Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Dear Maple users,

 

i have a set of 2 Lines: L1 (determined by the intersection of plane x + y -1=0 and plane x - z - 1=0), 

L2 ( intersection of plane x + y-7=0 and plane x-y+1 = 0 ).

which functions or commands of maple should I use "visualize" those 2 lines L1 and L2?

 

thanks for your help,

 

JJ

I want to compute binomial coefficients mod 2 in Maple.  My numbers are getting big and the standard function binomial(n, k) is very slow. Is there a maple procedure or function which will be fast for computing this mod 2?  (I know how to do this theoretically, but not in maple.) Thank you for your help.

Hello,

I am new to maple and coding so please bare the amateur coding.

 

I am trying to plot the following function:

 

When tgk < tb then I want it it to point a cross, where tgk and tb are functions that both have x and y values in them.

This is what I have:

My domain is x=-18..18 and range is y=0..12

I want x and y values to be integer values in degrees. And I want all possible combinations to be plotted (e.g (1,1) (1,2) (1.3) etc.) I do not know how to do any of this, but I need it for something I am modeling, and this software was recommended to me.

I am new to Maple and I have never really learned how to code. Any help would be really appreciated!

Thanks

Hi guys,

I am trying to fit some constants to an equation in maple but am very new to the software and am struggling somewhat to input he correct commands.

I have the following equation;

x=a(y^b)(z^c)

And I have data points for x, y and z

I need to calculate the best fit value for a, b and c based on this data.

These constants are material properties for calculating creep in a structures and the data is somewhat dirty, therefore my hand calcs lead to an unsolvable results so best fit values are my only hope!

Any suggestions or a nudge in the right direction would be wonderful!

Thanks 

Steve

Dear all;

 

Thanks ifor looking and help me in my work. Your remarks are welcome.Description:
 This routine uses the midpoint method to approximate the solution of
     the differential equation $y'=f(x,y)$ with the initial condition $y = y[0]$
     at $x = a$ and recursion starting value $y = y[1]$ at $x = a+h$.  The values
     are returned in $y[n]$, the value of $y$ evaluated at $x = a + nh$.       
                                                                          
Arguments:     
\begin{itemize}
\item  $f$  the integrand, a function of a two variables
                
                \item $y[]$ On input $y[0]$ is the initial value of $y$ at $x = a$, and $y[1]$
                is the value of $y$ at $x = a + h$,
                \item on output for $i \geqslant 2$
             $$ y[i] = y[i-2] + 2h f(x[i],y[i]); \quad \quad x[i] = a + i h.$$
             \end{itemize}

 
CODE USING MAPLE

 Midpoint-Method=proc(f,a,b, N)

h:=(b-a)/N;
x[0]:=a;
y[0]:=1:

 for n from 2 to N do
    x[n] := a+n*h;
    y[n+1] = y[n-1] +  2h f( x[n], y[n] );
od:
// Generate the sequence of approximations for the Improved Euler method
data_midpoint := [seq([x[n],y[n]],n=0..N)]:
//write the function;
F:=(t,y)-> value of function ;

//Generate plot which is not displayed but instead stored under the name out_fig for example
out_fig := plot(data_midpoint,style=point,color=blue)

 

Your remarks.

Thanks

 

 

 

Vector using package Physics, LinearAlgebra.

Vectores.mw     (in spanish)

I was recently asked about performing some General Relativity computations from a paper by Plamen Fiziev, posted in the arXiv in 2013. It crossed my mind that this question is also instrumental to illustrate how these General Relativity algebraic computations can be performed using the Physics package. The pdf and mw links at the end show the same contents but with the Sections expanded.

 

General Relativity using Computer Algebra

 

Problem: for the spacetime metric,

g[mu, nu] = (Matrix(4, 4, {(1, 1) = -exp(lambda(r)), (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = -r^2, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -r^2*sin(theta)^2, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = exp(nu(r))}))

 

a) Compute the trace of

 

"Z[alpha]^(beta)=Phi R[alpha]^(beta)+`&Dscr;`[alpha]`&Dscr;`[]^(beta) Phi+T[alpha]^(beta)"

 

where `&equiv;`(Phi, Phi(r)) is some function of the radial coordinate, R[alpha, `~beta`] is the Ricci tensor, `&Dscr;`[alpha] is the covariant derivative operator and T[alpha, `~beta`] is the stress-energy tensor

 

T[alpha, beta] = (Matrix(4, 4, {(1, 1) = 8*exp(lambda(r))*Pi, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = 8*r^2*Pi, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 8*r^2*sin(theta)^2*Pi, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 8*exp(nu(r))*Pi*epsilon}))

b) Compute the components of "W[alpha]^(beta)"" &equiv;"the traceless part of  "Z[alpha]^(beta)" of item a)

 

c) Compute an exact solution to the nonlinear system of differential equations conformed by the components of  "W[alpha]^(beta)" obtained in b)

 

Background: The equations of items a) and b) appear in a paper from February/2013, "Withholding Potentials, Absence of Ghosts and Relationship between Minimal Dilatonic Gravity and f(R) Theories", by Plamen Fiziev, a Maple user.  These equations model a problem in the context of a Branse-Dicke theory with vanishing parameter "omega." The Brans–Dicke theory is in many respects similar to Einstein's theory, but the gravitational "constant" is not actually presumed to be constant - it can vary from place to place and with time - and the gravitational interaction is mediated by a scalar field. Both Brans–Dicke's and Einstein's theory of general relativity are generally held to be in agreement with observation.

