Maple 2017 Questions and Posts

These are Posts and Questions associated with the product, Maple 2017

If I add "restart" to a program, then interface(imaginaryunit=j) don't work. Why? 

***********************************
restart;
interface(imaginaryunit = j);
j^2;
************************************
The output is j^2  but the output should be -1. 

 

Hello,
I am new to Maple and have some problems with fonts in Maple's forms. How can I increase the size of the monospaced font? (see the screenshot).

Hi!

I want to plot the approximation of a surface by polynomials. The surface is given by (x,y,f(x,y)) where f(x,y) is given by the following expression

proc (x) options operator, arrow; (sum(i*cos((i+1)*(-2+4*x[1])+i), i = 1 .. 5))*(sum(i*cos((i+1)*(-2+4*x[2])+i), i = 1 .. 5)) end proc

with both variables varying in the interval [0,1]. Then, by using the Bernstein polynomials of two variables (see, for instance, this paper for details  https://www.sciencedirect.com/science/article/pii/0021904589900956), the graph of the resulting (plot3d) surface (x,y,p(x,y))  it is not even like to the original surfaces.

Please, see this PDF of what I have done:  plots.pdf

Some idea or suggestion?

Thanks!

Dear all,

Following the comments I am editing this post:

I have a function F of variables (r1,r2,theta1,theta2,r,theta,a). r1, r2,theta1,theta2 are function of r,  theta and a. I want to take derivative of F with respect to a. r and theta are independent of a . I expressed everything in terms of 'a' as a function of 'a' at first. Then I use diff(F, a). I see there is an error in the final expression G .There is a restriction that theta1 should lie between -Pi to Pi and theta2 between 0 to 2*Pi. I speculate this is the source of error. Work sheet is attached. Reason: value of G: integration in 0 to pi/4 gives some  value but for 0 to pi it evaluates to zero and so is the case with 0 to 2*Pi. As "G "physically represents energy it must be a positive value.
 


restart;

theta1 := unapply(arctan(r*sin(theta)/(r*cos(theta)-a)), a);

proc (a) options operator, arrow; arctan(r*sin(theta)/(r*cos(theta)-a)) end proc

(1)

 

## theta1 -->[-Pi,Pi] and theta2-->[0,2*Pi]

NULL

theta2 := unapply(arctan(r*sin(theta)/(r*cos(theta)+a)), a);

proc (a) options operator, arrow; arctan(r*sin(theta)/(r*cos(theta)+a)) end proc

(2)

``

r1:=unapply(sqrt((r*cos(theta)-a)^2+r^2*(sin(theta))^2),a);r2:=unapply(sqrt((r*cos(theta)+a)^2+r^2*(sin(theta))^2),a);

proc (a) options operator, arrow; ((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2) end proc

 

proc (a) options operator, arrow; ((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2) end proc

(3)

sigma12:=0;sigma22:=sigma;

0

 

sigma

(4)

plot(arctan(tan(x)), x = (1/2)*Pi .. Pi)

 

## I have to use a constraint that

assume(theta1(a) < Pi, theta1(a) > -Pi, theta2(a) > 0, theta2(a) < 2*Pi, a>0,r>0)

u1:=(1+nu)*sigma22*sqrt(r1(a)*r2(a))*(4*(1-2*nu)*cos((theta1(a)+(theta2(a)))/2)-4*r*(1-nu)*cos(theta)/sqrt(r1(a)*r2(a))-2*r^2/(r1(a)*r2(a))*(cos((theta1(a)+(theta2(a)))/2)-cos(2*theta-theta1(a)/2-(theta2(a))/2)))/(4*E)+(1+nu)*sigma12*sqrt(r1(a)*r2(a))*(2*(1-2*nu)*sin((theta1(a)+(theta2(a)))/2)-2*r*(1-nu)*sin(theta)/sqrt(r1(a)*r2(a))+1*r^2/(r1(a)*r2(a))*sin(theta)*cos(theta-theta1(a)/2-(theta2(a))/2))/(E);

 

(1/4)*(1+nu)*sigma*(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)*(4*(1-2*nu)*cos((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-4*r*(1-nu)*cos(theta)/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)-2*r^2*(cos((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-cos(2*theta-(1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a))))/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2)))/E

(5)

