def _calc_sqrt(pattern_narr, signs, narr, rewrite_rules, output_tempalates):
x = get_atom_number(rewrite_rules['x'])
if x != None and x > 0 and x.is_integer():
m, n = sqrt_draw(x)
if n == 1:
rewrite_rules['c'] = gen_atom_number(m)
return rewrite_by_alpha(output_tempalates[0], rewrite_rules), True
elif m > 1:
rewrite_rules['m'] = gen_atom_number(m)
rewrite_rules['n'] = gen_atom_number(n)
return rewrite_by_alpha(output_tempalates[1], rewrite_rules), True
return narr, False
def _collapse_fraction(pattern_narr, signs, narr, rewrite_rules, output_tempalates):
a = get_atom_number(rewrite_rules['a'])
b = get_atom_number(rewrite_rules['b'])
if b != 0:
if a != None and b != None and not (a.is_integer() and b.is_integer()):
rewrite_rules['c'] = gen_atom_number(a / b)
return rewrite_by_alpha(output_tempalates[0], rewrite_rules), True
elif b != None and not b.is_integer():
rewrite_rules['k'] = gen_atom_number(1 / b)
rewrite_rules['x'] = rewrite_rules['a']
return rewrite_by_alpha(output_tempalates[1], rewrite_rules), True
return narr, False
def _fraction_int_addition(pattern_narr, signs, narr, rewrite_rules, output_tempalate):
a = get_atom_number(rewrite_rules['a'])
b = get_atom_number(rewrite_rules['b'])
c = get_atom_number(rewrite_rules['c'])
if a != None and a.is_integer():
return rewrite_by_alpha(output_tempalate, rewrite_rules), True
return narr, False
def _calc_abs(pattern_narr, signs, narr, rewrite_rules, output_tempalate):
x = get_atom_number(rewrite_rules['x'])
if x != None:
c = abs(x)
rewrite_rules['c'] = gen_atom_number(c)
return rewrite_by_alpha(output_tempalate, rewrite_rules), True
return narr, False
def _fraction_addition_same_denom(pattern_narr, signs, narr, rewrite_rules, output_tempalates):
a = get_atom_number(rewrite_rules['a'])
b = get_atom_number(rewrite_rules['b'])
c = get_atom_number(rewrite_rules['c'])
if a != None and b != None:
if a.is_integer() and b.is_integer():
a = a * signs[1]
b = b * signs[2]
z = a + b
if c != None and c.is_integer() and c != 0:
if (z / c).is_integer():
rewrite_rules['z'] = gen_atom_number(z / c)
return rewrite_by_alpha(output_tempalates[0], rewrite_rules), True
rewrite_rules['z'] = gen_atom_number(z)
return rewrite_by_alpha(output_tempalates[1], rewrite_rules), True
return narr, False
def _simplify_fraction(pattern_narr, signs, narr, rewrite_rules, output_tempalates):
a = get_atom_number(rewrite_rules['a'])
b = get_atom_number(rewrite_rules['b'])
if a != None and b != None and a.is_integer() and b.is_integer():
a, b = a, b
gcd = Euclidean_gcd(a, b)
if gcd != 0 and gcd != 1:
a = a / gcd
b = b / gcd
if b == 1:
rewrite_rules['c'] = gen_atom_number(a)
return rewrite_by_alpha(output_tempalates[0], rewrite_rules), True
elif b != 0:
rewrite_rules['c'] = gen_atom_number(a)
rewrite_rules['d'] = gen_atom_number(b)
return rewrite_by_alpha(output_tempalates[1], rewrite_rules), True
return narr, False
def _calc_mul(pattern_narr, signs, narr, rewrite_rules, output_tempalate):
a = get_atom_number(rewrite_rules['a'])
b = get_atom_number(rewrite_rules['b'])
if a != None and b != None:
c = a * b
rewrite_rules['c'] = gen_atom_number(c)
return rewrite_by_alpha(output_tempalate, rewrite_rules), True
return narr, False
def _canonicalize(pattern_narr, signs, narr, rewrite_rules, output_tempalate):
sign, Type = narr[0].get()
if Type in expression.commutative_operators():
new_narr, is_applied = expression.canonicalize(narr)
if is_applied:
rewrite_rules['X'] = new_narr
return rewrite_by_alpha(output_tempalate, rewrite_rules), True
else:
return new_narr, False
return narr, False
def _collapse_fraction_add_float(pattern_narr, signs, narr, rewrite_rules, output_tempalate):
a = get_atom_number(rewrite_rules['a'])
b = get_atom_number(rewrite_rules['b'])
c = get_atom_number(rewrite_rules['c'])
if a != None and b != None and c != None:
if b != 0 and not c.is_integer():
rewrite_rules['x'] = gen_atom_number(a / b)
return rewrite_by_alpha(output_tempalate, rewrite_rules), True
return narr, False
def _calc_pow(pattern_narr, signs, narr, rewrite_rules, output_tempalate):
a = get_atom_number(rewrite_rules['a'])
b = get_atom_number(rewrite_rules['b'])
if a != None and b != None:
try:
c = a ** b
if abs(c) > 2000: raise OverflowError
rewrite_rules['c'] = gen_atom_number(c)
return rewrite_by_alpha(output_tempalate, rewrite_rules), True
except OverflowError:
pass
except ZeroDivisionError:
pass
return narr, False
def _exact_apply(self, pattern, narr, debug=False):
# refuse to apply when rule is not animation compatible in animation mode.
if self.animation_mode and pattern not in self.animation:
return narr, False
# apply pattern transformation to nested array
pattern_narr = self.narrs[pattern]
is_match, rewrite_rules = test_alpha_equiv(pattern_narr,
narr,
debug=False)
if debug:
# Example:
# Axiom: (a+b)(a-b) => (a)^{2} - (b)^{2}
# pattern => destination
# narr: (-xy - z)(-xy + z)
# rewrite_rules:
# a -> -xy
# b -> -z
print()
if False:
print('pattern:', pattern_narr)
print('subject:', narr)
else:
print('pattern:', expression.narr2tex(pattern_narr))
print('subject:', expression.narr2tex(narr))
rich.print('match:', is_match)
if is_match:
if debug:
alpha_prettyprint(rewrite_rules[0])
dest = self.animation[
pattern] if self.animation_mode else self.rules[pattern]
dest_narr = [self.narrs[d] for d in dest] if isinstance(
dest, list) else self.narrs[dest]
if debug:
print('dest:', dest)
call = self.dp[pattern]
if call is not None: # dynamical axiom
signs = self.signs[pattern]
rewritten_narr, is_applied = call(pattern_narr, signs, narr,
rewrite_rules[0], dest_narr)
else:
rewritten_narr, is_applied = rewrite_by_alpha(
dest_narr, rewrite_rules[0]), True
if debug:
rich.print('applied:', is_applied, end=': ')
if False:
print(rewritten_narr)
else:
print(expression.narr2tex(rewritten_narr))
# if a rule with higher priority get applied, later ones are ignored
if is_applied:
# post processes
rewritten_narr = self._fraction_cancel(rewritten_narr)
return rewritten_narr, True
return narr, False