 

The computations below aim at illustrating how this type of computation can be performed using computer algebra, and so they focus only on the algebraic aspects, not the physical interpretation of the results.

a) The trace of "  Z[alpha]^(beta)=Phi R[alpha]^(beta)+`&Dscr;`[alpha]`&Dscr;`[]^(beta) Phi+T[alpha]^(beta)"

   

b) The components of "W[alpha]^(beta)"" &equiv;"the traceless part of " Z[alpha]^(beta)"

   

c) An exact solution for the nonlinear system of differential equations conformed by the components of  "W[alpha]^(beta)"

   

 

GeneralRelativit.pdf    GeneralRelativity.mw

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

I want to graph y=x^2, x>=0. but i want the axis to go from -2..2 so that you can see the restriction.  How do I go about this?

 

I am trying to solve these equations:

eq1:=cot(theta[n])=(omega[a]^2 - omega[n]^2)/omega[n];

eq2:=cot(theta[n]+ omega[n])=-(omega[b]^2 - omega[n]^2)/omega[n];

for some values of omega[a] and omega[b]. I will in the end create two 3d plots for omega[n] and theta[n] as a funciton of ometga[a] and omega[b]

So for example for some particular values have:

eqs:=subs(omega[a]=0.2, omega[b]=1, [eq1, eq2]);

Then solving,

solve(eqs, [omega[n],theta[n]]);

gives:

I'm however only interested in solutions where omega[n]>=0, but doing this:

solve(eqs, [omega[n],theta[n]], UseAssumptions) assuming omega[n]>=0.0;

returns an empty list. Adding the condition omega[n]>=0.0 to the list of equations also does not work.

Is this a bug or am I missing something? Note, I realize that i can manually go through the entries myself and pick the right solutions, I am just asking how to force maple to do this automagically.

thanks

 

Here is the full code:

restart:

eq1:=cot(theta[n])=(omega[a]^2 - omega[n]^2)/omega[n];

eq2:=cot(theta[n]+ omega[n])=-(omega[b]^2 - omega[n]^2)/omega[n];

eqs:=subs(omega[a]=0.2, omega[b]=1, [eq1, eq2]);

solve(eqs, [omega[n],theta[n]]);

solve(eqs, [omega[n],theta[n]], UseAssumptions) assuming omega[n]>=0.0;

Let a(1)=916 , a(2)=935 , a(3)=713  , a(4)=845  , a(5)=274  , a(6)=914 ,a(7)=255 . Find formula a(n)= ? ,n=1,2,3,....

Hello everyone,

 

I'm having some trouble overlaying a set of complex plots. I follow the usual procedure 'display(p0,p1)' I only get p1...

 

If i try with plots the display command works fine, here's the piece of code I'm trying to get working (r is defined elswhere as function of x and phi):

i := 0;

p := Array(0 .. 10);

for x from 0 by .2 to 2

do p[i] := complexplot(r, phi = -(1/2)*Pi .. (1/2)*Pi);

i := i+1

end do;

display(p[1], p[10]);

 

Any hints?

 

Cheers,

Felipe

I am a new user of Maple. Could anyone help me to know how to call a Maple function/procedure from a Matlab program with a simple example? And conversely, how to call a Matlab function from Maple.

I have 20 datapoints in two groups. I may name them as f[1],...,f[10];g[1],...,g[10]. f[1]:=[1.2,3.5] etc

I would like to plot these 20 points

(1) in one plot

(2) f[1]~f[10] in one color; g[1]~g[10] in another color.

 

I checked http://www.maplesoft.com/support/help/Maple/view.aspx?path=plots%2fpointplot

and did not get the point :(

 

Do you any suggestion what can I do to realize the aims (1) and (2)?

 

Thank you very much in advance!

Hi, 

 

  I tried to use generated random as following

*** 

for j from 1 to 5 do
    c:=rand(0..1):
    d:=c();
    print(`random number`,c(),d);

    if c()=1 then

       print(`Y`)
    else
     print(`N`);
    end if;
  end do:

***

 

  The output is

 

****

                      random number, 1, 0

                               Y

                      random number, 1, 1

                               Y

                      random number, 1, 1

                               N

                      random number, 1, 1

                               N

                      random number, 0, 0

                               N

****

  Why the output numbers in one line are different? And Using "if" sentence seems do not correspond to the printed "c()" value..

 

Thank you very much in advance!

 

Say we solve numerically and ODE using Maple. Say ode1:= { diff(Q(x),x)= Q(x)/3x , Q(1)=1 }

The solution is a procedure so now suppose we have another ODE where the solution appears.Say  ode2:= { diff(f(x),x)= Q(x)*x , f(1)=4}.

To extract the solution of the first ODE I set sol1:=dsolve(ode1,numeric) and Q:=proc(x) local s: return rhs(sol(x)[2]): end proc:

But now I got an error message when I trying sol2:=dsolve(ode2,numeric).

Is it possible to use a procedure in the definition of the ODE one wants to solve?

 

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