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rl/Lib/site-packages/sympy/parsing/__init__.py Normal file
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"""Used for translating a string into a SymPy expression. """
__all__ = ['parse_expr']
from .sympy_parser import parse_expr

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"""
This module implements the functionality to take any Python expression as a
string and fix all numbers and other things before evaluating it,
thus
1/2
returns
Integer(1)/Integer(2)
We use the ast module for this. It is well documented at docs.python.org.
Some tips to understand how this works: use dump() to get a nice
representation of any node. Then write a string of what you want to get,
e.g. "Integer(1)", parse it, dump it and you'll see that you need to do
"Call(Name('Integer', Load()), [node], [], None, None)". You do not need
to bother with lineno and col_offset, just call fix_missing_locations()
before returning the node.
"""
from sympy.core.basic import Basic
from sympy.core.sympify import SympifyError
from ast import parse, NodeTransformer, Call, Name, Load, \
fix_missing_locations, Constant, Tuple
class Transform(NodeTransformer):
def __init__(self, local_dict, global_dict):
NodeTransformer.__init__(self)
self.local_dict = local_dict
self.global_dict = global_dict
def visit_Constant(self, node):
if isinstance(node.value, int):
return fix_missing_locations(Call(func=Name('Integer', Load()),
args=[node], keywords=[]))
elif isinstance(node.value, float):
return fix_missing_locations(Call(func=Name('Float', Load()),
args=[node], keywords=[]))
return node
def visit_Name(self, node):
if node.id in self.local_dict:
return node
elif node.id in self.global_dict:
name_obj = self.global_dict[node.id]
if isinstance(name_obj, (Basic, type)) or callable(name_obj):
return node
elif node.id in ['True', 'False']:
return node
return fix_missing_locations(Call(func=Name('Symbol', Load()),
args=[Constant(node.id)], keywords=[]))
def visit_Lambda(self, node):
args = [self.visit(arg) for arg in node.args.args]
body = self.visit(node.body)
n = Call(func=Name('Lambda', Load()),
args=[Tuple(args, Load()), body], keywords=[])
return fix_missing_locations(n)
def parse_expr(s, local_dict):
"""
Converts the string "s" to a SymPy expression, in local_dict.
It converts all numbers to Integers before feeding it to Python and
automatically creates Symbols.
"""
global_dict = {}
exec('from sympy import *', global_dict)
try:
a = parse(s.strip(), mode="eval")
except SyntaxError:
raise SympifyError("Cannot parse %s." % repr(s))
a = Transform(local_dict, global_dict).visit(a)
e = compile(a, "<string>", "eval")
return eval(e, global_dict, local_dict)

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rl/Lib/site-packages/sympy/parsing/autolev/Autolev.g4 Normal file
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grammar Autolev;
options {
language = Python3;
}
prog: stat+;
stat: varDecl
| functionCall
| codeCommands
| massDecl
| inertiaDecl
| assignment
| settings
;
assignment: vec equals expr #vecAssign
| ID '[' index ']' equals expr #indexAssign
| ID diff? equals expr #regularAssign;
equals: ('='|'+='|'-='|':='|'*='|'/='|'^=');
index: expr (',' expr)* ;
diff: ('\'')+;
functionCall: ID '(' (expr (',' expr)*)? ')'
| (Mass|Inertia) '(' (ID (',' ID)*)? ')';
varDecl: varType varDecl2 (',' varDecl2)*;
varType: Newtonian|Frames|Bodies|Particles|Points|Constants
| Specifieds|Imaginary|Variables ('\'')*|MotionVariables ('\'')*;
varDecl2: ID ('{' INT ',' INT '}')? (('{' INT ':' INT (',' INT ':' INT)* '}'))? ('{' INT '}')? ('+'|'-')? ('\'')* ('=' expr)?;
ranges: ('{' INT ':' INT (',' INT ':' INT)* '}');
massDecl: Mass massDecl2 (',' massDecl2)*;
massDecl2: ID '=' expr;
inertiaDecl: Inertia ID ('(' ID ')')? (',' expr)+;
matrix: '[' expr ((','|';') expr)* ']';
matrixInOutput: (ID (ID '=' (FLOAT|INT)?))|FLOAT|INT;
codeCommands: units
| inputs
| outputs
| codegen
| commands;
settings: ID (EXP|ID|FLOAT|INT)?;
units: UnitSystem ID (',' ID)*;
inputs: Input inputs2 (',' inputs2)*;
id_diff: ID diff?;
inputs2: id_diff '=' expr expr?;
outputs: Output outputs2 (',' outputs2)*;
outputs2: expr expr?;
codegen: ID functionCall ('['matrixInOutput (',' matrixInOutput)*']')? ID'.'ID;
commands: Save ID'.'ID
| Encode ID (',' ID)*;
vec: ID ('>')+
| '0>'
| '1>>';
expr: expr '^'<assoc=right> expr # Exponent
| expr ('*'|'/') expr # MulDiv
| expr ('+'|'-') expr # AddSub
| EXP # exp
| '-' expr # negativeOne
| FLOAT # float
| INT # int
| ID('\'')* # id
| vec # VectorOrDyadic
| ID '['expr (',' expr)* ']' # Indexing
| functionCall # function
| matrix # matrices
| '(' expr ')' # parens
| expr '=' expr # idEqualsExpr
| expr ':' expr # colon
| ID? ranges ('\'')* # rangess
;
// These are to take care of the case insensitivity of Autolev.
Mass: ('M'|'m')('A'|'a')('S'|'s')('S'|'s');
Inertia: ('I'|'i')('N'|'n')('E'|'e')('R'|'r')('T'|'t')('I'|'i')('A'|'a');
Input: ('I'|'i')('N'|'n')('P'|'p')('U'|'u')('T'|'t')('S'|'s')?;
Output: ('O'|'o')('U'|'u')('T'|'t')('P'|'p')('U'|'u')('T'|'t');
Save: ('S'|'s')('A'|'a')('V'|'v')('E'|'e');
UnitSystem: ('U'|'u')('N'|'n')('I'|'i')('T'|'t')('S'|'s')('Y'|'y')('S'|'s')('T'|'t')('E'|'e')('M'|'m');
Encode: ('E'|'e')('N'|'n')('C'|'c')('O'|'o')('D'|'d')('E'|'e');
Newtonian: ('N'|'n')('E'|'e')('W'|'w')('T'|'t')('O'|'o')('N'|'n')('I'|'i')('A'|'a')('N'|'n');
Frames: ('F'|'f')('R'|'r')('A'|'a')('M'|'m')('E'|'e')('S'|'s')?;
Bodies: ('B'|'b')('O'|'o')('D'|'d')('I'|'i')('E'|'e')('S'|'s')?;
Particles: ('P'|'p')('A'|'a')('R'|'r')('T'|'t')('I'|'i')('C'|'c')('L'|'l')('E'|'e')('S'|'s')?;
Points: ('P'|'p')('O'|'o')('I'|'i')('N'|'n')('T'|'t')('S'|'s')?;
Constants: ('C'|'c')('O'|'o')('N'|'n')('S'|'s')('T'|'t')('A'|'a')('N'|'n')('T'|'t')('S'|'s')?;
Specifieds: ('S'|'s')('P'|'p')('E'|'e')('C'|'c')('I'|'i')('F'|'f')('I'|'i')('E'|'e')('D'|'d')('S'|'s')?;
Imaginary: ('I'|'i')('M'|'m')('A'|'a')('G'|'g')('I'|'i')('N'|'n')('A'|'a')('R'|'r')('Y'|'y');
Variables: ('V'|'v')('A'|'a')('R'|'r')('I'|'i')('A'|'a')('B'|'b')('L'|'l')('E'|'e')('S'|'s')?;
MotionVariables: ('M'|'m')('O'|'o')('T'|'t')('I'|'i')('O'|'o')('N'|'n')('V'|'v')('A'|'a')('R'|'r')('I'|'i')('A'|'a')('B'|'b')('L'|'l')('E'|'e')('S'|'s')?;
fragment DIFF: ('\'')*;
fragment DIGIT: [0-9];
INT: [0-9]+ ; // match integers
FLOAT: DIGIT+ '.' DIGIT*
| '.' DIGIT+;
EXP: FLOAT 'E' INT
| FLOAT 'E' '-' INT;
LINE_COMMENT : '%' .*? '\r'? '\n' -> skip ;
ID: [a-zA-Z][a-zA-Z0-9_]*;
WS: [ \t\r\n&]+ -> skip ; // toss out whitespace

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from sympy.external import import_module
from sympy.utilities.decorator import doctest_depends_on
@doctest_depends_on(modules=('antlr4',))
def parse_autolev(autolev_code, include_numeric=False):
"""Parses Autolev code (version 4.1) to SymPy code.
Parameters
=========
autolev_code : Can be an str or any object with a readlines() method (such as a file handle or StringIO).
include_numeric : boolean, optional
If True NumPy, PyDy, or other numeric code is included for numeric evaluation lines in the Autolev code.
Returns
=======
sympy_code : str
Equivalent SymPy and/or numpy/pydy code as the input code.
Example (Double Pendulum)
=========================
>>> my_al_text = ("MOTIONVARIABLES' Q{2}', U{2}'",
... "CONSTANTS L,M,G",
... "NEWTONIAN N",
... "FRAMES A,B",
... "SIMPROT(N, A, 3, Q1)",
... "SIMPROT(N, B, 3, Q2)",
... "W_A_N>=U1*N3>",
... "W_B_N>=U2*N3>",
... "POINT O",
... "PARTICLES P,R",
... "P_O_P> = L*A1>",
... "P_P_R> = L*B1>",
... "V_O_N> = 0>",
... "V2PTS(N, A, O, P)",
... "V2PTS(N, B, P, R)",
... "MASS P=M, R=M",
... "Q1' = U1",
... "Q2' = U2",
... "GRAVITY(G*N1>)",
... "ZERO = FR() + FRSTAR()",
... "KANE()",
... "INPUT M=1,G=9.81,L=1",
... "INPUT Q1=.1,Q2=.2,U1=0,U2=0",
... "INPUT TFINAL=10, INTEGSTP=.01",
... "CODE DYNAMICS() some_filename.c")
>>> my_al_text = '\\n'.join(my_al_text)
>>> from sympy.parsing.autolev import parse_autolev
>>> print(parse_autolev(my_al_text, include_numeric=True))
import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
<BLANKLINE>
q1, q2, u1, u2 = _me.dynamicsymbols('q1 q2 u1 u2')
q1_d, q2_d, u1_d, u2_d = _me.dynamicsymbols('q1_ q2_ u1_ u2_', 1)
l, m, g = _sm.symbols('l m g', real=True)
frame_n = _me.ReferenceFrame('n')
frame_a = _me.ReferenceFrame('a')
frame_b = _me.ReferenceFrame('b')
frame_a.orient(frame_n, 'Axis', [q1, frame_n.z])
frame_b.orient(frame_n, 'Axis', [q2, frame_n.z])
frame_a.set_ang_vel(frame_n, u1*frame_n.z)
frame_b.set_ang_vel(frame_n, u2*frame_n.z)
point_o = _me.Point('o')
particle_p = _me.Particle('p', _me.Point('p_pt'), _sm.Symbol('m'))
particle_r = _me.Particle('r', _me.Point('r_pt'), _sm.Symbol('m'))
particle_p.point.set_pos(point_o, l*frame_a.x)
particle_r.point.set_pos(particle_p.point, l*frame_b.x)
point_o.set_vel(frame_n, 0)
particle_p.point.v2pt_theory(point_o,frame_n,frame_a)
particle_r.point.v2pt_theory(particle_p.point,frame_n,frame_b)
particle_p.mass = m
particle_r.mass = m
force_p = particle_p.mass*(g*frame_n.x)
force_r = particle_r.mass*(g*frame_n.x)
kd_eqs = [q1_d - u1, q2_d - u2]
forceList = [(particle_p.point,particle_p.mass*(g*frame_n.x)), (particle_r.point,particle_r.mass*(g*frame_n.x))]
kane = _me.KanesMethod(frame_n, q_ind=[q1,q2], u_ind=[u1, u2], kd_eqs = kd_eqs)
fr, frstar = kane.kanes_equations([particle_p, particle_r], forceList)
zero = fr+frstar
from pydy.system import System
sys = System(kane, constants = {l:1, m:1, g:9.81},
specifieds={},
initial_conditions={q1:.1, q2:.2, u1:0, u2:0},
times = _np.linspace(0.0, 10, 10/.01))
<BLANKLINE>
y=sys.integrate()
<BLANKLINE>
"""
_autolev = import_module(
'sympy.parsing.autolev._parse_autolev_antlr',
import_kwargs={'fromlist': ['X']})
if _autolev is not None:
return _autolev.parse_autolev(autolev_code, include_numeric)

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# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
#
# Generated with antlr4
# antlr4 is licensed under the BSD-3-Clause License
# https://github.com/antlr/antlr4/blob/master/LICENSE.txt

