The initialization of fmpz_series and fmpq_series objects isn’t correct when another series is passed as the val.

[Jatinbhardwaj-093]

In the following routine:

python-flint/src/flint/types/fmpz_series.pyx

Lines 61 to 78 in c1ac8c9

	def __init__(self, val=None, prec=None):
	if prec is None:
	self._prec = getcap()
	else:
	self._prec = prec
	if self._prec < 0:
	self._prec = -1
	if val is not None:
	if typecheck(val, fmpz_series):
	fmpz_poly_set(self.val, (<fmpz_series>val).val)
	self._prec = min((<fmpz_series>val)._prec, getcap())
	elif typecheck(val, fmpz_poly):
	fmpz_poly_set(self.val, (<fmpz_poly>val).val)
	elif typecheck(val, list):
	fmpz_poly_set_list(self.val, val)
	else:
	fmpz_poly_set_list(self.val, [val])
	fmpz_poly_truncate(self.val, max(0, self._prec))

When setting the precision for a new series, the code currently compares the given series’s precision with the global cap. However, for correctness, it should compare it with self.prec (i.e., the already processed precision of the target object).

>>> from flint import fmpz_series
>>> x = fmpz_series([0,1], 5)
>>> fmpz_series(x, 4)
x + O(x^5)

It should be x + O(x^4) but instead, due to comparing with gcap (which is 10), the precision logic behaves incorrectly, producing an unintended result.

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Originally identified by @oscarbenjamin
Original comment: sympy/sympy#28109 (comment)