Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

THis is problem from textbook. Maple do not give solution. 

But when asked for implicit solution, it gives one.  Should it not have done this automatically?

interface(version);

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

ode:=y(x)*diff(y(x),x) = a;
ic:=y(0) = b;
sol:=dsolve([ode,ic]);

y(x)*(diff(y(x), x)) = a

y(0) = b

sol:=dsolve([ode,ic],'implicit')

-2*a*x+y(x)^2-b^2 = 0

 

 

Download why_no_solution_maple_2025_1.mw

We see now there are two solutions for y(x), since quadratic.

So why dsolve do not solve this and at least give implicit solution automatically? Should this be reported as defect?

is been a while i work on a test still i am study and there is a lot paper remain and is so important in PDEs, a lot paper explain in 2003 untill know and there is other way to find it too but i choose a easy one but is 2025 paper  which is explanation is so beeter than other paper, also some people write a package for take out this test with a second but maybe is not work for all i  search for that  but i didn't find it i will ask the question how we can find thus as shown in graph i did my train but need a little help while i am collect more information and style of solving 

Download p1.mw

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

Update

fyi, Here is yet another int() error Error, (in type/trig) too many levels of recursion in Maple 2025.1. (also reported to Maplesoft).

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:=(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2);

(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)

int(integrand,x)

Error, (in type/trig) too many levels of recursion

int(integrand,x)

(1/6)*(-c*(-1+sin(f*x+e)))^(1/2)*((3/4)*B*sin(f*x+e)*tan(f*x+e)*cos(2*f*x+2*e)+A*sin(2*f*x+2*e)-(3/8)*tan(f*x+e)*(((4/5)*B*sin(f*x+e)+A)*sin(3*f*x+3*e)+(44/15)*B*sin(f*x+e)^2+(5*A-6*B)*sin(f*x+e)-(32/3)*A))*a*c^2*(a*(1+sin(f*x+e)))^(1/2)/f

restart;

integrand:=(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2);
int(integrand,x)

(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)

Error, (in type/trig) too many levels of recursion

 

 

Download another_int_error_too_many_levels_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 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.

This post is written by a mathematics teacher who usually views Maple’s new initiatives from an educational perspective, and I’m well aware that others may see things differently. A single user might be delighted by a new feature that fits their personal workflow. An advanced user might not care if something requires a workaround.

There are also many preferences when it comes to how the interface should look. I often consider whether something will work well for our high school as a whole. We have students who are not very mathematically or scientifically inclined, and others who are. That’s why user-friendliness is essential. Some packages have been developed to make things easier for students. We try to avoid too many workarounds, since these often create problems for them.

Now, on to Maple 2025’s new interface:

When Microsoft introduced tabs and ribbons instead of menus and toolbars in Word many years ago, I personally thought it was a good idea. I can imagine it working well in Maple too — especially if the different elements are placed logically on the tabs, and frequently used functions are easy to access.

However, I just returned from summer vacation, ready for a new school year, only to discover something surprising: the Windows version comes with the new ribbon interface, while the Mac version still has the old one! For any teacher, this is a nightmare scenario: teaching a class where the Windows and Mac interfaces look completely different. Has Maplesoft ended up caught between two chairs here?

I’ve heard that a Mac version with tabs and ribbons is under development. But since it’s not ready yet, we can’t use it. On Windows, I also noticed a strange extra application called “Maple 2025 Screen Readers”. If you open it directly, you get an odd mix of modern 2D notation and old 1D Maple notation, which is simply unacceptable. If you instead click “Screen Reader Mode” in the top-right corner, it looks more normal. But does that mean it’s fully functional? If so, we might be able to combine this with the Mac version that still uses the old interface — and then switch next year to both Windows and Mac with tabs and ribbons. Still, I must say that Maplesoft is providing far too little information on this! Around 75% of our students use Macs, while only 25% use Windows.

Another issue: When saving a Maple file on a Windows computer, you’re forced into Maple’s own “Save As” window. I’ve previously suggested that it should instead open directly in Windows’ native File Explorer, which is far more powerful. In File Explorer, you can quickly use Quick Access shortcuts to save the file in the right folder. In Maple’s “Save As” window, however, it often takes 6–7 extra clicks to reach the desired location. For students who aren’t very tech-savvy, navigating through a deep folder tree can be a real challenge. Why doesn’t Maplesoft just use Windows’ own File Explorer, which students are already familiar with? Most other programs do. Perhaps someone can explain why Maplesoft insists on keeping their own limited “Save As” dialog.

Finally: I do believe that tabs and ribbons can be a good solution, but there’s still work to be done in placing items on appropriate tabs. For example, although I personally use the F5 keyboard shortcut to switch between Text, Non-executable Math, and Math mode, I know many students prefer to click on these options in Maple 2024. In the new interface, it now takes two or three clicks to do so. Since this is a function used very frequently, that’s a drawback. Couldn’t users be allowed to customize the Quick Access toolbar — via the Options menu — so these items can be placed there if needed?

 

 

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

Download simplify.mw

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?

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