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# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
#
# Generated with antlr4
# antlr4 is licensed under the BSD-3-Clause License
# https://github.com/antlr/antlr4/blob/master/LICENSE.txt
from antlr4 import *
from io import StringIO
import sys
if sys.version_info[1] > 5:
from typing import TextIO
else:
from typing.io import TextIO
def serializedATN():
return [
4,0,49,393,6,-1,2,0,7,0,2,1,7,1,2,2,7,2,2,3,7,3,2,4,7,4,2,5,7,5,
2,6,7,6,2,7,7,7,2,8,7,8,2,9,7,9,2,10,7,10,2,11,7,11,2,12,7,12,2,
13,7,13,2,14,7,14,2,15,7,15,2,16,7,16,2,17,7,17,2,18,7,18,2,19,7,
19,2,20,7,20,2,21,7,21,2,22,7,22,2,23,7,23,2,24,7,24,2,25,7,25,2,
26,7,26,2,27,7,27,2,28,7,28,2,29,7,29,2,30,7,30,2,31,7,31,2,32,7,
32,2,33,7,33,2,34,7,34,2,35,7,35,2,36,7,36,2,37,7,37,2,38,7,38,2,
39,7,39,2,40,7,40,2,41,7,41,2,42,7,42,2,43,7,43,2,44,7,44,2,45,7,
45,2,46,7,46,2,47,7,47,2,48,7,48,2,49,7,49,2,50,7,50,1,0,1,0,1,1,
1,1,1,2,1,2,1,3,1,3,1,3,1,4,1,4,1,4,1,5,1,5,1,5,1,6,1,6,1,6,1,7,
1,7,1,7,1,8,1,8,1,8,1,9,1,9,1,10,1,10,1,11,1,11,1,12,1,12,1,13,1,
13,1,14,1,14,1,15,1,15,1,16,1,16,1,17,1,17,1,18,1,18,1,19,1,19,1,
20,1,20,1,21,1,21,1,21,1,22,1,22,1,22,1,22,1,23,1,23,1,24,1,24,1,
25,1,25,1,26,1,26,1,26,1,26,1,26,1,27,1,27,1,27,1,27,1,27,1,27,1,
27,1,27,1,28,1,28,1,28,1,28,1,28,1,28,3,28,184,8,28,1,29,1,29,1,
29,1,29,1,29,1,29,1,29,1,30,1,30,1,30,1,30,1,30,1,31,1,31,1,31,1,
31,1,31,1,31,1,31,1,31,1,31,1,31,1,31,1,32,1,32,1,32,1,32,1,32,1,
32,1,32,1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,34,1,
34,1,34,1,34,1,34,1,34,3,34,232,8,34,1,35,1,35,1,35,1,35,1,35,1,
35,3,35,240,8,35,1,36,1,36,1,36,1,36,1,36,1,36,1,36,1,36,1,36,3,
36,251,8,36,1,37,1,37,1,37,1,37,1,37,1,37,3,37,259,8,37,1,38,1,38,
1,38,1,38,1,38,1,38,1,38,1,38,1,38,3,38,270,8,38,1,39,1,39,1,39,
1,39,1,39,1,39,1,39,1,39,1,39,1,39,3,39,282,8,39,1,40,1,40,1,40,
1,40,1,40,1,40,1,40,1,40,1,40,1,40,1,41,1,41,1,41,1,41,1,41,1,41,
1,41,1,41,1,41,3,41,303,8,41,1,42,1,42,1,42,1,42,1,42,1,42,1,42,
1,42,1,42,1,42,1,42,1,42,1,42,1,42,1,42,3,42,320,8,42,1,43,5,43,
323,8,43,10,43,12,43,326,9,43,1,44,1,44,1,45,4,45,331,8,45,11,45,
12,45,332,1,46,4,46,336,8,46,11,46,12,46,337,1,46,1,46,5,46,342,
8,46,10,46,12,46,345,9,46,1,46,1,46,4,46,349,8,46,11,46,12,46,350,
3,46,353,8,46,1,47,1,47,1,47,1,47,1,47,1,47,1,47,1,47,1,47,3,47,
364,8,47,1,48,1,48,5,48,368,8,48,10,48,12,48,371,9,48,1,48,3,48,
374,8,48,1,48,1,48,1,48,1,48,1,49,1,49,5,49,382,8,49,10,49,12,49,
385,9,49,1,50,4,50,388,8,50,11,50,12,50,389,1,50,1,50,1,369,0,51,
1,1,3,2,5,3,7,4,9,5,11,6,13,7,15,8,17,9,19,10,21,11,23,12,25,13,
27,14,29,15,31,16,33,17,35,18,37,19,39,20,41,21,43,22,45,23,47,24,
49,25,51,26,53,27,55,28,57,29,59,30,61,31,63,32,65,33,67,34,69,35,
71,36,73,37,75,38,77,39,79,40,81,41,83,42,85,43,87,0,89,0,91,44,
93,45,95,46,97,47,99,48,101,49,1,0,24,2,0,77,77,109,109,2,0,65,65,
97,97,2,0,83,83,115,115,2,0,73,73,105,105,2,0,78,78,110,110,2,0,
69,69,101,101,2,0,82,82,114,114,2,0,84,84,116,116,2,0,80,80,112,
112,2,0,85,85,117,117,2,0,79,79,111,111,2,0,86,86,118,118,2,0,89,
89,121,121,2,0,67,67,99,99,2,0,68,68,100,100,2,0,87,87,119,119,2,
0,70,70,102,102,2,0,66,66,98,98,2,0,76,76,108,108,2,0,71,71,103,
103,1,0,48,57,2,0,65,90,97,122,4,0,48,57,65,90,95,95,97,122,4,0,
9,10,13,13,32,32,38,38,410,0,1,1,0,0,0,0,3,1,0,0,0,0,5,1,0,0,0,0,
7,1,0,0,0,0,9,1,0,0,0,0,11,1,0,0,0,0,13,1,0,0,0,0,15,1,0,0,0,0,17,
1,0,0,0,0,19,1,0,0,0,0,21,1,0,0,0,0,23,1,0,0,0,0,25,1,0,0,0,0,27,
1,0,0,0,0,29,1,0,0,0,0,31,1,0,0,0,0,33,1,0,0,0,0,35,1,0,0,0,0,37,
1,0,0,0,0,39,1,0,0,0,0,41,1,0,0,0,0,43,1,0,0,0,0,45,1,0,0,0,0,47,
1,0,0,0,0,49,1,0,0,0,0,51,1,0,0,0,0,53,1,0,0,0,0,55,1,0,0,0,0,57,
1,0,0,0,0,59,1,0,0,0,0,61,1,0,0,0,0,63,1,0,0,0,0,65,1,0,0,0,0,67,
1,0,0,0,0,69,1,0,0,0,0,71,1,0,0,0,0,73,1,0,0,0,0,75,1,0,0,0,0,77,
1,0,0,0,0,79,1,0,0,0,0,81,1,0,0,0,0,83,1,0,0,0,0,85,1,0,0,0,0,91,
1,0,0,0,0,93,1,0,0,0,0,95,1,0,0,0,0,97,1,0,0,0,0,99,1,0,0,0,0,101,
1,0,0,0,1,103,1,0,0,0,3,105,1,0,0,0,5,107,1,0,0,0,7,109,1,0,0,0,
9,112,1,0,0,0,11,115,1,0,0,0,13,118,1,0,0,0,15,121,1,0,0,0,17,124,
1,0,0,0,19,127,1,0,0,0,21,129,1,0,0,0,23,131,1,0,0,0,25,133,1,0,
0,0,27,135,1,0,0,0,29,137,1,0,0,0,31,139,1,0,0,0,33,141,1,0,0,0,
35,143,1,0,0,0,37,145,1,0,0,0,39,147,1,0,0,0,41,149,1,0,0,0,43,151,
1,0,0,0,45,154,1,0,0,0,47,158,1,0,0,0,49,160,1,0,0,0,51,162,1,0,
0,0,53,164,1,0,0,0,55,169,1,0,0,0,57,177,1,0,0,0,59,185,1,0,0,0,
61,192,1,0,0,0,63,197,1,0,0,0,65,208,1,0,0,0,67,215,1,0,0,0,69,225,
1,0,0,0,71,233,1,0,0,0,73,241,1,0,0,0,75,252,1,0,0,0,77,260,1,0,
0,0,79,271,1,0,0,0,81,283,1,0,0,0,83,293,1,0,0,0,85,304,1,0,0,0,
87,324,1,0,0,0,89,327,1,0,0,0,91,330,1,0,0,0,93,352,1,0,0,0,95,363,
1,0,0,0,97,365,1,0,0,0,99,379,1,0,0,0,101,387,1,0,0,0,103,104,5,
91,0,0,104,2,1,0,0,0,105,106,5,93,0,0,106,4,1,0,0,0,107,108,5,61,
0,0,108,6,1,0,0,0,109,110,5,43,0,0,110,111,5,61,0,0,111,8,1,0,0,
0,112,113,5,45,0,0,113,114,5,61,0,0,114,10,1,0,0,0,115,116,5,58,
0,0,116,117,5,61,0,0,117,12,1,0,0,0,118,119,5,42,0,0,119,120,5,61,
0,0,120,14,1,0,0,0,121,122,5,47,0,0,122,123,5,61,0,0,123,16,1,0,
0,0,124,125,5,94,0,0,125,126,5,61,0,0,126,18,1,0,0,0,127,128,5,44,
0,0,128,20,1,0,0,0,129,130,5,39,0,0,130,22,1,0,0,0,131,132,5,40,
0,0,132,24,1,0,0,0,133,134,5,41,0,0,134,26,1,0,0,0,135,136,5,123,
0,0,136,28,1,0,0,0,137,138,5,125,0,0,138,30,1,0,0,0,139,140,5,58,
0,0,140,32,1,0,0,0,141,142,5,43,0,0,142,34,1,0,0,0,143,144,5,45,
0,0,144,36,1,0,0,0,145,146,5,59,0,0,146,38,1,0,0,0,147,148,5,46,
0,0,148,40,1,0,0,0,149,150,5,62,0,0,150,42,1,0,0,0,151,152,5,48,
0,0,152,153,5,62,0,0,153,44,1,0,0,0,154,155,5,49,0,0,155,156,5,62,
0,0,156,157,5,62,0,0,157,46,1,0,0,0,158,159,5,94,0,0,159,48,1,0,
0,0,160,161,5,42,0,0,161,50,1,0,0,0,162,163,5,47,0,0,163,52,1,0,
0,0,164,165,7,0,0,0,165,166,7,1,0,0,166,167,7,2,0,0,167,168,7,2,
0,0,168,54,1,0,0,0,169,170,7,3,0,0,170,171,7,4,0,0,171,172,7,5,0,
0,172,173,7,6,0,0,173,174,7,7,0,0,174,175,7,3,0,0,175,176,7,1,0,
0,176,56,1,0,0,0,177,178,7,3,0,0,178,179,7,4,0,0,179,180,7,8,0,0,
180,181,7,9,0,0,181,183,7,7,0,0,182,184,7,2,0,0,183,182,1,0,0,0,
183,184,1,0,0,0,184,58,1,0,0,0,185,186,7,10,0,0,186,187,7,9,0,0,
187,188,7,7,0,0,188,189,7,8,0,0,189,190,7,9,0,0,190,191,7,7,0,0,
191,60,1,0,0,0,192,193,7,2,0,0,193,194,7,1,0,0,194,195,7,11,0,0,
195,196,7,5,0,0,196,62,1,0,0,0,197,198,7,9,0,0,198,199,7,4,0,0,199,
200,7,3,0,0,200,201,7,7,0,0,201,202,7,2,0,0,202,203,7,12,0,0,203,
204,7,2,0,0,204,205,7,7,0,0,205,206,7,5,0,0,206,207,7,0,0,0,207,
64,1,0,0,0,208,209,7,5,0,0,209,210,7,4,0,0,210,211,7,13,0,0,211,
212,7,10,0,0,212,213,7,14,0,0,213,214,7,5,0,0,214,66,1,0,0,0,215,
216,7,4,0,0,216,217,7,5,0,0,217,218,7,15,0,0,218,219,7,7,0,0,219,
220,7,10,0,0,220,221,7,4,0,0,221,222,7,3,0,0,222,223,7,1,0,0,223,
224,7,4,0,0,224,68,1,0,0,0,225,226,7,16,0,0,226,227,7,6,0,0,227,
228,7,1,0,0,228,229,7,0,0,0,229,231,7,5,0,0,230,232,7,2,0,0,231,
230,1,0,0,0,231,232,1,0,0,0,232,70,1,0,0,0,233,234,7,17,0,0,234,
235,7,10,0,0,235,236,7,14,0,0,236,237,7,3,0,0,237,239,7,5,0,0,238,
240,7,2,0,0,239,238,1,0,0,0,239,240,1,0,0,0,240,72,1,0,0,0,241,242,
7,8,0,0,242,243,7,1,0,0,243,244,7,6,0,0,244,245,7,7,0,0,245,246,
7,3,0,0,246,247,7,13,0,0,247,248,7,18,0,0,248,250,7,5,0,0,249,251,
7,2,0,0,250,249,1,0,0,0,250,251,1,0,0,0,251,74,1,0,0,0,252,253,7,
8,0,0,253,254,7,10,0,0,254,255,7,3,0,0,255,256,7,4,0,0,256,258,7,
7,0,0,257,259,7,2,0,0,258,257,1,0,0,0,258,259,1,0,0,0,259,76,1,0,
0,0,260,261,7,13,0,0,261,262,7,10,0,0,262,263,7,4,0,0,263,264,7,
2,0,0,264,265,7,7,0,0,265,266,7,1,0,0,266,267,7,4,0,0,267,269,7,
7,0,0,268,270,7,2,0,0,269,268,1,0,0,0,269,270,1,0,0,0,270,78,1,0,
0,0,271,272,7,2,0,0,272,273,7,8,0,0,273,274,7,5,0,0,274,275,7,13,
0,0,275,276,7,3,0,0,276,277,7,16,0,0,277,278,7,3,0,0,278,279,7,5,
0,0,279,281,7,14,0,0,280,282,7,2,0,0,281,280,1,0,0,0,281,282,1,0,
0,0,282,80,1,0,0,0,283,284,7,3,0,0,284,285,7,0,0,0,285,286,7,1,0,
0,286,287,7,19,0,0,287,288,7,3,0,0,288,289,7,4,0,0,289,290,7,1,0,
0,290,291,7,6,0,0,291,292,7,12,0,0,292,82,1,0,0,0,293,294,7,11,0,
0,294,295,7,1,0,0,295,296,7,6,0,0,296,297,7,3,0,0,297,298,7,1,0,
0,298,299,7,17,0,0,299,300,7,18,0,0,300,302,7,5,0,0,301,303,7,2,
0,0,302,301,1,0,0,0,302,303,1,0,0,0,303,84,1,0,0,0,304,305,7,0,0,
0,305,306,7,10,0,0,306,307,7,7,0,0,307,308,7,3,0,0,308,309,7,10,
0,0,309,310,7,4,0,0,310,311,7,11,0,0,311,312,7,1,0,0,312,313,7,6,
0,0,313,314,7,3,0,0,314,315,7,1,0,0,315,316,7,17,0,0,316,317,7,18,
0,0,317,319,7,5,0,0,318,320,7,2,0,0,319,318,1,0,0,0,319,320,1,0,
0,0,320,86,1,0,0,0,321,323,5,39,0,0,322,321,1,0,0,0,323,326,1,0,
0,0,324,322,1,0,0,0,324,325,1,0,0,0,325,88,1,0,0,0,326,324,1,0,0,
0,327,328,7,20,0,0,328,90,1,0,0,0,329,331,7,20,0,0,330,329,1,0,0,
0,331,332,1,0,0,0,332,330,1,0,0,0,332,333,1,0,0,0,333,92,1,0,0,0,
334,336,3,89,44,0,335,334,1,0,0,0,336,337,1,0,0,0,337,335,1,0,0,
0,337,338,1,0,0,0,338,339,1,0,0,0,339,343,5,46,0,0,340,342,3,89,
44,0,341,340,1,0,0,0,342,345,1,0,0,0,343,341,1,0,0,0,343,344,1,0,
0,0,344,353,1,0,0,0,345,343,1,0,0,0,346,348,5,46,0,0,347,349,3,89,
44,0,348,347,1,0,0,0,349,350,1,0,0,0,350,348,1,0,0,0,350,351,1,0,
0,0,351,353,1,0,0,0,352,335,1,0,0,0,352,346,1,0,0,0,353,94,1,0,0,
0,354,355,3,93,46,0,355,356,5,69,0,0,356,357,3,91,45,0,357,364,1,
0,0,0,358,359,3,93,46,0,359,360,5,69,0,0,360,361,5,45,0,0,361,362,
3,91,45,0,362,364,1,0,0,0,363,354,1,0,0,0,363,358,1,0,0,0,364,96,
1,0,0,0,365,369,5,37,0,0,366,368,9,0,0,0,367,366,1,0,0,0,368,371,
1,0,0,0,369,370,1,0,0,0,369,367,1,0,0,0,370,373,1,0,0,0,371,369,
1,0,0,0,372,374,5,13,0,0,373,372,1,0,0,0,373,374,1,0,0,0,374,375,
1,0,0,0,375,376,5,10,0,0,376,377,1,0,0,0,377,378,6,48,0,0,378,98,
1,0,0,0,379,383,7,21,0,0,380,382,7,22,0,0,381,380,1,0,0,0,382,385,
1,0,0,0,383,381,1,0,0,0,383,384,1,0,0,0,384,100,1,0,0,0,385,383,
1,0,0,0,386,388,7,23,0,0,387,386,1,0,0,0,388,389,1,0,0,0,389,387,
1,0,0,0,389,390,1,0,0,0,390,391,1,0,0,0,391,392,6,50,0,0,392,102,
1,0,0,0,21,0,183,231,239,250,258,269,281,302,319,324,332,337,343,
350,352,363,369,373,383,389,1,6,0,0
]
class AutolevLexer(Lexer):
atn = ATNDeserializer().deserialize(serializedATN())
decisionsToDFA = [ DFA(ds, i) for i, ds in enumerate(atn.decisionToState) ]
T__0 = 1
T__1 = 2
T__2 = 3
T__3 = 4
T__4 = 5
T__5 = 6
T__6 = 7
T__7 = 8
T__8 = 9
T__9 = 10
T__10 = 11
T__11 = 12
T__12 = 13
T__13 = 14
T__14 = 15
T__15 = 16
T__16 = 17
T__17 = 18
T__18 = 19
T__19 = 20
T__20 = 21
T__21 = 22
T__22 = 23
T__23 = 24
T__24 = 25
T__25 = 26
Mass = 27
Inertia = 28
Input = 29
Output = 30
Save = 31
UnitSystem = 32
Encode = 33
Newtonian = 34
Frames = 35
Bodies = 36
Particles = 37
Points = 38
Constants = 39
Specifieds = 40
Imaginary = 41
Variables = 42
MotionVariables = 43
INT = 44
FLOAT = 45
EXP = 46
LINE_COMMENT = 47
ID = 48
WS = 49
channelNames = [ u"DEFAULT_TOKEN_CHANNEL", u"HIDDEN" ]
modeNames = [ "DEFAULT_MODE" ]
literalNames = [ "<INVALID>",
"'['", "']'", "'='", "'+='", "'-='", "':='", "'*='", "'/='",
"'^='", "','", "'''", "'('", "')'", "'{'", "'}'", "':'", "'+'",
"'-'", "';'", "'.'", "'>'", "'0>'", "'1>>'", "'^'", "'*'", "'/'" ]
symbolicNames = [ "<INVALID>",
"Mass", "Inertia", "Input", "Output", "Save", "UnitSystem",
"Encode", "Newtonian", "Frames", "Bodies", "Particles", "Points",
"Constants", "Specifieds", "Imaginary", "Variables", "MotionVariables",
"INT", "FLOAT", "EXP", "LINE_COMMENT", "ID", "WS" ]
ruleNames = [ "T__0", "T__1", "T__2", "T__3", "T__4", "T__5", "T__6",
"T__7", "T__8", "T__9", "T__10", "T__11", "T__12", "T__13",
"T__14", "T__15", "T__16", "T__17", "T__18", "T__19",
"T__20", "T__21", "T__22", "T__23", "T__24", "T__25",
"Mass", "Inertia", "Input", "Output", "Save", "UnitSystem",
"Encode", "Newtonian", "Frames", "Bodies", "Particles",
"Points", "Constants", "Specifieds", "Imaginary", "Variables",
"MotionVariables", "DIFF", "DIGIT", "INT", "FLOAT", "EXP",
"LINE_COMMENT", "ID", "WS" ]
grammarFileName = "Autolev.g4"
def __init__(self, input=None, output:TextIO = sys.stdout):
super().__init__(input, output)
self.checkVersion("4.11.1")
self._interp = LexerATNSimulator(self, self.atn, self.decisionsToDFA, PredictionContextCache())
self._actions = None
self._predicates = None

