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"""
Initial Author: Siddharth Kothiyal (sidkothiyal, https://github.com/sidkothiyal)
Other Authors:
Owner: AerospaceResearch.net
About: This module aims to create a sort of middleware module to call other modules which can handle/solve different types of equations and expressions.
This module is also responsible for performing tasks like simplification of equations/expressions, and individual functions like, addition, subtraction, multiplication and division in an equation/expression.
Communicates with polynomial roots module, to check if roots of the equation can be found.
Note: Please try to maintain proper documentation
Logic Description:
"""
import copy
from visma.functions.constant import Constant, Zero
from visma.functions.variable import Variable
from visma.functions.operator import Binary
from visma.functions.trigonometry import Trigonometric
from visma.io.checks import isEquation, getLevelVariables, getOperationsEquation, getOperationsExpression, postSimplification
from visma.io.parser import tokensToString
from visma.io.tokenize import tokenizer
from visma.simplify.addsub import addition, additionEquation, subtraction, subtractionEquation
from visma.simplify.muldiv import multiplication, multiplicationEquation, division, divisionEquation
from visma.functions.structure import Expression
def moveRTokensToLTokens(lTokens, rTokens):
"""Moves tokens in RHS to LHS
Arguments:
ltokens {list} -- LHS tokens list
rtokens {list} -- RHS tokens list
Returns:
ltokens {list} -- LHS tokens list
rtokens {list} -- RHS tokens list
"""
if len(lTokens) == 0 and len(rTokens) > 0:
return rTokens, lTokens
elif isEquation(lTokens, rTokens):
return lTokens, rTokens
elif len(lTokens) != 0:
for i, token in enumerate(rTokens):
if i == 0 and not isinstance(token, Binary):
binary = Binary()
binary.value = '-'
binary.scope = copy.copy(token.scope)
binary.scope[-1] -= 1
lTokens.append(binary)
if isinstance(token, Binary):
if token.value in ['+', '-']:
if token.value == '-':
token.value = '+'
else:
token.value = '-'
elif isinstance(token, Constant):
if token.value < 0:
if isinstance(lTokens[-1], Binary):
if lTokens[-1].value == '-':
token.value *= -1
lTokens[-1].value = '+'
elif lTokens[-1].value == '+':
token.value *= -1
lTokens[-1].value = '-'
elif isinstance(token, Variable):
if token.coefficient < 0:
if isinstance(lTokens[-1], Binary):
if lTokens[-1].value == '-':
token.coefficient *= -1
lTokens[-1].value = '+'
elif lTokens[-1].value == '+':
token.coefficient *= -1
lTokens[-1].value = '-'
lTokens.append(token)
rTokens = []
return lTokens, rTokens
def equationAnimationBuilder(lTokens, rTokens):
"""Given LHS & RHS tokens for an equation it builds the tokens of complete equation
Arguments:
lTokens {list} -- Tokens of LHS
rTokens {list} -- Tokens of RHS
Returns:
animBulder {list} -- list of tokens of complete equation
"""
animBuilder = []
lToks = copy.deepcopy(lTokens)
rToks = copy.deepcopy(rTokens)
animBuilder = lToks
lenToks = len(lToks)
equalTo = Binary()
equalTo.scope = [lenToks]
equalTo.value = '='
animBuilder.append(equalTo)
if len(rToks) == 0:
zero = Zero()
zero.scope = [lenToks + 1]
animBuilder.append(zero)
else:
animBuilder.extend(rToks)
return animBuilder
def simplifyEquation(lToks, rToks):
"""Simplifies given equation tokens
Arguments:
lToks {list} -- LHS tokens list
rToks {list} -- RHS tokens list
Returns:
lTokens {list} -- LHS tokens list
rTokens {list} -- RHS tokens list
availableOperations {list} -- list of operations
token_string {string} -- simplified result in string
animation {list} -- list of equation simplification progress
comments {list} -- list of solution steps
"""
lTokens = copy.deepcopy(lToks)
