MaplePrimes Questions

Hello everyone,
I hope this message finds you well. I am trying to plot a function f(x, y) and overlay its contour on a quarter ellipse using Maple 2015. However, I’ve encountered some difficulties and have not been successful so far. I would greatly appreciate any assistance in resolving this issue. Thank you!

Plotting in 2D

restart:with(plots):  aa := 4: bb := 2:  
f := -((x^(2))/(aa^(2))+(y^(2))/(bb^(2))-1)*((aa^(2)*bb^(2))/(aa^(2)+bb^(2))):  
plot3d(f,x = 0 .. aa/(2),y = 0 .. bb/(2),region = (x, y) -> ((2 x)/(aa))^(2) + ((2 y)/(bb))^(2)<= 1,axes = boxed,style = patchcontour, grid = [50, 50],orientation = [-120, 45],shading = zhue,title = "f(x,y) over quarter ellipse domain");

Contour plotting
xrange := 0 .. aa/(2): yrange := 0 .. bb/(2):  
nx := 100:   ny := 100:  
dx := (rhs(xrange) - lhs(xrange))/(nx-1):dy := (rhs(yrange) - lhs(yrange))/(ny-1):  
Z := Matrix(nx, ny, (i, j) -> local x, y, inside;x := lhs(xrange) + (i-1)*dx;y := lhs(yrange) + (j-1)*dy;inside := (((2 x)/aa)^2 + ((2 y)/bb)^2 <= 1);if inside then f(x, y) else NULL end if):  
contourplot(Z, xrange, yrange,contours = 15, filled = true, coloring = [blue, green, yellow, red], axes = boxed, title = "Contour plot over quarter ellipse", grid = [nx, ny]);  

Hi,
I would like to solve a system of 2 PDE with this code, but it does not work.
lin_eqs := {diff(h(x, t), t) + H*diff(u(x, t), x) = 0, diff(u(x, t), t) + g*diff(h(x, t), x) = 0};
sol := pdsolve(lin_eqs);
print('sol', sol);

Can you help me?Thanks
Best regards

Any idea why Maple simplifies 1+sin(x)^2 to 2-cos(x)^2?  Leaf count is larger also.

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

e1:=1+sin(x)^2;

1+sin(x)^2

e2:=simplify(e1)

-cos(x)^2+2

MmaTranslator:-Mma:-LeafCount(e1)

6

MmaTranslator:-Mma:-LeafCount(e2)

8

 

 

Download strange_simplification_august_20_2025.mw

Attached worksheet

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 29 and is the same as the version installed in this computer, created June 23, 2025, 10:25 hours Eastern Time.`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1877 and is the same as the version installed in this computer, created 2025, July 11, 19:24 hours Pacific Time.`

restart;

integrand:=1/2/x^(9/2)*2^(1/2)*Pi^(1/2)/(1/x)^(1/2)*cos(1/x);

(1/2)*2^(1/2)*Pi^(1/2)*cos(1/x)/(x^(9/2)*(1/x)^(1/2))

int(integrand,x)

Error, (in tools/eval_foo/do) too many levels of recursion

 

 

Download internal_error_on_int_august_20_2025_maple_2025_1.mw

Greetings

I trust that everyone is well here. I have an inquiry regarding the partitioning of a matrix BA, defined on both regular and irregular domains, into three matrices: Ad, Ab, and Ae, such that NewBA = Ad + Ab + Ae. Here, Ad comprises the entries of BA that reside within the domain, Ab includes the elements of BA located on the boundary, and Ae is derived as BA - Ad - Ab for any values of Mx and My. The specifics of matrix BA are contained in the attached document where NewBA constructed manually for different values of Mx and My for better understanding.
Splitting_a_matrix.mw
The attached file contains the matrix BA constructed in a square format. How may the BA matrix be adapted to create an irregular shape, such as a quarter circle?

The red dots indicate the mesh within the domain Ad, while the meshing along the blue line should occur in Ab.

I await your kind reply. Kindly ensure your well-being

I’m getting an error while solving the equations derived from the KKT conditions.
What syntax modifications should I make?
The decision variables are p1 and pr, with two constraints.

sheet: Q1_solve_equation.mw
 

I can't seem to find the "Stop Execution" symbol with the new Maple 2025.1 GUI.  Does anyone know where it went?

