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I have to plot in 2 different ways an ellipse that has been rotated in a plane. The equation of the ellipse is 

3x^2 - 3xy + 6y^2 -6x +7y =9

First of all I use the implicitplot which works great: 


For the second method I really am not sure if what I'm doing is good. I tried with the plot3d, but it gave me some sort of weird shape, I really don't think it is what I am looking for. 


The I tried to reduce the equation to the form x^2/a^2 + y^2/b^2 = 1, but I could not, maybe because of the rotation. Still, I tried to take the ellipse function from Maple with some empirical numbers I just tried to create an ellipse looking like the first one. 

This time I get an ellipse similar to the first, but I don't really think it is legit to do it that way, in a sort of trial-and-error.

So I was wondering if there was another way like implicitplot to create the graph of that ellipse. 

This is the code

This is the warning 

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters )"


How to solve it?

hi all

i have this code


theta1 := -arctan((Q*(-P*Q+sqrt(Q^2*W^2+W^4-W^2*P^2))/(Q^2+W^2)+P)/W):
Stheta1 := -(Q*(-P*Q+sqrt(Q^2*W^2+W^4-W^2*P^2))/(Q^2+W^2)+P)/(W*sqrt(1+(Q*(-P*Q+sqrt(Q^2*W^2+W^4-W^2*P^2))/(Q^2+W^2)+P)^2/W^2)):
Ctheta1 := 1/sqrt(1+(Q*(-P*Q+sqrt(Q^2*W^2+W^4-W^2*P^2))/(Q^2+W^2)+P)^2/W^2):


can i plot  qB vs  phiB1 while phiB1 bitween 0..pi ? if yes, how?

plz help

Hello everyone,


I am trying to extract the coefficients from a differential poynomial. In general, this poynomial is in two variables, say u and v along with their differentials, i.e D(u) or D@@2(u) or so on. 

Coefficients of this polynomials are rational funcitons.

For instance- consider the following example:


then output should be [a(x), 1, -1].


Thanks for your help.


I've got this error in my code and I don't know why as I didn't get it when I used a different xn function. Any help would be greatly appreciated! Thank you in advance!

Kind regards,

Gambia Man



boxcount := proc (data, N) local n, xmax, xmin, xrange, ymax, ymin, yrange, dx, dy, i, j, ix, iy, sum, res; n := (1/2)*ArrayNumElems(data); xmax := max(seq(data[i, 1], i = 1 .. n)); xmin := min(seq(data[i, 1], i = 1 .. n)); ymax := max(seq(data[i, 2], i = 1 .. n)); ymin := min(seq(data[i, 2], i = 1 .. n)); xrange := xmax-xmin; xmin := xmin+(-1)*0.1e-1*xrange; xmax := xmax+0.1e-1*xrange; xrange := 1.02*xrange; yrange := ymax-ymin; ymin := ymin+(-1)*0.1e-1*yrange; ymax := ymax+0.1e-1*yrange; yrange := 1.02*yrange; dx := xrange/N; dy := yrange/N; res := Array(0 .. N-1, 0 .. N-1, 0); for i to n do ix := trunc((data[i, 1]-xmin)/dx); iy := trunc((data[i, 2]-ymin)/dy); res[ix, iy] := 1 end do; add(add(res[i, j], i = 0 .. N-1), j = 0 .. N-1) end proc:


bicationplot := proc (N) local Nr, Nt, x0, rmin, rmax, bif, k, ir, r, xn, i; global pts; Nr := 100; Nt := 200; x0 := .1; rmin := .75; rmax := 3.5; bif := Array(1 .. Nr*N, 1 .. 2); k := 1; for ir to Nr do r := rmin+ir*(rmax-rmin)/Nr; xn := x0; for i to Nt do xn := xn^2-r end do; for i to N do xn := xn^2-r; bif[k, 1] := r; bif[k, 2] := xn; k := k+1 end do end do; pts := bif end proc:




fractaldimension := proc (Noofitterations::integer, Npoints::integer, Nmax::integer) local res, xv, yv, line, stderrors, avgstderrors, i, avgline; avgstderrors := 0; avgline := 0; for i to Noofitterations do bicationplot(Npoints); res := [seq([1.0/n, boxcount(pts, n)], n = 1 .. Nmax, 10)]; xv := [seq(log(res[i][1]), i = 1 .. nops(res))]; yv := [seq(log(res[i][2]), i = 1 .. nops(res))]; line[i] := Fit(m*x+const, xv, yv, x, output = [leastsquaresfunction]); stderrors[i] := Fit(m*x+const, xv, yv, x, output = standarderrors) end do; for i to Noofitterations do avgstderrors := avgstderrors+stderrors[i] end do; avgstderrors := avgstderrors/Noofitterations; for i to Noofitterations do avgline := avgline+line[i] end do; avgline := avgline/Noofitterations; return FD = -(diff(avgline, x)), avgline, avgstderrors, loglogplot(res) end proc:

fractaldimension(10, 100, 100)