NULL

u2:=(1+nu)*sigma*sqrt(r1(a)*r2(a))*(8*(1-nu)*sin((theta1(a)+(theta2(a)))/2)-4*r*(nu)*sin(theta)/sqrt(r1(a)*r2(a))-2*r^2/(r1(a)*r2(a))*(sin((theta1(a)+(theta2(a)))/2)+sin(2*theta-theta1(a)/2-(theta2(a))/2)))/(4*E)+(1+nu)*sigma12*sqrt(r1(a)*r2(a))*((1-2*nu)*cos((theta1(a)+theta2(a))/2)+2*r*(1-nu)*cos(theta)/sqrt(r1(a)*r2(a))-1*r^2/(r1(a)*r2(a))*sin(theta)*sin(theta-theta1(a)/2-theta2(a)/2))/(E);

 

(1/4)*(1+nu)*sigma*(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)*(8*(1-nu)*sin((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-4*r*nu*sin(theta)/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)-2*r^2*(sin((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))+sin(2*theta-(1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a))))/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2)))/E

(6)

 

## get u_r and u_theta as u[1] and u[2]

u[1] := u1*cos(theta)+u2*sin(theta);

(1/4)*(1+nu)*sigma*(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)*(4*(1-2*nu)*cos((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-4*r*(1-nu)*cos(theta)/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)-2*r^2*(cos((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-cos(2*theta-(1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a))))/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2)))*cos(theta)/E+(1/4)*(1+nu)*sigma*(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)*(8*(1-nu)*sin((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-4*r*nu*sin(theta)/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)-2*r^2*(sin((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))+sin(2*theta-(1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a))))/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2)))*sin(theta)/E

(7)

u[2] := -sin(theta)*u1+cos(theta)*u2;

-(1/4)*sin(theta)*(1+nu)*sigma*(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)*(4*(1-2*nu)*cos((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-4*r*(1-nu)*cos(theta)/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)-2*r^2*(cos((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-cos(2*theta-(1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a))))/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2)))/E+(1/4)*cos(theta)*(1+nu)*sigma*(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)*(8*(1-nu)*sin((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-4*r*nu*sin(theta)/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)-2*r^2*(sin((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))+sin(2*theta-(1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a))))/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2)))/E

(8)

Diff_ur := simplify(diff(u[1], a));

(1/2)*sigma*(1+nu)*a*(-(-2*cos(theta)*a*r+a^2+r^2)^(1/2)*(2*cos(theta)*a*r+a^2+r^2)^(1/2)*r^2*cos(theta)*(a-r)*(a+r)*cos(2*theta+(1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))+(-2*cos(theta)*a*r+a^2+r^2)^(1/2)*(2*cos(theta)*a*r+a^2+r^2)^(1/2)*r^2*sin(theta)*(a^2+r^2)*sin(2*theta+(1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))+((a^2*r^2-r^4)*(2*cos(theta)*a*r+a^2+r^2)^(1/2)*(-2*cos(theta)*a*r+a^2+r^2)^(1/2)-4*(-2*cos(theta)*a*r+a^2+r^2)*(2*cos(theta)*a*r+a^2+r^2)*(-4*r^2*(nu-3/4)*cos(theta)^2+(3*nu-5/2)*r^2+a^2*(nu-1/2)))*cos(theta)*cos((1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-sin(theta)*((2*cos(theta)*a*r+a^2+r^2)^(1/2)*r^2*(a^2+r^2)*(-2*cos(theta)*a*r+a^2+r^2)^(1/2)-4*(-2*cos(theta)*a*r+a^2+r^2)*(2*cos(theta)*a*r+a^2+r^2)*(-4*r^2*(nu-3/4)*cos(theta)^2+(a^2+r^2)*(nu-1)))*sin((1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a))))/((-2*cos(theta)*a*r+a^2+r^2)^(3/2)*(2*cos(theta)*a*r+a^2+r^2)^(3/2)*((-2*cos(theta)*a*r+a^2+r^2)^(1/2)*(2*cos(theta)*a*r+a^2+r^2)^(1/2))^(1/2)*E)

(9)

``

 

Diff_ut := simplify(diff(u[2], a));