I was wondering why there is no longer a separate section for Maple Flow under the tab "Products". As syntax is not always the same between Maple and Maple Flow it would be nice to ask specific questions. Also why is there no suggestion tag for maple flow?

Thank you for any information

I installed a free trial of Maple 2025, but I can't seem to get the (simple) sample test.java script to run using OpenMaple. It compiles fine, but when I try to run it I get a Segmentation Fault error. I've ensured that the environmental variables, as described in the installation documentation, are given properly. The documentation/example in the installation refers to an old version of Maple, so I wondered if perhaps the free trial version does not have all of the updated components? I was hoping to test my project compatibility with OpenMaple before purchasing Maple.

My OS is Ubuntu 24.04, and I'm using Java 21. It would be nice to get everything running in IntelliJ eventually, but for now even trying to run in the terminal is problematic.

In thus manuscript i got some reviewer comment which is asked to simplify this expresion and there is a lot of them maybe if i do by hand i  made a mistake becuase a lot of variable so how i can fix this issue and make thus square root are very simple as they demand

restart

B[2] := 0

0

(1)

K := sqrt(-(1/2)*sqrt(2)*sqrt(lambda*a[5]/a[4])+sqrt(-a[5]/(2*a[4]))*(B[1]*sqrt(-lambda)*sinh(xi*sqrt(-lambda))+B[2]*sqrt(-lambda)*cosh(xi*sqrt(-lambda)))/(B[1]*cosh(xi*sqrt(-lambda))+B[2]*sinh(xi*sqrt(-lambda))+mu/lambda)+sqrt(-(lambda^2*B[1]^2*a[5]-lambda^2*B[2]^2*a[5]-mu^2*a[5])/(2*lambda*a[4]))/(B[1]*cosh(xi*sqrt(-lambda))+B[2]*sinh(xi*sqrt(-lambda))+mu/lambda))*exp(I*(k*(xi+v*tau^alpha/alpha)+w*tau^alpha/alpha+gamma))

(1/2)*(-2*2^(1/2)*(lambda*a[5]/a[4])^(1/2)+2*(-2*a[5]/a[4])^(1/2)*B[1]*(-lambda)^(1/2)*sinh(xi*(-lambda)^(1/2))/(B[1]*cosh(xi*(-lambda)^(1/2))+mu/lambda)+2*(-2*(lambda^2*B[1]^2*a[5]-mu^2*a[5])/(lambda*a[4]))^(1/2)/(B[1]*cosh(xi*(-lambda)^(1/2))+mu/lambda))^(1/2)*exp(I*(k*(xi+v*tau^alpha/alpha)+w*tau^alpha/alpha+gamma))

(2)

simplify(K)

(1/2)*exp(I*((k*v+w)*tau^alpha+alpha*(k*xi+gamma))/alpha)*2^(3/4)*((lambda*(a[5]*(-lambda^2*B[1]^2+mu^2)/(lambda*a[4]))^(1/2)+(-B[1]*cosh(xi*(-lambda)^(1/2))*lambda-mu)*(lambda*a[5]/a[4])^(1/2)+sinh(xi*(-lambda)^(1/2))*lambda*(-a[5]/a[4])^(1/2)*(-lambda)^(1/2)*B[1])/(B[1]*cosh(xi*(-lambda)^(1/2))*lambda+mu))^(1/2)

(3)

subsindets(K, `&*`(rational, anything^(1/2)), proc (u) options operator, arrow; (u^2)^(1/2) end proc)

(1/2)*(-2*2^(1/2)*(lambda*a[5]/a[4])^(1/2)+2*(-2*a[5]/a[4])^(1/2)*B[1]*(-lambda)^(1/2)*sinh(xi*(-lambda)^(1/2))/(B[1]*cosh(xi*(-lambda)^(1/2))+mu/lambda)+2*(-2*(lambda^2*B[1]^2*a[5]-mu^2*a[5])/(lambda*a[4]))^(1/2)/(B[1]*cosh(xi*(-lambda)^(1/2))+mu/lambda))^(1/2)*exp(I*(k*(xi+v*tau^alpha/alpha)+w*tau^alpha/alpha+gamma))

(4)

latex(%)

