Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Let S be a set S={E1,E2,E3,E4,.....,Ek}  where E1 is a set of edges, E2 is another set of edges etc.

that like E1={{1,2},{2,3},..}, E2={{3,4},{1,2},....} , now we need to pick all possible  distinct sets of  size L  from the k sets of S such that the 

{E1,E2,E3,....,EL} are mutually disjoint with each other in other.

Ei intersect Ej is null no edge in common for i  not equal to j    where i, j varies from 1 to L.

F is the function which takes to parameters set S and L.

F(S,L)  then returns all possible sets which are such that {E1,E2,E3,....,EL} are mutually disjoint with each other in other.

Here mutually disjoint in graph theory terms they are edge-disjoint mutually 

I hava a recursive formula with variable n. The answer has the variable n and also N1.  What doe N1 mean?

Currrently maple exports it in huge fonts do the pdf is really big. I would like to make the pdf smaller by decreaseasing the font size. I cant seem to find any options for that online.


 

New generalized unit vectors in Physics:-Vectors

 

The Physics:-Vectors package, written many years ago to teach Vector Analysis to 1st year undergrad students in Physics courses, introduces several things that are unique in computer algebra software. Briefly, this package has the ability to compute sums, dot and cross products, and differentiation with

• 

abstract vectors, like `#mover(mi("A"),mo("→"))` or `#mover(mi("A"),mo("→"))`(x, y, z), symbols or functions with an arrow on top that indicates to the system that they are vectors, not scalars;

• 

projected vectors of algebraic (non-matrix) type in any of the Cartesian, cylindrical or spherical basis and/or associated systems of coordinates, including for that purpose an implementation of the corresponding unit vectors of the three bases;

• 

abstract or projected differential operators that involve Nabla, Gradient, Divergence, Laplacian and Curl;

• 

inert vectors or vectorial differential operators, including related expansion of operations and simplification; 

• 

path, surface and volume vector integrals.

 

In addition to the above, the display is as in textbooks, the input resembles paper and pencil handwriting, and examples of the use of Physics:-Vectors in Vector Analysis are presented in the Physics,Examples page.

 

Download New_generalized_unit_vectors.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Hi ---

      I know how to add the Angstrom symbol to a plot's axis label using my mouse and the palette menu.  How can I add the Angstroms symbol programmatically to the plot command?  Thanks!

David

Hi

I want to solve two equations (Eqmin and Eqmax) numerically  and plot curves of Mmin and Mmax versus "sigma" in one frame, But the  second curve (Mmax) is not plotted !  What should I do? 
(We know that only real and positive roots are acceptable)
Eq.mw

I can not spawn draw the circles C3 and C4

restart;
with(plots):
with(geometry):
_EnvHorizontalName := x:
_EnvVerticalName := y:
R := 7:
point(A, [0, R]):
line(L1, y = sqrt(3)*x + R):
line(L2, y = -sqrt(3)*x + R):
line(L3, y = R/3):
intersection(B, L1, L3):
intersection(C, L2, L3):
detail(C):
triangle(ABC, [A, B, C]):
circle(C1, [point(P1, [0, 0]), R]):
circle(C2, [point(P2, [0, R/3 + (2*R)/9]), (2*R)/9]):
detail(C2):
center(C2), coordinates(center(C2)):
reflection(P3, P2, C):
detail(P3):
reflection(C3, C2, C);
detail(C3):
Error, (in geometry:-reflection) unable to compute coeff
Error, (in geometry:-detail) unknown object:  C3
circle(C3, [point(P3*[(28*sqrt(3))/9, 7/9]), (2*R)/9]):
Error, (in geometry:-point) wrong number of arguments
reflection(C4, C2, B);
detail(C4);
Error, (in geometry:-reflection) unable to compute coeff
Error, (in geometry:-detail) unknown object:  C4
circle(C3*[point(P3, [(28*sqrt(3))/9, 7/9]), (2*R)/9]);
Error, (in geometry:-circle) wrong number of arguments


draw([L1(color = blue), 
ABC(color = red, transparency = 0.5, filled = true), 
L2(color = blue), L3(color = blue), 
C1(color = blue, thickness = 3), C1(color = yellow, transparency = 0.8, filled = true), C2(color = blue, filled = true)], 
axes = normal,
 view = [-R .. R, -R .. R], 
scaling = constrained);
Why these error messages. Thank you veru much.

Respected sir,

It looks like the Maple function IsSubgraphIsomorphic(G1,G2) function I think it is developled from the

phyton networkx package function 

GraphMatcher.subgraph_is_isomorphic()   The source python code for this is in this link below

networkx.algorithms.isomorphism.ismags — NetworkX 2.8.6 documentation

Now Can considering the Graphs G1 and G2 as vertex labeled graphs can we tweek the function in such way that rather than just to return true based on shape The function will now take a new parameter extra

IsSubgraphIsomorphic(G1,G2,Label=True or False)

If Label= True the then the function will return true if their is a subgraph G1 isomorphic in G2 with the same type of labels exists then it returns true and also returns that graph G1 edges based on those labels in G2.