rTokens = copy.deepcopy(rToks)
animation = []
comments = []
comments += [[]]
animation.append(equationAnimationBuilder(lTokens, rTokens))
lTokens = copy.deepcopy(lToks)
rTokens = copy.deepcopy(rToks)
expressionPresent = False
for toks in lTokens:
if isinstance(toks, Expression):
expressionPresent = True
if expressionPresent:
lTokens, _, _, _, _ = expressionSimplification(lTokens, [], lTokens)
comments += [['Opening brackets in the LHS']]
animation.append(equationAnimationBuilder(lTokens, rTokens))
expressionPresent = False
for toks in rTokens:
if isinstance(toks, Expression):
expressionPresent = True
if expressionPresent:
rTokens, _, _, _, _ = expressionSimplification(rTokens, [], rTokens)
comments += [['Opening brackets in the RHS']]
animation.append(equationAnimationBuilder(lTokens, rTokens))
lVariables = []
lVariables.extend(getLevelVariables(lTokens))
rVariables = []
rVariables.extend(getLevelVariables(rTokens))
availableOperations = getOperationsEquation(lVariables, lTokens, rVariables, rTokens)
while len(availableOperations) > 0:
if '/' in availableOperations:
lTokens, rTokens, availableOperations, token_string, anim, com = divisionEquation(
lTokens, rTokens)
animation.pop(len(animation) - 1)
animation.extend(anim)
comments.extend(com)
elif '*' in availableOperations:
lTokens, rTokens, availableOperations, token_string, anim, com = multiplicationEquation(
lTokens, rTokens)
animation.pop(len(animation) - 1)
animation.extend(anim)
comments.extend(com)
elif '+' in availableOperations:
lTokens, rTokens, availableOperations, token_string, anim, com = additionEquation(
lTokens, rTokens)
animation.pop(len(animation) - 1)
animation.extend(anim)
comments.extend(com)
elif '-' in availableOperations:
lTokens, rTokens, availableOperations, token_string, anim, com = subtractionEquation(
lTokens, rTokens)
animation.pop(len(animation) - 1)
animation.extend(anim)
comments.extend(com)
lVariables = getLevelVariables(lTokens)
rVariables = getLevelVariables(rTokens)
availableOperations = getOperationsEquation(lVariables, lTokens, rVariables, rTokens)
moved = False
if len(rTokens) > 0:
moved = True
lTokens, rTokens = moveRTokensToLTokens(lTokens, rTokens)
tokenToStringBuilder = copy.deepcopy(lTokens)
lenToks = len(lTokens)
equalTo = Binary()
equalTo.scope = [lenToks]
equalTo.value = '='
tokenToStringBuilder.append(equalTo)
if len(rTokens) == 0:
zero = Zero()
zero.scope = [lenToks + 1]
tokenToStringBuilder.append(zero)
else:
tokenToStringBuilder.extend(rTokens)
if moved:
animation.append(copy.deepcopy(tokenToStringBuilder))
comments.append(['Moving the rest of variables/constants to LHS'])
token_string = tokensToString(tokenToStringBuilder)
return lTokens, rTokens, availableOperations, token_string, animation, comments
def simplify(tokens):
"""
Main simplify function which is called from driver modules
Arguments:
tokens {list} -- list of tokens
Returns:
tokens {list} -- list of simplified
availableOperations {list} -- list of operations which can be performed on a equation token
token_string {string} -- final result stored in a string
animation {list} -- list of equation solving process
comments {list} -- list of comments in equation solving process
"""
tokens_orig = copy.deepcopy(tokens)
animation = [tokens_orig]
comments = [[]]
tokens, availableOperations, token_string, anim1, comment1 = expressionSimplification(tokens_orig, [], tokens)
animation.extend(anim1)
comments.extend(comment1)
return tokens, availableOperations, token_string, animation, comments
def expressionSimplification(tokens_now, scope, tokens1):
'''Makes an input equation free from Expressions, i.e. solving each Expression recursively to convert them in other tokens.
