SIXSEVEN

S_ymbolic I_{nterface for} X_-dimensional S_ystems, E_quations, V_{ectors, and} E_igen- N_etworks.

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A terrible linear algebra and symbolic math system, the result of an off-handed comment by a linear algebra professor and absolute insistence on not manually doing homework.

Featuring:

• Crazy static type safety
• Structural typing for different number systems (fields, rings, ...)
• Flexible matrices and vectors, supporting any* valid number system
• Symbolic arithmetic system for any* valid number system
• Almost no functional dependency (most dependencies are from the type system)

*Well that's the plan at least, we'll see where it goes

Example(s):

from lib import *

def S(n):
    return FieldSymbol(n, Fraction)

mat = Matrix(
    ("A" , 1 , -1) ,
    ("B" , 4 , 0 ) ,
    ("C" , 1 , 2 ),
    num_type=S
)

print(det(mat)) # this is the correct deteminant trust

TODOS:

• matrix.rank()
• Symbol number type
• Matrix needs to properly support commutative rings
  • Matrix methods use self.num_type(0) and self.num_type(1) for add and mult identity, make that part of number system
  • det and inverse uses division, replace with the fancy algorithm
• Maybe eigenvalue definition of sqrt of matrix
• Change Callable[[Any],T] to type[T] This seems too complicated, the other way gets the idea across
• Unary -/+
• Replace __init__ with __new__ (maybe but probably not)
• Implement equal for Matrix and Vector
• Symbol support for ops with int and float
• Refactor Zmod to bind pattern
• Implement default num_type for FieldSymbol or rework that system entirely
• Split up files and make some folders
• Update unit tests
• Rewrite the entire add and mult term grouping again
  • No more sorting as preprocessing, really expensive and doesn't work that well
  • Still need sorting for display mostly, so who knows?
• diagonalise