def multiplyMatrix(matA, matB):
"""Multiplies two matrices
Arguments:
matA {visma.matrix.structure.Matrix} -- matrix token
matB {visma.matrix.structure.Matrix} -- matrix token
Returns:
matPro {visma.matrix.structure.Matrix} -- product matrix token
Note:
Make mulitplyCheck before calling multiplyMatrix
Not commutative
"""
matPro = Matrix()
matPro.empty([matA.dim[0], matB.dim[1]])
for i in range(matA.dim[0]):
for j in range(matB.dim[1]):
for k in range(matA.dim[1]):
if matPro.value[i][j] != []:
matPro.value[i][j].append(Binary('+'))
if len(matA.value[i][k]) != 1:
matPro.value[i][j].append(Expression(matA.value[i][k]))
else:
matPro.value[i][j].extend(matA.value[i][k])
matPro.value[i][j].append(Binary('*'))
if len(matB.value[k][j]) != 1:
matPro.value[i][j].append(Expression(matB.value[k][j]))
else:
matPro.value[i][j].extend(matB.value[k][j])
matPro = simplifyMatrix(matPro)
return matPro
def __mul__(self, other):
"""Multiplies two matrices
Arguments:
self {visma.matrix.structure.Matrix} -- matrix token
other {visma.matrix.structure.Matrix} -- matrix token
Returns:
matPro {visma.matrix.structure.Matrix} -- product matrix token
Note:
Make mulitplyCheck before calling multiplyMatrix
Not commutative
"""
matPro = Matrix()
matPro.empty([self.dim[0], other.dim[1]])
for i in range(self.dim[0]):
for j in range(other.dim[1]):
for k in range(self.dim[1]):
if matPro.value[i][j] != []:
matPro.value[i][j].append(Binary('+'))
if len(self.value[i][k]) != 1:
matPro.value[i][j].append(Expression(self.value[i][k]))
else:
matPro.value[i][j].extend(self.value[i][k])
matPro.value[i][j].append(Binary('*'))
if len(other.value[k][j]) != 1:
matPro.value[i][j].append(Expression(
other.value[k][j]))
else:
matPro.value[i][j].extend(other.value[k][j])
from visma.matrix.operations import simplifyMatrix
matPro = simplifyMatrix(matPro)
return matPro
def integrate(self, wrtVar=None):
from visma.functions.constant import Constant
result = copy.deepcopy(self)
log = False
for i, var in enumerate(result.value):
if var == wrtVar:
if (result.power[i] == -1):
log = True
funcLog = Logarithm()
funcLog.operand = Variable()
funcLog.operand.coefficient = 1
funcLog.operand.value.append(result.value[i])
funcLog.operand.power.append(1)
del result.power[i]
del result.value[i]
if result.value == []:
result.__class__ = Constant
result.value = result.coefficient
result.coefficient = 1
result.power = 1
result = [result]
funcJoin = Binary()
funcJoin.value = '*'
result.append(funcJoin)
result.append(funcLog)
else:
result.power[i] += 1
result.coefficient /= result.power[i]
print(result)
return result, log
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 gauss_elim(mat):
"""
Returns calculated values of unknown variables
Arguments:
mat {visma.matrix.structure.Matrix} -- matrix token
Returns:
result {visma.matrix.structure.Matrix} -- result matrix token
Note: result is a Nx1 matrix
"""
echelon = Matrix()
echelon = row_echelon(mat)
result = Matrix()
result.empty([mat.dim[0], 1])
N = mat.dim[0]
M = mat.dim[1]
index = N - 1
for i in range(N - 1, -1, -1):
sum_ = []
temp = []
if echelon.value[i][i][
0].value == 0.0: # no unique solution for this case
return -1
for j in range(i + 1, M - 1):
temp = []
temp.extend(echelon.value[i][j])
temp.append(Binary('*'))
temp.extend(result.value[j][0])
temp, _, _, _, _ = simplify(temp)
sum_.extend(temp)