421
rl/Lib/site-packages/sympy/parsing/autolev/_antlr/autolevlistener.py Normal file
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@ -0,0 +1,421 @@
# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
#
# Generated with antlr4
# antlr4 is licensed under the BSD-3-Clause License
# https://github.com/antlr/antlr4/blob/master/LICENSE.txt
from antlr4 import *
if __name__ is not None and "." in __name__:
from .autolevparser import AutolevParser
else:
from autolevparser import AutolevParser
# This class defines a complete listener for a parse tree produced by AutolevParser.
class AutolevListener(ParseTreeListener):
# Enter a parse tree produced by AutolevParser#prog.
def enterProg(self, ctx:AutolevParser.ProgContext):
pass
# Exit a parse tree produced by AutolevParser#prog.
def exitProg(self, ctx:AutolevParser.ProgContext):
pass
# Enter a parse tree produced by AutolevParser#stat.
def enterStat(self, ctx:AutolevParser.StatContext):
pass
# Exit a parse tree produced by AutolevParser#stat.
def exitStat(self, ctx:AutolevParser.StatContext):
pass
# Enter a parse tree produced by AutolevParser#vecAssign.
def enterVecAssign(self, ctx:AutolevParser.VecAssignContext):
pass
# Exit a parse tree produced by AutolevParser#vecAssign.
def exitVecAssign(self, ctx:AutolevParser.VecAssignContext):
pass
# Enter a parse tree produced by AutolevParser#indexAssign.
def enterIndexAssign(self, ctx:AutolevParser.IndexAssignContext):
pass
# Exit a parse tree produced by AutolevParser#indexAssign.
def exitIndexAssign(self, ctx:AutolevParser.IndexAssignContext):
pass
# Enter a parse tree produced by AutolevParser#regularAssign.
def enterRegularAssign(self, ctx:AutolevParser.RegularAssignContext):
pass
# Exit a parse tree produced by AutolevParser#regularAssign.
def exitRegularAssign(self, ctx:AutolevParser.RegularAssignContext):
pass
# Enter a parse tree produced by AutolevParser#equals.
def enterEquals(self, ctx:AutolevParser.EqualsContext):
pass
# Exit a parse tree produced by AutolevParser#equals.
def exitEquals(self, ctx:AutolevParser.EqualsContext):
pass
# Enter a parse tree produced by AutolevParser#index.
def enterIndex(self, ctx:AutolevParser.IndexContext):
pass
# Exit a parse tree produced by AutolevParser#index.
def exitIndex(self, ctx:AutolevParser.IndexContext):
pass
# Enter a parse tree produced by AutolevParser#diff.
def enterDiff(self, ctx:AutolevParser.DiffContext):
pass
# Exit a parse tree produced by AutolevParser#diff.
def exitDiff(self, ctx:AutolevParser.DiffContext):
pass
# Enter a parse tree produced by AutolevParser#functionCall.
def enterFunctionCall(self, ctx:AutolevParser.FunctionCallContext):
pass
# Exit a parse tree produced by AutolevParser#functionCall.
def exitFunctionCall(self, ctx:AutolevParser.FunctionCallContext):
pass
# Enter a parse tree produced by AutolevParser#varDecl.
def enterVarDecl(self, ctx:AutolevParser.VarDeclContext):
pass
# Exit a parse tree produced by AutolevParser#varDecl.
def exitVarDecl(self, ctx:AutolevParser.VarDeclContext):
pass
# Enter a parse tree produced by AutolevParser#varType.
def enterVarType(self, ctx:AutolevParser.VarTypeContext):
pass
# Exit a parse tree produced by AutolevParser#varType.
def exitVarType(self, ctx:AutolevParser.VarTypeContext):
pass
# Enter a parse tree produced by AutolevParser#varDecl2.
def enterVarDecl2(self, ctx:AutolevParser.VarDecl2Context):
pass
# Exit a parse tree produced by AutolevParser#varDecl2.
def exitVarDecl2(self, ctx:AutolevParser.VarDecl2Context):
pass
# Enter a parse tree produced by AutolevParser#ranges.
def enterRanges(self, ctx:AutolevParser.RangesContext):
pass
# Exit a parse tree produced by AutolevParser#ranges.
def exitRanges(self, ctx:AutolevParser.RangesContext):
pass
# Enter a parse tree produced by AutolevParser#massDecl.
def enterMassDecl(self, ctx:AutolevParser.MassDeclContext):
pass
# Exit a parse tree produced by AutolevParser#massDecl.
def exitMassDecl(self, ctx:AutolevParser.MassDeclContext):
pass
# Enter a parse tree produced by AutolevParser#massDecl2.
def enterMassDecl2(self, ctx:AutolevParser.MassDecl2Context):
pass
# Exit a parse tree produced by AutolevParser#massDecl2.
def exitMassDecl2(self, ctx:AutolevParser.MassDecl2Context):
pass
# Enter a parse tree produced by AutolevParser#inertiaDecl.
def enterInertiaDecl(self, ctx:AutolevParser.InertiaDeclContext):
pass
# Exit a parse tree produced by AutolevParser#inertiaDecl.
def exitInertiaDecl(self, ctx:AutolevParser.InertiaDeclContext):
pass
# Enter a parse tree produced by AutolevParser#matrix.
def enterMatrix(self, ctx:AutolevParser.MatrixContext):
pass
# Exit a parse tree produced by AutolevParser#matrix.
def exitMatrix(self, ctx:AutolevParser.MatrixContext):
pass
# Enter a parse tree produced by AutolevParser#matrixInOutput.
def enterMatrixInOutput(self, ctx:AutolevParser.MatrixInOutputContext):
pass
# Exit a parse tree produced by AutolevParser#matrixInOutput.
def exitMatrixInOutput(self, ctx:AutolevParser.MatrixInOutputContext):
pass
# Enter a parse tree produced by AutolevParser#codeCommands.
def enterCodeCommands(self, ctx:AutolevParser.CodeCommandsContext):
pass
# Exit a parse tree produced by AutolevParser#codeCommands.
def exitCodeCommands(self, ctx:AutolevParser.CodeCommandsContext):
pass
# Enter a parse tree produced by AutolevParser#settings.
def enterSettings(self, ctx:AutolevParser.SettingsContext):
pass
# Exit a parse tree produced by AutolevParser#settings.
def exitSettings(self, ctx:AutolevParser.SettingsContext):
pass
# Enter a parse tree produced by AutolevParser#units.
def enterUnits(self, ctx:AutolevParser.UnitsContext):
pass
# Exit a parse tree produced by AutolevParser#units.
def exitUnits(self, ctx:AutolevParser.UnitsContext):
pass
# Enter a parse tree produced by AutolevParser#inputs.
def enterInputs(self, ctx:AutolevParser.InputsContext):
pass
# Exit a parse tree produced by AutolevParser#inputs.
def exitInputs(self, ctx:AutolevParser.InputsContext):
pass
# Enter a parse tree produced by AutolevParser#id_diff.
def enterId_diff(self, ctx:AutolevParser.Id_diffContext):
pass
# Exit a parse tree produced by AutolevParser#id_diff.
def exitId_diff(self, ctx:AutolevParser.Id_diffContext):
pass
# Enter a parse tree produced by AutolevParser#inputs2.
def enterInputs2(self, ctx:AutolevParser.Inputs2Context):
pass
# Exit a parse tree produced by AutolevParser#inputs2.
def exitInputs2(self, ctx:AutolevParser.Inputs2Context):
pass
# Enter a parse tree produced by AutolevParser#outputs.
def enterOutputs(self, ctx:AutolevParser.OutputsContext):
pass
# Exit a parse tree produced by AutolevParser#outputs.
def exitOutputs(self, ctx:AutolevParser.OutputsContext):
pass
# Enter a parse tree produced by AutolevParser#outputs2.
def enterOutputs2(self, ctx:AutolevParser.Outputs2Context):
pass
# Exit a parse tree produced by AutolevParser#outputs2.
def exitOutputs2(self, ctx:AutolevParser.Outputs2Context):
pass
# Enter a parse tree produced by AutolevParser#codegen.
def enterCodegen(self, ctx:AutolevParser.CodegenContext):
pass
# Exit a parse tree produced by AutolevParser#codegen.
def exitCodegen(self, ctx:AutolevParser.CodegenContext):
pass
# Enter a parse tree produced by AutolevParser#commands.
def enterCommands(self, ctx:AutolevParser.CommandsContext):
pass
# Exit a parse tree produced by AutolevParser#commands.
def exitCommands(self, ctx:AutolevParser.CommandsContext):
pass
# Enter a parse tree produced by AutolevParser#vec.
def enterVec(self, ctx:AutolevParser.VecContext):
pass
# Exit a parse tree produced by AutolevParser#vec.
def exitVec(self, ctx:AutolevParser.VecContext):
pass
# Enter a parse tree produced by AutolevParser#parens.
def enterParens(self, ctx:AutolevParser.ParensContext):
pass
# Exit a parse tree produced by AutolevParser#parens.
def exitParens(self, ctx:AutolevParser.ParensContext):
pass
# Enter a parse tree produced by AutolevParser#VectorOrDyadic.
def enterVectorOrDyadic(self, ctx:AutolevParser.VectorOrDyadicContext):
pass
# Exit a parse tree produced by AutolevParser#VectorOrDyadic.
def exitVectorOrDyadic(self, ctx:AutolevParser.VectorOrDyadicContext):
pass
# Enter a parse tree produced by AutolevParser#Exponent.
def enterExponent(self, ctx:AutolevParser.ExponentContext):
pass
# Exit a parse tree produced by AutolevParser#Exponent.
def exitExponent(self, ctx:AutolevParser.ExponentContext):
pass
# Enter a parse tree produced by AutolevParser#MulDiv.
def enterMulDiv(self, ctx:AutolevParser.MulDivContext):
pass
# Exit a parse tree produced by AutolevParser#MulDiv.
def exitMulDiv(self, ctx:AutolevParser.MulDivContext):
pass
# Enter a parse tree produced by AutolevParser#AddSub.
def enterAddSub(self, ctx:AutolevParser.AddSubContext):
pass
# Exit a parse tree produced by AutolevParser#AddSub.
def exitAddSub(self, ctx:AutolevParser.AddSubContext):
pass
# Enter a parse tree produced by AutolevParser#float.
def enterFloat(self, ctx:AutolevParser.FloatContext):
pass
# Exit a parse tree produced by AutolevParser#float.
def exitFloat(self, ctx:AutolevParser.FloatContext):
pass
# Enter a parse tree produced by AutolevParser#int.
def enterInt(self, ctx:AutolevParser.IntContext):
pass
# Exit a parse tree produced by AutolevParser#int.
def exitInt(self, ctx:AutolevParser.IntContext):
pass
# Enter a parse tree produced by AutolevParser#idEqualsExpr.
def enterIdEqualsExpr(self, ctx:AutolevParser.IdEqualsExprContext):
pass
# Exit a parse tree produced by AutolevParser#idEqualsExpr.
def exitIdEqualsExpr(self, ctx:AutolevParser.IdEqualsExprContext):
pass
# Enter a parse tree produced by AutolevParser#negativeOne.
def enterNegativeOne(self, ctx:AutolevParser.NegativeOneContext):
pass
# Exit a parse tree produced by AutolevParser#negativeOne.
def exitNegativeOne(self, ctx:AutolevParser.NegativeOneContext):
pass
# Enter a parse tree produced by AutolevParser#function.
def enterFunction(self, ctx:AutolevParser.FunctionContext):
pass
# Exit a parse tree produced by AutolevParser#function.
def exitFunction(self, ctx:AutolevParser.FunctionContext):
pass
# Enter a parse tree produced by AutolevParser#rangess.
def enterRangess(self, ctx:AutolevParser.RangessContext):
pass
# Exit a parse tree produced by AutolevParser#rangess.
def exitRangess(self, ctx:AutolevParser.RangessContext):
pass
# Enter a parse tree produced by AutolevParser#colon.
def enterColon(self, ctx:AutolevParser.ColonContext):
pass
# Exit a parse tree produced by AutolevParser#colon.
def exitColon(self, ctx:AutolevParser.ColonContext):
pass
# Enter a parse tree produced by AutolevParser#id.
def enterId(self, ctx:AutolevParser.IdContext):
pass
# Exit a parse tree produced by AutolevParser#id.
def exitId(self, ctx:AutolevParser.IdContext):
pass
# Enter a parse tree produced by AutolevParser#exp.
def enterExp(self, ctx:AutolevParser.ExpContext):
pass
# Exit a parse tree produced by AutolevParser#exp.
def exitExp(self, ctx:AutolevParser.ExpContext):
pass
# Enter a parse tree produced by AutolevParser#matrices.
def enterMatrices(self, ctx:AutolevParser.MatricesContext):
pass
# Exit a parse tree produced by AutolevParser#matrices.
def exitMatrices(self, ctx:AutolevParser.MatricesContext):
pass
# Enter a parse tree produced by AutolevParser#Indexing.
def enterIndexing(self, ctx:AutolevParser.IndexingContext):
pass
# Exit a parse tree produced by AutolevParser#Indexing.
def exitIndexing(self, ctx:AutolevParser.IndexingContext):
pass
del AutolevParser

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import os
import subprocess
import glob
from sympy.utilities.misc import debug
here = os.path.dirname(__file__)
grammar_file = os.path.abspath(os.path.join(here, "Autolev.g4"))
dir_autolev_antlr = os.path.join(here, "_antlr")
header = '''\
# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
#
# Generated with antlr4
# antlr4 is licensed under the BSD-3-Clause License
# https://github.com/antlr/antlr4/blob/master/LICENSE.txt
'''
def check_antlr_version():
debug("Checking antlr4 version...")
try:
debug(subprocess.check_output(["antlr4"])
.decode('utf-8').split("\n")[0])
return True
except (subprocess.CalledProcessError, FileNotFoundError):
debug("The 'antlr4' command line tool is not installed, "
"or not on your PATH.\n"
"> Please refer to the README.md file for more information.")
return False
def build_parser(output_dir=dir_autolev_antlr):
check_antlr_version()
debug("Updating ANTLR-generated code in {}".format(output_dir))
if not os.path.exists(output_dir):
os.makedirs(output_dir)
with open(os.path.join(output_dir, "__init__.py"), "w+") as fp:
fp.write(header)
args = [
"antlr4",
grammar_file,
"-o", output_dir,
"-no-visitor",
]
debug("Running code generation...\n\t$ {}".format(" ".join(args)))
subprocess.check_output(args, cwd=output_dir)
debug("Applying headers, removing unnecessary files and renaming...")
# Handle case insensitive file systems. If the files are already
# generated, they will be written to autolev* but Autolev*.* won't match them.
for path in (glob.glob(os.path.join(output_dir, "Autolev*.*")) or
glob.glob(os.path.join(output_dir, "autolev*.*"))):
# Remove files ending in .interp or .tokens as they are not needed.
if not path.endswith(".py"):
os.unlink(path)
continue
new_path = os.path.join(output_dir, os.path.basename(path).lower())
with open(path, 'r') as f:
lines = [line.rstrip().replace('AutolevParser import', 'autolevparser import') +'\n'
for line in f.readlines()]
os.unlink(path)
with open(new_path, "w") as out_file:
offset = 0
while lines[offset].startswith('#'):
offset += 1
out_file.write(header)
out_file.writelines(lines[offset:])
debug("\t{}".format(new_path))
return True
if __name__ == "__main__":
build_parser()

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from importlib.metadata import version
from sympy.external import import_module
autolevparser = import_module('sympy.parsing.autolev._antlr.autolevparser',
import_kwargs={'fromlist': ['AutolevParser']})
autolevlexer = import_module('sympy.parsing.autolev._antlr.autolevlexer',
import_kwargs={'fromlist': ['AutolevLexer']})
autolevlistener = import_module('sympy.parsing.autolev._antlr.autolevlistener',
import_kwargs={'fromlist': ['AutolevListener']})
AutolevParser = getattr(autolevparser, 'AutolevParser', None)
AutolevLexer = getattr(autolevlexer, 'AutolevLexer', None)
AutolevListener = getattr(autolevlistener, 'AutolevListener', None)
def parse_autolev(autolev_code, include_numeric):
antlr4 = import_module('antlr4')
if not antlr4 or not version('antlr4-python3-runtime').startswith('4.11'):
raise ImportError("Autolev parsing requires the antlr4 Python package,"
" provided by pip (antlr4-python3-runtime)"
" conda (antlr-python-runtime), version 4.11")
try:
l = autolev_code.readlines()
input_stream = antlr4.InputStream("".join(l))
except Exception:
input_stream = antlr4.InputStream(autolev_code)
if AutolevListener:
from ._listener_autolev_antlr import MyListener
lexer = AutolevLexer(input_stream)
token_stream = antlr4.CommonTokenStream(lexer)
parser = AutolevParser(token_stream)
tree = parser.prog()
my_listener = MyListener(include_numeric)
walker = antlr4.ParseTreeWalker()
walker.walk(my_listener, tree)
return "".join(my_listener.output_code)

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# parsing/tests/test_autolev.py uses the .al files in this directory as inputs and checks
# the equivalence of the parser generated codes and the respective .py files.
# By default, this directory contains tests for all rules of the parser.
# Additional tests consisting of full physics examples shall be made available soon in
# the form of another repository. One shall be able to copy the contents of that repo
# to this folder and use those tests after uncommenting the respective code in
# parsing/tests/test_autolev.py.

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CONSTANTS G,LB,W,H
MOTIONVARIABLES' THETA'',PHI'',OMEGA',ALPHA'
NEWTONIAN N
BODIES A,B
SIMPROT(N,A,2,THETA)
SIMPROT(A,B,3,PHI)
POINT O
LA = (LB-H/2)/2
P_O_AO> = LA*A3>
P_O_BO> = LB*A3>
OMEGA = THETA'
ALPHA = PHI'
W_A_N> = OMEGA*N2>
W_B_A> = ALPHA*A3>
V_O_N> = 0>
V2PTS(N, A, O, AO)
V2PTS(N, A, O, BO)
MASS A=MA, B=MB
IAXX = 1/12*MA*(2*LA)^2
IAYY = IAXX
IAZZ = 0
IBXX = 1/12*MB*H^2
IBYY = 1/12*MB*(W^2+H^2)
IBZZ = 1/12*MB*W^2
INERTIA A, IAXX, IAYY, IAZZ
INERTIA B, IBXX, IBYY, IBZZ
GRAVITY(G*N3>)
ZERO = FR() + FRSTAR()
KANE()
INPUT LB=0.2,H=0.1,W=0.2,MA=0.01,MB=0.1,G=9.81
INPUT THETA = 90 DEG, PHI = 0.5 DEG, OMEGA=0, ALPHA=0
INPUT TFINAL=10, INTEGSTP=0.02
CODE DYNAMICS() some_filename.c

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
g, lb, w, h = _sm.symbols('g lb w h', real=True)
theta, phi, omega, alpha = _me.dynamicsymbols('theta phi omega alpha')
theta_d, phi_d, omega_d, alpha_d = _me.dynamicsymbols('theta_ phi_ omega_ alpha_', 1)
theta_dd, phi_dd = _me.dynamicsymbols('theta_ phi_', 2)
frame_n = _me.ReferenceFrame('n')
body_a_cm = _me.Point('a_cm')
body_a_cm.set_vel(frame_n, 0)
body_a_f = _me.ReferenceFrame('a_f')
body_a = _me.RigidBody('a', body_a_cm, body_a_f, _sm.symbols('m'), (_me.outer(body_a_f.x,body_a_f.x),body_a_cm))
body_b_cm = _me.Point('b_cm')
body_b_cm.set_vel(frame_n, 0)
body_b_f = _me.ReferenceFrame('b_f')
body_b = _me.RigidBody('b', body_b_cm, body_b_f, _sm.symbols('m'), (_me.outer(body_b_f.x,body_b_f.x),body_b_cm))
body_a_f.orient(frame_n, 'Axis', [theta, frame_n.y])
body_b_f.orient(body_a_f, 'Axis', [phi, body_a_f.z])
point_o = _me.Point('o')
la = (lb-h/2)/2
body_a_cm.set_pos(point_o, la*body_a_f.z)
body_b_cm.set_pos(point_o, lb*body_a_f.z)
body_a_f.set_ang_vel(frame_n, omega*frame_n.y)
body_b_f.set_ang_vel(body_a_f, alpha*body_a_f.z)
point_o.set_vel(frame_n, 0)
body_a_cm.v2pt_theory(point_o,frame_n,body_a_f)
body_b_cm.v2pt_theory(point_o,frame_n,body_a_f)
ma = _sm.symbols('ma')
body_a.mass = ma
mb = _sm.symbols('mb')
body_b.mass = mb
iaxx = 1/12*ma*(2*la)**2
iayy = iaxx
iazz = 0
ibxx = 1/12*mb*h**2
ibyy = 1/12*mb*(w**2+h**2)
ibzz = 1/12*mb*w**2
body_a.inertia = (_me.inertia(body_a_f, iaxx, iayy, iazz, 0, 0, 0), body_a_cm)
body_b.inertia = (_me.inertia(body_b_f, ibxx, ibyy, ibzz, 0, 0, 0), body_b_cm)
force_a = body_a.mass*(g*frame_n.z)
force_b = body_b.mass*(g*frame_n.z)
kd_eqs = [theta_d - omega, phi_d - alpha]
forceList = [(body_a.masscenter,body_a.mass*(g*frame_n.z)), (body_b.masscenter,body_b.mass*(g*frame_n.z))]
kane = _me.KanesMethod(frame_n, q_ind=[theta,phi], u_ind=[omega, alpha], kd_eqs = kd_eqs)
fr, frstar = kane.kanes_equations([body_a, body_b], forceList)
zero = fr+frstar
from pydy.system import System
sys = System(kane, constants = {g:9.81, lb:0.2, w:0.2, h:0.1, ma:0.01, mb:0.1},
specifieds={},
initial_conditions={theta:_np.deg2rad(90), phi:_np.deg2rad(0.5), omega:0, alpha:0},
times = _np.linspace(0.0, 10, 10/0.02))
y=sys.integrate()

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MOTIONVARIABLES' Q{2}', U{2}'
CONSTANTS L,M,G
NEWTONIAN N
FRAMES A,B
SIMPROT(N, A, 3, Q1)
SIMPROT(N, B, 3, Q2)
W_A_N>=U1*N3>
W_B_N>=U2*N3>
POINT O
PARTICLES P,R
P_O_P> = L*A1>
P_P_R> = L*B1>
V_O_N> = 0>
V2PTS(N, A, O, P)
V2PTS(N, B, P, R)
MASS P=M, R=M
Q1' = U1
Q2' = U2
GRAVITY(G*N1>)
ZERO = FR() + FRSTAR()
KANE()
INPUT M=1,G=9.81,L=1
INPUT Q1=.1,Q2=.2,U1=0,U2=0
INPUT TFINAL=10, INTEGSTP=.01
CODE DYNAMICS() some_filename.c

