def multiplyVariables(variable1, variable2, coeff):
variable = Variable()
variable.value = []
variable.value.extend(variable1.value)
variable.power = []
variable.power.extend(variable1.power)
if isNumber(variable1.coefficient):
variable.coefficient = float(variable1.coefficient)
elif isinstance(variable1.coefficient, Function):
variable.coefficient = evaluateConstant(variable1.coefficient)
else:
variable.coefficient = variable1.coefficient
for j, var in enumerate(variable.value):
found = False
for k, var2 in enumerate(variable2.value):
if var == var2:
if isNumber(variable.power[j]) and isNumber(variable2.power[k]):
variable.power[j] += variable2.power[k]
found = True
break
if not found:
variable.value.append(variable2.value[j])
variable.power.append(variable2.power[j])
variable.coefficient *= variable2.coefficient
variable.coefficient *= coeff
# removeScopes.append(tokens[i].scope)
# removeScopes.append(tokens[i+1].scope)
return variable
def division_variable_constant(constant, variable, coeff):
variable1 = copy.deepcopy(variable)
variable1.coefficient /= evaluateConstant(constant)
variable1.coefficient *= coeff
# removeScopes.append(tokens[i].scope)
# removeScopes.append(tokens[i-1].scope)
return variable1
def multiplyVariableConstant(constant, variable, coeff):
variable1 = Variable()
variable1.value = []
variable1.value.extend(variable.value)
variable1.power = []
variable1.power.extend(variable.power)
if isNumber(variable.coefficient):
variable1.coefficient = float(variable.coefficient)
elif isinstance(variable.coefficient, Function):
variable1.coefficient = evaluateConstant(variable.coefficient)
else:
variable.coefficient = variable1.coefficient
variable1.coefficient *= evaluateConstant(constant)
variable1.coefficient *= coeff
# removeScopes.append(tokens[i].scope)
# removeScopes.append(tokens[i-1].scope)
return variable1
def division_constantVariable(constant, variable, coeff):
variable1 = Variable()
variable1.coefficient = (evaluateConstant(
constant) / variable.coefficient) * coeff
variable1.value = []
variable1.power = []
for i, var in enumerate(variable):
variable1.value.append(var)
variable1.power.append(-variable.power[i])
return variable1
def getCoefficients(lTokens, rTokens, degree):
'''Used by root finder modules to get a list of coefficients of equation
Argument:
lTokens {list} -- list of left side tokens
rTokens {list} -- list of right side tokens
degree {int} -- degree of equation
Returns:
coeffs {list} -- list of coefficients of equation (item at ith index is coefficient of x^i)
'''
coeffs = [0] * (degree + 1)
for i, token in enumerate(lTokens):
if isinstance(token, Constant):
cons = evaluateConstant(token)
if i != 0:
if isinstance(lTokens[i - 1], Binary):
if lTokens[i - 1].value in ['-', '+']:
if lTokens[i - 1].value == '-':
cons *= -1
if (i + 1) < len(lTokens):
if lTokens[i + 1].value not in ['*', '/']:
coeffs[0] += cons
else:
return []
else:
coeffs[0] += cons
if isinstance(token, Variable):
if len(token.value) == 1:
var = token.coefficient
if i != 0:
if isinstance(lTokens[i - 1], Binary):
if lTokens[i - 1].value in ['-', '+']:
if lTokens[i - 1].value == '-':
var *= -1
if (i + 1) < len(lTokens):
if lTokens[i + 1].value not in ['*', '/']:
if token.power[0] in [1, 2, 3, 4]:
coeffs[int(token.power[0])] += var
else:
return []
else:
return []
else:
if token.power[0] in [1, 2, 3, 4]:
coeffs[int(token.power[0])] += var
else:
return []
else:
return []
return coeffs
def division_expression_constant(constant, expression, coeff):
tokens = copy.deepcopy(expression)
tokens.coefficient /= (evaluateConstant(constant))
tokens.coefficient *= coeff
return tokens
def division_constants(constant1, constant2, coeff):
