[write up] {v.}
1. To write the story of; describe in writing; give a full account of.
* /Reporters from many newspapers are here to write up the game./* /The magazine is writing up the life of the President./
2. To put something thought or talked about into writing; finish writing (something).
* /John took notes of what the teacher said in class and he wrote them up when he got home./* /The author had an idea for a story when he saw the old house, and he wrote it up later./