I've just upgraded from Maple 15 to Maple 17, and discover that I cannot any longer write curly right braces in math mode. I use an international (Norwegian) keyboard, where curly right braces should be available by Ctrl+Alt+=, but nothing happens when I try to write this. I can work my way around it by using Copy and Paste, but this is inelegant, particularly when I want to demonstrate Maple for my class of 400 students.

Looking at older posts, I found this question, which concerns inline evaluation with international keyboard in Maple 16. Inline evaluation works fine for me, using Ctrl+Shift+=. So was this fixed at the expense of Ctrl+Alt+= ?

Well-known problem is the problem of placing eight shess queens on an 8×8 chessboard so that no two queens attack each other. In this post, we consider the same problem of placing  m  shess queens on an  n×n  chessboard. The problem has a solution if  n>3  and  m<=n .

Work consists of two procedures. The first procedure  Queens  returns the total number of solutions and saves a complete list of all solutions (global variable  S ). The second procedure  QueensPic  shows the user-defined solutions from the list  S  on the board. Formal argument  t  is the number of solutions in each row of the display. The second procedure should be used in the standard interface, rather than in the classic one, since in the latter it may not work properly.

Queens := proc (m::posint, n::posint)

local It, K, l, L, M, P;

global S, p, q;

It := proc (L)

local P, k, i, j;

M := []; k := nops(L[1]);

for i in L do

for j to n do

if convert([seq(j <> i[s, 2], s = 1 .. k)], `and`) and convert([seq(l[k+1]-i[s, 1] <> i[s, 2]-j, s = 1 .. k)], `and`) and convert([seq(l[k+1]-i[s, 1] <> j-i[s, 2], s = 1 .. k)], `and`) then M := [op(M), [op(i), [l[k+1], j]]]

fi;

od; od;

M;

end proc;

K := combinat:-choose([`$`(1 .. n)], m);

S := [];

for l in K do P := [];

L := [seq([[l[1], i]], i = 1 .. n)];

P := [op(P), op((It@@(m-1))(L))];

S := [op(S), op(P)]

od;

p := args[1]; q := args[2];

nops(S);

end proc:

QueensPic := proc (M, t::posint)

local m, n, HL, VL, T, A, N;

uses plottools, plots;

m := p; n := q; N := nops(args[1]);

HL := seq(line([.5, .5+k], [.5+n, .5+k], color = black, thickness = 2), k = 0 .. n);

VL := seq(line([.5+k, .5], [.5+k, .5+n], color = black, thickness = 2), k = 0 .. n);

T := [seq(textplot([seq([op(M[i, j]), Q], j = 1 .. m)], color = red, font = [TIMES, ROMAN, 24]), i = 1 .. N)];

if m <= n and 3 < n then

A := seq(display(HL, VL, T[k], axes = none, scaling = constrained), k = 1 .. N), seq(display(plot([[0, 0]]), axes = none, scaling = constrained), k = 1 .. t*ceil(N/t)-N);

Matrix(ceil(N/t), t, [A]);

display(%);

fi;

end proc:

Examples of work:

Queens(5, 6);  

S[70], S[140], S[210];

QueensPic([%], 3); 

                                                                            248

[[1, 5], [2, 3], [3, 6], [4, 4], [6, 1]], [[1, 3], [2, 5], [4, 1], [5, 4], [6, 2]], [[2, 1], [3, 4], [4, 2], [5, 5], [6, 3]]

Two solutions of classic problem:

Queens(8, 8); 

S[64..65];

QueensPic(%, 2);

                                                                                      92

[[[1, 5], [2, 8], [3, 4], [4, 1], [5, 7], [6, 2], [7, 6], [8, 3]], [[1, 6], [2, 1], [3, 5], [4, 2], [5, 8], [6, 3], [7, 7], [8, 4]]]

Queens_problem.mw

I would like to find the derivative for f(x)=min(x^2 +1, 2x+3) and plot f(x) and its derivative on the same graph. I know the "diff" command works on functions, but I'm not sure how to use it on this one. Suggestions would be appreciated. Thanks!

Fail to do Volume of Revolution when rotate in y-axis by using student calculus 1 packege.

It is good in any x-axis thorugh.

the erorr looks like this, I follow the direction on Maple website and enter axis = vertical, but it give me something like this.

