Certainly, hard to read as Maplesoft has not provided yet a TeX interface to its typesetting scheme, despite repeated claims. When you put this stuff in the command line and execute it, you get 2D typesetted output.

Certainly, hard to read as Maplesoft has not provided yet a TeX interface to its typesetting scheme, despite repeated claims. When you put this stuff in the command line and execute it, you get 2D typesetted output.

It may be the case that the methods/algorithms more convenient for computation by a serial computer are quite different from those most suitable to an intelligent human brain.

Additionally, the algorithms implemented in Maple are most frequently undocumented for the user. So, tracing as shown above, can give to the user, at most, a pale idea of what Maple really does, and why does it. It is not really thought for pedagogical purposes.

It may be the case that the methods/algorithms more convenient for computation by a serial computer are quite different from those most suitable to an intelligent human brain.

Additionally, the algorithms implemented in Maple are most frequently undocumented for the user. So, tracing as shown above, can give to the user, at most, a pale idea of what Maple really does, and why does it. It is not really thought for pedagogical purposes.

What precisely worries you?

Have you already found analytically the sum of the OP's series?, or demonstrated that no analytical expression exist?

What precisely worries you?

Have you already found analytically the sum of the OP's series?, or demonstrated that no analytical expression exist?

You can do something like:

J:=Int( N* Diff(psi(f, theta[1], theta[1]), theta[1]) * 
Diff(psi(f, theta[1], theta[2]), theta[2])* f^4,x):
indets(J,specfunc(anything,Diff)):
if nops(%)=1 then [%[],%[]]; else [%[]] end if:
op~(2,%):
typematch([op(%)],[theta['a'::posint],theta['b'::posint]],'s'):
l1:=s;
l2:=[alpha=op(2,indets(J,specop({name,integer},`^`))[])];

                         l1 := [a = 1, b = 2]

                          l2 := [alpha = 4]

subs([l1[],l2[]],K(alpha,a,b));
                              K(4, 1, 2)

You can do something like:

J:=Int( N* Diff(psi(f, theta[1], theta[1]), theta[1]) * 
Diff(psi(f, theta[1], theta[2]), theta[2])* f^4,x):
indets(J,specfunc(anything,Diff)):
if nops(%)=1 then [%[],%[]]; else [%[]] end if:
op~(2,%):
typematch([op(%)],[theta['a'::posint],theta['b'::posint]],'s'):
l1:=s;
l2:=[alpha=op(2,indets(J,specop({name,integer},`^`))[])];

                         l1 := [a = 1, b = 2]

                          l2 := [alpha = 4]

subs([l1[],l2[]],K(alpha,a,b));
                              K(4, 1, 2)

In fact, according to Maple, diff(conjugate(z),z) is undefined when z is not real or assumed real because then abs(1,z) is undefined. See above in this thread.

In fact, according to Maple, diff(conjugate(z),z) is undefined when z is not real or assumed real because then abs(1,z) is undefined. See above in this thread.

Note that, if a help link is enclosed by brackets, a space has to be left in between so that the automatic link script recognizes it. C.f. (?solve) vs ( ?solve ).

Yes, but no specification exists describing the capability of coulditbe. So, against my expectation, it is also a bug, but with this undocumentation level, Maplesoft can equally argue that it is a weakness or a "works as designed" case.

And is is in the same situation, though verify is better:

assume(f, RealRange(Open(0),infinity)):
coulditbe(f,'imaginary');

                                 FAIL

is(f,'imaginary');

                                 FAIL

verify(f,'imaginary');

                                false

Yes, but no specification exists describing the capability of coulditbe. So, against my expectation, it is also a bug, but with this undocumentation level, Maplesoft can equally argue that it is a weakness or a "works as designed" case.

And is is in the same situation, though verify is better:

assume(f, RealRange(Open(0),infinity)):
coulditbe(f,'imaginary');

                                 FAIL

is(f,'imaginary');

                                 FAIL

verify(f,'imaginary');

                                false

In ?assume it is stated:

The coulditbe routine returns FAIL if it cannot determine whether the property is true or false.  This is a result of insufficient information or an ability to compute the logical derivation.

In ?assume it is stated:

The coulditbe routine returns FAIL if it cannot determine whether the property is true or false.  This is a result of insufficient information or an ability to compute the logical derivation.