-(1/2)*sigma*(1+nu)*a*(-(-2*cos(theta)*a*r+a^2+r^2)^(1/2)*(2*cos(theta)*a*r+a^2+r^2)^(1/2)*r^2*sin(theta)*(a^2+r^2)*cos(2*theta+(1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-(-2*cos(theta)*a*r+a^2+r^2)^(1/2)*(2*cos(theta)*a*r+a^2+r^2)^(1/2)*r^2*cos(theta)*(a-r)*(a+r)*sin(2*theta+(1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))+sin(theta)*((2*cos(theta)*a*r+a^2+r^2)^(1/2)*r^2*(a^2+r^2)*(-2*cos(theta)*a*r+a^2+r^2)^(1/2)-4*(-2*cos(theta)*a*r+a^2+r^2)*(-4*r^2*(nu-3/4)*cos(theta)^2+(a^2+r^2)*(nu-1/2))*(2*cos(theta)*a*r+a^2+r^2))*cos((1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))+((a^2*r^2-r^4)*(2*cos(theta)*a*r+a^2+r^2)^(1/2)*(-2*cos(theta)*a*r+a^2+r^2)^(1/2)-4*(-2*cos(theta)*a*r+a^2+r^2)*(-4*r^2*(nu-3/4)*cos(theta)^2+(3*nu-2)*r^2+a^2*(nu-1))*(2*cos(theta)*a*r+a^2+r^2))*sin((1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))*cos(theta))/((-2*cos(theta)*a*r+a^2+r^2)^(3/2)*(2*cos(theta)*a*r+a^2+r^2)^(3/2)*((-2*cos(theta)*a*r+a^2+r^2)^(1/2)*(2*cos(theta)*a*r+a^2+r^2)^(1/2))^(1/2)*E)

(10)

``

# find the limiting case

Att := limit(Diff_ut*r*sin(2*theta), r = infinity);

(2*a*sigma*cos(theta)^3*sin(theta)^2*nu+2*a*sigma*cos(theta)*sin(theta)^4*nu+2*a*sigma*cos(theta)^3*sin(theta)^2+2*a*sigma*cos(theta)*sin(theta)^4-8*a*sigma*cos(theta)*sin(theta)^2*nu^2-6*a*sigma*cos(theta)*sin(theta)^2*nu+2*a*sigma*cos(theta)*sin(theta)^2)/(((cos(theta)^2+sin(theta)^2)/cos(theta)^2)^(1/2)*E)

(11)

Arr := limit(Diff_ur*r*(1-cos(2*theta)), r = infinity);

(-16*a*sigma*cos(theta)^6*nu^2-16*a*sigma*cos(theta)^4*sin(theta)^2*nu^2-6*a*sigma*cos(theta)^6*nu-6*a*sigma*cos(theta)^4*nu*sin(theta)^2+10*a*sigma*cos(theta)^6+10*a*sigma*sin(theta)^2*cos(theta)^4+28*a*sigma*cos(theta)^4*nu^2+20*a*sigma*cos(theta)^2*sin(theta)^2*nu^2+10*a*sigma*cos(theta)^4*nu+4*a*sigma*cos(theta)^2*sin(theta)^2*nu-18*a*sigma*cos(theta)^4-16*a*sigma*sin(theta)^2*cos(theta)^2-12*a*sigma*cos(theta)^2*nu^2-4*a*sigma*sin(theta)^2*nu^2-4*a*sigma*cos(theta)^2*nu+2*a*sigma*sin(theta)^2*nu+8*a*sigma*cos(theta)^2+6*a*sigma*sin(theta)^2)/(cos(theta)*((cos(theta)^2+sin(theta)^2)/cos(theta)^2)^(1/2)*E)

(12)

G := (1/8)*(int(Arr+Att, theta = 0 .. Pi/2))*sigma*4;

-(1/8)*Pi*a*sigma^2*(4*nu^2-nu-5)/E

(13)

simplify(G)

-(1/8)*Pi*a*sigma^2*(4*nu^2-nu-5)/E

(14)

 


Download Derivative_implicit_maplePrime.mw

 

Thanks,

Hello everyone!

I am trying to calculate the Killing vectors for the metric below. For such, I used the packages DifferentialGeometry and Physics. However, I found different results these packages. Could someone explain why?

