def commute(self, initIdx=None, finalIdx=None, assumptions=USE_DEFAULTS):
'''
From self, derive and return a form in which the operand
at index initIdx has been moved to finalIdx.
For example, given (A and B and ... and Y and Z) derive (A and ... and Y and B and Z)
via initIdx = 1 and finalIdx = -2.
'''
from ._theorems_ import commute, leftwardCommute, rightwardCommute
return apply_commutation_thm(self, initIdx, finalIdx, commute, leftwardCommute, rightwardCommute, assumptions)
def commutation(self, initIdx=None, finalIdx=None, assumptions=USE_DEFAULTS):
'''
Given Boolean operands, deduce that this expression is equal to a form in which the operand
at index initIdx has been moved to finalIdx.
For example, (A and B and ... and Y and Z) = (A and ... and Y and B and Z)
via initIdx = 1 and finalIdx = -2.
'''
from ._theorems_ import commutation, leftwardCommutation, rightwardCommutation
return apply_commutation_thm(self, initIdx, finalIdx, commutation, leftwardCommutation, rightwardCommutation, assumptions)
def commute(self, init_idx=None, final_idx=None, **defaults_config):
'''
From self, derive and return a form in which the operand
at index init_idx has been moved to final_idx.
For example, given (A or B or ... or Y or Z) derive (A or ... or Y or B or Z)
via init_idx = 1 and final_idx = -2.
'''
from . import commute, leftward_commute, rightward_commute
return apply_commutation_thm(self, init_idx, final_idx, commute,
leftward_commute, rightward_commute)
def commutation(self, init_idx=None, final_idx=None, **defaults_config):
'''
Given Boolean operands, deduce that this expression is equal to a form in which the operand
at index init_idx has been moved to final_idx.
For example, (A and B and ... and Y and Z) = (A and ... and Y and B and Z)
via init_idx = 1 and final_idx = -2.
'''
from . import commutation, leftward_commutation, rightward_commutation
return apply_commutation_thm(self, init_idx, final_idx, commutation,
leftward_commutation,
rightward_commutation)
def commutation(self,
init_idx=None,
final_idx=None,
assumptions=USE_DEFAULTS):
'''
Given Boolean operands, deduce that this expression is equal to a form in which the operand
at index init_idx has been moved to final_idx.
For example, (A or B or ... or Y or Z) = (A or ... or Y or B or Z)
via init_idx = 1 and final_idx = -2.
'''
from . import (commutation, leftward_commutation,
rightward_commutation)
return apply_commutation_thm(self, init_idx, final_idx, commutation,
leftward_commutation,
rightward_commutation, assumptions)
def permutation_move(self,
initIdx=None,
finalIdx=None,
assumptions=USE_DEFAULTS):
'''
Deduce that this Set expression is equal to a Set
in which the element at index initIdx has been moved to
finalIdx. For example, {a, b, c, d} = {a, c, b, d} via
initIdx = 1 (i.e. 'b') and finalIdx = -2. In traditional
cycle notation, this corresponds to an index-based cycle
(initIdx, initIdx+1, ..., finalIdx) where
0 ≤ initIdx ≤ finalIdx ≤ n - 1 for a set of size n.
'''
from ._theorems_ import (binaryPermutation, leftwardPermutation,
rightwardPermutation)
return apply_commutation_thm(self, initIdx, finalIdx,
binaryPermutation, leftwardPermutation,
rightwardPermutation, assumptions)