I type vertical := x = 0 somewhere, I was wondering the Maple think vertical = x = 0, so O change the
vertical := x = 0 to v := x = 0(like first image), but after I run the whole thing it still give me same error.

The weirdest part is I actually run the second one scuccess first time, but second time it failed and I don't know why. I input exactly samething but it failed, weird!!

How do you express sin(4x)^2 in terms of powers of cos(x) in Maple 17?

q[1] = sqrt(x)*alpha-lambda(sqrt(x)*alpha-lambda*q[1]*q[3]-p[2])*(sqrt(x)*alpha-lambda*q[1]*q[2]-p[3])-p[1]

I am looking for q[1] solution. When I solve for q[1], maple gives me following answer:

q[1] = RootOf(-_Z+sqrt(x)*alpha-lambda(sqrt(x)*alpha-lambda*_Z*q[3]-p[2])*sqrt(x)*alpha+lambda(sqrt(x)*alpha-lambda*_Z*q[3]-p[2])*lambda*_Z*q[2]+lambda(sqrt(x)*alpha-lambda*_Z*q[3]-p[2])*p[3]-p[1])

Is it possible to obtain a classical solution for the calculations above. (can not understand the meaning of: RootOf and _Z. I need q[1] in order to solve further in my system of eqautions for  q[2],  q[3]

could you help me please to find a solution for this issue...
I would like to thank you in advance 
Best regards,

D.L.

Hi folks,

from an experiment I gathered some data which I am now trying to display in a nice plot. The data contains x and y values (as well as errors for the y values, that are not part of my problem however). It appears that 'ErrorPlot' (Statistics package) seems to be the tool to use in my case, however I am not able to figure out how to assign the x values to the y values. By default Maple uses positive integers as the x values for any input set. Let's say my data is

x:=[1,5,8,9,10,15]

y:=[4,3,2,8,9,9] (with errors yr:=[0.5,0.5,0.5,0.5,0.5,0.5])

then, now matter how I try, the x values assigned are always 1,2,3,.. . Doing sth. like

> ErrorPlot([x,y]);

displays the sets of x and y each being assigned to integers rather than plotting y over x.
Can anybody help me with this issue?

tl;dr

How do I assign individual x values for my set of data using 'ErrorPlot' (from the Statistics pkg)?

Thank you very much!

Greets,
mulo

Hi 

Fairly new to Maple and having trouble with the result displayed when using exponential functions. 

So I have the following function h(r), in which f1 - f5 are unknown constants that are to be calculated. [I am attempting to set up the equations needed to do so]:

h := r → exp(f1 + f2r + f3r² + f4r³ + f5r⁴ + f6r⁵)

Firstly, I need to evaluate h(r) at the point A. But, on entering the evaluate command, the general expression for h is re-produced:

A := 0.2

evalf(h(A)) 

exp(f6r^5+f5r^4+f4r^3+f3r^2+f1+f2r)

Further, I need to take the natural logarithm of h(A), which produces:

evalf(ln(h(A))

ln(exp(f6r^5+f5r^4+f4r^3+f3r^2+f1+f2r))

How do I get Maple to output the actual result of the substitution of r=A and the logarithm?

i.e. how do I get maple to display:

f1 + 0.2f2 + 0.04f3 + 0.008f4 + 0.0016f5 + 0.00032f6

Apologies if this is a very basic question. 