Thanks in advance!

killing_test1.mw

killing_test2.mw

 

Dear Users,

I have difficulty in finding numerical integration of a function f(r,t) which is a function of position r and time t. Function f(r,t) consists 100 terms (for example : BesselJ(0, 151.5793716314014*r)+BesselJ(0, 151.5793716314014*r)*r^2+......100 terms). For a particular time t=t1, f(r,t1) is calculated and then integrated as follows:

I am using evalf(Int(f(r,t1),r=0..1)

Maple takes a lot of time  to evaluate it as it is integrating it in one shot!  Is there a way to

a) pick the terms individually and integrate it

b) then sum these individual terms up together

c) How reliable is evalf(int(f(r,t1),r=0..1)) is? Is evalf (Int()..)  the best way to evaluate integration?

thanks.

Hey there,

 

I'm trying to build a procedure that can function as an adapted form of Prim's algorithm. The idea is that on a graph with just vertices, the procedure has a starting point, and from there will find out which vertex is the cheapest to connect to (currently expressed purely by the lowest distance). Once this is found, the connected vertex is removed from a list that has vertices that aren't connected yet, and added to a list of vertices that are in the minimal spanning tree.

My problem is that I get an error returned that says "invalid Boolean expression", and I'm not sure how to solve it. Can anybody here point me in the right direction?

The procedure is defined as follows:

Primmetje := proc (aantal, posities, begin)
local knopenover, knopeninmst, huidig, V, kaart, e, a;
knopenover := [seq(i, i = 1 .. aantal)];
knopeninmst := {};
huidig := [0, 0];
if begin <> {} then
  V := [begin];
knopeninmst := knopeninmst union {V}
end if;
remove(V, knopenover);
kaart := Graph(aantal);
SetVertexPositions(kaart, posities);
while nops(knopeninmst) < aantal
do for e in knopeninmst
   do for a in knopenover
     do if huidig = [0, 0] or Distance(posities[e], posities[a]) < Distance(posities[huidig[1]], posities[huidig[2]]) then
   huidig := [e, a];
knopeninmst := knopeninmst union {a};
remove(a, knopenover);
AddEdge(kaart, huidig)
end if
end do
end do
end do
end proc

When I try to execute it with some parameters the return is this:

vp := [2.5, 21], [6, 13.5], [8, 10], [11, 24.5], [14.3, 19.4], [16.8, 26], [22, 21.5], [22, 17], [22.2, 12.5], [26.8, 23], [28, 20.5], [30, 25.5], [32, 21], [29.5, 16];
Primmetje(14, vp, 1);
Error, (in Primmetje) invalid boolean expression: [[6, 13.5]]

I think it has something to do with the double brackes, but I'm not sure how to solve it.
 

How to change the numbers shown in the diagram shapes from y=0.5- to rigth form y=-0.5a.mw

Download a.mw


 

 

 

 

 

 

For an Array A, say, and some positive integer n, say, Maple interpretes A^n as raising each entry separately to the same power n. Without the Physics package loaded, A^n can also be written as A . A . ... . A (n times). But with the Physics package loaded, this equality is broken (at least in Maple 2017): If A is a 2D square Array, A . A all of a sudden is no longer equal to A^2, but rather to convert(A,Matrix)^2, i.e., to the square of the Array considered as a Matrix. The presence of the dot operator seems to make the Physics enviroment convert A to a Matrix. This seems to me to be a bug.

Dear users,

I have an issue with finding real part of a complex variable function. In calculating the real part I see two arguments and the plot is not smooth. How to get real part correct. The worksheet is attached.
 

``

 

 

##Toya complex variable method

``

restart;

stress_c:=-(1+1/nu_c)*k*p2*zeta_c/2;

-(1/2)*(1+1/nu_c)*k*p2*zeta_c

(1.1)

p2:=(c0_c-d_1c/k)*(z-a*(cos(alpha)+2*lambda*sin(alpha)))+(1-k)/k*a*(N_infty-T_infty)*exp(2*I*phi_c+2*lambda*(alpha-Pi))*((a*(cos(alpha)-2*lambda*sin(alpha)))/z-a^2/z^2)

(c0_c-d_1c/k)*(z-a*(cos(alpha)+2*lambda*sin(alpha)))+(1-k)*a*(N_infty-T_infty)*exp((2*I)*phi_c+2*lambda*(alpha-Pi))*(a*(cos(alpha)-2*lambda*sin(alpha))/z-a^2/z^2)/k

