# coding: utf-8
# 2021/5/20 @ tongshiwei
from typing import List, Dict
from .katex import katex
__all__ = ["str2ast", "get_edges", "ast", "link_variable", "katex_parse"]
def katex_parse(formula):
return katex.katex.__parse(formula,{'displayMode':True,'trust': True}).to_list()
def str2ast(formula: str, *args, **kwargs):
return ast(formula, is_str=True, *args, **kwargs)
[docs]def ast(formula: (str, List[Dict]), index=0, forest_begin=0, father_tree=None, is_str=False):
"""
The origin code author is https://github.com/hxwujinze
Parameters
----------
formula: str or List[Dict]
公式字符串或通过katex解析得到的结构体
index: int
本子树在树上的位置
forest_begin: int
本树在森林中的起始位置
father_tree: List[Dict]
父亲树
is_str: bool
Returns
----------
tree: List[Dict]
重新解析形成的特征树
todo: finish all types
Notes
----------
Some functions are not supportd in ``katex``
e.g.,
1. tag
- ``\\begin{equation} \\tag{tagName} F=ma \\end{equation}``
- ``\\begin{align} \\tag{1} y=x+z \\end{align}``
- ``\\tag*{hi} x+y^{2x}``
2. dddot
- ``\\frac{ \\dddot y }{ x }``
For more information, refer to
`katex support table <https://github.com/KaTeX/KaTeX/blob/master/docs/support_table.md>`_
"""
tree = []
index += forest_begin
json_ast: List[Dict] = katex.katex.__parse(formula,{'displayMode':True,'trust': True}).to_list() if is_str else formula
last_node = None
for item in json_ast:
private_index = len(tree)
role = None
if 'role' in item:
role = item['role']
tree_node = {
'val': {'id': private_index + index, 'type': None, 'text': None, 'role': role},
'structure': {'bro': [None, None], 'child': None, 'father': None, 'forest': None}
}
tree_node['val']['type'] = item['type']
if index > forest_begin:
tree_node['structure']['father'] = index - 1
if tree_node['val']['type'] == "mathord" or tree_node['val']['type'] == "textord":
tree_node['val']['text'] = item['text'].replace('\\prime', '’')
tree.append(tree_node)
elif tree_node['val']['type'] == "atom":
tree_node['val']['text'] = item['text'].replace('\\cdotp', '·')
tree_node['val']['type'] = item['family']
tree.append(tree_node)
elif tree_node['val']['type'] == "op":
tree_node['val']['text'] = "\\op" if 'name' not in item else item['name']
if item['symbol'] and 'body' in item:
tree_node['structure']['child'] = [1 + private_index + index]
tree.append(tree_node)
tree += ast(item['body'], index=len(tree) + index, father_tree=tree)
else:
tree_node['val']['text'] = item['name']
tree.append(tree_node)
elif tree_node['val']['type'] == "genfrac":
item['numer']['role'] = 'numer'
item['denom']['role'] = 'denom'
tree_node['val']['text'] = '\\frac'
tree_node['structure']['child'] = [1 + private_index + index]
tree.append(tree_node)
tree += ast([item['numer'], item['denom']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == 'sqrt':
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = '\\sqrt'
tree.append(tree_node)
item['body']['role'] = 'body'
if item['index']:
item['index']['role'] = 'index'
tree += ast([item['body'], item['index']], index=len(tree) + index, father_tree=tree)
else:
tree += ast([item['body']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == 'array':
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['arraydims'] = item['arraystretch']
tree_node['val']['text'] = '\\begin {matrix} \\end {matrix}'
tree.append(tree_node)
bodys = []
for litem in item['body']:
for citem in litem:
citem['role'] = 'body'
bodys.append(citem)
tree += ast(bodys, index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == 'styling':
tree_node['structure']['child'] = [1 + private_index + index]
tree.append(tree_node)
for citem in item['body']:
citem['role'] = 'body'
tree += ast(item['body'], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == 'xArrow':
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = item['label']
tree.append(tree_node)
item['body']['role'] = 'body'
item['below']['role'] = 'below'
tree += ast([item['body'], item['below']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == 'overline':
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = '\\' + tree_node['val']['type']
tree.append(tree_node)
item['body']['role'] = 'body'
tree += ast([item['body']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "accent":
tree_node['val']['text'] = item['label']
tree_node['structure']['child'] = [1 + private_index + index]
tree.append(tree_node)
item['base']['role'] = 'base'
tree += ast([item['base']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "supsub":
_tree = []
if 'base' in item and item['base'] is not None:
item['base']['role'] = 'base'
_tree.append(item['base'])
if 'sub' in item and item['sub']:
item['sub']['role'] = 'sub'
_tree.append(item['sub'])
if 'sup' in item and item['sup']:
item['sup']['role'] = 'sup'
_tree.append(item['sup'])
tree_node['val']['text'] = "\\supsub"
if _tree != []:
tree_node['structure']['child'] = [1 + private_index + index]
tree.append(tree_node)
tree += ast(_tree, index=len(tree) + index, father_tree=tree)
else:
tree.append(tree_node)
elif tree_node['val']['type'] == "ordgroup":
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = '{ }'
tree.append(tree_node)
