how to find CharacteristicPolynomiall of matrix with vector entries? 

Download characpol.mw

Since C2=D1.D1inv should be equal to I. But return is just an expression (see attached). Further, how to obtain residue for a function C2?

residue.mw

I am solving 3 nonlinear equations for 3 variables: lambda_1, lambda_2, and lambda_3. I would expect these lambdas to be real and positive.

Instead of solving my original equations, which are convoluted and not in polynomial form, I try to solve for their numerators first (since their numerators are polynomials). Broadly speaking, such solutions should also solve the original non-polynomial system. More specifically, the solutions thus obtained may be a nontrivial superset of the solutions of the original system. They need to be verified, which should be a much much easier process than obtaining that superset. In the case at hand, my original system is rational functions, and thus the only thing that really needs to be verified is that the solutions do not make any of the original denominators zero.

1st question: How to actually implement such verification? In other words, how to verify that the polynomial solution that I obtain also solves the original non-polynomial system?

2nd question: As you can see from my attached script, I obtain one polynomial solution. How to analyze it? What can I say about its roots? In case there are an infinite number of roots, how can I pin down a closed-form, real, and positive expression of lambda_1, lambda_2, lambda_3 in terms of the four parameters gamma, p, sigma_e and sigma_v?*

*Please note that in SolveTools:-PolynomialSystem I set backsubstitute=false to favour compactness and computational efficiency (which means that I need to do the backsubstitution myself now - how to do it?).

**Perhaps is useful to know that gamma, sigma_e and sigma_v are all real and positive and that p is a real, positive number between 0 and 1 (it represents a probability).

SCRIPT: 141123_Problem_NoCorrelation.mw

Thanks a lot!

Dear Maple   help me to  to plot the graph please see and rectify.  thanks in advance

i am attaching the codes 

inf:=5:
pdes:= R(X,R,t)*diff(U(X,R,t),X)+U(X,R,t)*diff(R(X,R,t),X)+R(X,R,t)*diff(V(X,R,t),R)+V(X,R,t),
         diff(U(X,R,t),t)+U(X,R,t)*diff(U(X,R,t),X)+V(X,R,t)*diff(U(X,R,t),R)=Gr*T(X,R,t)+Gc*C(X,R,t)+(1/R(X,R,t))*diff(R*diff(U(X,R,t),R),R),
         diff(T(X,R,t),t)+U(X,R,t)*diff(T(X,R,t),X)+V(X,R,t)*diff(T(X,R,t),R)+(1/(Pr*R(X,R,t)))*diff(R*diff(T(X,R,t),R),R),diff(C(X,R,t),t)+U* diff(C(X,R,t),X)+V(X,R,t)*diff(C(X,R,t),R)+(1/(Sc*R(X,R,t)))*diff(R*diff(C(X,R,t),R),R):
conds:= U(X,R,0)=0, V(X,R,0)=0, T(X,R,0)=0,  C(X,R,0)=0,                                            
        U(X,1,t)=1, V(X,1,t)=0, T(X,1,t)=1,  C(X,1,t)=1,                                                                          U(0,R,t)=0, T(0,R,t)=0, C(0,R,t)=0,
        U(X,int,t)=0,T(X,int,t)=0,C(X,int,t)=0:
pars:= { Gr=5, Gc=10,Sc=2.0}        

              pars := {Gc = 10, Gr = 5, Sc = 2.0}

PrVals:=[0.71, 1.00, 1.25, 2.00]:
  colors:=[red, green, blue, black]:
  for j from 1 to numelems(PrVals) do
      pars1:=`union`( pars, {Pr=PrVals[j]}):
      pdSol:= pdsolve( eval([pdes], pars1),
                       eval([conds], pars1),
                       numeric
                     );
      plt[j]:=pdSol:-plot( U(X,R,t),X=1, t=2, R=0..inf, numpoints=200, color=colors[j]);
  od:
  plots:-display( [seq(plt[j], j=1..numelems(PrVals))]);

how I can find the solution of differential equations with dsolve?

Thesis_(1).mw

Download Thesis_(1).mw

I have a linear system of 3 equations in 3 variables and have no issues with solving it using solve().

I am having issues with solving it by imposing assumptions on my parameters. The infolevel[solve] now outputs "Entering solver with 6 equations in 3 variables", so I am likely making mistakes in the syntax solve(Eqs, Vars, UseAssumptions) assuming ... first of all, do I even need to do this given the assume statements that I set up on top of my script? How do I make sure that all the assumptions are preserved throughout all the calculations in my worksheet?

Moreover, I don't know why I get SolutionsLost: setting solutions lost flag.

My script: 061123_solving_with_assumptions.mw

How I put three coordinat node in a graph and capture it. I want to display the coordinat node for the same time with the red grapf for the blue and green graph.

grafik_solusi_AIS_ttk_kritis_8(AIS)tLB5.mw
 

Download grafik_solusi_AIS_ttk_kritis_8(AIS)tLB5.mw

My file is working, but I am not getting the idea of how to show it at the base as well.For refernce, please see attched picture

Surface_plot.mw

I'm scratching my head to understand this behaviour of MultiSeries. If I type

MultiSeries[series](diff(ln(GAMMA(1/x)), x), x)

Maple 2022.2 answers

But as is known (and maple confirms)

diff(ln(GAMMA(x)), x)=Psi(x)

But prompting in maple 

MultiSeries[series](Psi(1/x), x)

It answers

that is off by a x^2 factor with the former answer, while one expects to obtain the same answer as before. Why is this? (I tried assuming positivity, same discrepancy results).

Hello

I re-opened my maple file and got the following error code:

"There were problems during the loading process. Your worksheet may be incomplete"

I have attatched the original file and todays backup file.

Backup:

D_Maple_files_Mat_2_Hjemmeopgave_7_igen22_MAS_1_1.mw

Original:

Hjemmeopgave_7_igen.mw

I hope some of you can solve this issue for me, as I am at a loss. Appreciate any help I can get.

It seems like my maple document has been corrupted. When I tri to open the document I'm met with an error message "There were problems during the loading process. Your worksheet may be incomplete."

I have spent a great amount of time in this document, so if there was a way to recover it, that would be fantastic.

Thanks!

Download prac_exam_ece4179.mw

I am trying to separate a value by using solve common but could get the answer. Is there any way to get required expression

Simplification_Help.mw

Is there a way to directly code a complex conjugate such as z with overbar without using the verbose conjugate(z)?

I have solved a simple expression with different built-in methods.... I received differents answers ...What is the exact way to get the same answers by all methods

help_roots.mw.

I was wondering whether it is possible to execute Python code into Maple. As an example, I give a fairly simple code:

Concentration_calculation(C_0, Q, V_r, m_b, rho, R, Gamma_i, delta_t=1):
t = np.arange(0, 360*60, delta_t)
C_i = [C_0]
for i in range(len(t)-1):
dC = -(Q/V_r)*(1-math.exp(-3*m_b*math.sqrt(Gamma_i/(rho*t[i+1]))/(math.sqrt(math.pi)*Q*R)))*C_i[i]
C_i.append(C_i[i] + dC*delta_t)
return t, C_i

Any help in tis respect would be highly appreciated.