(1.2)

``

z := exp(I*theta)

exp(I*theta)

(1.3)

``

k := beta_c/(1+nu_c)

beta_c/(1+nu_c)

(1.4)

nu_c := (kappa2*mu+mu2)/(kappa*mu2+mu)

(kappa2*mu+mu2)/(kappa*mu2+mu)

(1.5)

d_1c := (N_infty+T_infty)*(1/2)

(1/2)*N_infty+(1/2)*T_infty

(1.6)

lambda := -evalf(ln(nu_c)/(2*Pi))

-.1591549430*ln((kappa2*mu+mu2)/(kappa*mu2+mu))

(1.7)

``

beta_c := mu*(1+kappa2)/(kappa*mu2+mu)

mu*(1+kappa2)/(kappa*mu2+mu)

(1.8)

zeta_c := ((z-a*exp(I*alpha))/(z-a*exp(-I*alpha)))^(I*lambda)/((z-a*exp(I*alpha))^.5*(z-a*exp(-I*alpha))^.5)

((exp(I*theta)-a*exp(I*alpha))/(exp(I*theta)-a*exp(-I*alpha)))^(-(.1591549430*I)*ln((kappa2*mu+mu2)/(kappa*mu2+mu)))/((exp(I*theta)-a*exp(I*alpha))^.5*(exp(I*theta)-a*exp(-I*alpha))^.5)

(1.9)

``

c0_c := G_c+I*H_c

G_c+I*H_c

(1.10)

G_c:=(0.5*(T_infty+N_infty)*(1-(cos(alpha)+2*lambda*sin(alpha))*exp(2*lambda*(evalf(Pi)-alpha)))-0.5*(1-k)*(1+4*lambda^2)*(N_infty-T_infty)*(sin(alpha))^2*cos(2*phi_c))/(2-k-k*(cos(alpha)+2*lambda*sin(alpha))*exp(evalf(2*lambda*(Pi-alpha))));

(.5*(N_infty+T_infty)*(1-(cos(alpha)-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*sin(alpha))*exp(-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*(3.141592654-alpha)))-.5*(1-mu*(1+kappa2)/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))))*(.1013211835*ln((kappa2*mu+mu2)/(kappa*mu2+mu))^2+1)*(N_infty-T_infty)*sin(alpha)^2*cos(2*phi_c))/(2-mu*(1+kappa2)/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu)))-mu*(1+kappa2)*(cos(alpha)-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*sin(alpha))*exp(-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*(3.141592654-1.*alpha))/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))))

(1.11)

H_c:=0.5*(1-k)*(1+4*lambda^2)*(-T_infty+N_infty)*(sin(alpha))^2*sin(2*phi_c)/(k*(1+(cos(alpha)+2*lambda*sin(alpha))*exp(2*lambda*(evalf(Pi)-alpha))));

.5*(1-mu*(1+kappa2)/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))))*(.1013211835*ln((kappa2*mu+mu2)/(kappa*mu2+mu))^2+1)*(N_infty-T_infty)*sin(alpha)^2*sin(2*phi_c)*(kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))/(mu*(1+kappa2)*(1+(cos(alpha)-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*sin(alpha))*exp(-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*(3.141592654-alpha))))

(1.12)

##Input

alpha:=evalf(Pi/6)

.5235987758

(1.13)

phi_c:=alpha;

.5235987758

(1.14)

N_infty:=0;

0

(1.15)

T_infty:=1;

1

(1.16)

a:=1;nu2:=22/100;kappa2:=3-4*nu2;nu:=35/100;kappa:=3-4*nu;mu:=239/100;mu2:=442/10;

1

 

11/50

 

53/25

 

7/20

 

8/5

 

239/100

 

221/5

(1.17)

