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"""
Initial Author: Siddharth Kothiyal (sidkothiyal, https://github.com/sidkothiyal)
Other Authors:
Owner: AerospaceResearch.net
About: This module hosts the functions used for finding roots of a quartic equation
Note: Please try to maintain proper documentation
Logic Description:
"""
import math
import copy
from visma.io.checks import getVariables
from visma.io.parser import tokensToString
from visma.functions.structure import Expression
from visma.functions.constant import Constant, Zero
from visma.functions.variable import Variable
from visma.functions.operator import Binary, Sqrt
from visma.simplify.simplify import simplifyEquation, moveRTokensToLTokens
from visma.config.values import ROUNDOFF
# FIXME: Extend to polynomials of all degrees
def getRootsQuadratic(coeffs):
'''Applies Quadratic Formula (https://en.wikipedia.org/wiki/Quadratic_formula) on the coefficients
of the quadratic equation
Arguments:
coeffs {list} -- list of coefficients of the quadratic equation
Returns:
roots {list} -- list of roots of quadratic equation
'''
animations = []
comments = []
roots = []
if len(coeffs) == 3:
d = (coeffs[1] * coeffs[1]) - (4 * coeffs[0] * coeffs[2])
if d == 0:
roots.append(-(coeffs[1] / (2 * coeffs[2])))
animations += [[]]
comments += [['Value of determinant is: ' + str(d) + ' thus, Only one roots']]
elif d > 0:
d = math.sqrt(d)
roots.append(-(coeffs[1] + d) / (2 * coeffs[2]))
roots.append(-(coeffs[1] - d) / (2 * coeffs[2]))
animations += [[]]
comments += [['Value of determinant is: ' + str(d) + ' thus, two (real) roots']]
else:
imaginary = [-(coeffs[1] / (2 * coeffs[2])), -1,
(math.sqrt(-d)) / (2 * coeffs[2])]
roots = imaginary
animations += [[]]
comments += [['Value of determinant is: ' + str(d) + ' thus, two (imaginary) roots']]
return roots, animations, comments
def quadraticRoots(lTokens, rTokens):
'''Used to get quadratic roots of an equation
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, 2)
var = getVariables(lTokens)
roots, animNew2, commentNew2 = getRootsQuadratic(coeffs)
animations.extend(animNew2)
comments.extend(commentNew2)
if len(roots) == 1:
tokens = []
expression = Expression(coefficient=1, power=2)
variable = Variable(1, var[0], 1)
tokens.append(variable)
binary = Binary()
if roots[0] < 0:
roots[0] *= -1
binary.value = '+'
else:
binary.value = '-'
tokens.append(binary)
constant = Constant(round(roots[0], ROUNDOFF), 1)
tokens.append(constant)
expression.tokens = tokens
lTokens = [expression]
elif len(roots) == 2:
tokens = []
expression = Expression(coefficient=1, power=1)
variable = Variable(1, var[0], 1)
tokens.append(variable)
binary = Binary()
if roots[0] < 0:
roots[0] *= -1
binary.value = '+'
else:
binary.value = '-'
tokens.append(binary)
constant = Constant(round(roots[0], ROUNDOFF), 1)
tokens.append(constant)
expression.tokens = tokens
tokens2 = []
expression2 = Expression(coefficient=1, power=1)
tokens2.append(variable)
binary2 = Binary()
if roots[1] < 0:
roots[1] *= -1
binary2.value = '+'
else:
binary2.value = '-'
tokens2.append(binary2)
constant2 = Constant(round(roots[1], ROUNDOFF), 1)
tokens2.append(constant2)
expression2.tokens = tokens2
binary3 = Binary()
binary3.value = '*'
lTokens = [expression, binary3, expression2]
elif len(roots) == 3:
binary4 = Binary()
if roots[0] < 0:
roots[0] *= -1
binary4.value = '+'
else:
binary4.value = '-'
constant3 = Constant(round(roots[0], ROUNDOFF), 1)
binary5 = Binary()
binary5.value = '*'
constant2 = Constant(round(roots[2], ROUNDOFF), 1)
tokens = []
expression = Expression(coefficient=1, power=1)
variable = Variable(1, var[0], 1)
tokens.extend([variable, binary4, constant3])
binary = Binary()
binary.value = '+'
tokens.extend([binary, constant2, binary5])
constant = Constant(round(roots[1], ROUNDOFF), 1)
sqrt = Sqrt(Constant(2, 1), constant)
tokens.append(sqrt)
expression.tokens = tokens
tokens2 = []
expression2 = Expression(coefficient=1, power=1)
variable2 = Variable(1, var[0], 1)
tokens2.extend([variable2, binary4, constant3])
binary2 = Binary()
binary2.value = '-'
tokens2.extend([binary2, constant2, binary5, sqrt])
expression2.tokens = tokens2
binary3 = Binary()
binary3.value = '*'
lTokens = [expression, binary3, expression2]
zero = Zero()
rTokens = [zero]
comments.append([])
tokenToStringBuilder = copy.deepcopy(lTokens)
tokLen = len(lTokens)
equalTo = Binary()
equalTo.scope = [tokLen]
equalTo.value = '='
tokenToStringBuilder.append(equalTo)
tokenToStringBuilder.extend(rTokens)
animations.append(copy.deepcopy(tokenToStringBuilder))
token_string = tokensToString(tokenToStringBuilder)
return lTokens, rTokens, [], token_string, animations, comments
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