Maple 2024.2 gives wrong inverse Laplace transform on expressions with exp(s) multiplied by Ei (the exponentional integral) with complex argument.

Below are two examples found so far. 

Inverse laplace of  exp(s)/2*Ei(1, s + I) gives exp(-I*(t + 1))/(2*(t + 2))  but the correct inverse should be exp(-I*(t + 1))/(2*(t + 1))

Inverse laplace of  exp(s)/2*Ei(1, s - I) gives exp(I*(t + 1))/(2*(t + 2))  but the correct inverse should be exp(I*(t + 1))/(2*(t + 1))

i.e. in both cases it gives 2*(t + 2) in denominator when denominator should be 2*(t + 1)

Below is worksheet

Download bug_in_inverse_laplace_transform.mw

Also Reported to Maple support.

Any idea why Maple returns empty string when asked for the latex of the Laplace of x(t)?  Am I doing anything wrong here? I do not see it

Download latex_of_laplace_nov_21_2024.mw

I was expecting something like this using another software

Did Maple always behave this way for Laplace? I do not have earlier version now to check.  Any workaround?

Is this a known error when using PDEtools:-Solve? I get no error using solve on same input, so thought to ask, just in case it should not happen.

For now, I will change my code to use solve for this.

I am basically solving two equations in Laplace domain for Y1(s) and Y2(s). But since there are initial conditions x(0) and y(0) in the equations, and Laplace has L(x(t),t,s)  then PDEtools:-Solve is not happy, as it sees x(t) and x(0) in same input.

But solve has no problem with this. Who is correct? solve or Solve?

Download differenece_between_solve_and_Solve_nov_20_2024.mw

I was not expecting odesteps to show steps for this ode, but crash the server each and everytime?

Anyone could find why? I am using Maple 2024.2 on windows 10 with latest Physics. This might indicate serious problem somewhere. Software should not really crash this easily.

Download crash_server_nov_18_2024.mw

here is small movie

I am learning patten matching in Maple. 

Any one could explain why patmatch(1, (x::anything)^(n::'nonunit'(anything)))   gives true but patmatch(2, (x::anything)^n::'nonunit'(anything)); gives false?

Download patmatch_question_nov_16_2024.mw

I was expecting result similar to using this other software

I do not understand Maple's result. How could I change the patmatch so it does not match 1 to the pattern x::anything^n::anything where n is not 1 ?

Update

To give context, I was trying to write this example from the other software  in Maple:

But when I wrote this

expr:=1 + x^2 + x^4;

F:=proc(X::anything,x::symbol)
    local la,y,n;
    if patmatch(X, (y::anything)^(n::'nonunit'(anything)) ,'la') then  
       f(eval(n,la));
     else
        X;
     fi;
end proc;

map(X->F(X,x), expr);

Maple gave 

So I modified the code now to check for explicit 1,  to avoid this bad match, like this

expr:=1 + x^2 + x^4;

F:=proc(X::anything,x::symbol)
    local la,y,n;
    if patmatch(X, (y::anything)^(n::'nonunit'(anything)) ,'la') then  
        if eval(y,la)=1 then #bug in maple?
           X;
        else
           f(eval(n,la));
        fi;
     else
        X;
     fi;
end proc;

map(X->F(X,x), expr);

And now it gives expected result