random math function generator

I am looking for a library that generates random math functions. For example, the library might include the following functions...

rand_poly would take in arguments like terms=3 and would output a random polynomial such as x^2 + 3x + 1.

rand_trig would output one of cos(x), sin(x), tan(x), etc, randomly.

For my specific needs, I much prefer Python. Also, I would like the output to be a string formatted in TeX. But these are not absolute requirements, as I could convert myself if necessary.

I was not able to find a suitable library in PyPI.