def tan_simplify(son1, son2):
if son1.value == '0.0':
return Node('0.0')
if (son1.value == '/' and son1.son1.value == 'pi'
and get_float_number_str_or_input_str(son1.son2.value) == '4.0'):
return Node('1.0')
return Node('tan', son1=son1)
def sin_simplify(son1, son2):
if (son1.value == '/' and son1.son1.value == 'pi'
and get_float_number_str_or_input_str(son1.son2.value) == '2.0'):
return Node('1.0')
if son1.value in ({'0.0'} | {'pi'}):
return Node('0.0')
return Node('sin', son1=son1)
def arcsin_simplify(son1, son2):
if son1.value == '0.0':
return Node('0.0')
if son1.value == '1.0':
return Node('pi/2', is_complex=True)
if son1.value == '-1.0':
return Node('3pi/2', is_complex=True)
return Node('arcsin', son1=son1)
def unary_minus_simplify(son1, son2):
if son1.value == '0.0':
return Node('0')
if is_number(son1.value):
return Node(str(-float(son1.value)))
cnt = 1
while son1.value == 'neg':
cnt += 1
son1 = son1.son1
return Node('neg', son1=son1, is_complex=True) if cnt % 2 != 0 else son1
def div_simplify(son1, son2):
if is_number(son1.value) and is_number(son2.value):
return Node(
str(get_truncated_value(float(son1.value) / float(son2.value), 7)))
if son2.value == '1.0':
return son1
if son1.value == '0.0':
return Node('0.0')
if son1.value == son2.value:
return Node('1.0')
return Node('/', son1=son1, son2=son2, is_complex=True)
def binary_plus_simplify(son1, son2):
if is_number(son1.value) and is_number(son2.value):
return Node(
str(get_truncated_value(float(son1.value) + float(son2.value), 7)))
if son1.value == '0.0':
return son2
if son2.value == '0.0':
return son1
return _deep_simplify_for_minus_and_plus('+', son1, son2)
def mult_simplify(son1, son2):
if is_number(son1.value) and is_number(son2.value):
return Node(
str(get_truncated_value(float(son1.value) * float(son2.value), 7)))
if son1.value == '0.0' or son2.value == '0.0':
return Node('0')
if son1.value == '1.0':
return son2
if son2.value == '1.0':
return son1
if son2.value == 'neg' and is_number(son1.value):
return mult_simplify(
Node(str(get_truncated_value(float(son1.value) * -1.0, 7))),
son2.son1)
if son1.value == 'neg' and is_number(son2.value):
return mult_simplify(
Node(str(get_truncated_value(float(son2.value) * -1.0, 7))),
son1.son1)
if (is_number(son1.value) and son2.value == '*'
and is_number(son2.son1.value)):
return mult_simplify(
Node(
str(
get_truncated_value(
float(son1.value) * float(son2.son1.value), 7))),
son2.son2)
if (is_number(son2.value) and son1.value == '*'
and is_number(son1.son1.value)):
return mult_simplify(
Node(
str(
get_truncated_value(
float(son2.value) * float(son1.son1.value), 7))))
if son1.value == '-1.0':
return Node('neg', son2)
if is_number(son2.value):
return Node('*', son1=son2, son2=son1, is_complex=True)
return Node('*', son1=son1, son2=son2, is_complex=True)
def arctan_simplify(son1, son2):
if son1.value == '0.0':
return Node('0.0')
if son1.value == '1.0':
return Node('pi/4', is_complex=True)
return Node('arctan', son1=son1)
def ln_simplify(son1, son2):
if son1.value == 'e':
return Node('1.0')
return Node('ln', son1=son1)
def lg_simplify(son1, son2):
if son1.value == '10.0':
return Node('1.0')
return Node('lg', son1=son1)
def _deep_simplify_for_minus_and_plus(operation, son1, son2):
bfs_arr = [(son1, 0)]
if operation == '-':
bfs_arr.append((son2, 1))
else:
bfs_arr.append((son2, 0))
nodes_to_sum = []
n = 2
i = 0
while i < n:
cur_node = bfs_arr[i][0]
cur_sign = bfs_arr[i][1]
if not is_operator(cur_node.value) and not cur_node.is_complex:
nodes_to_sum.append((cur_node, cur_sign))
elif cur_node.value != '+' and cur_node.value != '-':
if cur_node.value == 'neg':
cur_sign += 1
nodes_to_sum.append((cur_node, cur_sign))
else:
bfs_arr.append((cur_node.son1, cur_sign))
if cur_node.value == '-':
bfs_arr.append((cur_node.son2, cur_sign + 1))
else:
bfs_arr.append((cur_node.son2, cur_sign))
n += 2
i += 1
res_node = None
plus_dict = {'number': 0.0}
for cur_tuple in nodes_to_sum:
cur_node = cur_tuple[0]
cur_sign = float(pow(-1, cur_tuple[1]))
if (cur_node.value == '*' and (is_number(cur_node.son1.value)
and not is_number(cur_node.son2.value)
and not is_operator(cur_node.son2.value)
and not cur_node.son2.is_complex)):
coef = float(cur_node.son1.value) * cur_sign
if cur_node.son2.value in plus_dict.keys():
plus_dict[cur_node.son2.value] += coef
else:
plus_dict[cur_node.son2.value] = coef
elif not is_operator(cur_node.value) and not cur_node.is_complex:
if is_number(cur_node.value):
plus_dict['number'] = get_truncated_value(
plus_dict['number'] + float(cur_node.value) * cur_sign, 7)
elif cur_node.value in plus_dict.keys():
plus_dict[cur_node.value] += cur_sign
else:
plus_dict[cur_node.value] = cur_sign
else:
if cur_node.value == 'neg':
cur_node = cur_node.son1
if res_node is None:
if cur_sign < 0:
res_node = Node('neg', cur_node)
else:
res_node = cur_node
else:
if cur_sign < 0:
res_node = Node('-',
son1=res_node,
son2=cur_node,
is_complex=True)
else:
res_node = Node('+',
son1=res_node,
son2=cur_node,
is_complex=True)
if plus_dict['number'] != 0.0:
if res_node is not None:
if plus_dict['number'] < 0:
res_node = Node('-', res_node, Node(str(-plus_dict['number'])))
else:
res_node = Node('+', res_node, Node(str(plus_dict['number'])))
else:
res_node = Node(str(plus_dict['number']))
for x in plus_dict.keys():
if x != 'number':
if res_node is not None:
if plus_dict[x] < 0:
res_node = Node(
'-', res_node,
mult_simplify(Node(str(-plus_dict[x])), Node(x)))
else:
res_node = Node(
'+', res_node,
mult_simplify(Node(str(plus_dict[x])), Node(x)))
else:
if plus_dict[x] < 0:
res_node = Node(
'neg', mult_simplify(Node(str(plus_dict[x])), Node(x)))
else:
res_node = mult_simplify(Node(str(plus_dict[x])), Node(x))
res_node.is_complex = True
return res_node
def pow_simplify(son1, son2):
if son2.value == '0.0' or son1.value == '1.0':
return Node('1.0')
if son2.value == '1.0':
return son1
return Node('^', son1=son1, son2=son2, is_complex=True)
