Tensei Oujo to Tensai Reijou no Mahou Kakumei

Despite her supposed ineptitude with regular magic, Princess Anisphia defies the aristocracy's expectations by developing "magicology," a unique magical theory based on memories from her past commoner life. One day, she witnesses the brilliant noblewoman Euphyllia unjustly stripped of her title as the kingdom's next monarch. Thus Anisphia concocts a plan to help Euphyllia regain her good name somehow involving them living together and researching magic! Little do these two ladies know, however, that their chance encounter will alter not only their own futures, but those of the kingdom... and the entire world! ___ - Official Web Novel