my code can only do for one variable, 

how to make divisible checking for multivariable cases with the ordering such as plex

IsDivisible(LP(h, t), LP(g[i], t), x)

it is not only x when multivariable

f:=LP(y^2*x,plex(x, y))[2];
g:=LP(y*x-y,plex(x, y))[2];
Remainder(f, g, gcd(f,g));
degree(Remainder(f, g, x),x);
degree(g, x);

remainder has error expect its 3rd argument x, to be of type or but received y*x

how to do if have ordering

do it need to check whether both f and g have variable x using indets and then apply remainder?

do it need to check each variable starting from the first variable in the ordering? 

how about if f has variable x but g do not have variable x, or f do not have variable x and g have variable x

if so, i try to replace below code in the bottom code, it has error

Error, (in FindDivisble) cannot determine if this expression is true or false: 0 < Search(x, {x, y})

FindDivisble := proc(g, h, t)
with(ListTools):
result := 0;
for i from 1 to nops(g) do
mainvariable := 0;
for j from 1 to nops(t) do
mainvariable := op(j, t);
if mainvariable <> 0 then
if Search(mainvariable, indets(h)) > 0 and Search(mainvariable, indets(g[i])) > 0 then
if IsDivisible(LP(h,t), LP(g[i],t), mainvariable) = 0 then
return i;
else
result := 0;
end if:
end if:
end if:
od:
od:
return result;
end proc:

with(Groebner):
LP := proc(f, t)
return LeadingTerm(f, t)/LeadingCoefficient(f, t);
end proc:
IsDivisible := proc(f, g, x)
with(Algebraic):
if Remainder(f, g, x) = 0 or degree(Remainder(f, g, x),x) < degree(g, x) then
return 0;
else
return 1;
end if:
end proc:
FindDivisble := proc(g, h, t)
result := 0;
for i from 1 to nops(g) do
if IsDivisible(LP(h, t), LP(g[i], t), x) = 0 then
return i;
else
result := 0;
end if:
od:
return result;
end proc:
MD := proc(f, g, t)
r := 0;
u := Matrix(nops(g), 1);
for j from 1 to nops(g) do
u[j] := 0;
od:
h := f;
while h <> 0 do
i := FindDivisble(g, h, t);
if i > 0 then
u[i] := u[i] + LeadingTerm(h, t)/LeadingTerm(f[i], t);
h := h - LeadingTerm(h, t)/LeadingTerm(f[i], t)*f[i];
else
r := r + LeadingTerm(h, t);
h := h - LeadingTerm(h, t);
end if:
od:
end proc:
f:=y^2*x;
f1 := y*x-y;
f2 := y^2-x;
MD(f,[f1,f2],plex(x, y));

So I'm trying to make a procedure to tell is a sequence is graphical or not.
seqgraph:= proc (L::list)

local k::integer, i::integer, n::integer, a::integer, S;

n := numelems(L);

S := convert(L, `+`);

a := 0;

if type(S, odd) then print("not graphical")

else for k to n do

if add(L[i], i = 1 .. k) <= k(k-1)+add(min(k, L[i]), i = k+1 .. n) then a := a+1

else a := a+2

end if;

end do;

end if;
if n = a then print(graphical)

else print("not graphical")

end if;

end proc;

 I'm trying to say that if that equality (which is part of the erdos gallai theorem) holds for that value of k then we'll add one to a value (a). Thus, if a=n at the end then the ineuqality was true for each k and thus it would it should print "graphical" but every list I test it one prints 'not graphical'. Where is my mistake? I get an error saying it can't execute add?

From some scientific experiments, the following set of data is available
(1.0, 2.33),(2.0, 0.0626),(3.0, −2.16),(4.0, −2.45),(5.0, −0.357),(6.0, 2.21),(7.0, 2.75),(8.0, 0.636),(9.0, −2.45).

We need to use least squares method to fit the curve to the data
y = a + b cos(x) + c sin(x) + d cos(2x) + e sin(2x)

Show your solution procedure in Maple and get the best fit for the coefficients. Finally
plot the data and the y curve together on the same graph to visualize the fitting. For the
data, use blue circles while for the y curve, use red solid line style. Use the leastsquares
command we learned in LinearAlgebra package.

What is the solution to the following system? Is the solution unique? Use
the reduced row echelon form to explain why.
x + 2y + 3z = 1,
4x + 5y + 6z = 1,
7x + 8y + 9z = 1

Find the eigenvalues and eigenvectors for

A =
2 0.37 0
0 1.1 −4.29
1.6 0 2.2

Can you estimate the largest eigenvalues (in absolute value) using Power method for this
problem? Try to explain why if you can

Find the quadratic polynomial which interpolates (2, 0),(6, 1),(8, 0). Solve this with Maple. Start the problem by setting f(x) = ax2 + bx + c for example, then the unknowns are a, b, c.

