def calculate(self):
from visma.functions.constant import Constant
if isinstance(self.power, int) or isinstance(
self.power, float) or isinstance(self.power, Constant):
const = Constant()
if isinstance(self.power, Constant):
self.power = self.power.calculate()
const.value = self.coefficient * (self.base**self.power)
return const
else:
return self
def __mul__(self, other):
from visma.io.checks import isNumber
from visma.functions.constant import Constant
if isinstance(other, Variable):
for j, var in enumerate(other.value):
found = False
for k, var2 in enumerate(self.value):
self.coefficient *= other.coefficient
if var == var2:
if isNumber(other.power[j]) and isNumber(
self.power[k]):
self.power[k] += other.power[j]
if self.power[k] == 0:
del self.power[k]
del self.value[k]
found = True
break
if not found:
self.value.append(other.value[j])
self.power.append(other.power[j])
if len(self.value) == 0:
result = Constant(self.coefficient)
result.scope = self.scope
result.power = 1
result.value = self.coefficient
self = result
return self
elif isinstance(other, Constant):
self.coefficient *= other.calculate()
return self
elif isinstance(other, Expression):
result = Expression()
for _, token in enumerate(other.tokens):
if isinstance(token, Variable) or isinstance(token, Constant):
c = copy.deepcopy(self)
result.tokens.extend([c * token])
else:
result.tokens.extend([token])
return result
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 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:
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
def getLevelVariables(tokens):
"""Returns tokens of Function class from a list of function tokens
Arguments:
tokens {list} -- list of function tokens
Returns:
variables {list} -- list of tokens of Function class(Variable/Constant)
"""
variables = []
for i, term in enumerate(tokens):
if isinstance(term, Variable):
skip = False
for var in variables:
if var.value == term.value and var.power[0] == term.power:
var.power.append(term.power)
var.scope.append(term.scope)
var.coefficient.append(term.coefficient)
if i != 0 and isinstance(tokens[i - 1], Binary):
var.before.append(tokens[i - 1].value)
var.beforeScope.append(tokens[i - 1].scope)
else:
var.before.append('')
var.beforeScope.append('')
if i + 1 < len(tokens) and isinstance(tokens[i + 1], Binary):
var.after.append(tokens[i + 1].value)
var.afterScope.append(tokens[i + 1].scope)
else:
var.after.append('')
var.afterScope.append('')
skip = True
break
if not skip:
variable = Variable()
variable.value = term.value
variable.scope = [term.scope]
variable.power = []
variable.coefficient = []
variable.before = []
variable.beforeScope = []
variable.after = []
variable.afterScope = []
variable.power.append(term.power)
variable.coefficient.append(term.coefficient)
if i != 0 and isinstance(tokens[i - 1], Binary):
variable.before.append(tokens[i - 1].value)
variable.beforeScope.append(tokens[i - 1].scope)
else:
variable.before.append('')
variable.beforeScope.append('')
if i + 1 < len(tokens) and isinstance(tokens[i + 1], Binary):
variable.after.append(tokens[i + 1].value)
variable.afterScope.append(tokens[i + 1].scope)
else:
variable.after.append('')
variable.afterScope.append('')
variables.append(variable)
elif isinstance(term, Constant):
skip = False
for var in variables:
if isinstance(var.value, list) and isNumber(var.value[0]):
if var.power[0] == term.power:
var.value.append(term.value)
var.power.append(term.power)
var.scope.append(term.scope)
if i != 0 and isinstance(tokens[i - 1], Binary):
var.before.append(tokens[i - 1].value)
var.beforeScope.append(tokens[i - 1].scope)
else:
var.before.append('')
var.beforeScope.append('')
if i + 1 < len(tokens) and isinstance(tokens[i + 1], Binary):
var.after.append(tokens[i + 1].value)
var.afterScope.append(tokens[i + 1].scope)
else:
var.after.append('')
var.afterScope.append('')
skip = True
break
if not skip:
variable = Constant()
variable.power = []
if isinstance(term.value, list):
variable.value = [evaluateConstant(term)]
variable.power.append(1)
else:
variable.value = [term.value]
variable.power.append(term.power)
variable.scope = [term.scope]
variable.before = []
variable.beforeScope = []
variable.after = []
variable.afterScope = []
if i != 0 and isinstance(tokens[i - 1], Binary):
variable.before.append(tokens[i - 1].value)
variable.beforeScope.append(tokens[i - 1].scope)
else:
variable.before.append('')
variable.beforeScope.append('')
if i + 1 < len(tokens) and isinstance(tokens[i + 1], Binary):
variable.after.append(tokens[i + 1].value)
variable.afterScope.append(tokens[i + 1].scope)
else:
variable.after.append('')
variable.afterScope.append('')
variables.append(variable)
elif isinstance(term, Expression):
var = getLevelVariables(term.tokens)
retType, val = extractExpression(var)
if retType == "expression":
variable = Expression()
variable.value = val
variable.tokens = term.tokens
variables.append(variable)
elif retType == "constant":
skip = False
for var in variables:
if isinstance(var.value, list) and isNumber(var.value[0]):
if var.power == val.power:
var.value.append(val.value)
var.power.append(val.power)
