Consider the list [x,y,z], say. Does there in Maple exist some fundamental function for querying the position in the list of x,y, and z, respectively? I am unable to locate any such. Such a function can, of course, be constructed, an example being the following:

listPos := (l::list) -> table(zip(`=`,l,[$(1..nops(l))])):
pos := listPos([x,y,z]);
pos[x],
pos[y],
pos[z];

But that seems unsatisfactory. The same question concerning Vectors: Consider Vector([x,y,z]), say. Here, the following code, say, will perform the task:

VectorPos := (V::Vector) -> table([map(rhs = lhs,op(2,V))[]]):
pos := VectorPos(Vector([x,y,z]));
pos[x],
pos[y],
pos[z];

PS: Of course, list and Vectors can be converted into one another, so any one of the codes above can in practice be used to perform both tasks.

The following code is part of my attempt to answer the recent Question about the bifurcation of the map f:= x-> exp(x^2*(a-x)). Two very weird things are happening. They can be seen by applying trace to f. The first is that the input argument to f seems to be changed to a very large integer. The second is that for some real values of a and x, I get imaginary results from this obviously real-valued function. Why are these things happening?

Download bifurcation.mw

How to show what class of bifurcation is in this function :   exp(x²*(a-x)) ?

I have a long list of two element lists, for example,

A := [ [2,3], [4,5] ,[6,7]];

I want apply '/' to the elements of each sublist.

The result will be

R := [2/3, 4/5, 6/7];

I do not need the list, I could use vectors or matrices.

Is it possible to do this other than by iteration?

Tom Dean

I want to set up a couple of tables. One problem I have is setting up the list of names for the columns.  u0 etc are actual variables. Being trying to use  ` ` and ' ' to stop them evaluating. I have even more problems with  h₆ as a name and symbols Sigma etc.

How do you do this so it looks neat and the name preferably doesn`t display the  ` ` or " " or '  '?

Download Table_Headers.mw

greatings all,

I want to calculate energy momentum tensor for a given metric. is it possible to calculate it in the physics package?
thanks.

Hi

Please find the attached file

The command PolynomialInterpolation doesn't work, I will be appreciate if you can help me

Thanks

Question.mw

hi.i am a problem for solving this non linear algebric equation.

please help me...thanks

FSOLVE.mw

FSOLVE.mw

When I was editing the head of the question (? instead of .), its body disappeared. Please, insert it again.

Regard,

Markiyan Hirnyk

Maple 15.

I have a set of equations I can solve manually, but, solve fails.

restart;
eq1 := tgtX[1] = 0;
eq2 := tgtY[2] - y[2]    = m[2]*(tgtX[2]-x[2]);
eq3 := tgtY[3] - y[3]    = m[3]*(tgtX[3]-x[3]);
eq4 := tgtY[4] - y[4]    = m[4]*(tgtX[4]-x[4]);
eq5 := tgtY[2] - tgtY[1] = vy*t[2];
eq6 := tgtY[3] - tgtY[1] = vy*t[3];
eq7 := tgtY[4] - tgtY[1] = vy*t[4];
eq8 := tgtX[2]           = vx*t[2];
eq9 := tgtX[3]           = vx*t[3];
eq10:= tgtX[4]           = vx*t[4];
#
# solve the equations
eqs  := {eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10};

solvx := solve(eq10,vx);
solvy := solve(eq7,vy);
sol1  := subs(vx=solvx,{eq8,eq9});
sol2  := subs(vy=solvy,{eq5,eq6});

soln  := subs(sol1,{eq2,eq3});

soln  := subs(tgtY[2]=solve(sol2[1],tgtY[2]),soln);
soln  := subs(tgtY[3]=solve(sol2[2],tgtY[3]),soln);
soln  := subs(tgtY[1]=solve(soln[1],tgtY[1]),soln[2]);
soln  := solve({eq4,soln},{tgtX[4],tgtY[4]});

# this returns empty solution
solve(eqs,{tgtX[4],tgtY[4]});

Any ideas?

Tom Dean

Hello,

Is there an option/ or a way so as to ask pointplots to plot a interpolated curve for the points defined ?

Thank you for you help.

Below is the worksheet with the whole material presented yesterday in the webinar, “Applying the power of computer algebra to theoretical physics”, broadcasted by the “Institute of Physics” (IOP, England). The material was very well received, rated 4.5 out of 5 (around 30 voters among the more than 300 attendants), and generated a lot of feedback. The webinar was recorded so that it is possible to watch it (for free, of course, click the link above, it will ask you for registration, though, that’s how IOP works).