Cheers

((-1+lambda(lambda*k[2]*alpha[2]+alpha[1](k[2]*lambda^2-2*k[2]-2))^2)*k[1](lambda*k[2]*alpha[2]+alpha[1](k[2]*lambda^2-2*k[2]-2))+(-lambda*lambda(lambda*alpha[1]*k[1]+alpha[2](k[1]*lambda^2-2*k[1]-2))^2+lambda)*k[2](lambda*alpha[1]*k[1]+alpha[2](k[1]*lambda^2-2*k[1]-2))-k[1]*(-alpha[1]+lambda*alpha[2])*lambda(2+5*k[2])^2+lambda^5*alpha[2]*k[1]*k[2]-alpha[1]*k[1]*lambda^4*k[2]-2*lambda^3*alpha[2]*k[2]+2*alpha[1]*k[2]*lambda^2+(4*alpha[2]*(1+k[2])*k[1]+4*alpha[2]+4*k[2]*alpha[2]+2)*lambda-4*alpha[1]*(1+k[2])*k[1]-4*alpha[1]-4*alpha[1]*k[2]-2)*(-(lambda(lambda*k[2]*alpha[2]+alpha[1](k[2]*lambda^2-2*k[2]-2))-1)*(lambda(lambda*k[2]*alpha[2]+alpha[1](k[2]*lambda^2-2*k[2]-2))+1)*(-1+k[1]*lambda^2-k[1])*k[1](lambda*k[2]*alpha[2]+alpha[1](k[2]*lambda^2-2*k[2]-2))+(-lambda*lambda(lambda*alpha[1]*k[1]+alpha[2](k[1]*lambda^2-2*k[1]-2))^2+lambda)*k[2](lambda*alpha[1]*k[1]+alpha[2](k[1]*lambda^2-2*k[1]-2))-k[1]*(-alpha[1]+lambda*alpha[2])*lambda(2+5*k[2])^2+lambda^5*alpha[2]*k[1]*k[2]-alpha[1]*k[1]*lambda^4*k[2]-2*lambda^3*alpha[2]*k[2]+(2*k[1]+2*alpha[1]*k[2])*lambda^2+(4*alpha[2]*(1+k[2])*k[1]+4*alpha[2]+4*k[2]*alpha[2]+2)*lambda-(4*(1+k[1]))*(alpha[1]+alpha[1]*k[2]+1/2))*x

I am looking to simplify this long term...

could you help me please to find a solution for this issue...

I would like to thank you in advance

Best regards,

D.L.

Good afternoon sir.

I request your kind suggestion to the above cited query.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

Hi,

1-Triying to plot a function divided by its maximum value,sometimes it works with some parameters that means, the max.value of the plot is 1.

But when i change the data the max. value in the plot in graeter than 1 which is wrong!! should be 1.

dont know why??

2- Changing different data in the parameters, the programme takes long long time then i stop it?

please help me with these two problems.

restart:
>
------------------------- Defining the nature of the variables used ----------------------
assume(T,real):Digits:=25:n:=1:tau:=Pi:
theta:=0:phi:=0:
lambda:=n;Omega:=1:Gamma:=0.01:
--------------------- Input---------------------------------
1

J1

term1:=(exp((Gamma+I*d)*tau)-1)/(2*(Gamma+I*d)):
Ak1:=d->(exp((Gamma+I*(d+0.5*Omega-2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d+0.5*Omega-2*lambda*k/Gamma))+(exp((Gamma+I*(d-0.5*Omega+2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d-0.5*Omega+2*lambda*k/Gamma)):
Ak2:=d->(exp((Gamma+I*(d-0.5*Omega-2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d-0.5*Omega-2*lambda*k/Gamma))+(exp((Gamma+I*(d+0.5*Omega+2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d+0.5*Omega+2*lambda*k/Gamma)):
term2:=(evalf(-0.25*sum(BesselJ(k,Omega*Gamma/(4*n))*Ak1(d)+BesselJ(k,-(Omega*Gamma)/(4*n))*Ak2(d),k=0..50))):
J1:=(term1+term2):
J1mod:=(Re(J1))^2+(Im(J1))^2:
###### J2#########################
Ak1:=d->(exp((Gamma+I*(d+0.5*Omega-2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d+0.5*Omega-2*lambda*k/Gamma))-(exp((Gamma+I*(d-0.5*Omega+2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d-0.5*Omega+2*lambda*k/Gamma)):
Ak2:=d->(exp((Gamma+I*(d-0.5*Omega-2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d-0.5*Omega-2*lambda*k/Gamma))-(exp((Gamma+I*(d+0.5*Omega+2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d+0.5*Omega+2*lambda*k/Gamma)):

J2:=(evalf(-0.25*sum(BesselJ(k,Omega*Gamma/(4*n))*Ak1(d)+BesselJ(k,-Omega*Gamma/(4*n))*Ak2(d),k=0..100))):
######################