\frac{\sqrt{-2 \sqrt{2}\, \sqrt{\frac{\lambda  a_{5}}{a_{4}}}+\frac{2 \sqrt{-\frac{2 a_{5}}{a_{4}}}\, B_{1} \sqrt{-\lambda}\, \sinh \left(\xi  \sqrt{-\lambda}\right)}{B_{1} \cosh \left(\xi  \sqrt{-\lambda}\right)+\frac{\mu}{\lambda}}+\frac{2 \sqrt{-\frac{2 \left(\lambda^{2} B_{1}^{2} a_{5}-\mu^{2} a_{5}\right)}{\lambda  a_{4}}}}{B_{1} \cosh \left(\xi  \sqrt{-\lambda}\right)+\frac{\mu}{\lambda}}}\, {\mathrm e}^{\mathrm{I} \left(k \left(\xi +\frac{v \,\tau^{\alpha}}{\alpha}\right)+\frac{w \,\tau^{\alpha}}{\alpha}+\gamma \right)}}{2}

 

KK := sqrt(-(1/2)*sqrt(2)*sqrt(lambda*a[5]/a[4])+sqrt(-a[5]/(2*a[4]))*(B[1]*sqrt(-lambda)*sinh(xi*sqrt(-lambda))+B[2]*sqrt(-lambda)*cosh(xi*sqrt(-lambda)))/(B[1]*cosh(xi*sqrt(-lambda))+B[2]*sinh(xi*sqrt(-lambda))+mu/lambda)+sqrt(-(lambda^2*B[1]^2*a[5]-lambda^2*B[2]^2*a[5]-mu^2*a[5])/(2*lambda*a[4]))/(B[1]*cosh(xi*sqrt(-lambda))+B[2]*sinh(xi*sqrt(-lambda))+mu/lambda))*exp(I*(k*(xi+v*tau^alpha/alpha)+w*tau^alpha/alpha+gamma))

(1/2)*(-2*2^(1/2)*(lambda*a[5]/a[4])^(1/2)+2*(-2*a[5]/a[4])^(1/2)*B[1]*(-lambda)^(1/2)*sinh(xi*(-lambda)^(1/2))/(B[1]*cosh(xi*(-lambda)^(1/2))+mu/lambda)+2*(-2*(lambda^2*B[1]^2*a[5]-mu^2*a[5])/(lambda*a[4]))^(1/2)/(B[1]*cosh(xi*(-lambda)^(1/2))+mu/lambda))^(1/2)*exp((k*(xi+v*tau^alpha/alpha)+w*tau^alpha/alpha+gamma)*I)

(5)

latex(KK)

\frac{\sqrt{-2 \sqrt{2}\, \sqrt{\frac{\lambda  a_{5}}{a_{4}}}+\frac{2 \sqrt{-\frac{2 a_{5}}{a_{4}}}\, B_{1} \sqrt{-\lambda}\, \sinh \left(\xi  \sqrt{-\lambda}\right)}{B_{1} \cosh \left(\xi  \sqrt{-\lambda}\right)+\frac{\mu}{\lambda}}+\frac{2 \sqrt{-\frac{2 \left(\lambda^{2} B_{1}^{2} a_{5}-\mu^{2} a_{5}\right)}{\lambda  a_{4}}}}{B_{1} \cosh \left(\xi  \sqrt{-\lambda}\right)+\frac{\mu}{\lambda}}}\, {\mathrm e}^{\mathrm{I} \left(k \left(\xi +\frac{v \,\tau^{\alpha}}{\alpha}\right)+\frac{w \,\tau^{\alpha}}{\alpha}+\gamma \right)}}{2}

 

NULL

Download simplify.mw

I am trying to factor out I = sqrt(-1) from square roots in my Maple expression by using a substitution f2. However, after applying these substitutions to my final expression, there is no visible change. In addition, the term sqrt(2)/2 + sqrt(2)*I/2 also appear. How can I=sqrt(-1) can be properly factored out from the square roots?

