hoodmane / steenrod_modules

Python steenrod algebra implementation

Steenrod Modules

Requires Python 3 (tested in python 3.6.7). To use it you should download the repository and then run ./steenrod_modules in the root directory.

You can load a module from a file by saying M = SteenrodModule.from_Bruner_file(file_path), for instance file_path could be "Bruner-modules/CP-1". You can write a module to a file with M.to_Bruner_file(file_path).

The tensor product of modules M and N is M * N, the dual of a module M is ~M, and the truncation is M[min:max]. You can create a new empty module with M = SteenrodModule(p = a_prime) and then add basis vectors by saying x = M.add_basis_element("name", degree) and add relations with M.add_Sq_action(Sq_degree, basis_element, output_vector) You can check the relations define a correct action with M.validate().

So for instance:

A = AdemAlgebra(p=2)
M = SteenrodModule(p=2)
x0 = M.add_basis_element("x0", 0)
x1 = M.add_basis_element("x1", 1)
y1 = M.add_basis_element("y1", 1)
M.add_Sq_action(1, x0, x1 + y1)
M.validate()

Now A.Sq(1) * x0 will return x1 + y1.

You could build the same module by saying:

M = SteenrodModule(p=2)
x0 = M.add_basis_element("x0", 0)
x1 = M.add_basis_element("x1", 1)
M.add_Sq_action(1, x0, x1)
N = (M*M)[0:1]
x0x0 = N.get_basis_element("x0*x0")

though now the elements will be named x0*x0, x0*x1, and x1*x0. Now A.Sq(1) * x0x0 will return x0*x1 + x1*x0.

M.get_failed_relations() will return a list of the Adem relations that are violated in M.