Anyway, you can reproduce the presentation with the worksheet below (mw file linked at the end, or the corresponding pdf also linked with all the input lines executed). As usual, to reproduce the input/output you need to have installed the latest version of Physics, available in the Maplesoft R&D Physics webpage.

Physics_2016_IOP_webinar.mw     Physics_2016_IOP_webinar.pdf

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

Hello,

I have a complex set of non linear diff eqns in the form :

y1'' = f(y1',y1,y2'',y2',y2,y3'',y3',y3,y4'',....,y6'',y6',y6,u1,u2,u3,u4) ;

y2'' = f(y1'',y1',y1,y2',y2,y3'',y3',y3,y4'',....,y6'',y6',y6,u1,u2,u3,u4)

and so on ... y6''=(...)

As I want to resolve this coupled systeme in matlab using @ODE45... I wanted the equations in the form : y1''=f(y1',y1,y2',y2,....) and so on ... => X'[] = f(X[],U[])

How can I force maple to rearrange a system of coupled eqns with only the variables i want ?

I know this is possible beacause it is a nonlinear state space model but maple do not work with nonlinear state space model... It give me error when I tried to create statespace model with my non linear diff eqns.

Thanks a lot !

----------------------------------------------------------------------------------------------------------------------
Introduction

I have a matrix (named DC on the piece of code below) all the elements of which are complex numbers a+b*I with a and b floating point numbers.
I want to obtain the real part of DC.

Obviously, if you do something like :
DC := Matrix(2,2, [1.0+1.0*I, 1.0-1.0*I, -1.0+1.0*I, -1.0-1.0*I];
Re~(DC);

the result corresponds to the desired matrix

----------------------------------------------------------------------------------------------------------------------
Context

In fact this matrix DC comes from some computations  described in the piece of code below

# Purpose :
# Given N points in a plane (here  in [0,1]X[0,1]), compute the matrix DX of distances between these points
#
# Example : if Pi and Pj are two such points, DX[i,j]=DX[j,i] denotes the Euclidian distance between Pi and Pj
#
# As I did not be able to find any single function in MAPLE that would construct DX , I proceed that way :
#   1/ let X the (N,2) matrix that contains the coordinates of the N points
#   2/ I represent these  N points as N complex numbers (vector C)
#   3/ I construct the (N,N) matrix MC = <C | C …..| C>
#   4/ I put MC = C – Transpose(C) :
#   5/ I take the norm DX of each elements of DC : DX := abs~(DC)
#       At this point, DX should contain the desired distances
#       But, due to floating point arithmetics, each element of DX writes a+0.*I where a is some floating point number)
#   6/ Last stage : execute Re~(DX)
#

with(Statistics):
with(LinearAlgebra):

N := 4:
X := Matrix(N,2, convert(Sample(Uniform(0,1), 2*N), list)):  #just an example

C   := X[..,1] +~ X[..,2] *~I;
MC := Multiply(C, Vector[row](N, 1));
DC := MC - Transpose(MC);
DX := abs~(DC);
Re~(DX)


----------------------------------------------------------------------------------------------------------------------
 My observations : 

1/ Maple 2015, Windows XP, 64 bytes
Re~(DX) returns DX and does not remove the imaginary (0.*I) part
But  Matrix(N, N, Re~(convert(DC, list))) does (which is a satisfactory, even if not clever, stopgap)

Why (it is just a question to help me to understand correctly how MAPLE proceeds) Re~(DC) does not (seem) to work here ?


2/ Maple 2015.2, Mac OS X El Capitan
DX := abs~(DC) gives me this strange result :
If (for instance) DC[i, j] = -1 – 2*I, DX[i, j] = +1 + 2*I
According to the compatibility problems between Maple 2015.1 and “El Capitan” (fixed from February), could it remain a few other problems ?

Last but not lesat : Did I do any syntax error ?


 I look forward to your responses

Hello,

I have a little question about the property "local" or not of a index in a for loop.

I notice that when I make "for loop" the index i is not local. In the small example, when I ask to evaluate i after having done this loop, the answer is 5 and not i.

Example :

for i from 1 to 4 do
i^2
od;

i; --> 5

How can I do to ask Maple to use index as local ?

Thanks a lot for your help.