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import copy
from visma.functions.operator import Multiply
from visma.functions.structure import Expression
from visma.functions.variable import Variable
from visma.functions.constant import Constant
from visma.io.checks import isTokenInToken, getVariables
def substitute(initTok, subsTok, toklist):
"""Substitute given token in token list
Arguments:
initTok {functions.structure.Function} -- token to be substituted
subsTok {functions.structure.Function} -- substitute token
toklist {list} -- token list
Returns:
toklist {list} -- token list
"""
for i, token in enumerate(toklist):
if isTokenInToken(initTok, token):
toklist[i] = substituteTokens(initTok, subsTok, token)
return toklist
def substituteTokens(initTok, subsTok, givenTok):
"""Substitute initTok with subsTok in a givenTok.
For example: substitute x(initTok) with wyz^2(subsTok) in xyz(givenTok)
i.e. final_tok will be wy^2z^3
Arguments:
initTok {functions.structure.Function} -- token to be substituted
subsTok {functions.structure.Function} -- substitute token
givenTok {functions.structure.Function} -- given token
Returns:
givenTok {functions.structure.Function} -- given token after substitution
"""
if isinstance(givenTok, Variable):
if isinstance(initTok, Variable):
power = getPowerRatio(initTok, givenTok)
if isinstance(subsTok, Constant):
givenTok = removeValues(initTok, givenTok)
if len(givenTok.value) == 0:
givenTok = Constant((subsTok.value**power)*givenTok.coefficient)
else:
givenTok.coefficient *= subsTok.value**power
elif isinstance(subsTok, Variable):
givenTok.coefficient /= initTok.coefficient**power
givenTok.coefficient *= subsTok.coefficient**power
givenTok = replaceValues(initTok, subsTok, givenTok, power)
elif isinstance(subsTok, Expression):
subs_copy = copy.deepcopy(subsTok)
givenTok.coefficient /= initTok.coefficient**power
givenTok.coefficient *= subs_copy.coefficient**power
subs_copy.coefficient = 1
subs_copy.power = power
givenTok = removeValues(initTok, givenTok)
if len(givenTok.value) == 0:
subs_copy.coefficient = givenTok.coefficient
givenTok = subs_copy
else:
givenTok = Expression([givenTok, Multiply(), subs_copy])
elif isinstance(givenTok, Expression):
substitute(initTok, subsTok, Expression.toklist)
return givenTok
def getPowerRatio(initTok, givenTok):
"""Returns ratio of power of given token to power of token to be substituted
Arguments:
initTok {functions.structure.Function} -- token to be substituted
givenTok {functions.structure.Function} -- given token
Returns:
ratio {float} -- ratio of givenTok.power to initTok.power
"""
if isinstance(initTok, Variable) and isinstance(givenTok, Variable):
varA = getVariables([initTok])
varB = getVariables([givenTok])
if all(var in varB for var in varA):
ratios = []
for i, valA in enumerate(initTok.value):
for j, valB in enumerate(givenTok.value):
if valA == valB:
ratios.append(givenTok.power[j]/initTok.power[i])
break
if all(ratio == ratios[0] for ratio in ratios):
return ratios[0]
return 1
def removeValues(initTok, givenTok):
"""Removes token to be substituted from given token
Arguments:
initTok {functions.structure.Function} -- token to be substituted
givenTok {functions.structure.Function} -- given token
Returns:
givenTok {functions.structure.Function} -- given token after removing initTok
"""
for valI in initTok.value:
for i, valG in enumerate(givenTok.value):
if valI == valG:
givenTok.value.pop(i)
givenTok.power.pop(i)
break
return givenTok
def replaceValues(initTok, subsTok, givenTok, poweratio):
"""Replaces a token with a substitute token
Arguments:
initTok {functions.structure.Function} -- token to be substituted
subsTok {functions.structure.Function} -- substitute token
toklist {list} -- token list
poweratio {float} -- ratio of givenTok.power to initTok.power
Returns:
givenTok {functions.structure.Function} -- given token after replacing initTok with subsTok
"""
givenTok = removeValues(initTok, givenTok)
subs_copy = copy.deepcopy(subsTok)
subs_copy.power = [powr * poweratio for powr in subs_copy.power]
for val, powr in zip(subs_copy.value, subs_copy.power):
if val in givenTok.value:
valIndex = givenTok.value.index(val)
givenTok.power[valIndex] += powr
else:
givenTok.value.append(val)
givenTok.power.append(powr)
return givenTok
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