if j != M - 2:
sum_.append(Binary('+'))
sum_, _, _, _, _ = simplify(sum_)
result.value[index][0].extend(echelon.value[i][M - 1])
if sum_:
if sum_[0].value < 0:
result.value[index][0].append(
Binary('-')
) # negative sign makes the negative sign in value positive
else:
result.value[index][0].append(Binary('-'))
result.value[index][0].extend(sum_)
result.value[index][0], _, _, _, _ = simplify(result.value[index][0])
result.value[index][0].append(Binary('/'))
result.value[index][0].extend(echelon.value[i][i])
result.value[index][0], _, _, _, _ = simplify(result.value[index][0])
index -= 1
return result
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 scalarDiv(const, mat):
"""Divides constant terms with Matrix
Arguments:
const {string}--- constant value
mat {visma.matrix.structure.Matrix} -- matrix token
Returns:
matRes {visma.matrix.structure.Matrix} -- result matrix token
"""
if const != 0:
matRes = Matrix()
matRes.empty([mat.dim[0], mat.dim[1]])
for i in range(mat.dim[0]):
for j in range(mat.dim[1]):
if len(mat.value[i][j]) != 1:
matRes.value[i][j].append(Expression(mat.value[i][j]))
else:
matRes.value[i][j].extend(mat.value[i][j])
matRes.value[i][j].append(Binary('/'))
matRes.value[i][j].append(Constant(int(const)))
matRes = simplifyMatrix(matRes)
return matRes
else:
logger.error("ZeroDivisionError: Cannot divide matrix by zero")
def scalarSub(const, mat):
"""
Subtracts constant terms with Matrix
Arguments:
const {string}--- constant value
mat {visma.matrix.structure.Matrix} -- matrix token
Returns:
matRes {visma.matrix.structure.Matrix} -- subtracted matrix token
Note:
This scalar addition follows the following equation
{mat} - {lambda}{identity mat}
"""
matRes = Matrix()
matRes.empty([mat.dim[0], mat.dim[1]])
for i in range(mat.dim[0]):
for j in range(mat.dim[1]):
if i != j:
matRes.value[i][j].extend(mat.value[i][j])
else:
if len(mat.value[i][j]) != 1:
matRes.value[i][j].append(Expression(mat.value[i][j]))
else:
matRes.value[i][j].extend(mat.value[i][j])
matRes.value[i][j].append(Binary('-'))
matRes.value[i][j].append(Constant(int(const)))
matRes = simplifyMatrix(matRes)
return matRes
def row_echelon(mat):
"""
Returns the row echelon form of the given matrix
Arguments:
mat {visma.matrix.structure.Matrix} -- matrix token
Returns:
row_echelon {visma.matrix.structure.Matrix} -- result matrix token
"""
N = mat.dim[0]
M = mat.dim[1]
for k in range(0, N):
if abs(mat.value[k][k][0].value) == 0.0:
if k == N - 1:
return simplifyMatrix(mat)
else:
for i in range(0, N):
t = mat.value[k][i]
mat.value[k][i] = mat.value[k + 1][i]
mat.value[k + 1][i] = t
else:
for i in range(k + 1, N):
temp = []
temp.extend(mat.value[i][k])
temp.append(Binary('/'))
temp.extend(mat.value[k][k])
temp, _, _, _, _ = simplify(temp)
for j in range(k + 1, M):
temp2 = []
temp2.extend(mat.value[k][j])
temp2.append(Binary('*'))
temp2.extend(temp)
temp2, _, _, _, _ = simplify(temp2)
mat.value[i][j].append(Binary('-'))
mat.value[i][j].extend(temp2)
mat.value[i][k].append(Binary('*'))
mat.value[i][k].append(Constant(0))
mat = simplifyMatrix(mat)
return simplifyMatrix(mat)
def multiplyExpressions(expression1, expression2):
tokens = []
tokens1 = expression1.tokens
tokens2 = expression2.tokens
coeff = expression1.coefficient * expression2.coefficient
for i, token1 in enumerate(tokens1):
# print(token1.value)
op = 1
