covenant model.py

from fractions import Fraction as F
KEYS=['Q','T','qI','qX','xJ','jCall','callL','callZ','L_I','L_L','L_J','L_Z','L_A','Moses_birth','full_state_shift','L_Isaac','L_Kohath','L_Amram','phase']
def regular(v):
 Q=v['Q']
 r={'Q':Q,'terminal':v['T'],'Ishmael_birth':Q-v['qI'],'Isaac_birth':Q-v['qX']}
 r['Ishmael_death']=r['Ishmael_birth']-v['L_I']
 r['Jacob_birth']=r['Isaac_birth']-v['xJ']
 r['Jacob_call']=r['Jacob_birth']-v['jCall']
 r['Jacob_death']=r['Jacob_birth']-v['L_J']
 r['Levi_birth']=r['Jacob_call']-v['callL']
 r['Levi_death']=r['Levi_birth']-v['L_L']
 r['Joseph_birth']=r['Jacob_call']-v['callZ']
 r['Joseph_death']=r['Joseph_birth']-v['L_Z']
 return r
def claims(v):
 r=regular(v);S=r['Ishmael_birth']-r['Levi_birth'];Q=v['Q']
 return [v['xJ']+v['jCall']+v['callL']-v['L_J'],
 v['callL']+v['L_L']-v['L_J'],v['L_I']-v['L_L'],
 r['Ishmael_death']-2*r['Levi_death']+v['T'],
 r['Joseph_birth']-v['T']-2*v['L_J'],
 13*(Q-r['Joseph_death'])-12*(Q-r['Levi_death']),
 25*S-23*v['L_A'],2*S-v['L_J']-v['L_A'],S-v['L_J']-v['callZ']]
def cumulative(v):
 names=['Abraham','Isaac','Jacob','Levi','Kohath','Amram','Moses-interface']
 ls=[v[k] for k in ['L_A','L_Isaac','L_J','L_L','L_Kohath','L_Amram']]
 base=[v['Moses_birth']+sum(ls[i:]) for i in range(7)]
 D=regular(v)['Levi_death']+v['full_state_shift']
 d=base[4]-D;h=d/2
 return {'names':names,'base':base,'regular_full_Levi_death':D,'clutch':d,'half':h,
 'rails':[[base[i]+j*v['phase']-k*h for i in range(7)] for j in [0,1] for k in [0,1,2]]}
def coefficient_matrix(fn,keys):
 zero={k:F(0) for k in KEYS};origin=list(fn(zero));cols=[]
 for k in keys:
  v=zero.copy();v[k]=F(1);cols.append([a-b for a,b in zip(fn(v),origin)])
 return [list(row) for row in zip(*cols)]