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
q1, q2, u1, u2 = _me.dynamicsymbols('q1 q2 u1 u2')
q1_d, q2_d, u1_d, u2_d = _me.dynamicsymbols('q1_ q2_ u1_ u2_', 1)
l, m, g = _sm.symbols('l m g', real=True)
frame_n = _me.ReferenceFrame('n')
frame_a = _me.ReferenceFrame('a')
frame_b = _me.ReferenceFrame('b')
frame_a.orient(frame_n, 'Axis', [q1, frame_n.z])
frame_b.orient(frame_n, 'Axis', [q2, frame_n.z])
frame_a.set_ang_vel(frame_n, u1*frame_n.z)
frame_b.set_ang_vel(frame_n, u2*frame_n.z)
point_o = _me.Point('o')
particle_p = _me.Particle('p', _me.Point('p_pt'), _sm.Symbol('m'))
particle_r = _me.Particle('r', _me.Point('r_pt'), _sm.Symbol('m'))
particle_p.point.set_pos(point_o, l*frame_a.x)
particle_r.point.set_pos(particle_p.point, l*frame_b.x)
point_o.set_vel(frame_n, 0)
particle_p.point.v2pt_theory(point_o,frame_n,frame_a)
particle_r.point.v2pt_theory(particle_p.point,frame_n,frame_b)
particle_p.mass = m
particle_r.mass = m
force_p = particle_p.mass*(g*frame_n.x)
force_r = particle_r.mass*(g*frame_n.x)
kd_eqs = [q1_d - u1, q2_d - u2]
forceList = [(particle_p.point,particle_p.mass*(g*frame_n.x)), (particle_r.point,particle_r.mass*(g*frame_n.x))]
kane = _me.KanesMethod(frame_n, q_ind=[q1,q2], u_ind=[u1, u2], kd_eqs = kd_eqs)
fr, frstar = kane.kanes_equations([particle_p, particle_r], forceList)
zero = fr+frstar
from pydy.system import System
sys = System(kane, constants = {l:1, m:1, g:9.81},
specifieds={},
initial_conditions={q1:.1, q2:.2, u1:0, u2:0},
times = _np.linspace(0.0, 10, 10/.01))
y=sys.integrate()

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CONSTANTS M,K,B,G
MOTIONVARIABLES' POSITION',SPEED'
VARIABLES O
FORCE = O*SIN(T)
NEWTONIAN CEILING
POINTS ORIGIN
V_ORIGIN_CEILING> = 0>
PARTICLES BLOCK
P_ORIGIN_BLOCK> = POSITION*CEILING1>
MASS BLOCK=M
V_BLOCK_CEILING>=SPEED*CEILING1>
POSITION' = SPEED
FORCE_MAGNITUDE = M*G-K*POSITION-B*SPEED+FORCE
FORCE_BLOCK>=EXPLICIT(FORCE_MAGNITUDE*CEILING1>)
ZERO = FR() + FRSTAR()
KANE()
INPUT TFINAL=10.0, INTEGSTP=0.01
INPUT M=1.0, K=1.0, B=0.2, G=9.8, POSITION=0.1, SPEED=-1.0, O=2
CODE DYNAMICS() dummy_file.c

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
m, k, b, g = _sm.symbols('m k b g', real=True)
position, speed = _me.dynamicsymbols('position speed')
position_d, speed_d = _me.dynamicsymbols('position_ speed_', 1)
o = _me.dynamicsymbols('o')
force = o*_sm.sin(_me.dynamicsymbols._t)
frame_ceiling = _me.ReferenceFrame('ceiling')
point_origin = _me.Point('origin')
point_origin.set_vel(frame_ceiling, 0)
particle_block = _me.Particle('block', _me.Point('block_pt'), _sm.Symbol('m'))
particle_block.point.set_pos(point_origin, position*frame_ceiling.x)
particle_block.mass = m
particle_block.point.set_vel(frame_ceiling, speed*frame_ceiling.x)
force_magnitude = m*g-k*position-b*speed+force
force_block = (force_magnitude*frame_ceiling.x).subs({position_d:speed})
kd_eqs = [position_d - speed]
forceList = [(particle_block.point,(force_magnitude*frame_ceiling.x).subs({position_d:speed}))]
kane = _me.KanesMethod(frame_ceiling, q_ind=[position], u_ind=[speed], kd_eqs = kd_eqs)
fr, frstar = kane.kanes_equations([particle_block], forceList)
zero = fr+frstar
from pydy.system import System
sys = System(kane, constants = {m:1.0, k:1.0, b:0.2, g:9.8},
specifieds={_me.dynamicsymbols('t'):lambda x, t: t, o:2},
initial_conditions={position:0.1, speed:-1*1.0},
times = _np.linspace(0.0, 10.0, 10.0/0.01))
y=sys.integrate()

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MOTIONVARIABLES' Q{2}''
CONSTANTS L,M,G
NEWTONIAN N
POINT PN
V_PN_N> = 0>
THETA1 = ATAN(Q2/Q1)
FRAMES A
SIMPROT(N, A, 3, THETA1)
PARTICLES P
P_PN_P> = Q1*N1>+Q2*N2>
MASS P=M
V_P_N>=DT(P_P_PN>, N)
F_V = DOT(EXPRESS(V_P_N>,A), A1>)
GRAVITY(G*N1>)
DEPENDENT[1] = F_V
CONSTRAIN(DEPENDENT[Q1'])
ZERO=FR()+FRSTAR()
F_C = MAG(P_P_PN>)-L
CONFIG[1]=F_C
ZERO[2]=CONFIG[1]

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
q1, q2 = _me.dynamicsymbols('q1 q2')
q1_d, q2_d = _me.dynamicsymbols('q1_ q2_', 1)
q1_dd, q2_dd = _me.dynamicsymbols('q1_ q2_', 2)
l, m, g = _sm.symbols('l m g', real=True)
frame_n = _me.ReferenceFrame('n')
point_pn = _me.Point('pn')
point_pn.set_vel(frame_n, 0)
theta1 = _sm.atan(q2/q1)
frame_a = _me.ReferenceFrame('a')
frame_a.orient(frame_n, 'Axis', [theta1, frame_n.z])
particle_p = _me.Particle('p', _me.Point('p_pt'), _sm.Symbol('m'))
particle_p.point.set_pos(point_pn, q1*frame_n.x+q2*frame_n.y)
particle_p.mass = m
particle_p.point.set_vel(frame_n, (point_pn.pos_from(particle_p.point)).dt(frame_n))
f_v = _me.dot((particle_p.point.vel(frame_n)).express(frame_a), frame_a.x)
force_p = particle_p.mass*(g*frame_n.x)
dependent = _sm.Matrix([[0]])
dependent[0] = f_v
velocity_constraints = [i for i in dependent]
u_q1_d = _me.dynamicsymbols('u_q1_d')
u_q2_d = _me.dynamicsymbols('u_q2_d')
kd_eqs = [q1_d-u_q1_d, q2_d-u_q2_d]
forceList = [(particle_p.point,particle_p.mass*(g*frame_n.x))]
kane = _me.KanesMethod(frame_n, q_ind=[q1,q2], u_ind=[u_q2_d], u_dependent=[u_q1_d], kd_eqs = kd_eqs, velocity_constraints = velocity_constraints)
fr, frstar = kane.kanes_equations([particle_p], forceList)
zero = fr+frstar
f_c = point_pn.pos_from(particle_p.point).magnitude()-l
config = _sm.Matrix([[0]])
config[0] = f_c
zero = zero.row_insert(zero.shape[0], _sm.Matrix([[0]]))
zero[zero.shape[0]-1] = config[0]

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% ruletest1.al
CONSTANTS F = 3, G = 9.81
CONSTANTS A, B
CONSTANTS S, S1, S2+, S3+, S4-
CONSTANTS K{4}, L{1:3}, P{1:2,1:3}
CONSTANTS C{2,3}
E1 = A*F + S2 - G
E2 = F^2 + K3*K2*G

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
f = _sm.S(3)
g = _sm.S(9.81)
a, b = _sm.symbols('a b', real=True)
s, s1 = _sm.symbols('s s1', real=True)
s2, s3 = _sm.symbols('s2 s3', real=True, nonnegative=True)
s4 = _sm.symbols('s4', real=True, nonpositive=True)
k1, k2, k3, k4, l1, l2, l3, p11, p12, p13, p21, p22, p23 = _sm.symbols('k1 k2 k3 k4 l1 l2 l3 p11 p12 p13 p21 p22 p23', real=True)
c11, c12, c13, c21, c22, c23 = _sm.symbols('c11 c12 c13 c21 c22 c23', real=True)
e1 = a*f+s2-g
e2 = f**2+k3*k2*g

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% ruletest10.al
VARIABLES X,Y
COMPLEX ON
CONSTANTS A,B
E = A*(B*X+Y)^2
M = [E;E]
EXPAND(E)
EXPAND(M)
FACTOR(E,X)
FACTOR(M,X)
EQN[1] = A*X + B*Y
EQN[2] = 2*A*X - 3*B*Y
SOLVE(EQN, X, Y)
RHS_Y = RHS(Y)
E = (X+Y)^2 + 2*X^2
ARRANGE(E, 2, X)
CONSTANTS A,B,C
M = [A,B;C,0]
M2 = EVALUATE(M,A=1,B=2,C=3)
EIG(M2, EIGVALUE, EIGVEC)
NEWTONIAN N
FRAMES A
SIMPROT(N, A, N1>, X)
DEGREES OFF
SIMPROT(N, A, N1>, PI/2)
CONSTANTS C{3}
V> = C1*A1> + C2*A2> + C3*A3>
POINTS O, P
P_P_O> = C1*A1>
EXPRESS(V>,N)
EXPRESS(P_P_O>,N)
W_A_N> = C3*A3>
ANGVEL(A,N)
V2PTS(N,A,O,P)
PARTICLES P{2}
V2PTS(N,A,P1,P2)
A2PTS(N,A,P1,P)
BODIES B{2}
CONSTANT G
GRAVITY(G*N1>)
VARIABLE Z
V> = X*A1> + Y*A3>
P_P_O> = X*A1> + Y*A2>
X = 2*Z
Y = Z
EXPLICIT(V>)
EXPLICIT(P_P_O>)
FORCE(O/P1, X*Y*A1>)
FORCE(P2, X*Y*A1>)

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
x, y = _me.dynamicsymbols('x y')
a, b = _sm.symbols('a b', real=True)
e = a*(b*x+y)**2
m = _sm.Matrix([e,e]).reshape(2, 1)
e = e.expand()
m = _sm.Matrix([i.expand() for i in m]).reshape((m).shape[0], (m).shape[1])
e = _sm.factor(e, x)
m = _sm.Matrix([_sm.factor(i,x) for i in m]).reshape((m).shape[0], (m).shape[1])
eqn = _sm.Matrix([[0]])
eqn[0] = a*x+b*y
eqn = eqn.row_insert(eqn.shape[0], _sm.Matrix([[0]]))
eqn[eqn.shape[0]-1] = 2*a*x-3*b*y
print(_sm.solve(eqn,x,y))
rhs_y = _sm.solve(eqn,x,y)[y]
e = (x+y)**2+2*x**2
e.collect(x)
a, b, c = _sm.symbols('a b c', real=True)
m = _sm.Matrix([a,b,c,0]).reshape(2, 2)
m2 = _sm.Matrix([i.subs({a:1,b:2,c:3}) for i in m]).reshape((m).shape[0], (m).shape[1])
eigvalue = _sm.Matrix([i.evalf() for i in (m2).eigenvals().keys()])
eigvec = _sm.Matrix([i[2][0].evalf() for i in (m2).eigenvects()]).reshape(m2.shape[0], m2.shape[1])
frame_n = _me.ReferenceFrame('n')
frame_a = _me.ReferenceFrame('a')
frame_a.orient(frame_n, 'Axis', [x, frame_n.x])
frame_a.orient(frame_n, 'Axis', [_sm.pi/2, frame_n.x])
c1, c2, c3 = _sm.symbols('c1 c2 c3', real=True)
v = c1*frame_a.x+c2*frame_a.y+c3*frame_a.z
point_o = _me.Point('o')
point_p = _me.Point('p')
point_o.set_pos(point_p, c1*frame_a.x)
v = (v).express(frame_n)
point_o.set_pos(point_p, (point_o.pos_from(point_p)).express(frame_n))
frame_a.set_ang_vel(frame_n, c3*frame_a.z)
print(frame_n.ang_vel_in(frame_a))
point_p.v2pt_theory(point_o,frame_n,frame_a)
particle_p1 = _me.Particle('p1', _me.Point('p1_pt'), _sm.Symbol('m'))
particle_p2 = _me.Particle('p2', _me.Point('p2_pt'), _sm.Symbol('m'))
particle_p2.point.v2pt_theory(particle_p1.point,frame_n,frame_a)
point_p.a2pt_theory(particle_p1.point,frame_n,frame_a)
body_b1_cm = _me.Point('b1_cm')
body_b1_cm.set_vel(frame_n, 0)
body_b1_f = _me.ReferenceFrame('b1_f')
body_b1 = _me.RigidBody('b1', body_b1_cm, body_b1_f, _sm.symbols('m'), (_me.outer(body_b1_f.x,body_b1_f.x),body_b1_cm))
body_b2_cm = _me.Point('b2_cm')
body_b2_cm.set_vel(frame_n, 0)
body_b2_f = _me.ReferenceFrame('b2_f')
body_b2 = _me.RigidBody('b2', body_b2_cm, body_b2_f, _sm.symbols('m'), (_me.outer(body_b2_f.x,body_b2_f.x),body_b2_cm))
g = _sm.symbols('g', real=True)
force_p1 = particle_p1.mass*(g*frame_n.x)
force_p2 = particle_p2.mass*(g*frame_n.x)
force_b1 = body_b1.mass*(g*frame_n.x)
force_b2 = body_b2.mass*(g*frame_n.x)
z = _me.dynamicsymbols('z')
v = x*frame_a.x+y*frame_a.z
point_o.set_pos(point_p, x*frame_a.x+y*frame_a.y)
v = (v).subs({x:2*z, y:z})
point_o.set_pos(point_p, (point_o.pos_from(point_p)).subs({x:2*z, y:z}))
force_o = -1*(x*y*frame_a.x)
force_p1 = particle_p1.mass*(g*frame_n.x)+ x*y*frame_a.x

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VARIABLES X, Y
CONSTANTS A{1:2, 1:2}, B{1:2}
EQN[1] = A11*x + A12*y - B1
EQN[2] = A21*x + A22*y - B2
INPUT A11=2, A12=5, A21=3, A22=4, B1=7, B2=6
CODE ALGEBRAIC(EQN, X, Y) some_filename.c

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
x, y = _me.dynamicsymbols('x y')
a11, a12, a21, a22, b1, b2 = _sm.symbols('a11 a12 a21 a22 b1 b2', real=True)
eqn = _sm.Matrix([[0]])
eqn[0] = a11*x+a12*y-b1
eqn = eqn.row_insert(eqn.shape[0], _sm.Matrix([[0]]))
eqn[eqn.shape[0]-1] = a21*x+a22*y-b2
eqn_list = []
for i in eqn: eqn_list.append(i.subs({a11:2, a12:5, a21:3, a22:4, b1:7, b2:6}))
print(_sm.linsolve(eqn_list, x,y))

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VARIABLES X,Y
CONSTANTS A,B,R
EQN[1] = A*X^3+B*Y^2-R
EQN[2] = A*SIN(X)^2 + B*COS(2*Y) - R^2
INPUT A=2.0, B=3.0, R=1.0
INPUT X = 30 DEG, Y = 3.14
CODE NONLINEAR(EQN,X,Y) some_filename.c

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
x, y = _me.dynamicsymbols('x y')
a, b, r = _sm.symbols('a b r', real=True)
eqn = _sm.Matrix([[0]])
eqn[0] = a*x**3+b*y**2-r
eqn = eqn.row_insert(eqn.shape[0], _sm.Matrix([[0]]))
eqn[eqn.shape[0]-1] = a*_sm.sin(x)**2+b*_sm.cos(2*y)-r**2
matrix_list = []
for i in eqn:matrix_list.append(i.subs({a:2.0, b:3.0, r:1.0}))
print(_sm.nsolve(matrix_list,(x,y),(_np.deg2rad(30),3.14)))

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% ruletest2.al
VARIABLES X1,X2
SPECIFIED F1 = X1*X2 + 3*X1^2
SPECIFIED F2=X1*T+X2*T^2
VARIABLE X', Y''
MOTIONVARIABLES Q{3}, U{2}
VARIABLES P{2}'
VARIABLE W{3}', R{2}''
VARIABLES C{1:2, 1:2}
VARIABLES D{1,3}
VARIABLES J{1:2}
IMAGINARY N

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
x1, x2 = _me.dynamicsymbols('x1 x2')
f1 = x1*x2+3*x1**2
f2 = x1*_me.dynamicsymbols._t+x2*_me.dynamicsymbols._t**2
x, y = _me.dynamicsymbols('x y')
x_d, y_d = _me.dynamicsymbols('x_ y_', 1)
y_dd = _me.dynamicsymbols('y_', 2)
q1, q2, q3, u1, u2 = _me.dynamicsymbols('q1 q2 q3 u1 u2')
p1, p2 = _me.dynamicsymbols('p1 p2')
p1_d, p2_d = _me.dynamicsymbols('p1_ p2_', 1)
w1, w2, w3, r1, r2 = _me.dynamicsymbols('w1 w2 w3 r1 r2')
w1_d, w2_d, w3_d, r1_d, r2_d = _me.dynamicsymbols('w1_ w2_ w3_ r1_ r2_', 1)
r1_dd, r2_dd = _me.dynamicsymbols('r1_ r2_', 2)
c11, c12, c21, c22 = _me.dynamicsymbols('c11 c12 c21 c22')
d11, d12, d13 = _me.dynamicsymbols('d11 d12 d13')
j1, j2 = _me.dynamicsymbols('j1 j2')
n = _sm.symbols('n')
n = _sm.I

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% ruletest3.al
FRAMES A, B
NEWTONIAN N
VARIABLES X{3}
CONSTANTS L
V1> = X1*A1> + X2*A2> + X3*A3>
V2> = X1*B1> + X2*B2> + X3*B3>
V3> = X1*N1> + X2*N2> + X3*N3>
V> = V1> + V2> + V3>
POINTS C, D
POINTS PO{3}
PARTICLES L
PARTICLES P{3}
BODIES S
BODIES R{2}
V4> = X1*S1> + X2*S2> + X3*S3>
P_C_SO> = L*N1>