no_1 = False
no_2 = False
constant = Constant()
if isNumber(constant1.value):
no_1 = True
if isNumber(constant2.value):
no_2 = True
if no_1 and no_2:
constant.value = (evaluateConstant(
constant1) / evaluateConstant(constant2)) * coeff
constant.power = 1
# removeScopes.append(tokens[i].scope)
# removeScopes.append(tokens[i-1].scope)
elif no_1 and not no_2:
constant.value = [constant1.value]
constant.power = [constant1.power]
for i, val in enumerate(constant2.value):
done = False
for j, val2 in enumerate(constant.value):
if val == val2:
constant.power[j] -= constant2.power[i]
done = True
break
if not done:
constant.value.append(val)
constant.power.append(-constant2.power[i])
constant.value.append(coeff)
constant.power.append(1)
# removeScopes.append(tokens[i].scope)
# removeScopes.append(tokens[i-1].scope)
elif not no_1 and no_2:
constant.value = constant1.value
constant.power = constant1.power
done = False
for i, val in enumerate(constant.value):
if val == constant2.value:
constant.power[i] -= constant2.power
done = True
break
if not done:
constant.value.append(constant2.value)
constant.power.append(-constant2.power)
constant.value.append(coeff)
constant.power.append(1)
# removeScopes.append(tokens[i].scope)
# removeScopes.append(tokens[i+1].scope)
elif not no_1 and not no_2:
constant.value = constant1.value
constant.power = constant1.power
for i, val in enumerate(constant2.value):
done = False
for j, val2 in enumerate(constant.value):
if val == val2:
constant.power[j] -= constant2.power[i]
done = True
break
if not done:
constant.value.append(val)
constant.power.append(-constant2.power[i])
constant.value.append(coeff)
constant.power.append(1)
# removeScopes.append(tokens[i].scope)
# removeScopes.append(tokens[i-1].scope)
return constant
def multiply_expression_constant(constant, expression, coeff):
tokens = copy.deepcopy(expression)
tokens.coefficient *= (evaluateConstant(constant) * coeff)
return tokens
def expressionDivision(variables, tokens):
removeScopes = []
comments = []
for i, token in enumerate(tokens):
if isinstance(token, Binary):
if token.value in ['/']:
prev = False
nxt = False
if i != 0:
if tokens[i - 1].__class__ in [Variable, Constant]:
prev = True
if i + 1 < len(tokens):
if tokens[i + 1].__class__ in [Variable, Constant]:
nxt = True
if nxt and prev:
if isinstance(tokens[i + 1], Constant) and isinstance(tokens[i - 1], Constant):
comments.append("Dividing " + r"$" + tokens[i - 1].__str__() + r"$" + " by " + r"$" + tokens[i + 1].__str__() + r"$")
no_1 = False
no_2 = False
if isNumber(tokens[i - 1].value):
no_1 = True
if isNumber(tokens[i + 1].value):
no_2 = True
if no_1 and no_2:
tokens[i + 1].value = evaluateConstant(
tokens[i - 1]) / evaluateConstant(tokens[i + 1])
tokens[i + 1].power = 1
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i - 1].scope)
elif no_1 and not no_2:
value = tokens[i - 1].value
power = tokens[i - 1].power
tokens[i - 1].value = [value]
tokens[i - 1].power = [power]
for val in tokens[i + 1].value:
tokens[i - 1].value.append(val)
for pows in tokens[i + 1].power:
tokens[i - 1].power.append(-pows)
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
elif not no_1 and no_2:
tokens[i - 1].value.append(tokens[i + 1].value)
tokens[i - 1].power.append(-tokens[i + 1].power)
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
elif not no_1 and not no_2:
for vals in tokens[i + 1].value:
tokens[i - 1].value.append(vals)
for pows in tokens[i + 1].power:
tokens[i - 1].power.append(pows)
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
return variables, tokens, removeScopes, comments
elif isinstance(tokens[i + 1], Variable) and isinstance(tokens[i - 1], Variable):
