Accompanying a ballet warm-up exercise will also be the first thing a musician will play in the ballet studio. 
So, what type of music should we play ?
I personally keep it very SIMPLE and EASY :
after all, this is the moment for us, musicians to warm-up too, fingers and minds alike !
Improvising for ballet class can be a challenge on many levels, and it is important to :

• establish confidence from the start of the ballet class,
   
• look for a good sound,
   
• observe...or listen how the ballet teacher, the ballet dancers are reacting to the music.
  
  What will I play for a slow movement warming-up exercise ? 
   

1. The first thing I do is pick a style : 
   Will it be baroque, classical, neo-classical, romantic, jazz/blues... ?
   Will I get inspiration from a ballet, a story, a painting, a tune I heard on the radio ? 
   ...But how is the mood like in the ballet studio today ?
   What is the weather like, are the dancers tired or upbeat ?
   What time of the year is it ? What time of the day is it ??
   How is the ballet teacher ? How am I feeling myself ??
   The answers to these questions (If there are any!) will help me choose a style !
    
2. Once I pass this multi choice quizz, I quickly pick a key signature. 
   (generally a Major one to start the ballet class on a happy mood!)
   The time signature does not really matter unless the ballet teacher has been specific about it when marking the exercise.
   I just make sure I can be flexible and adapt quickly in case I was wrong !
    
3. I then pick a comfortable left hand accompanying pattern, and a simple melody
   (it does not matter if it is repetitive, in fact, repetition helps creativity, I find !)

THEN JUST PLAY, GO WITH THE FLOW AND ENJOY !

I try to think of the dancers and of the qualities they may like to find in the music at the start of a ballet class, to name a few,
stability, confidence, flexibility, mobility, strength, expression and focus..
I will need these too !!
To translate this into music, I try to choose simple harmonic structures, clear melodic lines and phrases, and also to give space to breathe, comforting bass lines on the left hand, repetitive patterns perhaps, yet allowing the right hand to evolve feely above. 

What will I play for a dynamic movement warming-up exercise ?

The process is more or less the same :
style, key signature, time signature, patterns.. BUT...I tend to keep it even simpler :
Very easy and clear harmonic structure, ABA type form, and very easy to play.
This varies for each musician of course but for me, this would be often a repetitive left hand and a bouncy phrasing, to keep loose and relaxed...
We need to last until the Grand Allegro !

For a combined slow and dynamic movement war-up exercise, the KEY THING is :

Be flexible, adapt, go with the flow ! 

I have selected a few of the pieces I composed for the three families of warm-up exercises below and hope they will inspire you to be creative !