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Finally, the returned quotient polynomial must be flipped for the same reason that the input polynomials needed to be flipped (to convert from left-to-right descending powers of in the returned result to ascending powers of ).
Our conditions are also different from those of Theorem 2.1 in the study by Kuczmaszewska [17]: is only required in Theorem 2.1, not in Theorem 2.1 of Kuczmaszewska [17]; the powers of in (b) and (c) of Theorem 2.1 are and, respectively, not in Theorem 2.1 of Kuczmaszewska [17].
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com