if i != 0:
if isinstance(tokens1[i - 1], Binary):
if tokens1[i - 1].value == '+':
op *= 1
elif tokens1[i - 1].value == '-':
op *= -1
if isinstance(token1, Variable) or isinstance(token1, Constant):
for j, token2 in enumerate(tokens2):
# print(token2.value)
op2 = op
if isinstance(token2, Variable) or isinstance(token2, Constant):
if j == 0 and i == 0:
pass
else:
if j != 0:
if isinstance(tokens2[j - 1], Binary):
if tokens2[j - 1].value == '+':
op2 *= 1
elif tokens2[j - 1].value == '-':
op2 *= -1
binary = Binary()
if op2 == -1:
binary.value = '-'
elif op2 == 1:
binary.value = '+'
tokens.append(binary)
tokens.append(multiplySelect(token1, token2, coeff))
def traceMat(self):
"""Returns the trace of a square matrix (sum of diagonal elements)
Arguments:
mat {visma.matrix.structure.Matrix} -- matrix token
Returns:
trace {visma.matrix.structure.Matrix} -- string token
"""
from visma.simplify.simplify import simplify
trace = []
for i in range(self.dim[0]):
trace.extend(self.value[i][i])
trace.append(Binary('+'))
trace.append(Constant(0))
trace, _, _, _, _ = simplify(trace)
return trace
def __add__(self, other):
"""Adds two matrices
Arguments:
self {visma.matrix.structure.Matrix} -- matrix token
other {visma.matrix.structure.Matrix} -- matrix token
Returns:
matSum {visma.matrix.structure.Matrix} -- sum matrix token
Note:
Make dimCheck before calling addMatrix
"""
matSum = Matrix()
matSum.empty(self.dim)
for i in range(self.dim[0]):
for j in range(self.dim[1]):
matSum.value[i][j].extend(self.value[i][j])
matSum.value[i][j].append(Binary('+'))
matSum.value[i][j].extend(other.value[i][j])
from visma.matrix.operations import simplifyMatrix
matSum = simplifyMatrix(matSum)
return matSum
def __sub__(self, other):
"""Subtracts two matrices
Arguments:
self {visma.matrix.structure.Matrix} -- matrix token
other {visma.matrix.structure.Matrix} -- matrix token
Returns:
matSub {visma.matrix.structure.Matrix} -- subtracted matrix token
Note:
Make dimCheck before calling subMatrix
"""
matSub = Matrix()
matSub.empty(self.dim)
for i in range(self.dim[0]):
for j in range(self.dim[1]):
matSub.value[i][j].extend(self.value[i][j])
matSub.value[i][j].append(Binary('-'))
matSub.value[i][j].extend(other.value[i][j])
from visma.matrix.operations import simplifyMatrix
matSub = simplifyMatrix(matSub)
return matSub
def subMatrix(matA, matB):
"""Subtracts two matrices
Arguments:
matA {visma.matrix.structure.Matrix} -- matrix token
matB {visma.matrix.structure.Matrix} -- matrix token
Returns:
matSub {visma.matrix.structure.Matrix} -- subtracted matrix token
Note:
Make dimCheck before calling subMatrix
"""
matSub = Matrix()
matSub.empty(matA.dim)
for i in range(matA.dim[0]):
for j in range(matA.dim[1]):
matSub.value[i][j].extend(matA.value[i][j])
matSub.value[i][j].append(Binary('-'))
matSub.value[i][j].extend(matB.value[i][j])
matSub = simplifyMatrix(matSub)
return matSub
def addMatrix(matA, matB):
"""Adds two matrices
Arguments:
matA {visma.matrix.structure.Matrix} -- matrix token
matB {visma.matrix.structure.Matrix} -- matrix token
Returns:
matSum {visma.matrix.structure.Matrix} -- sum matrix token
Note:
Make dimCheck before calling addMatrix
"""
matSum = Matrix()
matSum.empty(matA.dim)
for i in range(matA.dim[0]):
for j in range(matA.dim[1]):
matSum.value[i][j].extend(matA.value[i][j])