Error, (in boxcount) bad index into Array





Explore the values of km digit(n,m) using km list for all m, 0 ≤ m ≤ 8.
Look at the output until you can make a conjecture that concerns the pattern
obtained for each fixed m, 0 ≤ m ≤ 8 using 

km := proc (n::posint, m::nonnegint)

local k,

mySum := 0;

for k to n do

mySum := mySum+k^m

end do;

return mySum

end proc

using a list km list(m,6,20) when m is not a multiple of 4, and km list(m,6,50) when m is a multiple of 4.


any help appreciated..THank you


i have this problem -> f'^2 -ff''=f'''-k1(2f'f'''-ff''''-f''^2)+Ha^2(E1-f') with boundary conditions f(0)=0, f'(0)=1, f'(∞)=0.

since it is a fourth order equation, but only three bcs, it does not produce unique solution. so the solution of the equation may be seek in form of f=f0(eta)+k1f1(eta).

thus the equation will become 




boundary conditions are 



i had been clueless in solving this problem. please somebody help me with this problem.

Dear all,

I have the function


how can I plot y versus x with x in the interval (1000, 1001).

First, it's simple to verify that y(1000)=0; y(1001)=1;  So (1000, 0) and (1001,1)  belong to our graph.

I tried plot( y, x=1000..1001); but there is no curves.

Thank you in advance to help me to plot the graph of this function.

with brest regards,

defining f:=(t,a,b,c)->a*b/c*t^2 how can I give values for a,b and c inside the plot command?

plot(f(t,a,b,c),t=0..10 ????)




Hi Please I need help with making the output of my fslolve appear in a way that I can easily copy to an excel.

I am doing analysis for 3 countries and each time I produce a result I copy manually to excel and use 'text to column' and the 'transpose' excel options to arrange the results in order. I do this for almost 20 time because I want to see how hows in parameter affect the variables. is there a way I can convert this to a 32 by 3 matrix so that I can copy all at the same time instead of copying each variable at a time. here is my solve command

UK_SOL_FIRST:= fsolve(eval({eq||(1..32)}, Params_UK_FIRST), InitValue_UK_FIRST);
ES_SOL_FIRST:= fsolve(eval({eq||(1..32)}, Params_ES_FIRST), InitValue_ES_FIRST);
DK_SOL_FIRST:= fsolve(eval({eq||(1..32)}, Params_DK_FIRST), InitValue_DK_FIRST);

