MmaTranslator:-Mma:-Chop  does not seem to work as advertised.. It is supposed to work like Mathematica's Chop, but it does not. Is this by design or is it a bug?

restart;

MmaTranslator:-Mma:-Chop(((1.378834798932344*10^(-15))*I)*t) ;

returns the same input (1.378834799*10^(-15))*I*t but

MmaTranslator:-Mma:-Chop(((1.378834798932344*10^(-15))*I));

now returns 0.

But compare to Mathematica:

This makes it not very useful to use if one has to remove all symbols from an expression first, Any workaround? Here is an actual example where I wanted to use it

ode:=[diff(x(t), t) = -3*x(t) + 4*y(t), diff(y(t), t) = 5*x(t) + 9*z(t), diff(z(t), t) = y(t) + 6*z(t)];
sol:=dsolve(ode):
evalf[16](sol);

gives

Gives

{x(t) = (0.8172764110864494 - (7.853170607134887*10^(-16))*I)*c__1*exp((1.894304969211800 - (1.378834798932344*10^(-15))*I)*t) - (1.150854759654687 + (3.398186702482929*10^(-16))*I)*c__2*exp((-6.475677505300665 + (3.730232887526917*10^(-17))*I)*t) + (0.3780227930126823 + (9.268277369231981*10^(-16))*I)*c__3*exp((7.581372536088866 + (1.198480681985453*10^(-15))*I)*t), y(t) = c__1*exp((1.894304969211800 - (1.378834798932344*10^(-15))*I)*t) + c__2*exp((-6.475677505300665 + (3.730232887526917*10^(-17))*I)*t) + c__3*exp((7.581372536088866 + (1.198480681985453*10^(-15))*I)*t), z(t) = (-0.2435641206911610 + (1.431838044809606*10^(-16))*I)*c__1*exp((1.894304969211800 - (1.378834798932344*10^(-15))*I)*t) + (-0.08015596744746927 + (4.286632781083632*10^(-16))*I)*c__2*exp((-6.475677505300665 + (3.730232887526917*10^(-17))*I)*t) + (0.6323620634472722 - (5.261170533293161*10^(-16))*I)*c__3*exp((7.581372536088866 + (1.198480681985453*10^(-15))*I)*t)}

But Chop does not work on this. 

Maple 2023.2

Would Any one be able to give some explanation as to why calling a proc, which does not change anything globally but only acts on the input given, returns different answer the second time it is called with the same exact input? I am not able to understand this result at all. 

Maple 2023.2 on windows 10.

Download why_different_answer.mw

This is linear ode, third order, Euler type and inhomogeneous ode.

If I solve the homogeneous ode only, then ask Maple to give me a particular solution, then add these, I get much much smaller solution which Maple verifies is correct.

Now when asking Maple to solve the original inhomogeneous ode as is, the solution is much more complicated and much longer with unresolved integrals.

Why does not Maple give the simpler solution? Both are verified to be correct.

This is my theory: When asking maple to find only the particular solution, it seems to have used a different and advanced method to find yp. Which is new to me and trying to learn it. It is based on paper "D'Alembertian Solutions of Inhomogeneous Equations (differential, difference, and some other).

Undetermined coefficients method can't really be used on ode's such as this because its coefficients are not constant.

Now, when asking Maple to solve the inhomogeneous ode, it seems to have used variation of parameters method, which results in integrals, which can be hard to solve.

My question is: Why does not Maple give the same much shorter answer when asked to solve the ode as is? Should it not have done so? Any thoughts on why such large difference in answer? Why it did not use the same method to find yp when asked to solve the whole ode as that leads to much smaller and more elegant solution.

ps. debugging this, it uses LinearOperators:-dAsolver:-dAlembertianSolver which is called from ODEtools/particularsol/linear to find yp when calling DETools:-particularsol(ode); but for some reason, it does not do this when asking it to solve the whole ode directly (if it did, then one will expect same answer to result, right?)

Maple 2023.2 on windows 10.
 

Download why_such_difference_in_dsolve_answer.mw

THis came up in another maple forum.  Any one knows why

restart;
expr := -(r0+Delta_r)^2*(46*r0-41*Delta_r)*r0^5;
subsop(1=a,2=b,3=c,4=d, expr);

gives error Error, improper op or subscript selector

but changing the order works ok

subsop(4=d,3=c,2=b,1=a, expr);

               # a*b*c*d

Looked at help and nothing there I could see that would explain this. 

Maple 2023.2. 

Given

expr:=  (x^(-(44 + 12*sqrt(69))^(1/3)/6 + 10/(3*(44 + 12*sqrt(69))^(1/3)) + 2/3)) - (x^(sqrt(69)*2^(1/3)*((11 + 3*sqrt(69))^2)^(1/3)/100 - (11*(44 + 12*sqrt(69))^(2/3))/600 - (44 + 12*sqrt(69))^(1/3)/6 + 2/3))

could someone come with a trick to show this is zero using simplification and other methods? I know I can use is and coulditbe but I do not trust these too much due to false positives I've seen from them in some places.

Here is my attempts

restart;


expr:=  (x^(-(44 + 12*sqrt(69))^(1/3)/6 + 10/(3*(44 + 12*sqrt(69))^(1/3)) + 2/3)) - (x^(sqrt(69)*2^(1/3)*((11 + 3*sqrt(69))^2)^(1/3)/100 - (11*(44 + 12*sqrt(69))^(2/3))/600 - (44 + 12*sqrt(69))^(1/3)/6 + 2/3));
simplify(expr);
simplify(expr,size);
simplify(expr,symbolic);
simplify(normal(expr));
simplify(normal(expr),symbolic);
simplify(expr) assuming real;
simplify(expr) assuming positive;
is(expr=0);
coulditbe(expr=0);
evalb(expr=0);

Gives

This is for reference, the Mathematica attempt