Hi ! 

I want to know how to ask Maple to transform a system of ODE in cartesian coordinates (e.g. [x'(t)=u(t) , u'(t)=-x(t)])

into a system in polar coordinates (in my example [r'(t)=0, theta'(t)=-1]). 

Many thanks!

Kevin

Hi,

I am trying to evaluate the diff of a function at a parametric point. But the outcome seems wrong in comparison with a case that we evaluate diff at a numeric point. 

Please observe the attached picture to get my problem.

Thanks in advance.

have table like table(symmetric, [() = x]) from other code not mine, strange syntax

how to extract x from table thanks

I have the following code. I want to do the modify it so that:

1. The outputs of each for loop are merged in such a way that the outputs from the first loop (Es) that are also outputs of the second loop (Fs) are removed from the outputs of (Es).

2. The resulting outputs G= .... are saved to a text file, one to each line.

3. In between each output, I want to add 5 lines of text and a blank line, say

text1 text2 text3

text2 text2 text3

text3 text3 text3

text4 text4 text4

text5 text5 text5

(blank line)

so that in the text file, the format is (e.g.)

G={{1,2}};

text1 text2 text3

text2 text2 text3

text3 text3 text3

text4 text4 text4

text5 text5 text5

(blank line)

G={{1,2},{1,3}};

text1 text2 text3

text2 text2 text3

text3 text3 text3

text4 text4 text4

text5 text5 text5

(blank line)

etc.

What is the easiest way to accomplish this?

restart;
 
with(GraphTheory):
 n:= 4:
  L:= NonIsomorphicGraphs
      ( n,
        output=iterator,
        outputform=graph):
  Es:= Array
       ( [ seq
           (  Edges( L() ),
              j=1..NonIsomorphicGraphs
                   ( n,
                     output=count
                   )
           )
         ]
       ):


  M:= NonIsomorphicGraphs
      ( n-1,
        output=iterator,
        outputform=graph):
  Fs:= Array
       ( [ seq
           (  Edges( M() ),
              j=1..NonIsomorphicGraphs
                   ( n-1,
                     output=count
                   )
           )
         ]
       ):
;

numelems(Es): 
for i from 1 to numelems(Es) do G:=Es[i]:  od;
                           
numelems(Fs):
for i to numelems(Fs) do G := Fs[i]; od;
                        

Hey everyone ! 

I want to get the analytical function from a piecewise differential equation defined on 6 intervals but Maple returns me a numerical result... I think it hides a Runge Kutta method.. However, it returned me an analytical function for a similar piecewise differential equation defined on 3 intervals.

Do you know how I could get the analytical function defined on the 6 intervals ?

Thank you very much for your time ! 

Alex

Download cas_5v_F_inconnues.mw

Download test.mw

Hey everyone!

I would like to plot the integral of a discrete function. For simplicity, I choose the function sin(x) between –Pi and Pi, which has as an integral -cos(x). I tried to implement that in Maple using the Trapezoidal rule, but the result is simply wrong. Any help would be much appreciated!

I have the following Maplesoft code:

with(ImageTools);

with(IterativeMaps):
Crystal, xrange, yrange := Attractor([x, y], [[1/2 - y/2, x/2], [y/2 + 1/2, 1/2 - x/2], [x/2 + 1/4, y/2 + 1/2]], height = 400, width = 400, xmin = -1, xmax = 2, ymin = -1, ymax = 1, fixview = true, [0, 0], [0.33, 0.33, 0.33], greenexpression = 1 - 1/(1/(1 - G) + 1), iterations = 2500000);
xrange, yrange;
                        -1 .. 2, -1 .. 1

ColouringProcedures:-HueToRGB(Crystal);
                               0.

Embed(Crystal);

which yields the following image:

However, I should be seeing the following image:

Any help would be appreciated. Thanks!

Justify that 2 vectors (1,1) and (1,2) are an R² base; How to write calculations correctly ?
<x, y> = lambda*<1, 1> + mu*<1, 2>:
 solve({lambda+mu=x,lambda+2*mu=y},{lambda,mu}):
 <x, y> := (2*x - y)*<1, 1> + (-x + y)*<1, 2>:
Thank you.

I get this error when I try to use the ODE numeric solver, can anybody help me figure out what Im doing wrong? 

hi guys,

I have a question about computing reimann tensor in general relativity.

suppose we have schwarzschidl metric: ds^2=-(1-2*m*(r^-1))*dt^2+(1-2*m*(r^-1))^(-1)*dr^2+r^2*dtheta^2+r^2*sin^2(theta)*dphi^2.

I want to caclulate R[alpha,beta,mu,nu]*R[~alpha,~beta,~mu,~nu] where R[alpha,beta,mu,nu] is covariant form of Reimann tensor and also R[~alpha,~beta,~mu,~nu] is the contravariant form of Riemann tensor. I also want to calculate same thing for weyl tensor. please guide me.

with best regards.

graph.mw

How to reconstruct commutators like for example in Drinfeld associators (see (4.5) in https://arxiv.org/pdf/1310.3259.pdf)?

We have as computed in Drinfieldstuff_display.mw (note to run this it requires loading HyperInt package https://arxiv.org/pdf/1403.3385.pdf):

H[2] := a^2*(e[0]*e[1] - e[1]*e[0])*zeta[2]

H[3] := zeta[3]*a^3*(((e[0]*e[1]^2 + e[0]^2*e[1] - (2*e[1])*e[0]*e[1]) + e[1]^2*e[0]) - (2*e[0])*e[1]*e[0] + e[1]*e[0]^2)

H[4] := zeta[2]^2*a^4*((((((4*e[0])*e[1]^3 + (12*e[0])*e[1]*e[0]^2 - (5*e[1])*e[0]^2*e[1] - (4*e[1])*e[0]^3) - (4*e[1]^3)*e[0]) + (7*e[1])*e[0]*e[1]*e[0] + (12*e[1]^2)*e[0]*e[1] + (3*e[0])*e[1]*e[0]*e[1] - (12*e[0]^2)*e[1]*e[0] - (5*e[0])*e[1]^2*e[0] + e[0]^2*e[1]^2 - (12*e[1])*e[0]*e[1]^2) - e[1]^2*e[0]^2) + (4*e[0]^3)*e[1])/10

And we want maple rebuild them as  commutators as below ([x,y]=xy-yx). Correspondingly:

H[2] :=zeta[2] [e[0] , e[1] ]

H[3] :=zeta[ 3] ( [e[0] , [e[0], e[1] ]] − [e[1] , [e[0] , e[1] ]] )

H[4] :=zeta[4] [e[0] , [e[0], [e[0] , e[1]]]] −1/4* [e[0] , [e[1] , [e[0] ,e[1] ]]] + [e[1] , [e[1] , [e[0] , e[1] ]]] + 5/4*[e[0], e[1]] ^2

Does anyone know how to do it?

Hi

I got the error like this unable to convert to an explicit first-order system

please anyone can help me to solve this

I am attaching the worksheet

Download MapleOde.mw

Hi,

I try to display a different steps of an mathematical developpement with ShowSteps command, but But the command gives nothing in the new version Maple 2021?

Thanks for your Help

QShowSteps.mw