Arguments:
tokens_now {list} -- list of original tokens as function gets called recursively
scope {list} -- integers (bounds) indicating which Expression we are currently solving
tokens1 {list} -- list of current tokens as function gets called recursively
Returns:
simToks {list} -- list of simplified tokens of each Expression
availableOperations {list} -- list of operations which can be performed on a equation token
token_string {string} -- final result stored in a string
animation {list} -- list of equation solving process
comments {list} -- list of comments in equation solving process
'''
animation = []
comments = []
pfTokens = []
i = 0
while(i < len(tokens1)):
if (i + 1 < len(tokens1)):
if isinstance(tokens1[i], Binary) and tokens1[i].value == '^':
if isinstance(tokens1[i - 1], Expression):
tokens1[i - 1].tokens, _, _, _, _ = expressionSimplification(tokens_now, scope, tokens1[i - 1].tokens)
if isinstance(tokens1[i + 1], Expression):
tokens1[i + 1].tokens, _, _, _, _ = expressionSimplification(tokens_now, scope, tokens1[i + 1].tokens)
if len(tokens1[i + 1].tokens) == 1 and isinstance(tokens1[i + 1].tokens[0], Constant):
tokens1[i + 1] = Constant(tokens1[i + 1].tokens[0].calculate(), 1, 1)
if (isinstance(tokens1[i], Binary) and tokens1[i].value == '^') and isinstance(tokens1[i + 1], Constant):
if float(tokens1[i + 1].calculate()).is_integer():
rep = int(tokens1[i + 1].calculate())
for _ in range(rep - 1):
pfTokens.extend([Binary('*'), tokens1[i - 1]])
i += 1
else:
pfTokens.append(tokens1[i])
else:
pfTokens.append(tokens1[i])
else:
pfTokens.append(tokens1[i])
i += 1
tokens1 = copy.deepcopy(pfTokens)
animation.append(pfTokens)
comments.append(['Expanding the powers of expressions'])
mulFlag = True
expressionMultiplication = False
# Check for the case: {Non-Expression} * {Expression}
for _ in range(50):
for i, _ in enumerate(tokens1):
mulFlag = False
if isinstance(tokens1[i], Expression):
if (i > 1):
if (tokens1[i - 1].value == '*'):
scope.append(i)
tokens1[i].tokens, _, _, _, _ = expressionSimplification(tokens_now, scope, tokens1[i].tokens)
if isinstance(tokens1[i - 2], Expression):
scope.append(i - 2)
tokens1[i - 2].tokens, _, _, _, _ = expressionSimplification(tokens_now, scope, tokens1[i - 2].tokens)
a = tokens1[i - 2]
b = tokens1[i]
c = a * b
mulFlag = True
expressionMultiplication = True
if isinstance(c, Expression):
scope.append(i)
c.tokens, _, _, _, _ = expressionSimplification(tokens_now, scope, c.tokens)
tokens1[i] = c
del tokens1[i - 1]
del tokens1[i - 2]
break
trigonometricError = False
# Check for the case: {Expression} * {Non-Expression}
if not trigonometricError:
for _ in range(50):
for i, _ in enumerate(tokens1):
mulFlag = False
if isinstance(tokens1[i], Expression):
if i + 2 < len(tokens1):
if (tokens1[i + 1].value == '*'):
scope.append(i)
tokens1[i].tokens, _, _, _, _ = expressionSimplification(tokens_now, scope, tokens1[i].tokens)
if isinstance(tokens1[i + 2], Expression):
scope.append(i + 2)
tokens1[i + 2].tokens, _, _, _, _ = expressionSimplification(tokens_now, scope, tokens1[i + 2].tokens)
a = tokens1[i + 2]
b = tokens1[i]
trigonometricError = False
for ec in b.tokens:
if isinstance(ec, Trigonometric):
trigonometricError = True
break
if not trigonometricError:
c = a * b
mulFlag = True
expressionMultiplication = True
if isinstance(c, Expression):
scope.append(i)
c.tokens, _, _, _, _ = expressionSimplification(tokens_now, scope, c.tokens)
tokens1[i] = c
del tokens1[i + 1]
del tokens1[i + 1]
break
if not mulFlag:
break
if expressionMultiplication:
animation.append(tokens1)
comments.append(['Multiplying expressions'])
# TODO: Implement verbose multiplication steps.
simToks = []
expressionPresent = False
for i, _ in enumerate(tokens1):
if isinstance(tokens1[i], Expression):
expressionPresent = True
scope.append(i)
newToks, _, _, _, _ = expressionSimplification(tokens_now, scope, tokens1[i].tokens)
if not simToks:
simToks.extend(newToks)
elif (simToks[len(simToks) - 1].value == '+'):
if isinstance(newToks[0], Constant):
if (newToks[0].value < 0):
simToks.pop()
simToks.extend(newToks)
elif (simToks[len(simToks) - 1].value == '-'):
for _, x in enumerate(newToks):
if x.value == '+':
x.value = '-'
elif x.value == '-':
x.value = '+'
if (isinstance(newToks[0], Constant)):
if (newToks[0].value < 0):
simToks[-1].value = '+'
newToks[0].value = abs(newToks[0].value)
elif (isinstance(newToks[0], Variable)):
if (newToks[0].coefficient < 0):
simToks[-1].value = '+'
newToks[0].coefficient = abs(newToks[0].coefficient)
simToks.extend(newToks)
else:
simToks.extend([tokens1[i]])
simToks = tokenizer(tokensToString(simToks))
if expressionPresent:
animation += [simToks]
comments += [['Opening up all the brackets']]