So for the part of the erdos gallai theorem that says:

how could I translate this into maple? I'm assuming I'll need to use nested for...dos

If I have a list, how can I write a program to see is that list is graphical? So far I have

graphicalseq := proc (L::list)

local i::integer, N;

N := convert(L, `+`);

if type(N, odd) then print("Sequence is not graphical")

else if numelems(L)-1 < L[1] then print("Sequence is not graphical")
end if;

end if;

end proc;

I know I still have to keep going to determine whether the sequence is graphical, but I'm not sure how.

 I was thinking of trying to somehow use Havel-Hakimi's theorem, but again I'm not sure how. Any hints would be appreciated.  I can't use the is Graph Sequence function

Hi

I have to numerically solve this equation many (tens of thousands) of times for theta_n (as I vary different parameters, especially n):

tan(theta_n) - C_a*Z_0*(-v^2*(Pi*n-theta_n)^2/x_l^2+omega_a^2)*x_l/(v*(Pi*n-theta_n)) = 0

theta_n should be in [-pi/2, pi/2). It seems like solving this is the slowest single component of the chain of calculations (that follow this).

Currently I do it with this function:

get_theta_n_array:=proc(max_n::integer, omega_a::float, v::float, x_l::float, C_a::float, Z_0::float)
    local theta_n_array:=Array(
        select(x->Re(x)<evalf(Pi/2) and Re(x)>=-evalf(Pi/2), [seq(
        #NOTE: careful with fsolve - in some cases returns unevaluated equation
        fsolve(tan(theta_n) - C_a*Z_0*(-v^2*(Pi*n-theta_n)^2/x_l^2+omega_a^2)*x_l/(v*(Pi*n-theta_n)) = 0, theta_n) , n=1..max_n)]
        , real)
        ,datatype=float[8]);
    if ArrayNumElems(theta_n_array) <> max_n then
        printf("Bad Array Dimensions! Got too many or not enough solutions.");
        theta_n_array:="CHECK: get_theta_n_array()": #dirrrrty hack that will ring an alarm bell if array is not the right size
    end;
    theta_n_array;
end;

And call it like so (for say n=1000)

st:=time();
result:=get_theta_n_array(1000, 100e9, 1e8, 0.3, 20e-14, 50.0);
time()-st;

This will take say 3.5s on my PC.

Does anyone have any ideas how to speed this up? I would hope this to take at least an order of magnitude less time. I played with DirectSearch lib but that was not faster.

Also, I should note that this is the only portion of my code that is not thread safe (because of the fsolve call), which leads to "extra" slowdowns because I have to use Grid:-Map, instead of Thread:-Map when parallelizing, and more importantly because I can't compile the rest of the code (Grid:-Map is not compatible with compiled functions).

Let me know if you have any ideas...

thanks!

Hi all.

In the following program, i have normalized bernstein polynomials using gram- schmidt orthogonalization process and want to hybrid them with block pulse functions so that i have:

why the program is wrong?? where of it doesn't work properly?

please guide me

best wishes

OHB.mws

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

a := [x+1, x+2, x+3, x+4];

which command can remove polynomial x+2 from the list a;

to become

a := [x+1, x+3, x+4];

How can I find stepwise solution of the following integral?

Int(exp(-xi^2*b^2)*cos(xi^2*a*t)*cos(xi*x), xi = 0 .. infinity)

where xi greek letter.. 

Here was my search strategy to find the answer:

keyboard shortcut execute worksheet on http://www.mapleprimes.com/search/?term=keyboard%20shortcut%20execute%20worksheet

only found one thing http://www.mapleprimes.com/users/erik10/answers

Googled it found 

http://www.maplesoft.com/support/help/maple/view.aspx?path=worksheet%2Freference%2Fhotwin

http://www.maplesoft.com/support/help/Maple/view.aspx?path=worksheet/expressions/executeworksheet

http://scipp.ucsc.edu/~haber/webpage/maple_cheatsheet.pdf

Don't see a keyboard shortcut. 

What is the keyboard shortcut to execute entire worksheet? Is there a name for this action of executing the whole worksheet? 

What did you search and click to find the answer? 

Hello everybody,

I find a answer on that subject at this link: http://www.mapleprimes.com/maplesoftblog/95508-Monte-Carlo-Pi

But for starting easy, I try this:

with(RandomTools[MersenneTwister]);
directpi := proc (n)
local i, x, y, N;
N := 0;
Digits := 2;
for i to n do
x := GenerateFloat();
y := GenerateFloat();
if x^2+y^2 < 1 then
N := N+1:
end if:
end do:
N;
end proc;

evalf(directpi(4000)/(1000.0), 4);

                             3.176

I would like to know if this code is appropriate and if it is possible to have a random number between -1 to 1 so it will be easier to plot the points in the square with the circle inside.

Thank you.

--------------------------------------
Mario Lemelin

Maple 18 Ubuntu 13.10 - 64 bits
Maple 18 Win 7 -  64 bits
messagerie : mario.lemelin@cgocable.ca
téléphone :  (819) 376-0987

I am Maple 15 student edition user and the packages is not loaded when I use the execute all command from the GUI. I have to manually press the enter key to have by package loaded before I use a function defined in the package. How can I work around this issue?

Thanks

P.S: You can see the Maple document attached to this post.

NumericalSimulation.mw