What is the ruling on one who intentionally aroused her sexual desire by thinking during the daylight hours of Ramadan while she was menstruating, and then completed her fasting after becoming sure of her purity? And is expiation obligatory upon her?

Arousal of desire does not invalidate the fast nor necessitate expiation. The fast is only invalidated by intentionally discharging semen. There is a difference of opinion regarding the intentional discharge of prostatic fluid (madhy). A woman who becomes pure during the day in Ramadan (definition) is not obligated to fast the remainder of that day. A Muslim must utilize the blessing of thought in what benefits them in matters of their religion or their worldly life.