Welcome Thejasvi,

I cannot probably give you full help, but I modified your .input file a bit.

Note that ++ is for docstrings in .spad files. The usual comment starts
with --.

The first thing that I have noticed is that legendreP requires its first
argument to be a NonNegativeInteger. Unfortunately, FriCAS does not know
that n-1 for n: PositiveInteger would be of type NonNegativeInteger. You
have to help FriCAS here, i.e.,

(n-1)::NonNegativeInteger

(See start of the notebook. I have defined a few macros that I usually use.)

Still there is a problem with the aromberg function, but that comes from
the fact that its first argument must be of type F->F.

https://fricas.github.io/api/NumericalQuadrature.html#l4e756d65726963616c51756164726174757265-61726f6d62657267

You, however, give a type DoubleFloat -> Complex(DoubleFloat).
That cannot work.

Sorry, I have no time now to analyxe further, but according to

  F: FloatingPointSystem

for NumericalQuadrature(F), it will probably not work to use
Complex(DoubleFloat) since

(9) -> Complex(DoubleFloat) has FloatingPointSystem

   (9)  false

In other words, aromberg is not available for Complex(DF).

Sorry that I cannot be more clear.

Ralf

PS: Please subscribe to fricas-devel for further discussion.

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