The Results

UK_SOL_FIRST:={A_ss = 14.36104896, C_ss = 1.445842138, I_ss = 0.3136706500,

K_ss = 12.54682600, K_v_ss = 125.4682600,

LT_ss = 0.01061009037, L_ss = 4.014721807, N_ss = 0.9307582996,

P_a_ss = 0.9336893751, P_ss = 0.8625403648,

Surp = 0.9890479879, U_b_ss = 0.1781599919,

U_ss = 0.1046105158, V_ss = 0.05052687912, W_max = 1.476989982,

W_min = 0.4879419937, W_ss = 1.826907218,

W_tilde = 3.478049987, Y_ss = 2.428417935, aa_ss = 21.67403493,

chhi = 0.4523413798, f_c_ss = 0.04880034560,

m_ss = 0.03536881539, p_d_ss = 0.9907986980,

x_T = 0.7023268636, y_d_ss = 10.57030302, y_f_ss = 1.174478111,

y_x_ss = 10.57030300, z_ss = 21.14060602,

Profit_ss = 4.094720376, phi_prod = 0.9753885739,

theta_ss = 0.4830000000}

ES_SOL_FIRST:={A_ss = 10.91702785, C_ss = 2.038687975, I_ss = 0.3058575000,

K_ss = 12.23430000, LT_ss = 0.1309315222, L_ss = 2.857497927,

N_ss = 0.8398656215, P_a_ss = 0.9680877046,

P_ss = 0.8638978804, Surp = 2.541617932, U_b_ss = 0.9095925505,

U_ss = 0.1819708847, V_ss = 0.03119500880, W_max = 3.252738093,

W_min = 0.7111201606, W_ss = 3.605202340,

W_tilde = 3.665280790, Y_ss = 2.367929032, aa_ss = 15.67939783,

betta = 0.9909865708, chhi = 0.2898275349,

f_c_ss = 0.6743530978, m_ss = 0.02183650616,

p_d_ss = 0.9939322922, x_T = 0.005556307841,

y_d_ss = 7.853422751, y_f_ss = 1.195945300,

y_x_ss = 7.978400682, z_ss = 15.83182343,

Profit_ss = 3.084421270, phi_prod = 1.009721394,

theta_ss = 0.1714285714}

DK_SOL_FIRST:={A_ss = 16.18893837, C_ss = 1.359886068, I_ss = 0.2487000000,

K_ss = 9.948000000, LT_ss = 0.02282780783, L_ss = 5.834365727,

N_ss = 0.9399351536, P_a_ss = 0.7054445707,

P_ss = 0.8796237740, Surp = 0.6511024854,

U_b_ss = 0.4572819488, U_ss = 0.08450316042,

V_ss = 0.03491187713, W_max = 1.293898615,

W_min = 0.6427961298, W_ss = 2.363825013,

W_tilde = 2.758200925, Y_ss = 1.755529412, aa_ss = 34.56310241,

betta = 0.9851712031, chhi = 0.4499333284,

f_c_ss = 0.1898151486, m_ss = 0.02443831399,

p_d_ss = 1.032636460, x_T = 0.1506134910, y_d_ss = 11.17773688,

y_f_ss = 0.9144278497, y_x_ss = 13.74561008,

z_ss = 24.92334696, Profit_ss = 4.926248216,

phi_prod = 0.7210969276, theta_ss = 0.4131428571}

Hi all,

I want to rewrite the equation which is attached for you in order to have it in term of Nu. I want to write it such as below:

()*Nu^7+ ()*Nu^6+... +()*Nu+1=0

In the above equation the parameters in the parenthesis are function of k1&k2

Combining Plots...

Yesterday at 11:21 AM nMaple 50

Let say, I have two plots

P1:= plot(........):
P2:= plot(........):

We can display in one plot as



My question is, is there any way to combine these two plots into one and then display.

For example:  

P:= combine(P1, P2);



The reason for asking this question:

I am plotting multiple curves in a loop depending on some conditions but I can't display them in one plot. They are all appearing on different plots.



Hi, I'm new to Maple and I have to produce a recursive procedure with the nomenclature Puis:=proc(X,n::integer) which calculates X^n with:

for n<0   ->   1/(X^(-n))

for n=0  ->   1

for n being an even integer   ->   X^(n/2) * X^(n/2)

for n being an odd integer   ->   X*X^(n-1)

The procedure I produced is:

option remember;
if n<0 then Puis(X,-n);
elif n=0 then 1;
elif rem(n,2,x)=0 then Puis(X,n);
else X*Puis(X,n-1);
end if;
end proc;


i don't have any eror up to this point, but when I try to evaluate, only Puis(4,0) works

Error, (in content) too many levels of recursion
Error, (in content) too many levels of recursion
Error, (in content) too many levels of recursion


I was wondering what was wrong with my procedure, I changed the 1/(X^(-n)) with X^n and X^(n/2)*X^(n/2) for X^n because it is equivalent. I think I should put some sort of initial value to limit the recursion, but with that kind of function i really don't know how. I also tried with the X^(n/2)*X^(n/2) for the even numbers, but it says Puis expects its 2nd argument, n, to be of type integer, but received 1/2.


Hello everyone!

This is a procedure which I have writern. I know I write false, X=x because in maple, x is a table.although I did write x::Vector. Can you help me? Sorry, my English is not very good! :(


I''m looking to complete the following, and then use the 2nd to find what n for which Fn is divisible by f(3),  not sure where to start..any help much appreciated..


"Indicate divisibility of f(n) by s for n <= cr.",
"Write 'D' for divisible, else 'n'; r rows and c cols.";
local i, j, str, char;

for i from 0 to r-1 do
str := "";
for j from 1 to c do
if (f(c*i+j) mod s) = 0 then
str := cat(str,"D")
str := cat(str,"n")
end if
end do;
end do
end proc; # s_div_f


"Indicate divisibility of Fib(n) by m for n <= cr.",
"Write 'D' for divisible, else 'n'; r rows and c cols.";
end proc; # s_div_fib


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