for citem in item['body']:
citem['role'] = 'body'
tree += ast(item['body'], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "mclass":
tree_node['val']['text'] = item['mclass']
for citem in item['body']:
citem['role'] = 'body'
tree += ast(item['body'], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == 'leftright':
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = item['left']
tree_node['val']['right'] = item['right']
tree.append(tree_node)
for citem in item['body']:
citem['role'] = 'body'
tree += ast(item['body'], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] in {"kern"}:
# \quad
tree_node['val']['text'] = tree_node['val']['type']
tree_node['val']['type'] = "ignore"
tree.append(tree_node)
elif tree_node['val']['type'] == "text":
# \text{}
tree_node['val']['text'] = "".join([e['text'] for e in item["body"]])
tree.append(tree_node)
# --------------------- new node --------------------- #
elif tree_node['val']['type'] == "size":
# nknown usage : different from "sizing"
continue
elif tree_node['val']['type'] == "internal":
# unknown usage
continue
elif tree_node['val']['type'] == "cr":
# new line
continue
elif tree_node['val']['type'] == "infix":
continue
elif tree_node['val']['type'] == "rule":
# ignore layout setting
continue
elif tree_node['val']['type'] == "cdlabel":
tree_node['val']['text'] = item['side']
tree_node['structure']['child'] = [1 + private_index + index]
tree.append(tree_node)
item['label']['role'] = 'label'
tree += ast([item['label']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "cdlabelparent":
tree_node['val']['text'] = "\\cdlabelparent"
tree_node['structure']['child'] = [1 + private_index + index]
tree.append(tree_node)
item['fragment']['role'] = 'fragment'
tree += ast([item['fragment']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "color":
tree_node['val']['text'] = "\\color"
tree_node['structure']['child'] = [1 + private_index + index]
tree.append(tree_node)
tree += ast(item['body'], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "color-token":
tree_node['val']['text'] = "\\color-token"
tree_node['structure']['child'] = [1 + private_index + index]
tree.append(tree_node)
tree += ast([item['body']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "raw":
tree_node['val']['text'] = item['string']
tree.append(tree_node)
elif tree_node['val']['type'] == "styling":
# to be confirmed
tree_node['val']['text'] = "\\styling"
# tree_node['val']['text'] = item["style"] ！= None ? item["style"]: "\\styling"
tree_node['structure']['child'] = [1 + private_index + index]
tree.append(tree_node)
tree += ast(item['body'], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "tag":
continue
# not supported in Katex yet
# tree_node['structure']['child'] = [1 + private_index + index]
# tree_node['val']['text'] = '\\tag' # equations with order number
# tree.append(tree_node)
# body_item = {'type':'nodelist','role': 'body','body': item['body']}
# tag_item = {'type':'nodelist','role': 'tag','body': item['tag']}
# tree += ast([body_item, tag_item], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "verb":
tree_node['val']['text'] = item['body'] # "original copy", source code
tree.append(tree_node)
elif tree_node['val']['type'] in ["spacing","accent-token","op-token"]:
tree_node['val']['text'] = item['text']
tree.append(tree_node)
elif tree_node['val']['type'] in ["accent","accentUnder"]:
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = item["label"]
tree.append(tree_node)
item['base']['role'] = 'base'
tree += ast([item['base']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "delimsizing":
# contains symbols for size settings, including "(",")", etc
tree_node['val']['text'] = item['delim']
tree.append(tree_node)
elif tree_node['val']['type'] == "enclose":
# setting deleting line effect
tree_node['val']['text'] = item['label']
tree_node['structure']['child'] = [1 + private_index + index]
tree.append(tree_node)
tree += ast([item['body']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "environment":
tree_node['val']['text'] = item['name']
tree_node['structure']['child'] = [1 + private_index + index]
tree.append(tree_node)
item['nameGroup']['role'] = 'nameGroup'
tree += ast([item['nameGroup']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "url":
# continue
tree_node['val']['text'] = item['url']
tree.append(tree_node)
elif tree_node['val']['type'] == "href":
# continue
tree_node['val']['text'] = item['href']
tree_node['structure']['child'] = [1 + private_index + index]
tree.append(tree_node)
tree += ast(item['body'], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "html":
# continue
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = "\\html"
tree.append(tree_node)
tree += ast(item['body'], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "htmlmathml":
# continue
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = "\\htmlmathml"
tree.append(tree_node)
html_item = {'type':'nodelist','role': 'html','body': item['html']} # ?
mathml_item = {'type':'nodelist','role': 'mathml','body': item['mathml']} # ?