``

stress_c

-(9321/123167)*(((.5586916801-.5*(.8660254037-.1591549431*ln(123167/182775))*exp(-.8333333329*ln(123167/182775))+0.5946710490e-2*ln(123167/182775)^2)/(22817/11767-(717/11767)*(.8660254037-.1591549431*ln(123167/182775))*exp(-.8333333329*ln(123167/182775)))-(1.668336947*I)*(.1013211835*ln(123167/182775)^2+1)/(1+(.8660254037-.1591549431*ln(123167/182775))*exp(-.8333333329*ln(123167/182775)))-11767/1434)*(exp(I*theta)-.8660254037+.1591549431*ln(123167/182775))-(11050/717)*exp(1.047197552*I+.8333333328*ln(123167/182775))*((.8660254037+.1591549431*ln(123167/182775))/exp(I*theta)-1/(exp(I*theta))^2))*((exp(I*theta)+(-.8660254037-.5000000002*I))/(exp(I*theta)+(-.8660254037+.5000000002*I)))^(-(.1591549430*I)*ln(123167/182775))/((exp(I*theta)+(-.8660254037-.5000000002*I))^.5*(exp(I*theta)+(-.8660254037+.5000000002*I))^.5)

(1.18)

assume((1/6)*Pi < theta, theta < 2*Pi-(1/6)*Pi)

simplify(evalc(Re(stress_c)))

-0.8815855810e-10*((((1.000000000*cos(theta)^7+(0.5294827753e-2+.5671599115*sin(theta))*cos(theta)^6-4.533186669*cos(theta)^5+(-11.80630620+4.886343937*sin(theta))*cos(theta)^4+3.402782742*cos(theta)^3+(9213180122.+0.9866808100e-1*sin(theta))*cos(theta)^2+(-0.1055437876e11+0.1595769608e11*sin(theta))*cos(theta)-5794103792.*sin(theta)+1760041721.)*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(-.5600908440*cos(theta)^7+(0.6523625301e-2+1.134319823*sin(theta))*cos(theta)^6+4.644568297*cos(theta)^5+(-0.2905669688e-1+10.20004207*sin(theta))*cos(theta)^4-0.1774243515e-1*cos(theta)^3+(0.1595769609e11-9.082306669*sin(theta))*cos(theta)^2+(-7023191163.-9213180109.*sin(theta))*cos(theta)-3154310102.*sin(theta)-7408031461.)*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037)))*cos(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))+(-.5600908440*cos(theta)^7+(1.134319823*sin(theta)+0.4756356038e-2)*cos(theta)^6+4.644568284*cos(theta)^5+(11.37920491*sin(theta)-0.2640575516e-1)*cos(theta)^4-0.1774243890e-1*cos(theta)^3+(-11.39571957*sin(theta)+0.1595769607e11)*cos(theta)^2+(-9213180108.*sin(theta)-7023191160.)*cos(theta)-7408031458.-3154310086.*sin(theta))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(-1.000000000*cos(theta)^7+(-.5671599115*sin(theta)-0.5294826902e-2)*cos(theta)^6+4.531921682*cos(theta)^5+(-4.886343941*sin(theta)+11.76153292)*cos(theta)^4-3.358186195*cos(theta)^3+(-0.9866807692e-1*sin(theta)-9213180122.)*cos(theta)^2+(-0.1595769609e11*sin(theta)+0.1055437877e11)*cos(theta)-1760041726.+5794103798.*sin(theta))*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037)))*cos(0.314104002e-1*ln(1492820323.-1292820323.*cos(theta)+746410161.*sin(theta))-0.314104002e-1*ln(-1292820322.*cos(theta)-746410161.4*sin(theta)+1492820322.))+(((-.5600908440*cos(theta)^7+(1.134319823*sin(theta)+0.4756356038e-2)*cos(theta)^6+4.626658979*cos(theta)^5+(-0.2905667760e-1+10.24488508*sin(theta))*cos(theta)^4-.1341529536*cos(theta)^3+(0.1595769608e11-9.127079936*sin(theta))*cos(theta)^2+(-7023191161.-9213180109.*sin(theta))*cos(theta)-3154310089.*sin(theta)-7408031435.)*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(-1.134319823*cos(theta)^7-.5671599115*sin(theta)*cos(theta)^6+4.531921682*cos(theta)^5+(11.80860365-4.107288978*sin(theta))*cos(theta)^4-3.402959469*cos(theta)^3+(-9213180123.+0.1774243833e-1*sin(theta))*cos(theta)^2+(0.1055437876e11-0.1595769608e11*sin(theta))*cos(theta)+5794103807.*sin(theta)-1760041748.)*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037)))*cos(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))+(-1.000000000*cos(theta)^7-.5671599115*sin(theta)*cos(theta)^6+4.537223485*cos(theta)^5+(-4.886343950*sin(theta)+11.80860366)*cos(theta)^4-3.358186195*cos(theta)^3+(-0.9866807250e-1*sin(theta)-9213180123.)*cos(theta)^2+(0.1055437876e11-0.1595769608e11*sin(theta))*cos(theta)-1760041739.+5794103821.*sin(theta))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(.5600908440*cos(theta)^7+(-1.134319823*sin(theta)-0.4756356038e-2)*cos(theta)^6-4.644554360*cos(theta)^5+(-10.21771474*sin(theta)+0.2905668928e-1)*cos(theta)^4+0.1774243685e-1*cos(theta)^3+(9.082306650*sin(theta)-0.1595769608e11)*cos(theta)^2+(9213180109.*sin(theta)+7023191165.)*cos(theta)+7408031453.+3154310085.*sin(theta))*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037)))*sin(0.314104002e-1*ln(1492820323.-1292820323.*cos(theta)+746410161.*sin(theta))-0.314104002e-1*ln(-1292820322.*cos(theta)-746410161.4*sin(theta)+1492820322.)))/((-sin(theta)+2.-1.732050807*cos(theta))^(1/4)*(sin(theta)+2.-1.732050807*cos(theta))^(1/4))