Can anyone help please your help will be acknolwedged surely

Intially let it be for the undirected graph cases only.

Einstein's principle of relativity

 

The main difference between Newtonian mechanics and the mechanics based on Einstein's principle of relativity is that in the latter the velocity of light, c, is the same in all inertial reference systems. Therefore, when comparing the velocity of an object measured in two reference systems 1 and 2 that are moving relative to each other, the Newtonian rule of addition of velocities, v__2_ = v__1_+v__R_, where v__R_ is the velocity of one system with respect to the other one, is not valid; if it were, the speed v__1_ and v__2_ of light in the systems 1 and 2 would not be the same. This introduces surprising conceptual consequences, and algebraic complications in the formulas relating the values of measurements, in the systems 1 and 2, of time, space and everything else that is related to that.

 

This post is thus about Einstein's principle of relativity and the consequences of the velocity of light being the same in all inertial reference systems. Although the topic is often considered advanced, the concepts, as shocking as they are, are easy to understand, and the algebra is still tractable in simple terms. The presentation, following Landau & Lifshitz [1], Chapter 1, is at a basic level, with no prerequisite expertise required, and illustrates well how to handle the basic algebraic aspects of special relativity using computer algebra.

 

Finally, it seems to me not useful to just present the algebra when the concepts behind Einstein's theory are straightforward and surprising. For that reason, the short sections 1 and 2 are all about these concepts, and the algebra only starts in section 3, with the Lorentz transformations (which was recently the topic of a Mapleprimes post at a more advanced level ). To reproduce the computations shown in this worksheet, please install the Maplesoft Physics Updates v.1314 or any subsequent version.

 

Download Einstens_principle_of_relativity.mw

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

 

A "while" ago this was possible by commands. E.g.:

(from https://www.youtube.com/watch?v=uaQh_bXcIGA)

I consulted the help pages for Export and CodeGeneration options, but could not find anything suitable to generate a C code file.

Did I overlook something or searched for the wrong help pages?

If such options no longer exist, what is the preferred way to transfer C code from Maple to MapleSim?

Am I supposed to copy, paste & save with a third party editor? If I do so for a C code generated from a Maple procedure (generated with makeproc), I get

A complete example that works in 2022 versions would be helpfull. The tutorial "6.6 Tutorial 6: Using the External C Code/DLL Custom Component App" unfortuneately does not include code generated by Maple that can be imported, compiled, simulated and verified against a MapleSim model as in the example from youtube (which is still very instructive by the way). 

After loading the Physics package, I have define the langragian L this way:

L:=sqrt((1+(y')^2)/y)

After some algebra, I get the following integral:

((1+(y'(x))^2)^(-1)*1/y(x) = C

At that stage, I would like to isolate the term y'(x) and do the change of variable. But since I am under the Physics package, I try to isolate it with no succes and worst if I try to change the variable first. A little help would be appreciate.

Thank you in advance

Mario

Maple 2022 under Windows

Hello,

I have a nonlinear system of 12 SYMBOLIC equations in 6 variables. I am using solve() but it's taking me ages and will probably return the "Kernel connection has been lost" error after a half-day/ a day.

How do I solve it? Is it even possible to solve it? Is there a way to solve it approximately?

Thanks

Where is the problem within this procedure which I can not get the numerical values of V[1] , V[2], ...

restart

A := Matrix([[2*t, 2, 3], [4, 5*t, 6], [7, 8*t, 9]])

A := Matrix(3, 3, {(1, 1) = 2*t, (1, 2) = 2, (1, 3) = 3, (2, 1) = 4, (2, 2) = 5*t, (2, 3) = 6, (3, 1) = 7, (3, 2) = 8*t, (3, 3) = 9})

(1)

B := LinearAlgebra:-Transpose(Matrix([t, 2*t, 3*t]))

B := Matrix(3, 1, {(1, 1) = t, (2, 1) = 2*t, (3, 1) = 3*t})

(2)

``

test:=proc(n)
  local s,t,M,V;
  s:=1:
  for t from 1 to n do
    M:=A+A^(-1);
    V[s]:=(M.B):
    s:=s+1:
  end do;
  V;
end proc:

``

test(4)

V

(3)

V[1]

V[1]

(4)

``

``

Download ProcPropl.mw

fig([L1(color = blue), L2(color = blue), L3(color = green), C1(color = black), C2(color = black), C3(color = orange), C4(color = orange)]);
point(oo, [0, 0]);
                               oo

rotation(fig1, fig, oo, Pi/2, 'counterclockwise');
Error, (in geometry:-rotation) wrong type of arguments why thos error ? Thank you;
 

q := (f)->local ff := `if`(type(f,procedure),f,`x`->f); ff(z + (ff(k))):

Trying to create something so that I can do q(x) or q(x->x^2) or whatever.

Trying to understand the difference between an expression and a function as represented by maple. I thought I could just turn whatever is passed to q, such as x*cos(x) in to a function by x->x*cos(x) as one would do normally but this does not work.

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