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
frame_a = _me.ReferenceFrame('a')
frame_b = _me.ReferenceFrame('b')
frame_n = _me.ReferenceFrame('n')
x1, x2, x3 = _me.dynamicsymbols('x1 x2 x3')
l = _sm.symbols('l', real=True)
v1 = x1*frame_a.x+x2*frame_a.y+x3*frame_a.z
v2 = x1*frame_b.x+x2*frame_b.y+x3*frame_b.z
v3 = x1*frame_n.x+x2*frame_n.y+x3*frame_n.z
v = v1+v2+v3
point_c = _me.Point('c')
point_d = _me.Point('d')
point_po1 = _me.Point('po1')
point_po2 = _me.Point('po2')
point_po3 = _me.Point('po3')
particle_l = _me.Particle('l', _me.Point('l_pt'), _sm.Symbol('m'))
particle_p1 = _me.Particle('p1', _me.Point('p1_pt'), _sm.Symbol('m'))
particle_p2 = _me.Particle('p2', _me.Point('p2_pt'), _sm.Symbol('m'))
particle_p3 = _me.Particle('p3', _me.Point('p3_pt'), _sm.Symbol('m'))
body_s_cm = _me.Point('s_cm')
body_s_cm.set_vel(frame_n, 0)
body_s_f = _me.ReferenceFrame('s_f')
body_s = _me.RigidBody('s', body_s_cm, body_s_f, _sm.symbols('m'), (_me.outer(body_s_f.x,body_s_f.x),body_s_cm))
body_r1_cm = _me.Point('r1_cm')
body_r1_cm.set_vel(frame_n, 0)
body_r1_f = _me.ReferenceFrame('r1_f')
body_r1 = _me.RigidBody('r1', body_r1_cm, body_r1_f, _sm.symbols('m'), (_me.outer(body_r1_f.x,body_r1_f.x),body_r1_cm))
body_r2_cm = _me.Point('r2_cm')
body_r2_cm.set_vel(frame_n, 0)
body_r2_f = _me.ReferenceFrame('r2_f')
body_r2 = _me.RigidBody('r2', body_r2_cm, body_r2_f, _sm.symbols('m'), (_me.outer(body_r2_f.x,body_r2_f.x),body_r2_cm))
v4 = x1*body_s_f.x+x2*body_s_f.y+x3*body_s_f.z
body_s_cm.set_pos(point_c, l*frame_n.x)

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% ruletest4.al
FRAMES A, B
MOTIONVARIABLES Q{3}
SIMPROT(A, B, 1, Q3)
DCM = A_B
M = DCM*3 - A_B
VARIABLES R
CIRCLE_AREA = PI*R^2
VARIABLES U, A
VARIABLES X, Y
S = U*T - 1/2*A*T^2
EXPR1 = 2*A*0.5 - 1.25 + 0.25
EXPR2 = -X^2 + Y^2 + 0.25*(X+Y)^2
EXPR3 = 0.5E-10
DYADIC>> = A1>*A1> + A2>*A2> + A3>*A3>

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
frame_a = _me.ReferenceFrame('a')
frame_b = _me.ReferenceFrame('b')
q1, q2, q3 = _me.dynamicsymbols('q1 q2 q3')
frame_b.orient(frame_a, 'Axis', [q3, frame_a.x])
dcm = frame_a.dcm(frame_b)
m = dcm*3-frame_a.dcm(frame_b)
r = _me.dynamicsymbols('r')
circle_area = _sm.pi*r**2
u, a = _me.dynamicsymbols('u a')
x, y = _me.dynamicsymbols('x y')
s = u*_me.dynamicsymbols._t-1/2*a*_me.dynamicsymbols._t**2
expr1 = 2*a*0.5-1.25+0.25
expr2 = -1*x**2+y**2+0.25*(x+y)**2
expr3 = 0.5*10**(-10)
dyadic = _me.outer(frame_a.x, frame_a.x)+_me.outer(frame_a.y, frame_a.y)+_me.outer(frame_a.z, frame_a.z)

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% ruletest5.al
VARIABLES X', Y'
E1 = (X+Y)^2 + (X-Y)^3
E2 = (X-Y)^2
E3 = X^2 + Y^2 + 2*X*Y
M1 = [E1;E2]
M2 = [(X+Y)^2,(X-Y)^2]
M3 = M1 + [X;Y]
AM = EXPAND(M1)
CM = EXPAND([(X+Y)^2,(X-Y)^2])
EM = EXPAND(M1 + [X;Y])
F = EXPAND(E1)
G = EXPAND(E2)
A = FACTOR(E3, X)
BM = FACTOR(M1, X)
CM = FACTOR(M1 + [X;Y], X)
A = D(E3, X)
B = D(E3, Y)
CM = D(M2, X)
DM = D(M1 + [X;Y], X)
FRAMES A, B
A_B = [1,0,0;1,0,0;1,0,0]
V1> = X*A1> + Y*A2> + X*Y*A3>
E> = D(V1>, X, B)
FM = DT(M1)
GM = DT([(X+Y)^2,(X-Y)^2])
H> = DT(V1>, B)

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
x, y = _me.dynamicsymbols('x y')
x_d, y_d = _me.dynamicsymbols('x_ y_', 1)
e1 = (x+y)**2+(x-y)**3
e2 = (x-y)**2
e3 = x**2+y**2+2*x*y
m1 = _sm.Matrix([e1,e2]).reshape(2, 1)
m2 = _sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)
m3 = m1+_sm.Matrix([x,y]).reshape(2, 1)
am = _sm.Matrix([i.expand() for i in m1]).reshape((m1).shape[0], (m1).shape[1])
cm = _sm.Matrix([i.expand() for i in _sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)]).reshape((_sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)).shape[0], (_sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)).shape[1])
em = _sm.Matrix([i.expand() for i in m1+_sm.Matrix([x,y]).reshape(2, 1)]).reshape((m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[0], (m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[1])
f = (e1).expand()
g = (e2).expand()
a = _sm.factor((e3), x)
bm = _sm.Matrix([_sm.factor(i, x) for i in m1]).reshape((m1).shape[0], (m1).shape[1])
cm = _sm.Matrix([_sm.factor(i, x) for i in m1+_sm.Matrix([x,y]).reshape(2, 1)]).reshape((m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[0], (m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[1])
a = (e3).diff(x)
b = (e3).diff(y)
cm = _sm.Matrix([i.diff(x) for i in m2]).reshape((m2).shape[0], (m2).shape[1])
dm = _sm.Matrix([i.diff(x) for i in m1+_sm.Matrix([x,y]).reshape(2, 1)]).reshape((m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[0], (m1+_sm.Matrix([x,y]).reshape(2, 1)).shape[1])
frame_a = _me.ReferenceFrame('a')
frame_b = _me.ReferenceFrame('b')
frame_b.orient(frame_a, 'DCM', _sm.Matrix([1,0,0,1,0,0,1,0,0]).reshape(3, 3))
v1 = x*frame_a.x+y*frame_a.y+x*y*frame_a.z
e = (v1).diff(x, frame_b)
fm = _sm.Matrix([i.diff(_sm.Symbol('t')) for i in m1]).reshape((m1).shape[0], (m1).shape[1])
gm = _sm.Matrix([i.diff(_sm.Symbol('t')) for i in _sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)]).reshape((_sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)).shape[0], (_sm.Matrix([(x+y)**2,(x-y)**2]).reshape(1, 2)).shape[1])
h = (v1).dt(frame_b)

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% ruletest6.al
VARIABLES Q{2}
VARIABLES X,Y,Z
Q1 = X^2 + Y^2
Q2 = X-Y
E = Q1 + Q2
A = EXPLICIT(E)
E2 = COS(X)
E3 = COS(X*Y)
A = TAYLOR(E2, 0:2, X=0)
B = TAYLOR(E3, 0:2, X=0, Y=0)
E = EXPAND((X+Y)^2)
A = EVALUATE(E, X=1, Y=Z)
BM = EVALUATE([E;2*E], X=1, Y=Z)
E = Q1 + Q2
A = EVALUATE(E, X=2, Y=Z^2)
CONSTANTS J,K,L
P1 = POLYNOMIAL([J,K,L],X)
P2 = POLYNOMIAL(J*X+K,X,1)
ROOT1 = ROOTS(P1, X, 2)
ROOT2 = ROOTS([1;2;3])
M = [1,2,3,4;5,6,7,8;9,10,11,12;13,14,15,16]
AM = TRANSPOSE(M) + M
BM = EIG(M)
C1 = DIAGMAT(4, 1)
C2 = DIAGMAT(3, 4, 2)
DM = INV(M+C1)
E = DET(M+C1) + TRACE([1,0;0,1])
F = ELEMENT(M, 2, 3)
A = COLS(M)
BM = COLS(M, 1)
CM = COLS(M, 1, 2:4, 3)
DM = ROWS(M, 1)
EM = ROWS(M, 1, 2:4, 3)

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
q1, q2 = _me.dynamicsymbols('q1 q2')
x, y, z = _me.dynamicsymbols('x y z')
e = q1+q2
a = (e).subs({q1:x**2+y**2, q2:x-y})
e2 = _sm.cos(x)
e3 = _sm.cos(x*y)
a = (e2).series(x, 0, 2).removeO()
b = (e3).series(x, 0, 2).removeO().series(y, 0, 2).removeO()
e = ((x+y)**2).expand()
a = (e).subs({q1:x**2+y**2,q2:x-y}).subs({x:1,y:z})
bm = _sm.Matrix([i.subs({x:1,y:z}) for i in _sm.Matrix([e,2*e]).reshape(2, 1)]).reshape((_sm.Matrix([e,2*e]).reshape(2, 1)).shape[0], (_sm.Matrix([e,2*e]).reshape(2, 1)).shape[1])
e = q1+q2
a = (e).subs({q1:x**2+y**2,q2:x-y}).subs({x:2,y:z**2})
j, k, l = _sm.symbols('j k l', real=True)
p1 = _sm.Poly(_sm.Matrix([j,k,l]).reshape(1, 3), x)
p2 = _sm.Poly(j*x+k, x)
root1 = [i.evalf() for i in _sm.solve(p1, x)]
root2 = [i.evalf() for i in _sm.solve(_sm.Poly(_sm.Matrix([1,2,3]).reshape(3, 1), x),x)]
m = _sm.Matrix([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]).reshape(4, 4)
am = (m).T+m
bm = _sm.Matrix([i.evalf() for i in (m).eigenvals().keys()])
c1 = _sm.diag(1,1,1,1)
c2 = _sm.Matrix([2 if i==j else 0 for i in range(3) for j in range(4)]).reshape(3, 4)
dm = (m+c1)**(-1)
e = (m+c1).det()+(_sm.Matrix([1,0,0,1]).reshape(2, 2)).trace()
f = (m)[1,2]
a = (m).cols
bm = (m).col(0)
cm = _sm.Matrix([(m).T.row(0),(m).T.row(1),(m).T.row(2),(m).T.row(3),(m).T.row(2)])
dm = (m).row(0)
em = _sm.Matrix([(m).row(0),(m).row(1),(m).row(2),(m).row(3),(m).row(2)])

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% ruletest7.al
VARIABLES X', Y'
E = COS(X) + SIN(X) + TAN(X)&
+ COSH(X) + SINH(X) + TANH(X)&
+ ACOS(X) + ASIN(X) + ATAN(X)&
+ LOG(X) + EXP(X) + SQRT(X)&
+ FACTORIAL(X) + CEIL(X) +&
FLOOR(X) + SIGN(X)
E = SQR(X) + LOG10(X)
A = ABS(-1) + INT(1.5) + ROUND(1.9)
E1 = 2*X + 3*Y
E2 = X + Y
AM = COEF([E1;E2], [X,Y])
B = COEF(E1, X)
C = COEF(E2, Y)
D1 = EXCLUDE(E1, X)
D2 = INCLUDE(E1, X)
FM = ARRANGE([E1,E2],2,X)
F = ARRANGE(E1, 2, Y)
G = REPLACE(E1, X=2*X)
GM = REPLACE([E1;E2], X=3)
FRAMES A, B
VARIABLES THETA
SIMPROT(A,B,3,THETA)
V1> = 2*A1> - 3*A2> + A3>
V2> = B1> + B2> + B3>
A = DOT(V1>, V2>)
BM = DOT(V1>, [V2>;2*V2>])
C> = CROSS(V1>,V2>)
D = MAG(2*V1>) + MAG(3*V1>)
DYADIC>> = 3*A1>*A1> + A2>*A2> + 2*A3>*A3>
AM = MATRIX(B, DYADIC>>)
M = [1;2;3]
V> = VECTOR(A, M)

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
x, y = _me.dynamicsymbols('x y')
x_d, y_d = _me.dynamicsymbols('x_ y_', 1)
e = _sm.cos(x)+_sm.sin(x)+_sm.tan(x)+_sm.cosh(x)+_sm.sinh(x)+_sm.tanh(x)+_sm.acos(x)+_sm.asin(x)+_sm.atan(x)+_sm.log(x)+_sm.exp(x)+_sm.sqrt(x)+_sm.factorial(x)+_sm.ceiling(x)+_sm.floor(x)+_sm.sign(x)
e = (x)**2+_sm.log(x, 10)
a = _sm.Abs(-1*1)+int(1.5)+round(1.9)
e1 = 2*x+3*y
e2 = x+y
am = _sm.Matrix([e1.expand().coeff(x), e1.expand().coeff(y), e2.expand().coeff(x), e2.expand().coeff(y)]).reshape(2, 2)
b = (e1).expand().coeff(x)
c = (e2).expand().coeff(y)
d1 = (e1).collect(x).coeff(x,0)
d2 = (e1).collect(x).coeff(x,1)
fm = _sm.Matrix([i.collect(x)for i in _sm.Matrix([e1,e2]).reshape(1, 2)]).reshape((_sm.Matrix([e1,e2]).reshape(1, 2)).shape[0], (_sm.Matrix([e1,e2]).reshape(1, 2)).shape[1])
f = (e1).collect(y)
g = (e1).subs({x:2*x})
gm = _sm.Matrix([i.subs({x:3}) for i in _sm.Matrix([e1,e2]).reshape(2, 1)]).reshape((_sm.Matrix([e1,e2]).reshape(2, 1)).shape[0], (_sm.Matrix([e1,e2]).reshape(2, 1)).shape[1])
frame_a = _me.ReferenceFrame('a')
frame_b = _me.ReferenceFrame('b')
theta = _me.dynamicsymbols('theta')
frame_b.orient(frame_a, 'Axis', [theta, frame_a.z])
v1 = 2*frame_a.x-3*frame_a.y+frame_a.z
v2 = frame_b.x+frame_b.y+frame_b.z
a = _me.dot(v1, v2)
bm = _sm.Matrix([_me.dot(v1, v2),_me.dot(v1, 2*v2)]).reshape(2, 1)
c = _me.cross(v1, v2)
d = 2*v1.magnitude()+3*v1.magnitude()
dyadic = _me.outer(3*frame_a.x, frame_a.x)+_me.outer(frame_a.y, frame_a.y)+_me.outer(2*frame_a.z, frame_a.z)
am = (dyadic).to_matrix(frame_b)
m = _sm.Matrix([1,2,3]).reshape(3, 1)
v = m[0]*frame_a.x +m[1]*frame_a.y +m[2]*frame_a.z

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% ruletest8.al
FRAMES A
CONSTANTS C{3}
A>> = EXPRESS(1>>,A)
PARTICLES P1, P2
BODIES R
R_A = [1,1,1;1,1,0;0,0,1]
POINT O
MASS P1=M1, P2=M2, R=MR
INERTIA R, I1, I2, I3
P_P1_O> = C1*A1>
P_P2_O> = C2*A2>
P_RO_O> = C3*A3>
A>> = EXPRESS(I_P1_O>>, A)
A>> = EXPRESS(I_P2_O>>, A)
A>> = EXPRESS(I_R_O>>, A)
A>> = EXPRESS(INERTIA(O), A)
A>> = EXPRESS(INERTIA(O, P1, R), A)
A>> = EXPRESS(I_R_O>>, A)
A>> = EXPRESS(I_R_RO>>, A)
P_P1_P2> = C1*A1> + C2*A2>
P_P1_RO> = C3*A1>
P_P2_RO> = C3*A2>
B> = CM(O)
B> = CM(O, P1, R)
B> = CM(P1)
MOTIONVARIABLES U{3}
V> = U1*A1> + U2*A2> + U3*A3>
U> = UNITVEC(V> + C1*A1>)
V_P1_A> = U1*A1>
A> = PARTIALS(V_P1_A>, U1)
M = MASS(P1,R)
M = MASS(P2)
M = MASS()

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
frame_a = _me.ReferenceFrame('a')
c1, c2, c3 = _sm.symbols('c1 c2 c3', real=True)
a = _me.inertia(frame_a, 1, 1, 1)
particle_p1 = _me.Particle('p1', _me.Point('p1_pt'), _sm.Symbol('m'))
particle_p2 = _me.Particle('p2', _me.Point('p2_pt'), _sm.Symbol('m'))
body_r_cm = _me.Point('r_cm')
body_r_f = _me.ReferenceFrame('r_f')
body_r = _me.RigidBody('r', body_r_cm, body_r_f, _sm.symbols('m'), (_me.outer(body_r_f.x,body_r_f.x),body_r_cm))
frame_a.orient(body_r_f, 'DCM', _sm.Matrix([1,1,1,1,1,0,0,0,1]).reshape(3, 3))
point_o = _me.Point('o')
m1 = _sm.symbols('m1')
particle_p1.mass = m1
m2 = _sm.symbols('m2')
particle_p2.mass = m2
mr = _sm.symbols('mr')
body_r.mass = mr
i1 = _sm.symbols('i1')
i2 = _sm.symbols('i2')
i3 = _sm.symbols('i3')
body_r.inertia = (_me.inertia(body_r_f, i1, i2, i3, 0, 0, 0), body_r_cm)
point_o.set_pos(particle_p1.point, c1*frame_a.x)
point_o.set_pos(particle_p2.point, c2*frame_a.y)
point_o.set_pos(body_r_cm, c3*frame_a.z)
a = _me.inertia_of_point_mass(particle_p1.mass, particle_p1.point.pos_from(point_o), frame_a)
a = _me.inertia_of_point_mass(particle_p2.mass, particle_p2.point.pos_from(point_o), frame_a)
a = body_r.inertia[0] + _me.inertia_of_point_mass(body_r.mass, body_r.masscenter.pos_from(point_o), frame_a)
a = _me.inertia_of_point_mass(particle_p1.mass, particle_p1.point.pos_from(point_o), frame_a) + _me.inertia_of_point_mass(particle_p2.mass, particle_p2.point.pos_from(point_o), frame_a) + body_r.inertia[0] + _me.inertia_of_point_mass(body_r.mass, body_r.masscenter.pos_from(point_o), frame_a)
a = _me.inertia_of_point_mass(particle_p1.mass, particle_p1.point.pos_from(point_o), frame_a) + body_r.inertia[0] + _me.inertia_of_point_mass(body_r.mass, body_r.masscenter.pos_from(point_o), frame_a)
a = body_r.inertia[0] + _me.inertia_of_point_mass(body_r.mass, body_r.masscenter.pos_from(point_o), frame_a)
a = body_r.inertia[0]
particle_p2.point.set_pos(particle_p1.point, c1*frame_a.x+c2*frame_a.y)
body_r_cm.set_pos(particle_p1.point, c3*frame_a.x)
body_r_cm.set_pos(particle_p2.point, c3*frame_a.y)
b = _me.functions.center_of_mass(point_o,particle_p1, particle_p2, body_r)
b = _me.functions.center_of_mass(point_o,particle_p1, body_r)
b = _me.functions.center_of_mass(particle_p1.point,particle_p1, particle_p2, body_r)
u1, u2, u3 = _me.dynamicsymbols('u1 u2 u3')
v = u1*frame_a.x+u2*frame_a.y+u3*frame_a.z
u = (v+c1*frame_a.x).normalize()
particle_p1.point.set_vel(frame_a, u1*frame_a.x)
a = particle_p1.point.partial_velocity(frame_a, u1)
m = particle_p1.mass+body_r.mass
m = particle_p2.mass
m = particle_p1.mass+particle_p2.mass+body_r.mass