matSum.value[i][j].append(Binary('+'))
matSum.value[i][j].extend(matB.value[i][j])
matSum = simplifyMatrix(matSum)
return matSum
def scalarMult(const, mat):
"""Multiplies constant terms with Matrix
Arguments:
const {string}--- constant value
mat {visma.matrix.structure.Matrix} -- matrix token
Returns:
matRes {visma.matrix.structure.Matrix} -- product matrix token
"""
matRes = Matrix()
matRes.empty([mat.dim[0], mat.dim[1]])
for i in range(mat.dim[0]):
for j in range(mat.dim[1]):
if len(mat.value[i][j]) != 1:
matRes.value[i][j].append(Expression(mat.value[i][j]))
else:
matRes.value[i][j].extend(mat.value[i][j])
matRes.value[i][j].append(Binary('*'))
matRes.value[i][j].append(Constant(int(const)))
matRes = simplifyMatrix(matRes)
return matRes
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
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 inverse(self):
"""Calculates the inverse of the matrix using Gauss-Jordan Elimination
Arguments:
matrix {visma.matrix.structure.Matrix} -- matrix token
Returns:
inv {visma.matrix.structure.Matrix} -- result matrix token
"""
from visma.simplify.simplify import simplify
from visma.io.tokenize import tokenizer
from visma.io.parser import tokensToString
if tokensToString(self.determinant()) == "0":
return -1
self.dim[0] = len(self.value)
self.dim[1] = len(self.value[0])
n = self.dim[0]
mat = Matrix()
mat.empty([n, 2 * n])
for i in range(0, n):
for j in range(0, 2 * n):
if j < n:
mat.value[i][j] = self.value[i][j]
else:
mat.value[i][j] = []
for i in range(0, n):
for j in range(n, 2 * n):
if j == (i + n):
mat.value[i][j].extend(tokenizer('1'))
else:
mat.value[i][j].extend(tokenizer("0"))
for i in range(n - 1, 0, -1):
if mat.value[i - 1][0][0].value < mat.value[i][0][0].value:
for j in range(0, 2 * n):
temp = mat.value[i][j]
mat.value[i][j] = mat.value[i - 1][j]
mat.value[i - 1][j] = temp
for i in range(0, n):
for j in range(0, n):
if j != i:
temp = []
if len(mat.value[j][i]) != 1:
temp.append(Expression(mat.value[j][i]))
else:
temp.extend(mat.value[j][i])
temp.append(Binary('/'))
if len(mat.value[i][i]) != 1:
temp.append(Expression(mat.value[i][i]))
else:
temp.extend(mat.value[i][i])
temp, _, _, _, _ = simplify(temp)
for k in range(0, 2 * n):
t = []
if mat.value[i][k][0].value != 0:
if len(mat.value[i][k]) != 1:
t.append(Expression(mat.value[i][k]))
else:
t.extend(mat.value[i][k])
t.append(Binary('*'))
if len(temp) != 1:
t.append(Expression(temp))
else:
t.extend(temp)
t, _, _, _, _ = simplify(t)
mat.value[j][k].append(Binary('-'))
if len(t) != 1:
mat.value[j][k].append(Expression(t))
else:
mat.value[j][k].extend(t)
mat.value[j][k], _, _, _, _ = simplify(
mat.value[j][k])
for i in range(0, n):
temp = []
temp.extend(mat.value[i][i])
for j in range(0, 2 * n):
if mat.value[i][j][0].value != 0:
mat.value[i][j].append(Binary('/'))
mat.value[i][j].extend(temp)
mat.value[i][j], _, _, _, _ = simplify(mat.value[i][j])
inv = SquareMat()
inv.empty([n, n])
for i in range(0, n):
for j in range(n, 2 * n):
inv.value[i][j - n] = mat.value[i][j]
return inv
def divisionEquation(lToks, rToks, direct=False):
lTokens = copy.deepcopy(lToks)
rTokens = copy.deepcopy(rToks)
animation = []
comments = []
if direct:
comments = [[]]
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)
animation.append(copy.deepcopy(animBuilder))
lVariables = []
lVariables.extend(getLevelVariables(lTokens))