var.scope.append(val.scope)
var.before.append(val.before)
var.beforeScope.append(val.beforeScope)
var.after.append(val.after)
var.afterScope.append(val.afterScope)
skip = True
break
if not skip:
var = Constant()
var.value = [val.value]
var.power = [val.power]
var.scope = [val.scope]
var.before = [val.before]
var.beforeScope = [val.beforeScope]
var.after = []
var.afterScope = ['']
variables.append(var)
elif retType == "variable":
skip = False
for var in variables:
if var.value == val.value:
var.power.append(val.power)
var.before.append('')
var.beforeScope.append('')
var.after.append('')
var.afterScope.append('')
var.coefficient.append(val.coefficient)
var.scope.append(val.scope)
skip = True
break
if not skip:
var = Constant()
var.coefficient = [val.coefficient]
var.value = val.value
var.power = [val.power]
var.scope = [val.scope]
var.before = ['']
var.beforeScope = ['']
var.after = ['']
var.afterScope = ['']
variables.append(var)
elif retType == "mixed":
for v in val:
if isinstance(v, Variable):
skip = False
for var in variables:
if var.value == v.value:
var.power.extend(v.power)
var.before.extend(v.before)
var.beforeScope.extend(v.beforeScope)
var.after.extend(v.after)
var.afterScope.extend(v.afterScope)
var.coefficient.extend(v.coefficient)
var.scope.extend(v.scope)
skip = True
break
if not skip:
var = Constant()
var.coefficient = [v.coefficient]
var.value = v.value
var.power = [v.power]
var.scope = [v.scope]
var.before = [v.before]
var.beforeScope = [v.beforeScope]
var.after = [v.after]
var.afterScope = [v.afterScope]
variables.append(var)
elif isinstance(v, Constant):
for var in variables:
if isinstance(var.value, list) and isNumber(var.value[0]):
if var.power == v.power:
var.value.extend(v.value)
var.power.extend(v.power)
var.before.extend(v.before)
var.beforeScope.extend(
v.beforeScope)
var.after.extend(v.after)
var.afterScope.extend(v.afterScope)
var.coefficient.extend(v.coefficient)
var.scope.extend(v.scope)
skip = True
break
if not skip:
var = Constant()
var.coefficient = [v.coefficient]
var.value = [v.value]
var.power = [v.power]
var.scope = [v.scope]
var.before = [v.before]
var.beforeScope = [v.beforeScope]
var.after = [v.after]
var.afterScope = [v.afterScope]
variables.append(var)
elif isinstance(v, Expression):
variables.append(v)
return variables
def cubicRoots(lTokens, rTokens):
'''Used to get roots of a cubic equation
This functions also translates roots {list} into final result of solution
Argument:
lTokens {list} -- list of LHS tokens
rTokens {list} -- list of RHS tokens
Returns:
lTokens {list} -- list of LHS tokens
rTokens {list} -- list of RHS tokens
{empty list}
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
'''
from visma.solvers.polynomial.roots import getCoefficients
animations = []
comments = []
lTokens, rTokens, _, token_string, animNew1, commentNew1 = simplifyEquation(
lTokens, rTokens)
animations.extend(animNew1)
comments.extend(commentNew1)
if len(rTokens) > 0:
lTokens, rTokens = moveRTokensToLTokens(lTokens, rTokens)
coeffs = getCoefficients(lTokens, rTokens, 3)
var = getVariables(lTokens)
roots, animNew2, commentNew2 = getRootsCubic(coeffs)
animations.extend(animNew2)
comments.extend(commentNew2)
tokens1 = []
expression1 = Expression(coefficient=1, power=3)
variable = Variable(1, var[0], 1)
tokens1.append(variable)
if roots[0][1] == 0:
binary = Binary()
if roots[0][0] < 0:
roots[0][0] *= -1
binary.value = '+'
else:
binary.value = '-'
tokens1.append(binary)
constant = Constant(round(roots[0][0], ROUNDOFF), 1)
tokens1.append(constant)
expression1.tokens = tokens1
lTokens = [expression1, Binary('*')]
if len(roots) > 1:
expression1.power = 1
for _, root in enumerate(roots[1:]):
tokens2 = []
expression2 = Expression(coefficient=1, power=1)
variable = Variable(1, var[0], 1)
tokens2.append(variable)
binary = Binary()
if root[1] == 0:
if root[0] < 0:
root[0] *= -1
binary.value = '+'
else:
binary.value = '-'
tokens2.append(binary)
constant = Constant(round(root[0], ROUNDOFF), 1)
tokens2.append(constant)
else:
binary.value = '-'
tokens2.append(binary)
expressionResult = Expression(coefficient=1, power=1)
tokensResult = []
real = Constant(round(root[0], ROUNDOFF), 1)
tokensResult.append(real)
imaginary = Constant(round(root[1], ROUNDOFF), 1)
if imaginary.value < 0:
tokensResult.append(Minus())
imaginary.value = abs(imaginary.value)
tokensResult.append(imaginary)
else:
tokensResult.extend([Plus(), imaginary])
sqrt = Sqrt(Constant(2, 1), Constant(-1, 1))
tokensResult.append(Binary('*'))
tokensResult.append(sqrt)
expressionResult.tokens = tokensResult
tokens2.append(expressionResult)
expression2.tokens = tokens2
lTokens.extend([expression2, Binary('*')])
lTokens.pop()
rTokens = [Zero()]
tokenToStringBuilder = copy.deepcopy(lTokens)
tokLen = len(lTokens)
equalTo = Binary()
equalTo.scope = [tokLen]
equalTo.value = '='
tokenToStringBuilder.append(equalTo)
tokenToStringBuilder.extend(rTokens)
token_string = tokensToString(tokenToStringBuilder)
animations.append(copy.deepcopy(tokenToStringBuilder))
comments.append([])
return lTokens, rTokens, [], token_string, animations, comments
