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    Splitting a matrix defined on regular and irregula...

    Asked by: Muhammad Usman 240
    matrix partition
    3 hours ago
    0  0

    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

    Showing error will solving KKT equations...

    Asked by: Andiguys 65
    optimization constraints
    4 hours ago
    0  1

    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
     

    Where Has The "Stop Execution" Symbol Gone?...

    Asked by: WD0HHU 40
    interrupt gui ribbon
    15 hours ago
    0  3

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

    Why is there no longer a section for Maple Flow un...

    Asked by: FDS 190
    19 hours ago
    0  2

    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

    Does OpenMaple work in the Free Trial?...

    Asked by: benshaw2 5
    openmaple ubuntu
    Yesterday at 12:48 AM
    1  0

    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.

    How make simplify the fractional expresion?...

    Asked by: salim-barzani 1575
    radical simplify simplification
    August 15 2025
    2  1

    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

    How can I=sqrt(-1) can be properly factored out fr...

    Asked by: Ahmed111 140
    radical simplify simplification
    August 15 2025
    1  3

    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(`ω__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)*`ω__0`*t)+(2*I)*exp(-I*(A__c^2*g*l__0^2-1/2)*`ω__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*`ω__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)*`ω__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*`ω__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*`ω__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)*`ω__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*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))+exp(-(2*(l__0^2*(I*delta1+delta2)*t*`ω__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*`ω__0`+(1/2)*x))+exp(sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(x+(2*I)*`ω__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*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))-exp(-(2*(l__0^2*(I*delta1+delta2)*t*`ω__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)*`ω__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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