[2]   C6XTY @ sa: this Thursday:

(sa: is where I've taught Martian Math before)



​In this post I'm merging two threads:  

(i) introduce some of the high end 3rd party stuff early e.g. science stack numpy and pandas

(ii) segue a geometry that requires some rethinking of familiar orthodoxies.

Example:


pd.options.display.float_format = '{:,.3f}'.format    
data = pd.DataFrame(vectors, columns = index)
print(data)
Vtype    ivm                      xyz              
Coords     a     b     c     d      x      y      z
0      0.000 1.000 1.000 2.000  0.000 -0.707 -0.707
1      1.000 0.000 1.000 2.000  0.707  0.000 -0.707
2      2.000 0.000 1.000 1.000  0.707  0.707  0.000
3      0.000 2.000 1.000 1.000 -0.707 -0.707  0.000
4      0.000 1.000 2.000 1.000 -0.707  0.000 -0.707
5      1.000 2.000 1.000 0.000 -0.707  0.000  0.707
6      1.000 1.000 2.000 0.000 -0.707  0.707  0.000
7      2.000 1.000 1.000 0.000  0.000  0.707  0.707
8      1.000 0.000 2.000 1.000  0.000  0.707 -0.707
9      1.000 2.000 0.000 1.000  0.000 -0.707  0.707
10     2.000 1.000 0.000 1.000  0.707  0.000  0.707
11     1.000 1.000 0.000 2.000  0.707 -0.707  0.000

​
Getting such multi-indexing requires such as:


arrays = [['ivm', 'ivm', 'ivm', 'ivm', 'xyz', 'xyz', 'xyz'],
          ['a', 'b', 'c', 'd', 'x', 'y', 'z',]]

tuples = list(zip(*arrays))
index = pd.MultiIndex.from_tuples(tuples, names=['Vtype', 'Coords'])

Call it business math if you like, micro-management of data tables via some command line interface.

https://en.wikipedia.org/wiki/In_the_Beginning..._Was_the_Command_Line

That's using the multi-indexing phenomenon (object) the pandas dataframes provide.  

Above, I'm showing vectors in two notations, side by side, with a link to their colorful depictions, in terms of ball packings, at this still improving Jupyter Notebook:

https://github.com/4dsolutions/Python5/blob/master/Generating%20the%20FCC.ipynb

Next challenge is to segment the dataframe vertically, into nucleus (1) plus successive layers (12, 42, 92...).

Kirby