Found integration problem which causes server.exe to crash each time. I hope this can be used to help find why server.exe keeps crashing much more than before in Maple 2022.

This happens each time. The above is a typical example of what I have been saying all the time above server.exe crashing. It should not do that. If it can not solve the problem, it should simply return.

I hope these problems will be fixed in Maple 2023.

Any one can figure why it crashes?

Attached worksheet.

Download crash_feb_3_2023.mw

I am converting some code from Mathematica. In it there is this solution

eqs={2c2+c0==1,6c3+2c1==2,3c2+12c4==1};
FindInstance[eqs,{c0,c1,c2,c3,c4}]

Which gives

{{c0 -> 0, c1 -> 0, c2 -> 1/2, c3 -> 1/3, c4 -> -(1/24)}}

Maple's solve gives

eqs := [2*c2 + c0 = 1, 6*c3 + 2*c1 = 2, 3*c2 + 12*c4 = 1];
sol:=solve(eqs, {c0, c1, c2, c3, c4})

Gives

sol := {c0 = 1/3 + 8*c4, c1 = -3*c3 + 1, c2 = 1/3 - 4*c4, c3 = c3, c4 = c4}

I know that both are correct solutions. But I'am asking if there is a command or an option I overlooked that will generate the same result as the above from FindInstance, which will make it easier for me.

May be there is another solver package or command I could try?

I am not sure what algorithm FindInstance uses. The documentation page does not say.

I have only seen big O show up in series solutions, as in 

series(sin(x),x)

I've never seen it before show up in result of solve

restart;
eq:=x=p*(a*ln(p+sqrt(p^2-2))+2*_C1)/(2*sqrt(p^2-2));
sol:=solve(eq,p);

What does it actually mean when the solution has  O(RootOf(....))?  

Should not result of solve be exact? isn't having big O means an approximation?

Maple 2022.2 on windows 10

Could you suggest a more elegent way to remove any entry in piecewise which has undefined in it?

expr:=(s+exp(-Pi*s)-exp(-2*Pi*s))/(s*(s^2+2*s+2));
inttrans:-invlaplace(expr,s,t);
Y:=convert(%,piecewise);
#remove all entries in piecwise which has undefined

To obtain this

I can;t just apply select on piecewise. So currently I convert piecwise to list of lists, each sublist has the 2 entries you see above in each row.

Next apply select. Then use piecewise again on the result. This works, but wondering if there is a better way.

Attached worksheet.

Download remove_undefined.mw

Another very strange result from simplify.  Consider

simplify(a*f(x) + b*f(x) + a*g(x))

Which is what is expected. Now 

expr := a*f(x) + b*f(x) + a*g(x) + 1/(a*f(x) + b*f(x) + a*g(x));
simplify(expr)

gives

why?  I expected (a+b)*f(x) also in the first expression. Compare for reference the same thing in Mathematica where it does them both the same way:

You see it simplified it to (a+b)*f(x)+a*g(x) in both places as expected.

I tried using size option for simplify, but it had no effect.

How can one obtain same result shown above using Maple? And why it does not automatically produce this result?

Maple 2022.2