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% ruletest9.al
NEWTONIAN N
FRAMES A
A> = 0>
D>> = EXPRESS(1>>, A)
POINTS PO{2}
PARTICLES P{2}
MOTIONVARIABLES' C{3}'
BODIES R
P_P1_PO2> = C1*A1>
V> = 2*P_P1_PO2> + C2*A2>
W_A_N> = C3*A3>
V> = 2*W_A_N> + C2*A2>
W_R_N> = C3*A3>
V> = 2*W_R_N> + C2*A2>
ALF_A_N> = DT(W_A_N>, A)
V> = 2*ALF_A_N> + C2*A2>
V_P1_A> = C1*A1> + C3*A2>
A_RO_N> = C2*A2>
V_A> = CROSS(A_RO_N>, V_P1_A>)
X_B_C> = V_A>
X_B_D> = 2*X_B_C>
A_B_C_D_E> = X_B_D>*2
A_B_C = 2*C1*C2*C3
A_B_C += 2*C1
A_B_C := 3*C1
MOTIONVARIABLES' Q{2}', U{2}'
Q1' = U1
Q2' = U2
VARIABLES X'', Y''
SPECIFIED YY
Y'' = X*X'^2 + 1
YY = X*X'^2 + 1
M[1] = 2*X
M[2] = 2*Y
A = 2*M[1]
M = [1,2,3;4,5,6;7,8,9]
M[1, 2] = 5
A = M[1, 2]*2
FORCE_RO> = Q1*N1>
TORQUE_A> = Q2*N3>
FORCE_RO> = Q2*N2>
F> = FORCE_RO>*2

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import sympy.physics.mechanics as _me
import sympy as _sm
import math as m
import numpy as _np
frame_n = _me.ReferenceFrame('n')
frame_a = _me.ReferenceFrame('a')
a = 0
d = _me.inertia(frame_a, 1, 1, 1)
point_po1 = _me.Point('po1')
point_po2 = _me.Point('po2')
particle_p1 = _me.Particle('p1', _me.Point('p1_pt'), _sm.Symbol('m'))
particle_p2 = _me.Particle('p2', _me.Point('p2_pt'), _sm.Symbol('m'))
c1, c2, c3 = _me.dynamicsymbols('c1 c2 c3')
c1_d, c2_d, c3_d = _me.dynamicsymbols('c1_ c2_ c3_', 1)
body_r_cm = _me.Point('r_cm')
body_r_cm.set_vel(frame_n, 0)
body_r_f = _me.ReferenceFrame('r_f')
body_r = _me.RigidBody('r', body_r_cm, body_r_f, _sm.symbols('m'), (_me.outer(body_r_f.x,body_r_f.x),body_r_cm))
point_po2.set_pos(particle_p1.point, c1*frame_a.x)
v = 2*point_po2.pos_from(particle_p1.point)+c2*frame_a.y
frame_a.set_ang_vel(frame_n, c3*frame_a.z)
v = 2*frame_a.ang_vel_in(frame_n)+c2*frame_a.y
body_r_f.set_ang_vel(frame_n, c3*frame_a.z)
v = 2*body_r_f.ang_vel_in(frame_n)+c2*frame_a.y
frame_a.set_ang_acc(frame_n, (frame_a.ang_vel_in(frame_n)).dt(frame_a))
v = 2*frame_a.ang_acc_in(frame_n)+c2*frame_a.y
particle_p1.point.set_vel(frame_a, c1*frame_a.x+c3*frame_a.y)
body_r_cm.set_acc(frame_n, c2*frame_a.y)
v_a = _me.cross(body_r_cm.acc(frame_n), particle_p1.point.vel(frame_a))
x_b_c = v_a
x_b_d = 2*x_b_c
a_b_c_d_e = x_b_d*2
a_b_c = 2*c1*c2*c3
a_b_c += 2*c1
a_b_c = 3*c1
q1, q2, u1, u2 = _me.dynamicsymbols('q1 q2 u1 u2')
q1_d, q2_d, u1_d, u2_d = _me.dynamicsymbols('q1_ q2_ u1_ u2_', 1)
x, y = _me.dynamicsymbols('x y')
x_d, y_d = _me.dynamicsymbols('x_ y_', 1)
x_dd, y_dd = _me.dynamicsymbols('x_ y_', 2)
yy = _me.dynamicsymbols('yy')
yy = x*x_d**2+1
m = _sm.Matrix([[0]])
m[0] = 2*x
m = m.row_insert(m.shape[0], _sm.Matrix([[0]]))
m[m.shape[0]-1] = 2*y
a = 2*m[0]
m = _sm.Matrix([1,2,3,4,5,6,7,8,9]).reshape(3, 3)
m[0,1] = 5
a = m[0, 1]*2
force_ro = q1*frame_n.x
torque_a = q2*frame_n.z
force_ro = q1*frame_n.x + q2*frame_n.y
f = force_ro*2

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"""Used for translating C source code into a SymPy expression"""

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"""Used for translating Fortran source code into a SymPy expression. """

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from sympy.external import import_module
lfortran = import_module('lfortran')
if lfortran:
from sympy.codegen.ast import (Variable, IntBaseType, FloatBaseType, String,
Return, FunctionDefinition, Assignment)
from sympy.core import Add, Mul, Integer, Float
from sympy.core.symbol import Symbol
asr_mod = lfortran.asr
asr = lfortran.asr.asr
src_to_ast = lfortran.ast.src_to_ast
ast_to_asr = lfortran.semantic.ast_to_asr.ast_to_asr
"""
This module contains all the necessary Classes and Function used to Parse
Fortran code into SymPy expression
The module and its API are currently under development and experimental.
It is also dependent on LFortran for the ASR that is converted to SymPy syntax
which is also under development.
The module only supports the features currently supported by the LFortran ASR
which will be updated as the development of LFortran and this module progresses
You might find unexpected bugs and exceptions while using the module, feel free
to report them to the SymPy Issue Tracker
The API for the module might also change while in development if better and
more effective ways are discovered for the process
Features Supported
==================
- Variable Declarations (integers and reals)
- Function Definitions
- Assignments and Basic Binary Operations
Notes
=====
The module depends on an external dependency
LFortran : Required to parse Fortran source code into ASR
References
==========
.. [1] https://github.com/sympy/sympy/issues
.. [2] https://gitlab.com/lfortran/lfortran
.. [3] https://docs.lfortran.org/
"""
class ASR2PyVisitor(asr.ASTVisitor): # type: ignore
"""
Visitor Class for LFortran ASR
It is a Visitor class derived from asr.ASRVisitor which visits all the
nodes of the LFortran ASR and creates corresponding AST node for each
ASR node
"""
def __init__(self):
"""Initialize the Parser"""
self._py_ast = []
def visit_TranslationUnit(self, node):
"""
Function to visit all the elements of the Translation Unit
created by LFortran ASR
"""
for s in node.global_scope.symbols:
sym = node.global_scope.symbols[s]
self.visit(sym)
for item in node.items:
self.visit(item)
def visit_Assignment(self, node):
"""Visitor Function for Assignment
Visits each Assignment is the LFortran ASR and creates corresponding
assignment for SymPy.
Notes
=====
The function currently only supports variable assignment and binary
operation assignments of varying multitudes. Any type of numberS or
array is not supported.
Raises
======
NotImplementedError() when called for Numeric assignments or Arrays
"""
# TODO: Arithmetic Assignment
if isinstance(node.target, asr.Variable):
target = node.target
value = node.value
if isinstance(value, asr.Variable):
new_node = Assignment(
Variable(
target.name
),
Variable(
value.name
)
)
elif (type(value) == asr.BinOp):
exp_ast = call_visitor(value)
for expr in exp_ast:
new_node = Assignment(
Variable(target.name),
expr
)
else:
raise NotImplementedError("Numeric assignments not supported")
else:
raise NotImplementedError("Arrays not supported")
self._py_ast.append(new_node)
def visit_BinOp(self, node):
"""Visitor Function for Binary Operations
Visits each binary operation present in the LFortran ASR like addition,
subtraction, multiplication, division and creates the corresponding
operation node in SymPy's AST
In case of more than one binary operations, the function calls the
call_visitor() function on the child nodes of the binary operations
recursively until all the operations have been processed.
Notes
=====
The function currently only supports binary operations with Variables
or other binary operations. Numerics are not supported as of yet.
Raises
======
NotImplementedError() when called for Numeric assignments
"""
# TODO: Integer Binary Operations
op = node.op
lhs = node.left
rhs = node.right
if (type(lhs) == asr.Variable):
left_value = Symbol(lhs.name)
elif(type(lhs) == asr.BinOp):
l_exp_ast = call_visitor(lhs)
for exp in l_exp_ast:
left_value = exp
else:
raise NotImplementedError("Numbers Currently not supported")
if (type(rhs) == asr.Variable):
right_value = Symbol(rhs.name)
elif(type(rhs) == asr.BinOp):
r_exp_ast = call_visitor(rhs)
for exp in r_exp_ast:
right_value = exp
else:
raise NotImplementedError("Numbers Currently not supported")
if isinstance(op, asr.Add):
new_node = Add(left_value, right_value)
elif isinstance(op, asr.Sub):
new_node = Add(left_value, -right_value)
elif isinstance(op, asr.Div):
new_node = Mul(left_value, 1/right_value)
elif isinstance(op, asr.Mul):
new_node = Mul(left_value, right_value)
self._py_ast.append(new_node)
def visit_Variable(self, node):
"""Visitor Function for Variable Declaration
Visits each variable declaration present in the ASR and creates a
Symbol declaration for each variable
Notes
=====
The functions currently only support declaration of integer and
real variables. Other data types are still under development.
Raises
======
NotImplementedError() when called for unsupported data types
"""
if isinstance(node.type, asr.Integer):
var_type = IntBaseType(String('integer'))
value = Integer(0)
elif isinstance(node.type, asr.Real):
var_type = FloatBaseType(String('real'))
value = Float(0.0)
else:
raise NotImplementedError("Data type not supported")
if not (node.intent == 'in'):
new_node = Variable(
node.name
).as_Declaration(
type = var_type,
value = value
)
self._py_ast.append(new_node)
def visit_Sequence(self, seq):
"""Visitor Function for code sequence
Visits a code sequence/ block and calls the visitor function on all the
children of the code block to create corresponding code in python
"""
if seq is not None:
for node in seq:
self._py_ast.append(call_visitor(node))
def visit_Num(self, node):
"""Visitor Function for Numbers in ASR
This function is currently under development and will be updated
with improvements in the LFortran ASR
"""
# TODO:Numbers when the LFortran ASR is updated
# self._py_ast.append(Integer(node.n))
pass
def visit_Function(self, node):
"""Visitor Function for function Definitions
Visits each function definition present in the ASR and creates a
function definition node in the Python AST with all the elements of the
given function
The functions declare all the variables required as SymPy symbols in
the function before the function definition
This function also the call_visior_function to parse the contents of
the function body
"""
# TODO: Return statement, variable declaration
fn_args = [Variable(arg_iter.name) for arg_iter in node.args]
fn_body = []
fn_name = node.name
for i in node.body:
fn_ast = call_visitor(i)
try:
fn_body_expr = fn_ast
except UnboundLocalError:
fn_body_expr = []
for sym in node.symtab.symbols:
decl = call_visitor(node.symtab.symbols[sym])
for symbols in decl:
fn_body.append(symbols)
for elem in fn_body_expr:
fn_body.append(elem)
fn_body.append(
Return(
Variable(
node.return_var.name
)
)
)
if isinstance(node.return_var.type, asr.Integer):
ret_type = IntBaseType(String('integer'))
elif isinstance(node.return_var.type, asr.Real):
ret_type = FloatBaseType(String('real'))
else:
raise NotImplementedError("Data type not supported")
new_node = FunctionDefinition(
return_type = ret_type,
name = fn_name,
parameters = fn_args,
body = fn_body
)
self._py_ast.append(new_node)
def ret_ast(self):
"""Returns the AST nodes"""
return self._py_ast
else:
class ASR2PyVisitor(): # type: ignore
def __init__(self, *args, **kwargs):
raise ImportError('lfortran not available')
def call_visitor(fort_node):
"""Calls the AST Visitor on the Module
This function is used to call the AST visitor for a program or module
It imports all the required modules and calls the visit() function
on the given node
Parameters
==========
fort_node : LFortran ASR object
Node for the operation for which the NodeVisitor is called
Returns
=======
res_ast : list
list of SymPy AST Nodes
"""
v = ASR2PyVisitor()
v.visit(fort_node)
res_ast = v.ret_ast()
return res_ast
def src_to_sympy(src):
"""Wrapper function to convert the given Fortran source code to SymPy Expressions
Parameters
==========
src : string
A string with the Fortran source code
Returns
=======
py_src : string
A string with the Python source code compatible with SymPy
"""
a_ast = src_to_ast(src, translation_unit=False)
a = ast_to_asr(a_ast)
py_src = call_visitor(a)
return py_src

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The MIT License (MIT)
Copyright 2016, latex2sympy
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

312
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/*
ANTLR4 LaTeX Math Grammar
Ported from latex2sympy by @augustt198 https://github.com/augustt198/latex2sympy See license in
LICENSE.txt
*/
/*
After changing this file, it is necessary to run `python setup.py antlr` in the root directory of
the repository. This will regenerate the code in `sympy/parsing/latex/_antlr/*.py`.
*/
grammar LaTeX;
options {
language = Python3;
}
WS: [ \t\r\n]+ -> skip;
THINSPACE: ('\\,' | '\\thinspace') -> skip;
MEDSPACE: ('\\:' | '\\medspace') -> skip;
THICKSPACE: ('\\;' | '\\thickspace') -> skip;
QUAD: '\\quad' -> skip;
QQUAD: '\\qquad' -> skip;
NEGTHINSPACE: ('\\!' | '\\negthinspace') -> skip;
NEGMEDSPACE: '\\negmedspace' -> skip;
NEGTHICKSPACE: '\\negthickspace' -> skip;
CMD_LEFT: '\\left' -> skip;
CMD_RIGHT: '\\right' -> skip;
IGNORE:
(
'\\vrule'
| '\\vcenter'
| '\\vbox'
| '\\vskip'
| '\\vspace'
| '\\hfil'
| '\\*'
| '\\-'
| '\\.'
| '\\/'
| '\\"'
| '\\('
| '\\='
) -> skip;
ADD: '+';
SUB: '-';
MUL: '*';
DIV: '/';
L_PAREN: '(';
R_PAREN: ')';
L_BRACE: '{';
R_BRACE: '}';
L_BRACE_LITERAL: '\\{';
R_BRACE_LITERAL: '\\}';
L_BRACKET: '[';
R_BRACKET: ']';
BAR: '|';
R_BAR: '\\right|';
L_BAR: '\\left|';
L_ANGLE: '\\langle';
R_ANGLE: '\\rangle';
FUNC_LIM: '\\lim';
LIM_APPROACH_SYM:
'\\to'
| '\\rightarrow'
| '\\Rightarrow'
| '\\longrightarrow'
| '\\Longrightarrow';
FUNC_INT:
'\\int'
| '\\int\\limits';
FUNC_SUM: '\\sum';
FUNC_PROD: '\\prod';
FUNC_EXP: '\\exp';
FUNC_LOG: '\\log';
FUNC_LG: '\\lg';
FUNC_LN: '\\ln';
FUNC_SIN: '\\sin';
FUNC_COS: '\\cos';
FUNC_TAN: '\\tan';
FUNC_CSC: '\\csc';
FUNC_SEC: '\\sec';
FUNC_COT: '\\cot';
FUNC_ARCSIN: '\\arcsin';
FUNC_ARCCOS: '\\arccos';
FUNC_ARCTAN: '\\arctan';
FUNC_ARCCSC: '\\arccsc';
FUNC_ARCSEC: '\\arcsec';
FUNC_ARCCOT: '\\arccot';
FUNC_SINH: '\\sinh';
FUNC_COSH: '\\cosh';
FUNC_TANH: '\\tanh';
FUNC_ARSINH: '\\arsinh';
FUNC_ARCOSH: '\\arcosh';
FUNC_ARTANH: '\\artanh';
L_FLOOR: '\\lfloor';
R_FLOOR: '\\rfloor';
L_CEIL: '\\lceil';
R_CEIL: '\\rceil';
FUNC_SQRT: '\\sqrt';
FUNC_OVERLINE: '\\overline';
CMD_TIMES: '\\times';
CMD_CDOT: '\\cdot';
CMD_DIV: '\\div';
CMD_FRAC:
'\\frac'
| '\\dfrac'
| '\\tfrac';
CMD_BINOM: '\\binom';
CMD_DBINOM: '\\dbinom';
CMD_TBINOM: '\\tbinom';
CMD_MATHIT: '\\mathit';
UNDERSCORE: '_';
CARET: '^';
COLON: ':';
fragment WS_CHAR: [ \t\r\n];
DIFFERENTIAL: 'd' WS_CHAR*? ([a-zA-Z] | '\\' [a-zA-Z]+);
LETTER: [a-zA-Z];
DIGIT: [0-9];
EQUAL: (('&' WS_CHAR*?)? '=') | ('=' (WS_CHAR*? '&')?);
NEQ: '\\neq';
LT: '<';
LTE: ('\\leq' | '\\le' | LTE_Q | LTE_S);
LTE_Q: '\\leqq';
LTE_S: '\\leqslant';
GT: '>';
GTE: ('\\geq' | '\\ge' | GTE_Q | GTE_S);
GTE_Q: '\\geqq';
GTE_S: '\\geqslant';
BANG: '!';
SINGLE_QUOTES: '\''+;
SYMBOL: '\\' [a-zA-Z]+;
math: relation;
relation:
relation (EQUAL | LT | LTE | GT | GTE | NEQ) relation
| expr;
equality: expr EQUAL expr;
expr: additive;
additive: additive (ADD | SUB) additive | mp;
// mult part
mp:
mp (MUL | CMD_TIMES | CMD_CDOT | DIV | CMD_DIV | COLON) mp
| unary;
mp_nofunc:
mp_nofunc (
MUL
| CMD_TIMES
| CMD_CDOT
| DIV
| CMD_DIV
| COLON
) mp_nofunc
| unary_nofunc;
unary: (ADD | SUB) unary | postfix+;
unary_nofunc:
(ADD | SUB) unary_nofunc
| postfix postfix_nofunc*;
postfix: exp postfix_op*;
postfix_nofunc: exp_nofunc postfix_op*;
postfix_op: BANG | eval_at;
eval_at:
BAR (eval_at_sup | eval_at_sub | eval_at_sup eval_at_sub);
eval_at_sub: UNDERSCORE L_BRACE (expr | equality) R_BRACE;
eval_at_sup: CARET L_BRACE (expr | equality) R_BRACE;
exp: exp CARET (atom | L_BRACE expr R_BRACE) subexpr? | comp;
exp_nofunc:
exp_nofunc CARET (atom | L_BRACE expr R_BRACE) subexpr?
| comp_nofunc;
comp:
group
| abs_group
| func
| atom
| floor
| ceil;
comp_nofunc:
group
| abs_group
| atom
| floor
| ceil;
group:
L_PAREN expr R_PAREN
| L_BRACKET expr R_BRACKET
| L_BRACE expr R_BRACE
| L_BRACE_LITERAL expr R_BRACE_LITERAL;
abs_group: BAR expr BAR;
number: DIGIT+ (',' DIGIT DIGIT DIGIT)* ('.' DIGIT+)?;
atom: (LETTER | SYMBOL) (subexpr? SINGLE_QUOTES? | SINGLE_QUOTES? subexpr?)
| number
| DIFFERENTIAL
| mathit
| frac
| binom
| bra
| ket;
bra: L_ANGLE expr (R_BAR | BAR);
ket: (L_BAR | BAR) expr R_ANGLE;
mathit: CMD_MATHIT L_BRACE mathit_text R_BRACE;
mathit_text: LETTER*;
frac: CMD_FRAC (upperd = DIGIT | L_BRACE upper = expr R_BRACE)
(lowerd = DIGIT | L_BRACE lower = expr R_BRACE);
binom:
(CMD_BINOM | CMD_DBINOM | CMD_TBINOM) L_BRACE n = expr R_BRACE L_BRACE k = expr R_BRACE;
floor: L_FLOOR val = expr R_FLOOR;
ceil: L_CEIL val = expr R_CEIL;
func_normal:
FUNC_EXP
| FUNC_LOG
| FUNC_LG
| FUNC_LN
| FUNC_SIN
| FUNC_COS
| FUNC_TAN
| FUNC_CSC
| FUNC_SEC
| FUNC_COT
| FUNC_ARCSIN
| FUNC_ARCCOS
| FUNC_ARCTAN
| FUNC_ARCCSC
| FUNC_ARCSEC
| FUNC_ARCCOT
| FUNC_SINH
| FUNC_COSH
| FUNC_TANH
| FUNC_ARSINH
| FUNC_ARCOSH
| FUNC_ARTANH;
func:
func_normal (subexpr? supexpr? | supexpr? subexpr?) (
L_PAREN func_arg R_PAREN
| func_arg_noparens
)
| (LETTER | SYMBOL) (subexpr? SINGLE_QUOTES? | SINGLE_QUOTES? subexpr?) // e.g. f(x), f_1'(x)
L_PAREN args R_PAREN
| FUNC_INT (subexpr supexpr | supexpr subexpr)? (
additive? DIFFERENTIAL
| frac
| additive
)
| FUNC_SQRT (L_BRACKET root = expr R_BRACKET)? L_BRACE base = expr R_BRACE
| FUNC_OVERLINE L_BRACE base = expr R_BRACE
| (FUNC_SUM | FUNC_PROD) (subeq supexpr | supexpr subeq) mp
| FUNC_LIM limit_sub mp;
args: (expr ',' args) | expr;
limit_sub:
UNDERSCORE L_BRACE (LETTER | SYMBOL) LIM_APPROACH_SYM expr (
CARET ((L_BRACE (ADD | SUB) R_BRACE) | ADD | SUB)
)? R_BRACE;
func_arg: expr | (expr ',' func_arg);
func_arg_noparens: mp_nofunc;
subexpr: UNDERSCORE (atom | L_BRACE expr R_BRACE);
supexpr: CARET (atom | L_BRACE expr R_BRACE);
subeq: UNDERSCORE L_BRACE equality R_BRACE;
supeq: UNDERSCORE L_BRACE equality R_BRACE;

