how to solve optimal system of vector   fields in lie theory in maple?

Am trying to draw a series of triangles for animation.  I try to construct the triangles in a loop using:

triangle(cat(T1,`a`),[A,B,C]):

  so that the names of the triangles are meant to beT14, T15, T16

I have tried unsuccessfully to use the plots and draw commands ie

draw({seq(tabl[i], i=4..6)}, insequence=true, scaling=constrained);

plots[display({seq(tabl[i], i=4..6)}, insequence=true, scaling=constrained);

  Can the animation be done in either?  

It seems to want a variable in a list/set format - How do I set that up?  Any comments, or help gratefully received.  The program is below.  Part of the output does give triangles - but they all seem identical:-(

restart:

# # # # # # # # # # # # # # # # # # # # # # # # # # # #

# Altitude exploration  program

#Trying to draw a sequence of triangles for animation

# # # # # # # # # # # # # # # # # # # # # # # # # # # #

with(plots):

with(geometry):

for a from 4 to 6 do

b:=a+1: c:=a+2:

angA:=arccos((a+5)/2/(a+2));

point(A,0,0),point(B,c*cos(angA),c*sin(angA)),point(C,a+1,0):

tabl[a]:=triangle(cat(T1,`a`),[A,B,C]):

printf("a=%d\n",a);

triangle(cat(T1,`a`),[A,B,C]):

end do:
 

for i from 4 to 6 do

draw({seq(tabl[i], i=4..6)}, scaling=constrained);

printf("a=%d\n",i);

end do;
 

print(`After do`);

draw({seq(tabl[i], i=4..6)}, insequence=true, scaling=constrained);

Warning, the name changecoords has been redefined

Warning, the name arrow has been redefined

Warning, these names have been redefined: circle, ellipse, homothety, hyperbola, line, point

a=4

a=5

a=6

a=4

a=5

a=6

What is a suitable replacement for eliminate?

Here is my code:

In the older versions of Maple the first example of eliminate would return same result as the solve example, but with current version I need to resort to the second example.

Maple 13:

t:=(a0+a1*x+a2*x^2)/(b0+b1*x+b2*x^2);
t*exp(t)=c;

x=solve(%,x); yields with c<>0:

x=-(a0*b2-b0*a2)/(a1*b2-b1*a2)

Is this an error? The solution is the same in each case - it is independent of c. I would expect x as solution of t=LambertW(c).

Mathematica 7.0 says correctly: "The equations appear to involve the variables to be solved for in an essentially non-algebraic way."

Is this bug corrected in higher versions of Maple?

Hello, I have been attempting to plot a sequence of arrows in order to display how the vectors of the Frenet-Serret frame change throughout an helix-like trajectory. I came up with the following:

(With p1 being a plot I made earlier)

for t from 0 by 0.1e-1 to 12.5663706144 do plots[display](p1, plottools[arrow](Vector([cos(t), sin(t), t/(7.5)]), Vector([-(1/2)*sqrt(2)*sin(t), (1/2)*sqrt(2)*cos(t), (1/2)*sqrt(2)]), .1, .2, .3, cylindrical_arrow)) end do

This plots the desired arrow representing the tangent vector; however, it creates a plot for each step, while what I want is for it to display the arrow on each step in the same plot (as an animation).

I have attempted using the seq command, but I can't seem to get it right.

plots[display](p1, plottools[arrow](seq([Vector([cos(t), sin(t), t/(7.5)]), Vector([-(1/2)*sqrt(2)*sin(t), (1/2)*sqrt(2)*cos(t), (1/2)*sqrt(2)]), .1, .2, .3, cylindrical_arrow], t = 0 .. 4*Pi, 0.1e-1)))

With this code, the sequence won't be able to be executed.

Any ideas on how to do this? How can I use the sequence command in combination with plottools[arrow]?

Dear Guys

I want to solve this integral by maple:

p := sqrt(ln(t)*(ln(t))^(-2))*t^(-1)*(1-(ln(t))^(2)/(t^2))^(-1/4);

I used these expressions, but they don't work:

int(p, t);

int(simplify(p),t);

int(simplify(p, symbolic), t);

Could you please guide me?

Thanks

Hi,

I asked a question before, how to shift subscript of u(i,j):

P: u[i,j] -->  u[i+1,j]

https://www.mapleprimes.com/questions/223136-How-To-Define-An-Operator

How about an arbitrary expression?

P: u[i,j]^2 v[i,j]+u[i-1,j]  -->  u[i+1,j]^2 v[i,j]+u[i,j]

thanks.

See below, why the difference + what is the distinction between the 2?  Notice that they yield different results with the is command.

Download sum_versus_Sum.mw

where i can change the value?

I'd like to find the harmonic mean of the lengths of the three altitudes of a triangle.  I believe this to be equal to the radius of the incenter of the triangle.  I haven't used the geometry package  much, but notice it has some interesting features like Harmonic mean. (Incidentally, it has a vertex, and vertices command, but these don't seem to be recognised in Maple 7 - not even in the Help section.)  I would normally tackle thissue  problem using coordinate geometry, and give a diagram of the triangle using the plots [display] command.  Id like some advice about the interactivity of commands in geometry and plots packages eg  can I find the coordinates of the base of an altitudemail using the geometry package?  There is an altitude command which gives the àltitude's equation.  For this the coding would be

:triangle(ABC, [point (A,0,0),point (B,,2,0), point (C,1,3)]:

altitude (hA1,A, ABC);

detail (hA1);

   I think I have answered my own question!  I see there is a DefinedAs command which would give me the coords.   Am I correct in thinking the geometry package is the best method of doing this.  Later I was hoping to display animation, to see how the Harmonic mean changes with varying different triangles.

Thanks for reading this and Happy New Year.

David  

Hallo,

I have a list of graphs made correctly with the package GraphTheory: g=[g[1],g[2],g[3]], where g[1], g[2] and g[3] are graph objects. GraphTheory[DrawGraph] inside a for-loop doesn't work. GraphTheory[DrawGraph](g) draws all graphs simultaneously. How can I draw the single graphs of the list successively when the number of members in g is a variable?

Thanks.

Hello everyone,

Compliment of the season. I received the error message while trying to solve some Pade approximant problem and try to find what could possibly be the error but could not.

Please, anyone with good informations on the possible solutions should help.

Thanks. The Link is below

 Error.mw

Hello.
Can I somehow print several matrices next to each other without getting the quotations marks printet too?
Attached what I currently have.

Download matrix_print_attempt.mw

 Hi,  

Is there a way of determining whether a function of two variables is continuous or not? Can we find the discontinuity points 

of such multivariable functions? (Considering the graphs of the function is not always helpful.)

Hi, I need to calculate some discrete variational problems, but it's a hard work just by hand.

Is there any toolboxes about the discrete variational computation? Or how to design a program to do that?

In particular, I need to realize the functions:

1. the linearized operator and the adjoint operator of some expressions.

       For example:

       the linearized operator of u(n,m+1)u(n+1,m) is u(n+1,m)Tm+u(n,m+1)Tn

       the adjoint operator is u(n+1,m-1)T^(-1)m+u(n-1,m+1)T^(-1)n,

       (The latter is just the discrete Euler operator.)

      Tm, Tn is the shift operator, T^(-1) is the inverse operator of T.

2. discrete Euler-Lagrange equation.

I am not familar with the maple, please help!

Thanks.