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Merge pull request #38 from 8hantanu/master
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Round-off error fixed and complex roots simplified
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@sidkothiyal
sidkothiyal authored Mar 5, 2018
2 parents 6736d6a + 6c74ab8 commit 6b21ad7
Showing 1 changed file with 37 additions and 34 deletions.
71 changes: 37 additions & 34 deletions find_roots.py
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Original file line number Diff line number Diff line change
@@ -1,17 +1,20 @@
"""
Initial Author: Siddharth Kothiyal (sidkothiyal, https://github.com/sidkothiyal)
Other Authors:
Other Authors:
Owner: AerospaceResearch.net
About: This module is aimed at first checking if quadratic roots can be found for the given equation, and then in the next step find the quadratic roots and
display them.
About: This module is aimed at first checking if quadratic roots can be found for the given equation, and then in the next step find the quadratic roots and display them.
Note: Please try to maintain proper documentation
Logic Description:
"""

from __future__ import division
import solve
import math
import copy

ROUND_OFF = 3

def avaiable_variables(tokens):
variables = []
for token in tokens:
Expand All @@ -20,7 +23,7 @@ def avaiable_variables(tokens):
if val not in variables:
variables.append(val)
return variables

def highest_power(tokens, variable):
maxPow = 0
for token in tokens:
Expand All @@ -34,7 +37,7 @@ def highest_power(tokens, variable):
def preprocess_check_quadratic_roots(lTokens, rTokens):
lTokens, rTokens, avaiableOperations, token_string, animation, comments = solve.simplify_equation(lTokens, rTokens)
return check_for_quadratic_roots(lTokens, rTokens)

def check_for_quadratic_roots(lTokens, rTokens):
lVariables = avaiable_variables(lTokens)
rVariables = avaiable_variables(rTokens)
Expand All @@ -46,40 +49,40 @@ def check_for_quadratic_roots(lTokens, rTokens):
if token["type"] == 'binary':
if token["value"] in ['*', '/']:
return False

if len(lVariables) == 1 and len(rVariables) == 1:
if lVariables[0] == rVariables[0]:
if highest_power(lTokens, lVariables[0]) == 2 or highest_power(rTokens, rVariables[0]) == 2:
return True
return True
elif len(lVariables) == 1 and len(rVariables) == 0:
if highest_power(lTokens, lVariables[0]) == 2:
return True

elif len(lVariables) == 0 and len(rVariables) == 1:
if highest_power(lTokens, lVariables[0]) == 2:
return True

return False

def get_roots(coeffs):
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])))
roots.append(-(coeffs[1]/(2 * coeffs[2])))
elif d > 0:
d = math.sqrt(d)
roots.append(-(coeffs[1] + d)/(2*coeffs[2]))
roots.append(-(coeffs[1] - d)/(2*coeffs[2]))
else:
imaginary = [-(coeffs[1]/(2 * coeffs[2])), d, (2 * coeffs[2])]
imaginary = [-(coeffs[1]/(2 * coeffs[2])), -1, (math.sqrt(-d))/(2 * coeffs[2])]
roots = imaginary
return roots

def quadratic_roots(lTokens, rTokens):
lTokens, rTokens, availableOperations, token_string, animation, comments = solve.simplify_equation(lTokens, rTokens)
roots, var = find_quadratic_roots(lTokens, rTokens)
if len(roots) == 1:
if len(roots) == 1:
tokens = []
expression = {}
expression["type"] = 'expression'
Expand All @@ -97,11 +100,11 @@ def quadratic_roots(lTokens, rTokens):
roots[0] *= -1
binary["value"] = '+'
else:
binary["value"] = '-'
binary["value"] = '-'
tokens.append(binary)
constant = {}
constant["type"] = 'constant'
constant["value"] = math.ceil(roots[0]*100)/100
constant["value"] = round(roots[0],ROUND_OFF)
constant["power"] = 1
tokens.append(constant)
expression["tokens"] = tokens
Expand All @@ -125,11 +128,11 @@ def quadratic_roots(lTokens, rTokens):
roots[0] *= -1
binary["value"] = '+'
else:
binary["value"] = '-'
binary["value"] = '-'
tokens.append(binary)
constant = {}
constant["type"] = 'constant'
constant["value"] = math.ceil(roots[0]*100)/100
constant["value"] = round(roots[0],ROUND_OFF)
constant["power"] = 1
tokens.append(constant)
expression["tokens"] = tokens
Expand All @@ -151,11 +154,11 @@ def quadratic_roots(lTokens, rTokens):
roots[1] *= -1
binary2["value"] = '+'
else:
binary2["value"] = '-'
binary2["value"] = '-'
tokens2.append(binary2)
constant2 = {}
constant2["type"] = 'constant'
constant2["value"] = math.ceil(roots[1]*100)/100
constant2["value"] = round(roots[1],ROUND_OFF)
constant2["power"] = 1
tokens2.append(constant2)
expression2["tokens"] = tokens2
Expand All @@ -164,24 +167,24 @@ def quadratic_roots(lTokens, rTokens):
binary3["type"] = 'binary'
binary3["value"] = '*'
lTokens = [expression, binary3, expression2]