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from sympy.external import import_module
from sympy.utilities.decorator import doctest_depends_on
from sympy.parsing.latex.lark import LarkLaTeXParser, TransformToSymPyExpr, parse_latex_lark # noqa
from .errors import LaTeXParsingError # noqa
__doctest_requires__ = {('parse_latex',): ['antlr4', 'lark']}
@doctest_depends_on(modules=('antlr4', 'lark'))
def parse_latex(s, strict=False, backend="antlr"):
r"""Converts the input LaTeX string ``s`` to a SymPy ``Expr``.
Parameters
==========
s : str
The LaTeX string to parse. In Python source containing LaTeX,
*raw strings* (denoted with ``r"``, like this one) are preferred,
as LaTeX makes liberal use of the ``\`` character, which would
trigger escaping in normal Python strings.
backend : str, optional
Currently, there are two backends supported: ANTLR, and Lark.
The default setting is to use the ANTLR backend, which can be
changed to Lark if preferred.
Use ``backend="antlr"`` for the ANTLR-based parser, and
``backend="lark"`` for the Lark-based parser.
The ``backend`` option is case-sensitive, and must be in
all lowercase.
strict : bool, optional
This option is only available with the ANTLR backend.
If True, raise an exception if the string cannot be parsed as
valid LaTeX. If False, try to recover gracefully from common
mistakes.
Examples
========
>>> from sympy.parsing.latex import parse_latex
>>> expr = parse_latex(r"\frac {1 + \sqrt {\a}} {\b}")
>>> expr
(sqrt(a) + 1)/b
>>> expr.evalf(4, subs=dict(a=5, b=2))
1.618
>>> func = parse_latex(r"\int_1^\alpha \dfrac{\mathrm{d}t}{t}", backend="lark")
>>> func.evalf(subs={"alpha": 2})
0.693147180559945
"""
if backend == "antlr":
_latex = import_module(
'sympy.parsing.latex._parse_latex_antlr',
import_kwargs={'fromlist': ['X']})
if _latex is not None:
return _latex.parse_latex(s, strict)
elif backend == "lark":
return parse_latex_lark(s)
else:
raise NotImplementedError(f"Using the '{backend}' backend in the LaTeX" \
" parser is not supported.")

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# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
#
# Generated from ../LaTeX.g4, derived from latex2sympy
# latex2sympy is licensed under the MIT license
# https://github.com/augustt198/latex2sympy/blob/master/LICENSE.txt
#
# Generated with antlr4
# antlr4 is licensed under the BSD-3-Clause License
# https://github.com/antlr/antlr4/blob/master/LICENSE.txt