comments.append("Dividing " + r"$" + tokens[i - 1].__str__() + r"$" + " by " + r"$" + tokens[i + 1].__str__() + r"$")
for j, var in enumerate(tokens[i + 1].value):
found = False
for k, var2 in enumerate(tokens[i - 1].value):
tokens[i-1].coefficient /= tokens[i+1].coefficient
if var == var2:
if isNumber(tokens[i + 1].power[j]) and isNumber(tokens[i - 1].power[k]):
tokens[i - 1].power[k] -= tokens[i + 1].power[j]
if tokens[i - 1].power[k] == 0:
del tokens[i - 1].power[k]
del tokens[i - 1].value[k]
found = True
break
if not found:
tokens[i - 1].value.append(tokens[i + 1].value[j])
tokens[i - 1].power.append(-tokens[i + 1].power[j])
if len(tokens[i - 1].value) == 0:
constant = Constant()
constant.scope = tokens[i - 1].scope
constant.power = 1
constant.value = tokens[i - 1].coefficient
tokens[i - 1] = constant
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
return variables, tokens, removeScopes, comments
elif (isinstance(tokens[i + 1], Variable) and isinstance(tokens[i - 1], Constant)):
comments.append("Dividing " + r"$" + tokens[i - 1].__str__() + r"$" + " by " + r"$" + tokens[i + 1].__str__() + r"$")
val = evaluateConstant(tokens[i - 1])
scope = tokens[i - 1].scope
tokens[i - 1] = Variable()
tokens[i - 1].value = tokens[i + 1].value
tokens[i - 1].coefficient = val / \
tokens[i + 1].coefficient
tokens[i - 1].power = []
tokens[i - 1].scope = scope
for pows in tokens[i + 1].power:
tokens[i - 1].power.append(-pows)
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
return variables, tokens, removeScopes, comments
elif (isinstance(tokens[i - 1], Variable) and isinstance(tokens[i + 1], Constant)):
comments.append("Dividing " + r"$" + tokens[i - 1].__str__() + r"$" + " by " + r"$" + tokens[i + 1].__str__() + r"$")
tokens[i - 1].coefficient /= evaluateConstant(tokens[i + 1])
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
return variables, tokens, removeScopes, comments
return variables, tokens, removeScopes, comments
def expressionMultiplication(variables, tokens):
removeScopes = []
comments = []
for i, token in enumerate(tokens):
if isinstance(token, Binary):
if token.value in ['*']:
prev = False
nxt = False
if i != 0:
if tokens[i - 1].__class__ in [Variable, Constant]:
prev = True
if i + 1 < len(tokens):
if tokens[i + 1].__class__ in [Variable, Constant]:
nxt = True
if nxt and prev:
if isinstance(tokens[i + 1], Constant) and isinstance(tokens[i - 1], Constant):
comments.append("Multiplying " + r"$" + tokens[i-1].__str__() + r"$" + " and " + r"$" + tokens[i+1].__str__() + r"$")
no_1 = False
no_2 = False
if isNumber(tokens[i - 1].value):
no_1 = True
if isNumber(tokens[i + 1].value):
no_2 = True
if no_1 and no_2:
tokens[i + 1].value = evaluateConstant(
tokens[i - 1]) * evaluateConstant(tokens[i + 1])
tokens[i + 1].power = 1
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i - 1].scope)
elif no_1 and not no_2:
tokens[i + 1].value.append(tokens[i - 1].value)
tokens[i + 1].power.append(tokens[i - 1].power)
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i - 1].scope)
elif not no_1 and no_2:
tokens[i - 1].value.append(tokens[i + 1].value)
tokens[i - 1].power.append(tokens[i + 1].power)
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
elif not no_1 and not no_2:
for vals in tokens[i - 1].value:
tokens[i + 1].value.append(vals)
for pows in tokens[i - 1].power:
tokens[i + 1].power.append(pows)
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i - 1].scope)
return variables, tokens, removeScopes, comments
elif isinstance(tokens[i + 1], Variable) and isinstance(tokens[i - 1], Variable):
comments.append("Multiplying " + r"$" + tokens[i - 1].__str__() + r"$" + " and " + r"$" + tokens[i + 1].__str__() + r"$")
