# MaplePrimes Questions

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### convert Matlab code to Maple...

February 23 2014
0 1

Dear all

I would like to convert Matlab code to Maple, is there anu idea, this is the code.

% Usage: [y t] = abm4(f,a,b,ya,n) or y = abm4(f,a,b,ya,n)
% Adams-Bashforth-Moulton 4-th order predictor-corrector method for initial value problems
% It uses
% Adams-Bashforth 4-step method as a precdictor,
% Adams-Moulton 3-step method as a corrector, and
% Runge-Kutta method of order 4 as a starter
%
% Input:
% f - Matlab inline function f(t,y)
% a,b - interval
% ya - initial condition
% n - number of subintervals (panels)
%
% Output:
% y - computed solution
% t - time steps
%
% Examples:
% [y t]=abm4(@myfunc,0,1,1,10);          here 'myfunc' is a user-defined function in M-file
% y=abm4(inline('sin(y*t)','t','y'),0,1,1,10);
% f=inline('sin(y(1))-cos(y(2))','t','y');
% y=abm4(f,0,1,1,10);

function [y t] = abm4(f,a,b,ya,n)
h = (b - a) / n;
h24 = h / 24;

y(1,:) = ya;
t(1) = a;

m = min(3,n);

for i = 1 : m % start-up phase, using Runge-Kutta of order 4
t(i+1) = t(i) + h;
s(i,:) = f(t(i), y(i,:));
s2 = f(t(i) + h / 2, y(i,:) + s(i,:) * h /2);
s3 = f(t(i) + h / 2, y(i,:) + s2 * h /2);
s4 = f(t(i+1), y(i,:) + s3 * h);
y(i+1,:) = y(i,:) + (s(i,:) + s2+s2 + s3+s3 + s4) * h / 6;
end;

for i = m + 1 : n % main phase
s(i,:) = f(t(i), y(i,:));
y(i+1,:) = y(i,:) + (55 * s(i,:) - 59 * s(i-1,:) + 37 * s(i-2,:) - 9 * s(i-3,:)) * h24; % predictor
t(i+1) = t(i) + h;
y(i+1,:) = y(i,:) + (9 * f(t(i+1), y(i+1,:)) + 19 * s(i,:) - 5 * s(i-1,:) + s(i-2,:)) * h24; % corrector
end;

### Adams–Moulton methods to solve ODE...

February 23 2014
0 3

Dear all

Is there any one can help me to find  the Maple code to solve ODE : y'(x)=f(x,y(x))  using n-step  Adams-Moulton Methods.

The code exist  with mathematica in this link:

there is also the code of this method with Matlab, see please:

http://www.math.mcgill.ca/gantumur/math579w10/matlab/abm4.m

But I want file.mw ( with maple)

Thank you very much for helping me.

### Combining two fractions with a radical in the nume...

February 23 2014
1 4

I'd like to get MAPLE to take this as an input: 1/2+(1/3)*sqrt(2) and give this as an output: (3+2sqrt(2))/6. For the life of me, I can't get it to do that.  I fieel like an idiot; it should be easy.

### Write a function that diagonalises a complex (2x2)...

February 23 2014
0 5

so we have to Write a function that diagonalises a complex (2x2) matrix if possible,

we need the argument to be a (2x2) matrix say A.   and we need the return value to be a list [a1 ;a2 ;b1;b2] of two complex numbers followed by two 2-vectors such that {b1,b2} is a basis for C^2 and so that

Ab1 =a1b1 , Ab2=a2b2  if these exist. if not then the function should return an empty list []

also, the thing is that we're not allowed to load any maple packages, we have to do it by hand :'(

thanks <3

### A straight line in 3D...

February 23 2014
1 4

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?

JJ

### Binomial coefficients...

February 22 2014
1 4

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.

### plotpoint with if operator possible?...

February 22 2014
1 5

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

### Fitting constants to equation...

February 22 2014
2 8

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

### Midpoint Method using for solving Ordinary differe...

February 22 2014
1 16

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)

Thanks

### Write a procedure whose input is a binary list an...

February 21 2014
1 5

m:=proc(n::list)
local N, S, i:
N:=nops(n);
S:={};
for i from 1 to N do
if n[i]=1 then do
S:=S union {i}; break; od; fi; od;
for i from 1 to N do
if n[i]=0 then do
S:=S union {}; break; od; fi; od;
end proc;

the procedure works if the last member of a list is 0, for example

m(1,0,1,0);

returns {1,3}

but if it ends in 1, nothing gets returned, example: m(1,0,1);

I can also get it to work the other way around, where it'll return the set if the list ends in 1 but not zero. I need it to work for both.

### How do you create a function with restricted domai...

February 20 2014
2 2

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?

### StandardDeviation does not the job... HELP!...

February 20 2014
3 16

Sorry for the last post:

StandardDeviation not StandardVariation

with(Statistics);

L := [3, 2, 2];

W := [7, 5, 8];

StandardDeviation(L, weights=W);

The results by Maple 17 is 0.589345606817264

But the value of the standard deviation value must be : 0.489360484929593

What is the problem?

### solve with assumptions - is this a bug?...

February 20 2014
0 6

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;

### Sequence of integers...

February 20 2014
0 1

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,....

### Cannot paste into this site from Chromium browser...

February 20 2014
0 6

I cannot copy and paste into this site using the Google Chromium brower (v 32). Has anyone had this problem and know of a work-around? What I'd really like to do is use Edit-with-Emacs (a chromium extension). It works for other sites.  I can open it from this site, but nothing I enter gets transferred. I'm guessing this is related to the inability to cut/paste.

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