(y^2 - 1)^3*(x^2 - 1)^2*x - 6*z^4*(1 - z)^3*(-x^2 + 1)^2*(-y^2 + 1)^3*x*(-3*z^2*(7*z - 4)*(z - 1)^2*(y^2 - 1)^3*(x^2 - 1)^3 - 7*z^3*(z - 1)^2*(y^2 - 1)^3*(x^2 - 1)^3 - 2*z^3*(7*z - 4)*(z - 1)*(y^2 - 1)^3*(x^2 - 1)^3) - (1 - z^3*(7*z - 4)*(z - 1)^2*(y^2 - 1)^3*(x^2 - 1)^3)*(-24*z^3*(1 - z)^3*(-x^2 + 1)^2*(-y^2 + 1)^3*x + 18*z^4*(1 - z)^2*(-x^2 + 1)^2*(-y^2 + 1)^3*x))*z^4*(1 - z)^3*(-x^2 + 1)^2*(-y^2 + 1)^3*x*(1 - z^3*(7*z - 4)*(z - 1)^2*(y^2 - 1)^3*(x^2 - 1)^3)

The 4th item eval as:
cf(2, 4, 2, t, x, y, z)[4] = -36*z^10*x^2*(x^2 - 1)^7*(7*z^2 - 8*z + 4)*(z - 1)^7*(y^2 - 1)^9*(-1 + z^3*(7*z - 4)*(z - 1)^2*(y^2 - 1)^3*(x^2 - 1)^3)

But when I define another function by just changing the seq operator with a sum operator:

cf2:=(k,l,m,t,x,y,z)->sum(lie(p,e[k](t,x,y,z),e[l](t,x,y,z))*G(t,x,y,z)[p,m],p=1..4);
cf2(2,4,2,t,x,y,z);

I get 0.

What do I miss ?

I want to define an alias L_2 in terms of another alias L_1, the latter being a RootOf(). I noticed that doing the following does not work: alias_in_alias.mw. How to fix it? Should I define the two alias sequantially? That is, L_1 first and then (in a follow up alias()) L_2?

Sorry for the super complicated expressions. You could perhaps show me with a simpler example. Thanks!

This is my code
 

restart;
with(Student:-MultivariateCalculus);
A := [0, 0, 0];
B := [a, 0, 0];
C := [a, a, 0];
DD := [0, a, 0];
S := [0, 0, h];
d1 := Line(A, C);
d2 := Line(S, DD);
(Distance(d1, d2) assuming (a::positive and h::positive));

I got 

abs(a)^2*abs(h)/sqrt(2*abs(a*h)^2 + abs(a)^4)

How can I remove abs?

Using with(plots) and with(plottools), how do you change the color of the line enclosing a disk? I can change the line style of the line, but I can't figure out how to change the color of the line. I didn't find anything in plot options that would fit my purpose.

how_do_i_change_the_color_of_the_line_around_a_disk_while_using_plottools.mw

I am trying to verify a solution by checking whether eval() returns 0 but it's taking me forever. If I recall correctly it once returned [0,0] so I am quite confident that the first and only positive root of that polynomial solves my system. I am now running again the same calculation but somehow eval() is stuck in "Evaluating...". I am not sure if it matters here, but parameters gamma, sigma_v, and sigma_d are strictly positive while -1<rho<+1 (rho is a correlation coefficient). 

How else can I verify such solution?

EDIT: THIS IS NOT A DUPLICATE QUESTION AND SHOULDN'T BE TAGGED AS SUCH

Download solution_check.mw

Hi,

I was just wondering if there is a init file for the Windows version of Maple, like there is one for the LInux version.

I'm not talking about the Maple.ini file located in the user's Application Data folder. In the Linux version, there is a file, .mapleinit, where you can place all of your initialization setups, like the packages you want to automatically load with the worksheet, defining constants, etc.

If someone has any ideas, I really appreciate it. Thanks very much in advance.

Hi,

is there any package out there to calculate Wigner J symbols and Clebsch-Gordon coefficients in Maple

Good day to all of you nice people.
I'm currently attempting to plot a vector field where each component of the vector is defined by the equations S_x, S_y, and S_z, which are functions of the radial coordinate. Here is a depiction of how the vectors change with respect to r:

The next step, which I'm unsure how to do, is to plot the vectors around the z-direction, or I should say, in phi direction, to achieve something similar to this example:

Thank you a lot for your kind help. 

Here is my code:
Maple_Question.mw

I am running Maple 2023 - yes I should update - and I found a weird "bug" if you could call it that. For different versions of the Physics package I am getting different answers on the same problem. 
 

This is what I was getting when I run Version 1410:

And this is what I get if I used the latet update for 2023, Version 1683:

Strange right? I bring this up because it makes me wonder about potential errors in other computations...

The answer - equation 6 - in 1410 is the correct answer. This is simply a derivation of the Einstein Tensor. 

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