restart;
with(geometry):
with(plots):
_EnvHorizontalName = 'x':
_EnvVerticalName = 'y':
EQ := proc(M, N) 
local eq, sol; 
eq := simplify(expand((y - M[2])/(x - M[1]) - (N[2] - M[2])/(N[1] - M[1]))); 
sol := solve(eq, y); 
RETURN(y = sol); end proc:
_local(D);
point(A, [-2, 7]):
point(B, [-5, -2]):
point(C, [8, -7]):
point(E, [1, 4]):
EQ([-5, -2], [8, -7]):
point(D, [1, subs(x = 1, rhs(%))]):
dsegment(sgAD, [A, D]):
BD := distance(B, D):
DC := distance(C, D):
triangle(ABC, [A, B, C]):
area(ABC):
triangle(ABD, [A, B, D]):
area(ABD):
triangle(ADC, [A, D, C]):
area(ADC):
is(area(ABD)/area(ADC) = BD/DC):
triangle(EBD, [E, B, D]):
area(EBD):
triangle(EDC, [E, D, C]):
area(EDC):
triangle(AEC, [A, E, C]):
area(AEC):
triangle(ABE, [A, B, E]):
area(ABE):
is(area(ABE)/area(AEC) = BD/DC):
display*([draw*[A(color = black, symbol = solidcircle, symbolsize = 6), 
B(color = black, symbol = solidcircle, symbolsize = 6), 
C(color = black, symbol = solidcircle, symbolsize = 6), 
ABC(color = blue)], 
textplot*([[coordinates(A)[], "A"], 
[coordinates(B)[], "B"], 
[coordinates(C)[], "C3"]], 
align = [above, right])], 
axes = none, 
title = "Lemme du Chevron");
The program simply reproduces display...Why; Thank you.
display*([draw*[A(color = black, symbol = solidcircle, symbolsize = 12), B(color = black, symbol = solidcircle, symbolsize = 12), C(color = black, symbol = solidcircle, symbolsize = 12), ABC(color = blue)], textplot*([[-2, 7, "A"], [-5, -2, "B"], [8, -7, "C3"]], align = [above, right])], axes = none, title = "Lemme du Chevron")

Download Equality_of_Elliptic_expressions.mw

Download surface_dinesh_paper.mw  please help me to solve the problem

Hi, I would appreciate some help in solving the following system of partial differential equations. The particularity of the system is that only the individual variables (i.e. a, c, and l) depend on two arguments (t: current time period and v: date of birth). The other variables are either rates or aggregates. The aggregate variables (i.e. K, L, and Y) depend only on time, t, because they are the integrals of the individual variables over v. Thanks for your help.

Download OLG.mw

Hi!

This might sound like a simple question, but I have looked pretty hard in the documentation and can't find a solution.  I want to plot functions in spherical coordinates in such a way that they are actually spherical.  For example, r = 1 should be a sphere.  All I can do is get the "cube" with sides labelled as the traditional variables r, theta, and phi.  That's not really spherical coordinates, it's just relabelled Cartesian.

I didn't make a worksheet for this topic.

Thanks in advance for your help!

Hi,

I have been bothered lately by the number format for axis labels in Maple. My problem existed before, but it apparently didn't bother me before. I have spent many hours trying to find an answer in the program help, in MaplePrimes, and in general online searches. I am not having any luck at all (good luck, that is).

I want to change the format of the axis numbering. Maple seems to default to 2 decimal places in my graph, and I really need more. Oddly, when I export the graph to PDF, I get another decimal place (even though I didn't explicitly ask for one). 

How do I change the axis-label format? Any idea what I might get when I export the graph?

Thanks for your help,

Jno.

How can I change the order of variables in a polynomial as I want? For example, I want to assign a polynomial G of 3 variables a,b,c. Then I want to compute G(a,b,c) (exchange the variable a to b, exchange variable b to a)?

Hello everybody

I would like to check, with Spacetime Tensors computation , if  a transfomation is a Lorentz transformation , i.e that leavs Minkosky metric invariant 

For esample a boost  or axis rotation transformation

Some could help me ? ( Maple 2016)

Thank's a lot

I've probably asked about this long time ago but I do not remember now. But it is still a problem any way in 2022.2

Compare these two results

code is

restart;

alias(seq(c[k] = _C||k, k = 0..10));
c[1]*h(x);
Int(c[1]*h(x),x);


restart;
c[1]*h(x);
Int(c[1]*h(x),x);

I tried with typesetting level as extended and standard and same result.