rVariables = []
rVariables.extend(getLevelVariables(rTokens))
availableOperations = getOperationsExpression(lVariables, lTokens)
while '/' in availableOperations:
_, tok, rem, com = expressionDivision(lVariables, lTokens)
lTokens = removeToken(tok, rem)
comments.append(com)
animBuilder = copy.deepcopy(lTokens)
lenToks = len(lTokens)
equalTo = Binary()
equalTo.scope = [lenToks]
equalTo.value = '='
animBuilder.append(equalTo)
if len(rTokens) == 0:
zero = Zero()
zero.scope = [lenToks + 1]
animBuilder.append(zero)
else:
animBuilder.extend(rTokens)
animation.append(copy.deepcopy(animBuilder))
lVariables = getLevelVariables(lTokens)
availableOperations = getOperationsExpression(lVariables, lTokens)
availableOperations = getOperationsExpression(rVariables, rTokens)
while '/' in availableOperations:
_, tok, rem, com = expressionDivision(rVariables, rTokens)
rTokens = removeToken(tok, rem)
comments.append(com)
animBuilder = copy.deepcopy(lTokens)
lenToks = len(lTokens)
equalTo = Binary()
equalTo.scope = [lenToks]
equalTo.value = '='
animBuilder.append(equalTo)
if len(rTokens) == 0:
zero = Zero()
zero.scope = [lenToks + 1]
animBuilder.append(zero)
else:
animBuilder.extend(rTokens)
animation.append(copy.deepcopy(animBuilder))
rVariables = getLevelVariables(rTokens)
availableOperations = getOperationsExpression(rVariables, 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)
token_string = tokensToString(tokenToStringBuilder)
lVariables = getLevelVariables(lTokens)
rVariables = getLevelVariables(rTokens)
availableOperations = getOperationsEquation(
lVariables, lTokens, rVariables, rTokens)
return lTokens, rTokens, availableOperations, token_string, animation, comments
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
def divisionEquation(lToks, rToks, direct=False):
"""Function deals with division related operations FOR EQUATIONS (driver function in division module)
Arguments:
rtoks {list} -- list of right tokens
ltoks {list} -- list of left tokens
direct {bool} -- True when we are only concerned about multiplications terms in the input
Returns:
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
"""
lTokens = copy.deepcopy(lToks)
rTokens = copy.deepcopy(rToks)
animation = []
comments = []
if direct:
comments = [[]]
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)
animation.append(copy.deepcopy(animBuilder))
lVariables = []
lVariables.extend(getLevelVariables(lTokens))
rVariables = []
rVariables.extend(getLevelVariables(rTokens))
availableOperations = getOperationsExpression(lVariables, lTokens)
while '/' in availableOperations:
_, tok, rem, com = expressionDivision(lVariables, lTokens)
lTokens = removeToken(tok, rem)
comments.append(com)
animBuilder = copy.deepcopy(lTokens)
lenToks = len(lTokens)
equalTo = Binary()
equalTo.scope = [lenToks]
equalTo.value = '='
animBuilder.append(equalTo)
if len(rTokens) == 0:
zero = Zero()
zero.scope = [lenToks + 1]
animBuilder.append(zero)
else:
animBuilder.extend(rTokens)
animation.append(copy.deepcopy(animBuilder))
lVariables = getLevelVariables(lTokens)
availableOperations = getOperationsExpression(lVariables, lTokens)
availableOperations = getOperationsExpression(rVariables, rTokens)
while '/' in availableOperations:
_, tok, rem, com = expressionDivision(rVariables, rTokens)
rTokens = removeToken(tok, rem)