J2mod:=(Re(J2))^2+(Im(J2))^2:
J3 same as J1differ in sign
term1:=(exp((Gamma+I*d)*tau)-1)/(2*(Gamma+I*d)):
Ak1:=d->(exp((Gamma+I*(d+0.5*Omega-2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d+0.5*Omega-2*lambda*k/Gamma))+(exp((Gamma+I*(d-0.5*Omega+2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d-0.5*Omega+2*lambda*k/Gamma)):
Ak2:=d->(exp((Gamma+I*(d-0.5*Omega-2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d-0.5*Omega-2*lambda*k/Gamma))+(exp((Gamma+I*(d+0.5*Omega+2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d+0.5*Omega+2*lambda*k/Gamma)):
term2:=(evalf(0.25*sum(BesselJ(k,Omega*Gamma/(4*n))*Ak1(d)+BesselJ(k,-Omega*Gamma/(4*n))*Ak2(d),k=0..100))):
J3:=term1+term2:
J3mod:=(Re(J3))^2+(Im(J3))^2:
J4 same as J2 but -0.25-->2

J4:=-2*J2:
######################

J4mod:=(Re(J4))^2+(Im(J4))^2:

calculate the spectrum

Spec:=d->(exp(-2*Gamma*tau)*(J1mod*cos(theta/2)^2+J2mod+J3mod*sin(theta/2)^2-0.5*Re(J3*J4*sin(theta)*exp(I*phi))+0.5*Re(J1*J4*sin(theta)*exp(-I*phi)))):

with(plots):

tit:=sprintf("l=%g,W=%g,G=%g",lambda,Omega,Gamma):
Smax1:=max(seq(evalf(Spec(d)),d=-100..100)):
plot(evalf(Spec(d)/Smax1),d=-15..15,axes=boxed,title=tit,color=black,font=[2,3,18],thickness=2,tickmarks=[3,3],titlefont=[SYMBOL,14],font=[1,1,18],linestyle=1);

I have a multivariate polynomial P (written with the order "tdeg")in the (x_i)_i ; the coefficients are functions of the (a_i)_i. I'd want the set of the monomials that appear in the development of P. For instance P=a_1xy^2z^3+a_2x^4yz^2+a_3 is associated to {xy^2z^3,x^4yz^2,1}. Does there exist a command to do that ?

In a second time, I'd want the coefficients of {xy^2z^3,x^4yz^2,1} in the same order. Does there exist a command to do that ?

Thanks in advance.

HI,

Here is my question,

I want to plot dependent variable or say function f(x) on x-axis and independent variable x on x-axis. But dont know how to do it. Please help me for this.

Regards

Sunit

Hello,

I look for solving a DAE system i obtain after having determined the equations of a mechanical system with kinematic closed loops.

For that, thanks to the partitioning method, i could transform my DAE in ODE system.

But now, i don't manage to solve my ODE system.

The first issue was the calculation of big matrix with trigonometric functions. With your help in the post "Resolution of a big product of matrix with trigonometric function" (http://www.mapleprimes.com/questions/200012-Rsolution-Of-A-Big-Product-Of-Matrix) , i could calculate the different matrix involved are calculated.

Now, the resolution with my differential system is very long and never finished.

@Carl Love 3670 gives me good advices. He asked me to try to avoid symbolic calculations of the matrix.

Do not use the output option for dsolve.

Then the following procedure evaluates the Matrix AA:

AA:= proc(S,t)
local Cu_inv:= eval(Cu, S(t))^(-1), tCu_inv:= eval(tCu, S(t))^(1);
     eval(Avv - Avu.Cu_inv.Cv + tCv.tCu_inv.Auu.Cu_inv.Cv - tCv.tCu_inv.Auv, S(t))
end proc:

           To use it, invoke AA(Sol, t) where t is an actual numeric value.

Unfortunately, i don't see how i can use this method for the moment? But, i think that there is a step i don't understand. For me, i have to make the calculation of the big matrix AA and QQ before solving my differentiel system because my differentiel system is composed with AA and QQ.

Here you can find the system i try to solve.

and here you can find the maple file without the steps leading to the setting of the equations

calcul_des_matrices_.mw

Find a loop do define these matrices, even for large values of n. Record the Matrix Mn 

all i,j=1,2,13,..,n for example 

N := `<|>`(`<,>`(1, 2), `<,>`(2, 2))

P := `<|>`(`<,>`(1, 2, 3), `<,>`(2, 2, 3), `<,>`(3, 3, 3))

Q := `<|>`(`<,>`(1, 2, 3, 4), `<,>`(2, 2, 3, 4), `<,>`(3, 3, 3, 4), `<,>`(4, 4, 4, 4))

Please help!!!