for j, var in enumerate(tokens[i + 1].value):
found = False
for k, var2 in enumerate(tokens[i - 1].value):
tokens[i - 1].coefficient *= tokens[i + 1].coefficient
if var == var2:
if tokens[i + 1].power[j] == tokens[i - 1].power[k]:
if isNumber(tokens[i + 1].power[j]) and isNumber(tokens[i - 1].power[k]):
tokens[i - 1].power[k] += tokens[i + 1].power[j]
found = True
break
if not found:
tokens[i - 1].value.append(tokens[i + 1].value[j])
tokens[i - 1].power.append(tokens[i + 1].power[j])
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
return variables, tokens, removeScopes, comments
elif (isinstance(tokens[i + 1], Variable) and isinstance(tokens[i - 1], Constant)):
comments.append("Multiplying " + r"$" + tokens[i - 1].__str__() + "}" + r"$" + " and " + r"$" + tokens[i + 1].__str__() + r"$")
tokens[i + 1].coefficient *= evaluateConstant(tokens[i - 1])
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i - 1].scope)
return variables, tokens, removeScopes, comments
elif (isinstance(tokens[i - 1], Variable) and isinstance(tokens[i + 1], Constant)):
comments.append("Multiplying " + r"$" + tokens[i - 1].__str__() + r"$" + " and " + r"$" + tokens[i + 1].__str__() + r"$")
tokens[i - 1].coefficient *= evaluateConstant(tokens[i + 1])
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
return variables, tokens, removeScopes, comments
return variables, tokens, removeScopes, comments
def expressionMultiplication(variables, tokens):
removeScopes = []
comments = []
for i, token in enumerate(tokens):
if isinstance(token, Binary):
if token.value in ['*']:
prev = False
nxt = False
if i != 0:
if tokens[i - 1].__class__ in [Variable, Constant]:
prev = True
if i + 1 < len(tokens):
if tokens[i + 1].__class__ in [Variable, Constant]:
nxt = True
if nxt and prev:
comments.append("Multiplying " + r"$" +
tokens[i - 1].__str__() + r"$" + " and " +
r"$" + tokens[i + 1].__str__() + r"$")
if isinstance(tokens[i + 1], Constant) and isinstance(
tokens[i - 1], Constant):
tokens[i + 1].value = evaluateConstant(
tokens[i - 1]) * evaluateConstant(tokens[i + 1])
tokens[i + 1].power = 1
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i - 1].scope)
return variables, tokens, removeScopes, comments
elif isinstance(tokens[i + 1], Variable) and isinstance(
tokens[i - 1], Variable):
for j, var in enumerate(tokens[i + 1].value):
found = False
for k, var2 in enumerate(tokens[i - 1].value):
tokens[i -
1].coefficient *= tokens[i +
1].coefficient
if var == var2:
if isNumber(
tokens[i +
1].power[j]) and isNumber(
tokens[i - 1].power[k]):
tokens[i - 1].power[k] += tokens[
i + 1].power[j]
if tokens[i - 1].power[k] == 0:
del tokens[i - 1].power[k]
del tokens[i - 1].value[k]
found = True
break
if not found:
tokens[i - 1].value.append(tokens[i +
1].value[j])
tokens[i - 1].power.append(tokens[i +
1].power[j])
if len(tokens[i - 1].value) == 0:
constant = Constant()
constant.scope = tokens[i - 1].scope
constant.power = 1
constant.value = tokens[i - 1].coefficient
tokens[i - 1] = constant
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
return variables, tokens, removeScopes, comments
elif (isinstance(tokens[i + 1], Variable)
and isinstance(tokens[i - 1], Constant)):
tokens[i + 1].coefficient *= evaluateConstant(
tokens[i - 1])
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i - 1].scope)
return variables, tokens, removeScopes, comments
elif (isinstance(tokens[i - 1], Variable)
and isinstance(tokens[i + 1], Constant)):
tokens[i - 1].coefficient *= evaluateConstant(
tokens[i + 1])
removeScopes.append(tokens[i].scope)
removeScopes.append(tokens[i + 1].scope)
return variables, tokens, removeScopes, comments
return variables, tokens, removeScopes, comments