Your studying together has also gone rather well. While the subject of slide evolution isn't the exact same as High Programming the basic points are similar enough for a grounding of the subject to occur quickly. According to frigimon's manual a digimon's base code isn't made from 0's and 1's like the lines in Sorcery. But rather living beings such as digimon run on trinary type coding, i.e. zero, one and two. It's only a small difference at the base level, but it allows for far more complex designs to function.
Ardat is really good at learning this type of theory for some reason. From where you're standing it almost seems as if her new form took away her aptitude for magic and replaced it with this new field.
Now, the process of slide evolution isn't quite an exact science that can simply be taught en-masse. Rather the manual explains that the process is drastically different from mon to mon depending on their current and previous forms. It requires not only a basic understanding of oneself but a certain amount of instinct to guide oneself back to their previous form. Which is luckily enough, something you've gained in spades upon evolving to Gryzmon.