Is this a know issue? It is not a big deal as it only affects display but it will be nice to find why it happens when using alias.

This a more a math question than  a maple programming question. But interesting.

I have a point P=[x,y] on a line y= 2+3x. The point maps to Pn=[f(x, y), g(x, y)]. That represents a conic.

I want to find the equation of the conic. I did it by calculating 5 points and that works fine but only because I know I'm looking for a conic. 

Can the problem by solved without having to get the five points?
I copied and pasted the equations for the lines because they were generated by commands in a pagkage I have.

Download Q_23-03-04_how_to_find_conic_from_mapping.mw

Dears,
I have a problem whem try to solve a optimization probolem.
The equations are "complex" (G1 equation), and this error is showed "Error, (in Optimization:-NLPSolve) could not store 0.1749271137e-1*(588.000000000000+72.0000000000000*(-3.03333333+.333333333333333*MM)*(MM-17.80)+72.0000000000000*(.333333333333333*NN-3.5666666666667)*(17.00-1.*NN)+24.50000000*(2.90+4.666666667*tan(1.000000000*arctan(.166666666666667*MM-2.96666666666667)))*(18.00+5.627472876000*sin(-1.570796327+1.000000000*arctan(.166666666666667*MM-2.96666666666667))/sin(-1.745329252+1.000000000*arctan(.166666666666667*MM-2.96666666666667)))*cos(-.5235987756000+1.000000000*arctan(.166666666666667*MM-2.96666666666667))^2*sin(.3490658504000+1.000000000*arctan(.166666666666667*MM-2.9666 ... 756000+1.000000000*arctan(.166666666666667*MM-2.96666666666667))^2)-1. in a floating-point rtable".
Someone can help me?

ATS := proc(NN::float, MM::float) 
L[7]*H[4] + L[4]*H[2] + L[1]*(H[1] - H[2]) + 1/2*(P[X1] - NN)*(H[1] - H[2]) + 1/2*(MM - P[XF])*(H[1] - H[2]); 
end proc;
bounds := 14.90 .. 16.90, 17.90 .. 19.90;
cstr8 := proc(NN::float, MM::float) 
G1 - FS; 
end proc;

NLPSolve(ATS, {cstr8}, bounds, initialpoint = [15.90, 18.90], assume = nonnegative)

Hi MaplePrimes, 

I am interested in obtaining some gravitational field equations from an action using the FunDiff command. I have been able to write what I think is a pretty short and quick worksheet(with an arbitrary metric) and I am easily able to obtain the Einstein Field Equations. However, when I introduce some new more complicated terms into the action and apply the Simplify command maple does not appear to be able to evaluate and I end up halting the computation. When I specify a metric Maple, for example Schwarzschild, Maple will easily be able to Simplify my expression but it will use metric components during the process. Where what I am interested in is just the Tensor expression with respective indices. 

I was wondering if anyone had any thoughts on how I could resolve this. 

I have attached the worksheet that I am working with. I look forward to your thoughts/comments.

Thank you.  

ActionFieldEquations.mw

If we use, for example, pointplot3d with an mx3 matrix we get a 3d plot. I can click on the plot and choose the lighting. But how do we do that with code?

Maple continuously shows 'Evaluating' and there is no output. How to fix it?

Download sol1det.mw

Hello. I work with vector fields and 1-forms with the package DifferentialGeometry. I need to copy the output in a latex file, but when I use copy paste what I get is the internal representation of the 1-forms, for example, something like

_DG([[\"form\", M, 1], [[[1], x2/x4], [[2], -1]]])

But what I need is something like:

x2/x4 dx1-(`*`(dx2))

which is what I see at the screen. I have tried lot of commands but I don't get what I want.

Here is the basic code:

restart;

with(DifferentialGeometry);

with(JetCalculus);

DGsetup([x1, x2, x3], M);

w:=evalDG(x2/x4 dx1-dx2)