restart

with(Student[Precalculus])

interface(showassumed = 0)

assume(x::real); assume(t::real); assume(lambda1::complex); assume(lambda2::complex); assume(a::real); assume(A__c::real); assume(B1::real); assume(B2::real); assume(delta1::real); assume(delta2::real); assume(`&omega;__0`::real); assume(g::real); assume(l__0::real)

expr := (0*A__c)*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*`&omega;__0`*t)+(2*I)*exp(-I*(A__c^2*g*l__0^2-1/2)*`&omega;__0`*t)*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*exp(-2*sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(l__0^2*(I*delta1-delta2)*t*`&omega;__0`+(1/2)*x))-sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*exp(sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(x+(2*I)*`&omega;__0`*l__0^2*(delta1+I*delta2)*t)))*(sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))*exp((2*(l__0^2*(I*delta1+delta2)*t*`&omega;__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))-sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*exp(-(2*(l__0^2*(I*delta1+delta2)*t*`&omega;__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2)))*delta2/(exp(I*(A__c^2*g*l__0^2-1/2)*`&omega;__0`*t)*(((-sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))-sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2)))*exp((2*(l__0^2*(I*delta1+delta2)*t*`&omega;__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))+exp(-(2*(l__0^2*(I*delta1+delta2)*t*`&omega;__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))))*exp(-2*sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(l__0^2*(I*delta1-delta2)*t*`&omega;__0`+(1/2)*x))+exp(sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(x+(2*I)*`&omega;__0`*l__0^2*(delta1+I*delta2)*t))*((sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2)))*exp((2*(l__0^2*(I*delta1+delta2)*t*`&omega;__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))-exp(-(2*(l__0^2*(I*delta1+delta2)*t*`&omega;__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2)))))*(-delta1+I*delta2)*(delta1+I*delta2))

(2*I)*exp(-I*(A__c^2*g*l__0^2-1/2)*omega__0*t)*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*exp(-2*(-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(l__0^2*(I*delta1-delta2)*t*omega__0+(1/2)*x))-(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*exp((-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(x+(2*I)*omega__0*l__0^2*(delta1+I*delta2)*t)))*((-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))-(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2)))*delta2/(exp(I*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(((-(delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)-(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2))*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))+exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)))*exp(-2*(-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(l__0^2*(I*delta1-delta2)*t*omega__0+(1/2)*x))+exp((-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(x+(2*I)*omega__0*l__0^2*(delta1+I*delta2)*t))*(((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2))*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))-exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2))))*(I*delta2-delta1)*(delta1+I*delta2))

(1)

`assuming`([simplify(combine(simplify(convert(combine(eval(expr, delta1 = 0)), trigh))))], [delta2 > g*A__c and g*A__c > 0])

(cos((2*A__c^2*g*l__0^2-1)*omega__0*t)-I*sin((2*A__c^2*g*l__0^2-1)*omega__0*t))*(-I*cosh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*(-A__c^2*g-delta2^2)^(1/2))*delta2+(I*delta2-(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(I*delta2+(-A__c^2*g-delta2^2)^(1/2))^(1/2)+sinh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*(-A__c^2*g-delta2^2)^(1/2))*(-A__c^2*g-delta2^2)^(1/2))/(delta2*(I*(I*delta2-(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(I*delta2+(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*(-A__c^2*g-delta2^2)^(1/2))+delta2))

(2)

f1 := simplify(convert(numer(%),exp))/factor(denom(%))

I*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(-I*cosh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*(-A__c^2*g-delta2^2)^(1/2))*delta2+(I*delta2-(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(I*delta2+(-A__c^2*g-delta2^2)^(1/2))^(1/2)+sinh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*(-A__c^2*g-delta2^2)^(1/2))*(-A__c^2*g-delta2^2)^(1/2))/((-(I*delta2-(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(I*delta2+(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh(2*(2*delta2*l__0^2*t*omega__0-x)*(-A__c^2*g-delta2^2)^(1/2))+I*delta2)*delta2)

(3)

sqrtterms := indets(%, sqrt)

{(I*delta2-(-A__c^2*g-delta2^2)^(1/2))^(1/2), (I*delta2+(-A__c^2*g-delta2^2)^(1/2))^(1/2), (-A__c^2*g-delta2^2)^(1/2)}

(4)

f2 := subs({sqrtterms[1] = sqrt(I)*sqrt(delta2-sqrt(-A__c^2*g-delta2^2)/(I)), sqrtterms[2] = sqrt(I)*sqrt(delta2+sqrt(-A__c^2*g-delta2^2)/(I)), sqrtterms[3] = sqrt(I)*sqrt(A__c^2*g+delta2^2)})

{(I*delta2-(-A__c^2*g-delta2^2)^(1/2))^(1/2) = ((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2), (I*delta2+(-A__c^2*g-delta2^2)^(1/2))^(1/2) = ((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2), (-A__c^2*g-delta2^2)^(1/2) = ((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*(A__c^2*g+delta2^2)^(1/2)}