(1.19)

plot(%, theta = (1/6)*Pi .. 2*Pi-(1/6)*Pi)

 


 

Download Toya_complexPlot2.mw

I am trying to put a number of related 2-d plots into a 3-d frame so I can see them stacked up in the third dimension (which follows a parameter) and rotate things around.

The way I once did this successfully was to create the 2-d plots and then use plottools:-transform to move the individual plots in the third dimension, like so:

plt:=plot(something);

tr:=plottools:-transform((x,y) -> [x,2,y]); # the "2" gets changed for the other plots (not shown here).

plots:-display(tr(plt));

The only effect I can get is that the GUI gets confused and I have to close and reload the sheet to get it back again. I have a (complicated) sheet where this actually works, but I am not able to make it work even in the small example I am posting below.

Any hint of where I am going off trail is appreciated. Incidentally, this problem is what led to the corrupted sheet I had maybe a week ago.

Thanks,

Mac Dude.

display3d.mw

 

I got bit by Maple when I tried to combine a number of 2-d plots into one 3-d plot, using plottools:-transform to space the plots out in the third dimentsion. I have done such things before. This time, the first time I executed the final plot statement the GUI got clobbered and somehow also the whole worksheet (I may have saved it). Now, when I load it nothing shows up and worse, I cannot enter anything in the worksheet, it is completely screwy. I looked at the XML code in Emacs and it validates and I cannot find anything obviously wrong with it, i.e. no dangling tags or similar.

I used Maple 2017. In Maple 2015 the same worksheet overprints itself & makes a big mess on the screen. It is similarly unuseable.

Can one of the experts have a look at this? Although rare I have experienced similar issues on occasion before & would like to know how to get this into a sane state.

TIA,

Mac Dude

triangle_analysis.mw

I am having problems when trying to sue de colorscheme opiton. I always get an error message. The example below is from the Maple homepage:

plot3d(sin(x)*cos(y), x = 0 .. 4*Pi, y = 0 .. 4*Pi, view = [default, default, -3 .. 3], colorscheme = ["xgradient", ["Green", "Purple", "Blue"]]);
Error, (in plot3d) unexpected option: colorscheme = ["xgradient", ["Green", "Purple", "Blue"]]


Any hint?

I'm using the differential operator D to differentiate variables and look at the structure of the equations, i.e. turn things like

D[1]u-vt+v^2=0 into

D[1,2](u)-D[2](v)*t+v*D[1](t)+2*v*D[2](v)=0

However, it is assumed that this is a commutative operator, i.e. D[1,2]=D[2,1]. Can I use an option to have it not commute, or should I look into using the DETools package?

Thanks,

Mike

Hello,

 

Assume we have the following "intervals" (I am not sure what is its formal name in Maple)

 

C :=[0,1/11],[1/11,1/9],[1/9, 1/7],[1/3,1/2],[1/2,1]

 

How can we get the "union" of these intervals? That is to say, obtain  [0,1/7],[1/3,1] 

 

Many thanks in advance for your comments and suggestions.

 

 

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