def gen_atom_number(num):
"""
生成一个常量表达式，输入是数字。小数点后至多保留 3 位。
"""
num = float(num)
if not num.is_integer():
num = round(num, 3) # avoid infinity decimals
if num >= .0:
return [NarrRoot(+1, 'NUMBER'), abs(num)]
else:
return [NarrRoot(-1, 'NUMBER'), abs(num)]
def _apply_sign(narr, apply_product):
"""
apply sign to `narr', distribute sign in addition case.
"""
if apply_product > 0:
return
root = narr[0]
old_sign, Type = root.get()
narr[0].apply_sign(apply_product)
if Type == 'add':
# Distribute signs (i.e., make addition root positive)
narr[:], _ = expression.passchildren(NarrRoot(+1, Type), [narr])
def _level_apply(self, narr, debug=False):
ret_narrs = [] # store possible results
ani_narrs = [] # store transition animations
root_sign, root_type = narr[0].get()
# ignore terminal tokens (no rule has a single terminal token as pattern)
if root_type in expression.terminal_tokens():
return [], []
for pattern in self.rules:
wildcards_idx = self.wildcards_idx[pattern]
no_permute = (wildcards_idx !=
None) or root_type in expression.no_permute_tokens()
if debug:
rich.print(
f'\n[red]level apply[/] {pattern} wildcards_idx={wildcards_idx},'
+ f' no_permute={no_permute} [red]to[/]',
expression.narr2tex(narr))
# extract and try partial one or two operands to match against pattern
for construct_tree, brothers, ani_tree in self._children_permutation(
narr, no_permute=no_permute):
rewritten_narr, is_applied = self._exact_apply(pattern,
construct_tree,
debug=debug)
if is_applied:
new_narr = [] # construct a new father
if len(brothers) > 0:
if self.root_sign_reduce:
# always positive new father, in case the negative
# sign of father is also reduced, e.g. -abc => (ab)c
new_root = NarrRoot(+1, root_type)
else:
# in addition case, we will need to keep father sign,
# e.g. -(1+2+3) => -(3+3)
new_root = NarrRoot(root_sign, root_type)
new_narr = [new_root, None, *brothers]
expression.replace_or_pass_children(
new_narr, 0, rewritten_narr)
else:
# the entire expression in this level gets reduced
new_narr = rewritten_narr
if not self.root_sign_reduce and root_sign < 0:
new_narr[0].apply_sign(-1)
#print('[animat]', expression.narr2tex(ani_tree))
#print('[result]', expression.narr2tex(new_narr))
#print()
if False:
rich.print('[red]level apply[/]:')
print('[origin]', expression.narr2tex(narr))
print('[pattern]', pattern)
print('[result]', expression.narr2tex(new_narr))
print()
_, append = Axiom()._uniq_append(ret_narrs, new_narr,
self.max_results)
if append: ani_narrs.append(ani_tree)
return ret_narrs, ani_narrs
def gen_num(n):
return [NarrRoot(+1 if n >= 0 else -1, 'NUMBER'), float(abs(n))]
def test_alpha_equiv(narr1, narr2, alpha_universe=[{}], debug=False):
root1, root2 = narr1[0], narr2[0]
sign1, sign2 = root1[0], root2[0]
type1, type2 = root1[1], root2[1]
if debug:
print('test_alpha_equiv')
#for alpha in alpha_universe:
# alpha_prettyprint(alpha)
rich.print('[bold green]1[/]', end=" ")
expression.narr_prettyprint(narr1)
rich.print('[bold red]2[/]', end=" ")
expression.narr_prettyprint(narr2)
if type1 == 'NUMBER':
return type1 == type2 and sign1 == sign2 and narr1[1] == narr2[
1], alpha_universe
elif type1 in ['VAR', 'WILDCARDS']:
name1 = narr1[1] if type1 == 'VAR' else '*' + narr1[1]
narr2 = deepcopy(narr2)
# handle sign
_apply_sign(narr2, sign1)
#print(name1, end=' --> ')
#print(narr2)
#print()
# uppercase pattern such as X, Y only match variables / polynomials
if name1.isupper() and type2 not in ['VAR', 'sup']:
return False, []
# same variables must match same structures
else:
return alpha_universe_add_constraint(alpha_universe, name1, narr2)
# quick test of identicalness for non-wildcards pattern
wildcards_index = expression.get_wildcards_index(narr1)
if root1 != root2:
return False, []
elif len(narr1[1:]) != len(narr2[1:]) and wildcards_index is None:
return False, []
alpha_universe_new = []
