You need to have sage installed for this, which you can get here, as well as using
sudo apt-get install sagemath
Then you run it by running sage in interactive mode and calling load("mpl.sage"), which will print
[(v_1, 0), (v_2, 0), (v_3, 0), (v_4, 0)] [(v_u, 0), (v_v, 0)]
[(v_1, 1), (v_2, 0), (v_3, 0), (v_4, 0)] [(v_u, 0), (v_v, 0)]
[(v_1, 0), (v_2, 1), (v_3, 0), (v_4, 0)] [(v_u, 0), (v_v, 0)]
[(v_1, 0), (v_2, 0), (v_3, 1), (v_4, 0)] [(v_u, 0), (v_v, 0)]
[(v_1, 0), (v_2, 0), (v_3, 0), (v_4, 1)] [(v_u, 0), (v_v, 0)]
[(v_1, 1), (v_2, 1), (v_3, 0), (v_4, 0)] [(v_u, 1), (v_v, 0)]
The usual example we use is in the variable data = [3, 1, 1, 1, 1, 2]
Here's some random data: random_data = [3, 4, 3, 6, 7, 4]
Usage:
summarize_lumps(data)
int_max, border_max = sort_functions(data); find_lumps(int_max, border_max)
The sort_functions procedure takes a long time, so you can get intermediate values.
print_lumps(find_lumps(int_max, border_max)) # prints LaTeX tables.
You can make your own data, it just needs to be a list of length 6.
You can also switch to a different tree by typingg = tree5 or g = tree3 but you need to make your own if you want some other trees. Printing out g will provide helpful information for this.
This code will find all of the critical points of your function and sort through them to determine which ones are lumps.