comments.append(com)
animBuilder = copy.deepcopy(lTokens)
lenToks = len(lTokens)
equalTo = Binary()
equalTo.scope = [lenToks]
equalTo.value = '='
animBuilder.append(equalTo)
if len(rTokens) == 0:
zero = Zero()
zero.scope = [lenToks + 1]
animBuilder.append(zero)
else:
animBuilder.extend(rTokens)
animation.append(copy.deepcopy(animBuilder))
rVariables = getLevelVariables(rTokens)
availableOperations = getOperationsExpression(rVariables, 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)
token_string = tokensToString(tokenToStringBuilder)
lVariables = getLevelVariables(lTokens)
rVariables = getLevelVariables(rTokens)
availableOperations = getOperationsEquation(lVariables, lTokens,
rVariables, rTokens)
return lTokens, rTokens, availableOperations, token_string, animation, comments
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 = [[]]
lVariables = []
lVariables.extend(getLevelVariables(lTokens))
rVariables = []
rVariables.extend(getLevelVariables(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)
animation.append(copy.deepcopy(animBuilder))
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 integrateTokens(funclist, wrtVar):
"""Integrates given tokens wrt given variable
Arguments:
funclist {list} -- list of funtion tokens
wrtVar {string} -- with respect to variable
Returns:
intFunc {list} -- list of integrated tokens
animNew {list} -- equation tokens for step-by-step
commentsNew {list} -- comments for step-by-step
"""
intFunc = []
animNew = []
commentsNew = [
"Integrating with respect to " + r"$" + wrtVar + r"$" + "\n"
]
for func in funclist:
if isinstance(func, Operator): # add isFuntionOf
intFunc.append(func)
else:
newfunc = []
while (isinstance(func, Function)):
commentsNew[0] += r"$" + "\int \ " + "( " + func.__str__(
) + ")" + " d" + wrtVar + r"$"
funcCopy = copy.deepcopy(func)
if wrtVar in funcCopy.functionOf():
if not isinstance(funcCopy, Constant):
for i, var in enumerate(funcCopy.value):
log = False
if var == wrtVar:
if (funcCopy.power[i] == -1):
log = True
funcLog = Logarithm()
funcLog.operand = Variable()
funcLog.operand.coefficient = 1
funcLog.operand.value.append(
funcCopy.value[i])
funcLog.operand.power.append(1)
del funcCopy.power[i]
del funcCopy.value[i]
if funcCopy.value == []:
funcCopy.__class__ = Constant
funcCopy.value = funcCopy.coefficient
funcCopy.coefficient = 1
funcCopy.power = 1
funcCopy = [funcCopy]
funcJoin = Binary()
funcJoin.value = '*'
funcCopy.append(funcJoin)
funcCopy.append(funcLog)
else:
funcCopy.power[i] += 1
funcCopy.coefficient /= funcCopy.power[i]
if log:
commentsNew[0] += r"$" + "= " + funcCopy[0].__str__(
) + "*" + funcCopy[2].__str__() + "\ ;\ " + r"$"
newfunc.extend(funcCopy)
else:
commentsNew[0] += r"$" + "= " + funcCopy.__str__(
) + "\ ;\ " + r"$"
newfunc.append(funcCopy)
else:
if isinstance(funcCopy, Variable):
funcCopy.value.append(wrtVar)
funcCopy.power.append(1)
if isinstance(funcCopy, Constant):
coeff = funcCopy.value
funcCopy = Variable()
funcCopy.coefficient = coeff
funcCopy.value.append(wrtVar)
funcCopy.power.append(1)
newfunc.append(funcCopy)
commentsNew[0] += r"$" + "= " + funcCopy.__str__(
) + "\ ;\ " + r"$"
if func.operand is None:
break
else:
func = func.operand
if isinstance(func, Constant):
intFunc = Zero()
break
intFunc.extend(newfunc)
animNew.extend(intFunc)
return intFunc, animNew, commentsNew