# TODO: Implement Trigonometric functions in the simplify module.
trigonometricError = False
for tk in simToks:
if isinstance(tk, Trigonometric):
trigonometricError = True
break
if not trigonometricError:
if scope == []:
simToks, availableOperations, token_string, animExtra, commentExtra = simplifification(simToks)
animExtra.pop(0)
animation += animExtra
comments += commentExtra
else:
availableOperations = ''
token_string = ''
else:
availableOperations = []
token_string = tokensToString(simToks)
# TODO: Implement verbose steps in simplification of Expressions (steps shown can be varied depending on length of expression)
if scope != []:
scope.pop()
return simToks, availableOperations, token_string, animation, comments
def simplifification(tokens):
"""Simplifies given expression tokens
Arguments:
tokens {list} -- tokens list
Returns:
tokens {list} -- tokens list
availableOperations {list} -- list of operations
token_string {string} -- simplified result in string
animation {list} -- list of equation simplification progress
comments {list} -- list of solution steps
"""
tokens_orig = copy.deepcopy(tokens)
animation = [tokens_orig]
variables = []
comments = []
variables.extend(getLevelVariables(tokens))
availableOperations = getOperationsExpression(variables, tokens)
while len(availableOperations) > 0:
if '/' in availableOperations:
tokens_temp = copy.deepcopy(tokens)
tokens, availableOperations, token_string, anim, com = division(
tokens_temp)
animation.pop(len(animation) - 1)
animation.extend(anim)
comments.extend(com)
elif '*' in availableOperations:
tokens_temp = copy.deepcopy(tokens)
tokens, availableOperations, token_string, anim, com = multiplication(
tokens_temp)
animation.pop(len(animation) - 1)
animation.extend(anim)
comments.extend(com)
elif '+' in availableOperations:
tokens_temp = copy.deepcopy(tokens)
tokens, availableOperations, token_string, anim, com = addition(
tokens_temp)
animation.pop(len(animation) - 1)
animation.extend(anim)
comments.extend(com)
elif '-' in availableOperations:
tokens_temp = copy.deepcopy(tokens)
tokens, availableOperations, token_string, anim, com = subtraction(
tokens_temp)
animation.pop(len(animation) - 1)
animation.extend(anim)
comments.extend(com)
tokens, animation = postSimplification(tokens, animation)
token_string = tokensToString(tokens)
return tokens, availableOperations, token_string, animation, comments
'''
def defineScopeVariable(variable, scope):
token = copy.deepcopy(variable)
local_scope = copy.deepcopy(scope)
if isinstance(token.value, list):
for j, val in enumerate(token.value):
if val.__class__ in [Binary, Variable, Constant, Expression]:
local_scope_value = copy.deepcopy(local_scope)
local_scope_value.extend(-1)
local_scope_value.extend(j)
val.scope = local_scope_value
if isinstance(token.power, list):
for j, val in enumerate(token.value):
if val.__class__ in [Binary, Variable, Constant, Expression]:
local_scope_value = copy.deepcopy(local_scope)
local_scope_value.extend(-2)
local_scope_value.extend(j)
val.scope = local_scope_value
return token
def defineScopeConstant(constant, scope):
token = copy.deepcopy(constant)
local_scope = copy.deepcopy(scope)
if isinstance(token.value, list):
for j, val in enumerate(token.value):
if val.__class__ in [Binary, Variable, Constant, Expression]:
local_scope_value = copy.deepcopy(local_scope)
local_scope_value.extend(-1)
local_scope_value.extend(j)
val.scope = local_scope_value
if isinstance(token.power, list):
for j, val in enumerate(token.value):
if val.__class__ in [Binary, Variable, Constant, Expression]:
local_scope_value = copy.deepcopy(local_scope)
local_scope_value.extend(-2)
local_scope_value.extend(j)
val.scope = local_scope_value
return token
def defineScope(tokens, scope=None):
if scope is None:
scope = []
i = 0
for token in tokens:
local_scope = copy.deepcopy(scope)
local_scope.extend(i)
token.scope = local_scope
if isinstance(token, Variable):
token = defineScopeVariable(token, copy.deepcopy(local_scope))
elif isinstance(token, Constant):
token = defineScopeConstant(token, copy.deepcopy(local_scope))
elif isinstance(token, Expression):
token.tokens = defineScope(token.tokens, local_scope)
elif isinstance(token, Binary):
pass
i += 1
return tokens
'''
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