elif len(roots) == 3:
sqrtPow = {}
sqrtPow["type"] = 'constant'
sqrtPow["value"] = 2
sqrtPow["power"] = 1

binary4 = {}
binary4["type"] = 'binary'
if roots[0] < 0:
roots[0] *= -1
binary4["value"] = '+'
else:
binary4["value"] = '-'

constant3 = {}
constant3["type"] = 'constant'
constant3["value"] = roots[0]
constant3["value"] = round(roots[0],ROUND_OFF)
constant3["power"] = 1

binary5 = {}
Expand All @@ -190,7 +193,7 @@ def quadratic_roots(lTokens, rTokens):

constant2 = {}
constant2["type"] = 'constant'
constant2["value"] = 1/roots[2]
constant2["value"] = round(roots[2],ROUND_OFF)
constant2["power"] = 1

tokens = []
Expand All @@ -214,12 +217,12 @@ def quadratic_roots(lTokens, rTokens):
tokens.append(binary5)
constant = {}
constant["type"] = 'constant'
constant["value"] = math.ceil(roots[1]*100)/100
constant["value"] = round(roots[1],ROUND_OFF)
constant["power"] = 1
sqrt = {}
sqrt["type"] = 'sqrt'
sqrt["power"] = sqrtPow
sqrt["expression"] = constant
sqrt["expression"] = constant
tokens.append(sqrt)
expression["tokens"] = tokens

Expand All @@ -238,7 +241,7 @@ def quadratic_roots(lTokens, rTokens):
tokens2.append(constant3)
binary2 = {}
binary2["type"] = 'binary'
binary2["value"] = '-'
binary2["value"] = '-'
tokens2.append(binary2)
tokens2.append(constant2)
tokens2.append(binary5)
Expand All @@ -249,12 +252,12 @@ def quadratic_roots(lTokens, rTokens):
binary3["type"] = 'binary'
binary3["value"] = '*'
lTokens = [expression, binary3, expression2]

zero = {}
zero["type"] = 'constant'
zero["value"] = 0
zero["power"] = 1
rTokens = [zero]
rTokens = [zero]
comments.append([])
tokenToStringBuilder = copy.deepcopy(lTokens)
l = len(lTokens)
Expand All @@ -268,7 +271,7 @@ def quadratic_roots(lTokens, rTokens):
tokenToStringBuilder.append(zero)
else:
tokenToStringBuilder.extend(rTokens)
animation.append(copy.deepcopy(tokenToStringBuilder))
animation.append(copy.deepcopy(tokenToStringBuilder))
token_string = solve.tokens_to_string(tokenToStringBuilder)
return lTokens, rTokens, [], token_string, animation, comments

Expand All @@ -291,7 +294,7 @@ def find_quadratic_roots(lTokens, rTokens):
else:
return roots
else:
coeffs[0] += cons
coeffs[0] += cons
if token["type"] == 'variable':
if len(token["value"]) == 1:
var = token["coefficient"]
Expand All @@ -305,18 +308,18 @@ def find_quadratic_roots(lTokens, rTokens):
if token["power"][0] == 1 or token["power"][0] == 2:
coeffs[int(token["power"][0])] += var
else:
return roots
return roots
else:
return roots
else:
if token["power"][0] == 1 or token["power"][0] == 2:
coeffs[int(token["power"][0])] += var
else:
return roots
return roots
else:
return roots

return get_roots(coeffs), avaiable_variables(lTokens)
return get_roots(coeffs), avaiable_variables(lTokens)

if __name__ == '__main__':
pass

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