A little error in the ornament popups: typing either mor or invmor gets you a mordent. Typing shorttrill gets you an inverted mordent. (The way I learned it the mordent has a slash and goes to the lower neighbor, while an inverted mordent gets you no slash and goes to the upper neighbor.
The precise meaning of mordent has changed over the years. In the Baroque period, a mordent was a lower mordent and an upper mordent was a pralltriller or schneller. In the 19th century, however, the name mordent was generally applied to what is now called the upper mordent, and the lower mordent became known as an inverted mordent.
In other languages the situation is different: for example in German Pralltriller and Mordent are still the upper and lower mordents respectively. Also note that this ornament in French, and sometimes in German, is spelled mordant.
from Wikipedia
as you can see, there is not an easy solution to this…