# use exact order for concrete match or permuted order for wildcards match.
# (the latter will possibly generate multiple universes/possibilities)
permutations = [
narr2[1:]
] if wildcards_index == None else children_wildcards_permutation(narr2)
for perm_children in permutations:
match_perm = True # require all children get matched.
alpha_universe_copy = deepcopy(alpha_universe)
for i, c1 in enumerate(narr1[1:]):
# safe-guard for long wildcards, e.g., 'abc*' matching 'ab'
if i >= len(perm_children):
match_perm = False
break
if c1[0][1] == 'WILDCARDS':
# wildcards match (no sign reduce here)
c2 = [NarrRoot(+1, type2)] + perm_children[i:]
# unwrap matched group if necessary
if len(c2[1:]) == 1:
c2 = c2[1]
else:
# concrete child match
c2 = perm_children[i]
# test subtree
match_any, alpha_universe_copy = test_alpha_equiv(
c1, c2, alpha_universe=alpha_universe_copy, debug=debug)
if match_any:
# stop early for wildcards match
if c1[0][1] == 'WILDCARDS':
break
else:
match_perm = False
break
if match_perm:
alpha_universe_new += alpha_universe_copy
return len(alpha_universe_new) > 0, alpha_universe_new
#narr2 = expression.tex2narr('-(\\sqrt{x})^{2}')
#narr1 = expression.tex2narr('0 (-n)')
#narr2 = expression.tex2narr('- 0 n')
#narr1 = expression.tex2narr('-x \\times *{1} + x \\times *{2}')
#narr2 = expression.tex2narr('-25 \\times 51 + 25 \\times 48')
#narr1 = expression.tex2narr('+(-X)(-X)')
#narr2 = expression.tex2narr('-yy')
#narr1 = expression.tex2narr('a + *{1}')
#narr1 = expression.tex2narr('- a - *{1}')
narr1 = expression.tex2narr('-a')
narr2 = [
NarrRoot(1, 'add'), [NarrRoot(1, 'NUMBER'), 30.0],
[
NarrRoot(1, 'add'), [NarrRoot(1, 'NUMBER'), 1.0],
[NarrRoot(1, 'NUMBER'), 3.0]
]
]
is_equiv, rewrite_rules = test_alpha_equiv(narr1, narr2, debug=True)
if is_equiv:
rich.print('[bold green]Is alpha-equivalent')
alpha = rewrite_rules[0]
alpha_prettyprint(alpha)
rewritten_narr = rewrite_by_alpha(narr1, alpha)
rich.print('[[rewritten]]', expression.narr2tex(rewritten_narr))
else:
rich.print('[bold red]Not alpha-equivalent')
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
canonicalize = (
Axiom(name='去括号')
.add_rule('# a *{1}', 'X', animation='`#1 a *{1}`[replace]{X}', dynamic_procedure=_canonicalize)
.add_rule('# a # *{1}', 'X', animation='`#1 a #2 *{1}`[replace]{X}', dynamic_procedure=_canonicalize)
.add_rule('a', 'X', animation='`a`[replace]{X}', dynamic_procedure=_canonicalize)
.add_test(
[NarrRoot(1, "eq"),
[NarrRoot(1, "add"),
[NarrRoot(1, "mul"),
[NarrRoot(1, "NUMBER"), 3.0],
[NarrRoot(1, "VAR"), 'x']
],
[NarrRoot(1, "NUMBER"), 3.0],
[NarrRoot(1, "add"),
[NarrRoot(-1, "mul"),
[NarrRoot(1, "NUMBER"), 2.0],
[NarrRoot(1, "VAR"), 'x']
],
[NarrRoot(1, "NUMBER"), 1.0]
]
],
[NarrRoot(1, "NUMBER"), 0.0]