tree += ast([html_item,mathml_item], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "includegraphics":
# continue
tree_node['val']['text'] = item['src']
tree.append(tree_node)
elif tree_node['val']['type'] == "font":
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = item["font"] # font name
tree.append(tree_node)
item['body']['role'] = 'body'
tree += ast([item['body']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "hbox":
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = '\\hbox' # box layout
tree.append(tree_node)
tree += ast(item['body'], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "vcenter":
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = '\\vcenter' # box layout
tree.append(tree_node)
tree += ast([item['body']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "horizBrace":
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = item['label']
tree.append(tree_node)
item['base']['role'] = 'base'
tree += ast([item['base']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "lap":
# layout setting (overlap)
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = item["alignment"] # methods of overlap (llap | rlap)
tree.append(tree_node)
tree += ast([item['body']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "sizing":
# consider ignoring size
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = "\\sizing"
tree.append(tree_node)
tree += ast(item['body'], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "smash":
# layout setting : smash (height | width)
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = "\\smash"
tree.append(tree_node)
tree += ast([item['body']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "mathchoice":
# provides content that is dependent on the current style (display, text, script, or scriptscript).
# eg: \mathchoice {#1}{#2}{#3}{#4}
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = "\\mathchoice"
tree.append(tree_node)
mathchoiceList = []
for choice in ["display","text","script","scriptscript"]:
citem = {'type':'nodelist','role':choice, 'body':item[choice]}
mathchoiceList.append(citem)
tree += ast(mathchoiceList, index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "operatorname":
# unknown usage
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = "\\operatorname"
tree.append(tree_node)
tree += ast(item['body'], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] in ["overline","underline"]:
# consider ignoring line
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = "\\" + tree_node['val']['type']
tree.append(tree_node)
tree += ast([item['body']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "raisebox":
# raise or lower the height of the text
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = "\\raisebox"
tree.append(tree_node)
tree += ast([item['body']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == "leftright-right":
# paired with leftright
tree_node['val']['text'] = item["delim"]
tree.append(tree_node)
elif tree_node['val']['type'] == "middle":
# symbols with height setting, such as "|"
tree_node['val']['text'] = item["delim"]
tree.append(tree_node)
elif tree_node['val']['type'] in ["phantom","hphantom","vphantom"]:
# set space distance by the length of content
# continue
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = "\\" + tree_node['val']['type']
tree.append(tree_node)
tree += ast([item['body']], index=len(tree) + index, father_tree=tree)
elif tree_node['val']['type'] == 'nodelist':
# process node list specially
tree_node['structure']['child'] = [1 + private_index + index]
tree_node['val']['text'] = "\\" + item["role"]
tree.append(tree_node)
tree += ast(item['body'], index=len(tree) + index, father_tree=tree)
else:
tree_node['structure']['child'] = [1 + private_index + index]
if "text" in item:
tree_node['val']['text'] = item["text"]
else:
tree_node['val']['text'] = item["type"]
tree_node['val']['type'] = "other"
tree.append(tree_node)
Role = ['body', 'base', 'sup', 'sub', 'numer', 'denom', 'index', 'below','nameGroup','fragment','label', 'other']
childrole = []
for role_item in Role:
if role_item in item:
if role_item == "body" and isinstance(item[role_item], dict) is False:
# \text{}
childrole.extend(item[role_item])
else:
item[role_item]['role'] = role_item
childrole.append(item[role_item])
tree += ast(childrole, index=len(tree) + index, father_tree=tree)
if item:
if item != json_ast[0]:
tree[private_index]['structure']['bro'][0] = last_node + index
last_node = private_index
else:
last_node = private_index
if item != json_ast[-1]:
tree[private_index]['structure']['bro'][1] = len(tree) + index
if father_tree:
father_tree[tree[private_index]['structure']['father'] - index]['structure']['child'].append(
len(tree) + index
)
return tree
[docs]def link_variable(forest):
"""
建森林
Parameters
----------
forest: List[Dict]
Returns
-------
trees: List[Dict]
"""
forest_connect_dict = {}
for node in forest:
if node['val']['type'] == 'mathord':
if node['val']['text'] not in forest_connect_dict:
forest_connect_dict[node['val']['text']] = []
forest_connect_dict[node['val']['text']].append(forest.index(node))
for k, v in forest_connect_dict.items():
if len(v) > 1:
for i in range(0, len(v)):
l_v = [] + v
index = l_v.pop(i)
forest[index]['structure']['forest'] = l_v
variable_connect_dict = {
"var2id": forest_connect_dict,
"var_code": {}
}
return variable_connect_dict
[docs]def get_edges(forest):
"""
构造边集合
Parameters
----------
forest: List[Dict]
森林
Returns
----------
edges: list of tuple(src,dst,type)
边集合
"""
edges = []
for node in forest:
index = node["val"]["id"]
edges.append((index, index, 1))
if node['structure']['bro'][1] is not None:
edges.append((index, node['structure']['bro'][1], 2))
if node['structure']['bro'][0] is not None:
edges.append((index, node['structure']['bro'][0], 2))
if node['structure']['child'] is not None:
for item in node['structure']['child']:
edges.append((index, item, 3))
if node['structure']['father'] is not None:
edges.append((index, node['structure']['father'], 4))
if node['structure']['forest'] is not None:
for item in node['structure']['forest']:
edges.append((index, item, 5))
return edges