(5)

f3 := subs(f2, f1)

I*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(-I*cosh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*(A__c^2*g+delta2^2)^(1/2))*delta2+((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))^2*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)+sinh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*(A__c^2*g+delta2^2)^(1/2))*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*(A__c^2*g+delta2^2)^(1/2))/((-((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))^2*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh(2*(2*delta2*l__0^2*t*omega__0-x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*(A__c^2*g+delta2^2)^(1/2))+I*delta2)*delta2)

(6)

f4 := subs({sqrt(A__c^2*g+delta2^2) = Z}, f3)

I*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(-I*cosh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)*delta2+((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))^2*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)+sinh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)/((-((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))^2*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh(2*(2*delta2*l__0^2*t*omega__0-x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)+I*delta2)*delta2)

(7)

f4f := A__c*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*`&omega;__0`*t)+f4

A__c*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)+I*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(-I*cosh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)*delta2+((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))^2*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)+sinh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)/((-((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))^2*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh(2*(2*delta2*l__0^2*t*omega__0-x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)+I*delta2)*delta2)

(8)

f4fnl := subs({I = -I, x = -x}, f4f)

A__c*exp((2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)-I*exp((2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(I*cosh(4*(l__0^2*delta2*t*omega__0+(1/2)*x)*((1/2)*2^(1/2)-((1/2)*I)*2^(1/2))*Z)*delta2+((1/2)*2^(1/2)-((1/2)*I)*2^(1/2))^2*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)+sinh(4*(l__0^2*delta2*t*omega__0+(1/2)*x)*((1/2)*2^(1/2)-((1/2)*I)*2^(1/2))*Z)*((1/2)*2^(1/2)-((1/2)*I)*2^(1/2))*Z)/((-((1/2)*2^(1/2)-((1/2)*I)*2^(1/2))^2*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh(2*(2*delta2*l__0^2*t*omega__0+x)*((1/2)*2^(1/2)-((1/2)*I)*2^(1/2))*Z)-I*delta2)*delta2)

(9)

Mdensity := simplify(f4f*f4fnl)

(1/4)*(2*(1-I*A__c*cosh((1-I)*(2*delta2*l__0^2*t*omega__0+x)*2^(1/2)*Z)*delta2)*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)-2*cosh((1-I)*(2*delta2*l__0^2*t*omega__0+x)*2^(1/2)*Z)*delta2+(1+I)*2^(1/2)*Z*sinh((1-I)*(2*delta2*l__0^2*t*omega__0+x)*2^(1/2)*Z)+(2*I)*A__c*delta2^2)*(2*(I*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*A__c-1)*delta2*cosh((1+I)*(2*delta2*l__0^2*t*omega__0-x)*2^(1/2)*Z)+(1-I)*2^(1/2)*Z*sinh((1+I)*(2*delta2*l__0^2*t*omega__0-x)*2^(1/2)*Z)-(2*I)*A__c*delta2^2+2*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2))/(delta2^2*((delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh((1+I)*(2*delta2*l__0^2*t*omega__0-x)*2^(1/2)*Z)-delta2)*((delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh((1-I)*(2*delta2*l__0^2*t*omega__0+x)*2^(1/2)*Z)-delta2))

(10)

NULL

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Using Eigenvalues and Eigenvectors commands with symmetric matrices (so real eigenvalues) I get something like

Can I avoid "+0.I"?
Thanks

...flies around in the spatial Cartesian coordinate system and impacts the coordinate planes xy, xz, and yz with exactly one impact. This creates circular impressions on the coordinate planes in this order, with the radii r1, r2, and r3, which are assumed to be known. From these, the sphere's radius r and the coordinates of its center can be determined?

Is there a short-cut for jumping to a specific output label in a Maple worksheet?

I have a Maple worksheet with over 200 labels:  (1), (2), ....., (236) etc?

"Find" does not seem to work.

Thanks

Frank Garvan

In the 3D figure, the z-axis currently extends only to zero; please extend it to include positive values. Also help needed in setting the optimal point which is not clearly visible now—how to adjust the view and labeling to highlight only its z-value. How can we Improve the overall clarity and positioning of the figure to enhance visual readability.

Q_figure.mw

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