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# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
#
# Generated from ../LaTeX.g4, derived from latex2sympy
# latex2sympy is licensed under the MIT license
# https://github.com/augustt198/latex2sympy/blob/master/LICENSE.txt
#
# Generated with antlr4
# antlr4 is licensed under the BSD-3-Clause License
# https://github.com/antlr/antlr4/blob/master/LICENSE.txt
from antlr4 import *
from io import StringIO
import sys
if sys.version_info[1] > 5:
from typing import TextIO
else:
from typing.io import TextIO
def serializedATN():
return [
4,0,91,911,6,-1,2,0,7,0,2,1,7,1,2,2,7,2,2,3,7,3,2,4,7,4,2,5,7,5,
2,6,7,6,2,7,7,7,2,8,7,8,2,9,7,9,2,10,7,10,2,11,7,11,2,12,7,12,2,
13,7,13,2,14,7,14,2,15,7,15,2,16,7,16,2,17,7,17,2,18,7,18,2,19,7,
19,2,20,7,20,2,21,7,21,2,22,7,22,2,23,7,23,2,24,7,24,2,25,7,25,2,
26,7,26,2,27,7,27,2,28,7,28,2,29,7,29,2,30,7,30,2,31,7,31,2,32,7,
32,2,33,7,33,2,34,7,34,2,35,7,35,2,36,7,36,2,37,7,37,2,38,7,38,2,
39,7,39,2,40,7,40,2,41,7,41,2,42,7,42,2,43,7,43,2,44,7,44,2,45,7,
45,2,46,7,46,2,47,7,47,2,48,7,48,2,49,7,49,2,50,7,50,2,51,7,51,2,
52,7,52,2,53,7,53,2,54,7,54,2,55,7,55,2,56,7,56,2,57,7,57,2,58,7,
58,2,59,7,59,2,60,7,60,2,61,7,61,2,62,7,62,2,63,7,63,2,64,7,64,2,
65,7,65,2,66,7,66,2,67,7,67,2,68,7,68,2,69,7,69,2,70,7,70,2,71,7,
71,2,72,7,72,2,73,7,73,2,74,7,74,2,75,7,75,2,76,7,76,2,77,7,77,2,
78,7,78,2,79,7,79,2,80,7,80,2,81,7,81,2,82,7,82,2,83,7,83,2,84,7,
84,2,85,7,85,2,86,7,86,2,87,7,87,2,88,7,88,2,89,7,89,2,90,7,90,2,
91,7,91,1,0,1,0,1,1,1,1,1,2,4,2,191,8,2,11,2,12,2,192,1,2,1,2,1,
3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,3,3,209,8,3,1,3,1,
3,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,3,4,224,8,4,1,4,1,
4,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,1,5,3,5,241,8,
5,1,5,1,5,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1,7,1,7,1,7,1,7,1,7,1,
7,1,7,1,7,1,7,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,8,1,
8,1,8,1,8,3,8,277,8,8,1,8,1,8,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,9,1,
9,1,9,1,9,1,9,1,9,1,9,1,9,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,
1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,10,1,11,1,11,1,11,1,11,
1,11,1,11,1,11,1,11,1,12,1,12,1,12,1,12,1,12,1,12,1,12,1,12,1,12,
1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,
1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,
1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,
1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,1,13,3,13,
381,8,13,1,13,1,13,1,14,1,14,1,15,1,15,1,16,1,16,1,17,1,17,1,18,
1,18,1,19,1,19,1,20,1,20,1,21,1,21,1,22,1,22,1,22,1,23,1,23,1,23,
1,24,1,24,1,25,1,25,1,26,1,26,1,27,1,27,1,27,1,27,1,27,1,27,1,27,
1,27,1,28,1,28,1,28,1,28,1,28,1,28,1,28,1,29,1,29,1,29,1,29,1,29,
1,29,1,29,1,29,1,30,1,30,1,30,1,30,1,30,1,30,1,30,1,30,1,31,1,31,
1,31,1,31,1,31,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,
1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,
1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,
1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,1,32,
1,32,1,32,1,32,1,32,1,32,1,32,3,32,504,8,32,1,33,1,33,1,33,1,33,
1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,33,1,33,3,33,521,
8,33,1,34,1,34,1,34,1,34,1,34,1,35,1,35,1,35,1,35,1,35,1,35,1,36,
1,36,1,36,1,36,1,36,1,37,1,37,1,37,1,37,1,37,1,38,1,38,1,38,1,38,
1,39,1,39,1,39,1,39,1,40,1,40,1,40,1,40,1,40,1,41,1,41,1,41,1,41,
1,41,1,42,1,42,1,42,1,42,1,42,1,43,1,43,1,43,1,43,1,43,1,44,1,44,
1,44,1,44,1,44,1,45,1,45,1,45,1,45,1,45,1,46,1,46,1,46,1,46,1,46,
1,46,1,46,1,46,1,47,1,47,1,47,1,47,1,47,1,47,1,47,1,47,1,48,1,48,
1,48,1,48,1,48,1,48,1,48,1,48,1,49,1,49,1,49,1,49,1,49,1,49,1,49,
1,49,1,50,1,50,1,50,1,50,1,50,1,50,1,50,1,50,1,51,1,51,1,51,1,51,
1,51,1,51,1,51,1,51,1,52,1,52,1,52,1,52,1,52,1,52,1,53,1,53,1,53,
1,53,1,53,1,53,1,54,1,54,1,54,1,54,1,54,1,54,1,55,1,55,1,55,1,55,
1,55,1,55,1,55,1,55,1,56,1,56,1,56,1,56,1,56,1,56,1,56,1,56,1,57,
1,57,1,57,1,57,1,57,1,57,1,57,1,57,1,58,1,58,1,58,1,58,1,58,1,58,
1,58,1,58,1,59,1,59,1,59,1,59,1,59,1,59,1,59,1,59,1,60,1,60,1,60,
1,60,1,60,1,60,1,60,1,61,1,61,1,61,1,61,1,61,1,61,1,61,1,62,1,62,
1,62,1,62,1,62,1,62,1,63,1,63,1,63,1,63,1,63,1,63,1,63,1,63,1,63,
1,63,1,64,1,64,1,64,1,64,1,64,1,64,1,64,1,65,1,65,1,65,1,65,1,65,
1,65,1,66,1,66,1,66,1,66,1,66,1,67,1,67,1,67,1,67,1,67,1,67,1,67,
1,67,1,67,1,67,1,67,1,67,1,67,1,67,1,67,1,67,1,67,3,67,753,8,67,
1,68,1,68,1,68,1,68,1,68,1,68,1,68,1,69,1,69,1,69,1,69,1,69,1,69,
1,69,1,69,1,70,1,70,1,70,1,70,1,70,1,70,1,70,1,70,1,71,1,71,1,71,
1,71,1,71,1,71,1,71,1,71,1,72,1,72,1,73,1,73,1,74,1,74,1,75,1,75,
1,76,1,76,5,76,796,8,76,10,76,12,76,799,9,76,1,76,1,76,1,76,4,76,
804,8,76,11,76,12,76,805,3,76,808,8,76,1,77,1,77,1,78,1,78,1,79,
1,79,5,79,816,8,79,10,79,12,79,819,9,79,3,79,821,8,79,1,79,1,79,
1,79,5,79,826,8,79,10,79,12,79,829,9,79,1,79,3,79,832,8,79,3,79,
834,8,79,1,80,1,80,1,80,1,80,1,80,1,81,1,81,1,82,1,82,1,82,1,82,
1,82,1,82,1,82,1,82,1,82,3,82,852,8,82,1,83,1,83,1,83,1,83,1,83,
1,83,1,84,1,84,1,84,1,84,1,84,1,84,1,84,1,84,1,84,1,84,1,85,1,85,
1,86,1,86,1,86,1,86,1,86,1,86,1,86,1,86,1,86,3,86,881,8,86,1,87,
1,87,1,87,1,87,1,87,1,87,1,88,1,88,1,88,1,88,1,88,1,88,1,88,1,88,
1,88,1,88,1,89,1,89,1,90,4,90,902,8,90,11,90,12,90,903,1,91,1,91,
4,91,908,8,91,11,91,12,91,909,3,797,817,827,0,92,1,1,3,2,5,3,7,4,
9,5,11,6,13,7,15,8,17,9,19,10,21,11,23,12,25,13,27,14,29,15,31,16,
33,17,35,18,37,19,39,20,41,21,43,22,45,23,47,24,49,25,51,26,53,27,
55,28,57,29,59,30,61,31,63,32,65,33,67,34,69,35,71,36,73,37,75,38,
77,39,79,40,81,41,83,42,85,43,87,44,89,45,91,46,93,47,95,48,97,49,
99,50,101,51,103,52,105,53,107,54,109,55,111,56,113,57,115,58,117,
59,119,60,121,61,123,62,125,63,127,64,129,65,131,66,133,67,135,68,
137,69,139,70,141,71,143,72,145,73,147,74,149,75,151,0,153,76,155,
77,157,78,159,79,161,80,163,81,165,82,167,83,169,84,171,85,173,86,
175,87,177,88,179,89,181,90,183,91,1,0,3,3,0,9,10,13,13,32,32,2,
0,65,90,97,122,1,0,48,57,949,0,1,1,0,0,0,0,3,1,0,0,0,0,5,1,0,0,0,
0,7,1,0,0,0,0,9,1,0,0,0,0,11,1,0,0,0,0,13,1,0,0,0,0,15,1,0,0,0,0,
17,1,0,0,0,0,19,1,0,0,0,0,21,1,0,0,0,0,23,1,0,0,0,0,25,1,0,0,0,0,
27,1,0,0,0,0,29,1,0,0,0,0,31,1,0,0,0,0,33,1,0,0,0,0,35,1,0,0,0,0,
37,1,0,0,0,0,39,1,0,0,0,0,41,1,0,0,0,0,43,1,0,0,0,0,45,1,0,0,0,0,
47,1,0,0,0,0,49,1,0,0,0,0,51,1,0,0,0,0,53,1,0,0,0,0,55,1,0,0,0,0,
57,1,0,0,0,0,59,1,0,0,0,0,61,1,0,0,0,0,63,1,0,0,0,0,65,1,0,0,0,0,
67,1,0,0,0,0,69,1,0,0,0,0,71,1,0,0,0,0,73,1,0,0,0,0,75,1,0,0,0,0,
77,1,0,0,0,0,79,1,0,0,0,0,81,1,0,0,0,0,83,1,0,0,0,0,85,1,0,0,0,0,
87,1,0,0,0,0,89,1,0,0,0,0,91,1,0,0,0,0,93,1,0,0,0,0,95,1,0,0,0,0,
97,1,0,0,0,0,99,1,0,0,0,0,101,1,0,0,0,0,103,1,0,0,0,0,105,1,0,0,
0,0,107,1,0,0,0,0,109,1,0,0,0,0,111,1,0,0,0,0,113,1,0,0,0,0,115,
1,0,0,0,0,117,1,0,0,0,0,119,1,0,0,0,0,121,1,0,0,0,0,123,1,0,0,0,
0,125,1,0,0,0,0,127,1,0,0,0,0,129,1,0,0,0,0,131,1,0,0,0,0,133,1,
0,0,0,0,135,1,0,0,0,0,137,1,0,0,0,0,139,1,0,0,0,0,141,1,0,0,0,0,
143,1,0,0,0,0,145,1,0,0,0,0,147,1,0,0,0,0,149,1,0,0,0,0,153,1,0,
0,0,0,155,1,0,0,0,0,157,1,0,0,0,0,159,1,0,0,0,0,161,1,0,0,0,0,163,
1,0,0,0,0,165,1,0,0,0,0,167,1,0,0,0,0,169,1,0,0,0,0,171,1,0,0,0,
0,173,1,0,0,0,0,175,1,0,0,0,0,177,1,0,0,0,0,179,1,0,0,0,0,181,1,
0,0,0,0,183,1,0,0,0,1,185,1,0,0,0,3,187,1,0,0,0,5,190,1,0,0,0,7,
208,1,0,0,0,9,223,1,0,0,0,11,240,1,0,0,0,13,244,1,0,0,0,15,252,1,
0,0,0,17,276,1,0,0,0,19,280,1,0,0,0,21,295,1,0,0,0,23,312,1,0,0,
0,25,320,1,0,0,0,27,380,1,0,0,0,29,384,1,0,0,0,31,386,1,0,0,0,33,
388,1,0,0,0,35,390,1,0,0,0,37,392,1,0,0,0,39,394,1,0,0,0,41,396,
1,0,0,0,43,398,1,0,0,0,45,400,1,0,0,0,47,403,1,0,0,0,49,406,1,0,
0,0,51,408,1,0,0,0,53,410,1,0,0,0,55,412,1,0,0,0,57,420,1,0,0,0,
59,427,1,0,0,0,61,435,1,0,0,0,63,443,1,0,0,0,65,503,1,0,0,0,67,520,
1,0,0,0,69,522,1,0,0,0,71,527,1,0,0,0,73,533,1,0,0,0,75,538,1,0,
0,0,77,543,1,0,0,0,79,547,1,0,0,0,81,551,1,0,0,0,83,556,1,0,0,0,
85,561,1,0,0,0,87,566,1,0,0,0,89,571,1,0,0,0,91,576,1,0,0,0,93,581,
1,0,0,0,95,589,1,0,0,0,97,597,1,0,0,0,99,605,1,0,0,0,101,613,1,0,
0,0,103,621,1,0,0,0,105,629,1,0,0,0,107,635,1,0,0,0,109,641,1,0,
0,0,111,647,1,0,0,0,113,655,1,0,0,0,115,663,1,0,0,0,117,671,1,0,
0,0,119,679,1,0,0,0,121,687,1,0,0,0,123,694,1,0,0,0,125,701,1,0,
0,0,127,707,1,0,0,0,129,717,1,0,0,0,131,724,1,0,0,0,133,730,1,0,
0,0,135,752,1,0,0,0,137,754,1,0,0,0,139,761,1,0,0,0,141,769,1,0,
0,0,143,777,1,0,0,0,145,785,1,0,0,0,147,787,1,0,0,0,149,789,1,0,
0,0,151,791,1,0,0,0,153,793,1,0,0,0,155,809,1,0,0,0,157,811,1,0,
0,0,159,833,1,0,0,0,161,835,1,0,0,0,163,840,1,0,0,0,165,851,1,0,
0,0,167,853,1,0,0,0,169,859,1,0,0,0,171,869,1,0,0,0,173,880,1,0,
0,0,175,882,1,0,0,0,177,888,1,0,0,0,179,898,1,0,0,0,181,901,1,0,
0,0,183,905,1,0,0,0,185,186,5,44,0,0,186,2,1,0,0,0,187,188,5,46,
0,0,188,4,1,0,0,0,189,191,7,0,0,0,190,189,1,0,0,0,191,192,1,0,0,
0,192,190,1,0,0,0,192,193,1,0,0,0,193,194,1,0,0,0,194,195,6,2,0,
0,195,6,1,0,0,0,196,197,5,92,0,0,197,209,5,44,0,0,198,199,5,92,0,
0,199,200,5,116,0,0,200,201,5,104,0,0,201,202,5,105,0,0,202,203,
5,110,0,0,203,204,5,115,0,0,204,205,5,112,0,0,205,206,5,97,0,0,206,
207,5,99,0,0,207,209,5,101,0,0,208,196,1,0,0,0,208,198,1,0,0,0,209,
210,1,0,0,0,210,211,6,3,0,0,211,8,1,0,0,0,212,213,5,92,0,0,213,224,
5,58,0,0,214,215,5,92,0,0,215,216,5,109,0,0,216,217,5,101,0,0,217,
218,5,100,0,0,218,219,5,115,0,0,219,220,5,112,0,0,220,221,5,97,0,
0,221,222,5,99,0,0,222,224,5,101,0,0,223,212,1,0,0,0,223,214,1,0,
0,0,224,225,1,0,0,0,225,226,6,4,0,0,226,10,1,0,0,0,227,228,5,92,
0,0,228,241,5,59,0,0,229,230,5,92,0,0,230,231,5,116,0,0,231,232,
5,104,0,0,232,233,5,105,0,0,233,234,5,99,0,0,234,235,5,107,0,0,235,
236,5,115,0,0,236,237,5,112,0,0,237,238,5,97,0,0,238,239,5,99,0,
0,239,241,5,101,0,0,240,227,1,0,0,0,240,229,1,0,0,0,241,242,1,0,
0,0,242,243,6,5,0,0,243,12,1,0,0,0,244,245,5,92,0,0,245,246,5,113,
0,0,246,247,5,117,0,0,247,248,5,97,0,0,248,249,5,100,0,0,249,250,
1,0,0,0,250,251,6,6,0,0,251,14,1,0,0,0,252,253,5,92,0,0,253,254,
5,113,0,0,254,255,5,113,0,0,255,256,5,117,0,0,256,257,5,97,0,0,257,
258,5,100,0,0,258,259,1,0,0,0,259,260,6,7,0,0,260,16,1,0,0,0,261,
262,5,92,0,0,262,277,5,33,0,0,263,264,5,92,0,0,264,265,5,110,0,0,
265,266,5,101,0,0,266,267,5,103,0,0,267,268,5,116,0,0,268,269,5,
104,0,0,269,270,5,105,0,0,270,271,5,110,0,0,271,272,5,115,0,0,272,
273,5,112,0,0,273,274,5,97,0,0,274,275,5,99,0,0,275,277,5,101,0,
0,276,261,1,0,0,0,276,263,1,0,0,0,277,278,1,0,0,0,278,279,6,8,0,
0,279,18,1,0,0,0,280,281,5,92,0,0,281,282,5,110,0,0,282,283,5,101,
0,0,283,284,5,103,0,0,284,285,5,109,0,0,285,286,5,101,0,0,286,287,
5,100,0,0,287,288,5,115,0,0,288,289,5,112,0,0,289,290,5,97,0,0,290,
291,5,99,0,0,291,292,5,101,0,0,292,293,1,0,0,0,293,294,6,9,0,0,294,
20,1,0,0,0,295,296,5,92,0,0,296,297,5,110,0,0,297,298,5,101,0,0,
298,299,5,103,0,0,299,300,5,116,0,0,300,301,5,104,0,0,301,302,5,
105,0,0,302,303,5,99,0,0,303,304,5,107,0,0,304,305,5,115,0,0,305,
306,5,112,0,0,306,307,5,97,0,0,307,308,5,99,0,0,308,309,5,101,0,
0,309,310,1,0,0,0,310,311,6,10,0,0,311,22,1,0,0,0,312,313,5,92,0,
0,313,314,5,108,0,0,314,315,5,101,0,0,315,316,5,102,0,0,316,317,
5,116,0,0,317,318,1,0,0,0,318,319,6,11,0,0,319,24,1,0,0,0,320,321,
5,92,0,0,321,322,5,114,0,0,322,323,5,105,0,0,323,324,5,103,0,0,324,
325,5,104,0,0,325,326,5,116,0,0,326,327,1,0,0,0,327,328,6,12,0,0,
328,26,1,0,0,0,329,330,5,92,0,0,330,331,5,118,0,0,331,332,5,114,
0,0,332,333,5,117,0,0,333,334,5,108,0,0,334,381,5,101,0,0,335,336,
5,92,0,0,336,337,5,118,0,0,337,338,5,99,0,0,338,339,5,101,0,0,339,
340,5,110,0,0,340,341,5,116,0,0,341,342,5,101,0,0,342,381,5,114,
0,0,343,344,5,92,0,0,344,345,5,118,0,0,345,346,5,98,0,0,346,347,
5,111,0,0,347,381,5,120,0,0,348,349,5,92,0,0,349,350,5,118,0,0,350,
351,5,115,0,0,351,352,5,107,0,0,352,353,5,105,0,0,353,381,5,112,
0,0,354,355,5,92,0,0,355,356,5,118,0,0,356,357,5,115,0,0,357,358,
5,112,0,0,358,359,5,97,0,0,359,360,5,99,0,0,360,381,5,101,0,0,361,
362,5,92,0,0,362,363,5,104,0,0,363,364,5,102,0,0,364,365,5,105,0,
0,365,381,5,108,0,0,366,367,5,92,0,0,367,381,5,42,0,0,368,369,5,
92,0,0,369,381,5,45,0,0,370,371,5,92,0,0,371,381,5,46,0,0,372,373,
5,92,0,0,373,381,5,47,0,0,374,375,5,92,0,0,375,381,5,34,0,0,376,
377,5,92,0,0,377,381,5,40,0,0,378,379,5,92,0,0,379,381,5,61,0,0,
380,329,1,0,0,0,380,335,1,0,0,0,380,343,1,0,0,0,380,348,1,0,0,0,
380,354,1,0,0,0,380,361,1,0,0,0,380,366,1,0,0,0,380,368,1,0,0,0,
380,370,1,0,0,0,380,372,1,0,0,0,380,374,1,0,0,0,380,376,1,0,0,0,
380,378,1,0,0,0,381,382,1,0,0,0,382,383,6,13,0,0,383,28,1,0,0,0,
384,385,5,43,0,0,385,30,1,0,0,0,386,387,5,45,0,0,387,32,1,0,0,0,
388,389,5,42,0,0,389,34,1,0,0,0,390,391,5,47,0,0,391,36,1,0,0,0,
392,393,5,40,0,0,393,38,1,0,0,0,394,395,5,41,0,0,395,40,1,0,0,0,
396,397,5,123,0,0,397,42,1,0,0,0,398,399,5,125,0,0,399,44,1,0,0,
0,400,401,5,92,0,0,401,402,5,123,0,0,402,46,1,0,0,0,403,404,5,92,
0,0,404,405,5,125,0,0,405,48,1,0,0,0,406,407,5,91,0,0,407,50,1,0,
0,0,408,409,5,93,0,0,409,52,1,0,0,0,410,411,5,124,0,0,411,54,1,0,
0,0,412,413,5,92,0,0,413,414,5,114,0,0,414,415,5,105,0,0,415,416,
5,103,0,0,416,417,5,104,0,0,417,418,5,116,0,0,418,419,5,124,0,0,
419,56,1,0,0,0,420,421,5,92,0,0,421,422,5,108,0,0,422,423,5,101,
0,0,423,424,5,102,0,0,424,425,5,116,0,0,425,426,5,124,0,0,426,58,
1,0,0,0,427,428,5,92,0,0,428,429,5,108,0,0,429,430,5,97,0,0,430,
431,5,110,0,0,431,432,5,103,0,0,432,433,5,108,0,0,433,434,5,101,
0,0,434,60,1,0,0,0,435,436,5,92,0,0,436,437,5,114,0,0,437,438,5,
97,0,0,438,439,5,110,0,0,439,440,5,103,0,0,440,441,5,108,0,0,441,
442,5,101,0,0,442,62,1,0,0,0,443,444,5,92,0,0,444,445,5,108,0,0,
445,446,5,105,0,0,446,447,5,109,0,0,447,64,1,0,0,0,448,449,5,92,
0,0,449,450,5,116,0,0,450,504,5,111,0,0,451,452,5,92,0,0,452,453,
5,114,0,0,453,454,5,105,0,0,454,455,5,103,0,0,455,456,5,104,0,0,
456,457,5,116,0,0,457,458,5,97,0,0,458,459,5,114,0,0,459,460,5,114,
0,0,460,461,5,111,0,0,461,504,5,119,0,0,462,463,5,92,0,0,463,464,
5,82,0,0,464,465,5,105,0,0,465,466,5,103,0,0,466,467,5,104,0,0,467,
468,5,116,0,0,468,469,5,97,0,0,469,470,5,114,0,0,470,471,5,114,0,
0,471,472,5,111,0,0,472,504,5,119,0,0,473,474,5,92,0,0,474,475,5,
108,0,0,475,476,5,111,0,0,476,477,5,110,0,0,477,478,5,103,0,0,478,
479,5,114,0,0,479,480,5,105,0,0,480,481,5,103,0,0,481,482,5,104,
0,0,482,483,5,116,0,0,483,484,5,97,0,0,484,485,5,114,0,0,485,486,
5,114,0,0,486,487,5,111,0,0,487,504,5,119,0,0,488,489,5,92,0,0,489,
490,5,76,0,0,490,491,5,111,0,0,491,492,5,110,0,0,492,493,5,103,0,
0,493,494,5,114,0,0,494,495,5,105,0,0,495,496,5,103,0,0,496,497,
5,104,0,0,497,498,5,116,0,0,498,499,5,97,0,0,499,500,5,114,0,0,500,
501,5,114,0,0,501,502,5,111,0,0,502,504,5,119,0,0,503,448,1,0,0,
0,503,451,1,0,0,0,503,462,1,0,0,0,503,473,1,0,0,0,503,488,1,0,0,
0,504,66,1,0,0,0,505,506,5,92,0,0,506,507,5,105,0,0,507,508,5,110,
0,0,508,521,5,116,0,0,509,510,5,92,0,0,510,511,5,105,0,0,511,512,
5,110,0,0,512,513,5,116,0,0,513,514,5,92,0,0,514,515,5,108,0,0,515,
516,5,105,0,0,516,517,5,109,0,0,517,518,5,105,0,0,518,519,5,116,
0,0,519,521,5,115,0,0,520,505,1,0,0,0,520,509,1,0,0,0,521,68,1,0,
0,0,522,523,5,92,0,0,523,524,5,115,0,0,524,525,5,117,0,0,525,526,
5,109,0,0,526,70,1,0,0,0,527,528,5,92,0,0,528,529,5,112,0,0,529,
530,5,114,0,0,530,531,5,111,0,0,531,532,5,100,0,0,532,72,1,0,0,0,
533,534,5,92,0,0,534,535,5,101,0,0,535,536,5,120,0,0,536,537,5,112,
0,0,537,74,1,0,0,0,538,539,5,92,0,0,539,540,5,108,0,0,540,541,5,
111,0,0,541,542,5,103,0,0,542,76,1,0,0,0,543,544,5,92,0,0,544,545,
5,108,0,0,545,546,5,103,0,0,546,78,1,0,0,0,547,548,5,92,0,0,548,
549,5,108,0,0,549,550,5,110,0,0,550,80,1,0,0,0,551,552,5,92,0,0,
552,553,5,115,0,0,553,554,5,105,0,0,554,555,5,110,0,0,555,82,1,0,
0,0,556,557,5,92,0,0,557,558,5,99,0,0,558,559,5,111,0,0,559,560,
5,115,0,0,560,84,1,0,0,0,561,562,5,92,0,0,562,563,5,116,0,0,563,
564,5,97,0,0,564,565,5,110,0,0,565,86,1,0,0,0,566,567,5,92,0,0,567,
568,5,99,0,0,568,569,5,115,0,0,569,570,5,99,0,0,570,88,1,0,0,0,571,
572,5,92,0,0,572,573,5,115,0,0,573,574,5,101,0,0,574,575,5,99,0,
0,575,90,1,0,0,0,576,577,5,92,0,0,577,578,5,99,0,0,578,579,5,111,
0,0,579,580,5,116,0,0,580,92,1,0,0,0,581,582,5,92,0,0,582,583,5,
97,0,0,583,584,5,114,0,0,584,585,5,99,0,0,585,586,5,115,0,0,586,
587,5,105,0,0,587,588,5,110,0,0,588,94,1,0,0,0,589,590,5,92,0,0,
590,591,5,97,0,0,591,592,5,114,0,0,592,593,5,99,0,0,593,594,5,99,
0,0,594,595,5,111,0,0,595,596,5,115,0,0,596,96,1,0,0,0,597,598,5,
92,0,0,598,599,5,97,0,0,599,600,5,114,0,0,600,601,5,99,0,0,601,602,
5,116,0,0,602,603,5,97,0,0,603,604,5,110,0,0,604,98,1,0,0,0,605,
606,5,92,0,0,606,607,5,97,0,0,607,608,5,114,0,0,608,609,5,99,0,0,
609,610,5,99,0,0,610,611,5,115,0,0,611,612,5,99,0,0,612,100,1,0,
0,0,613,614,5,92,0,0,614,615,5,97,0,0,615,616,5,114,0,0,616,617,
5,99,0,0,617,618,5,115,0,0,618,619,5,101,0,0,619,620,5,99,0,0,620,
102,1,0,0,0,621,622,5,92,0,0,622,623,5,97,0,0,623,624,5,114,0,0,
624,625,5,99,0,0,625,626,5,99,0,0,626,627,5,111,0,0,627,628,5,116,
0,0,628,104,1,0,0,0,629,630,5,92,0,0,630,631,5,115,0,0,631,632,5,
105,0,0,632,633,5,110,0,0,633,634,5,104,0,0,634,106,1,0,0,0,635,
636,5,92,0,0,636,637,5,99,0,0,637,638,5,111,0,0,638,639,5,115,0,
0,639,640,5,104,0,0,640,108,1,0,0,0,641,642,5,92,0,0,642,643,5,116,
0,0,643,644,5,97,0,0,644,645,5,110,0,0,645,646,5,104,0,0,646,110,
1,0,0,0,647,648,5,92,0,0,648,649,5,97,0,0,649,650,5,114,0,0,650,
651,5,115,0,0,651,652,5,105,0,0,652,653,5,110,0,0,653,654,5,104,
0,0,654,112,1,0,0,0,655,656,5,92,0,0,656,657,5,97,0,0,657,658,5,
114,0,0,658,659,5,99,0,0,659,660,5,111,0,0,660,661,5,115,0,0,661,
662,5,104,0,0,662,114,1,0,0,0,663,664,5,92,0,0,664,665,5,97,0,0,
665,666,5,114,0,0,666,667,5,116,0,0,667,668,5,97,0,0,668,669,5,110,
0,0,669,670,5,104,0,0,670,116,1,0,0,0,671,672,5,92,0,0,672,673,5,
108,0,0,673,674,5,102,0,0,674,675,5,108,0,0,675,676,5,111,0,0,676,
677,5,111,0,0,677,678,5,114,0,0,678,118,1,0,0,0,679,680,5,92,0,0,
680,681,5,114,0,0,681,682,5,102,0,0,682,683,5,108,0,0,683,684,5,
111,0,0,684,685,5,111,0,0,685,686,5,114,0,0,686,120,1,0,0,0,687,
688,5,92,0,0,688,689,5,108,0,0,689,690,5,99,0,0,690,691,5,101,0,
0,691,692,5,105,0,0,692,693,5,108,0,0,693,122,1,0,0,0,694,695,5,
92,0,0,695,696,5,114,0,0,696,697,5,99,0,0,697,698,5,101,0,0,698,
699,5,105,0,0,699,700,5,108,0,0,700,124,1,0,0,0,701,702,5,92,0,0,
702,703,5,115,0,0,703,704,5,113,0,0,704,705,5,114,0,0,705,706,5,
116,0,0,706,126,1,0,0,0,707,708,5,92,0,0,708,709,5,111,0,0,709,710,
5,118,0,0,710,711,5,101,0,0,711,712,5,114,0,0,712,713,5,108,0,0,
713,714,5,105,0,0,714,715,5,110,0,0,715,716,5,101,0,0,716,128,1,
0,0,0,717,718,5,92,0,0,718,719,5,116,0,0,719,720,5,105,0,0,720,721,
5,109,0,0,721,722,5,101,0,0,722,723,5,115,0,0,723,130,1,0,0,0,724,
725,5,92,0,0,725,726,5,99,0,0,726,727,5,100,0,0,727,728,5,111,0,
0,728,729,5,116,0,0,729,132,1,0,0,0,730,731,5,92,0,0,731,732,5,100,
0,0,732,733,5,105,0,0,733,734,5,118,0,0,734,134,1,0,0,0,735,736,
5,92,0,0,736,737,5,102,0,0,737,738,5,114,0,0,738,739,5,97,0,0,739,
753,5,99,0,0,740,741,5,92,0,0,741,742,5,100,0,0,742,743,5,102,0,
0,743,744,5,114,0,0,744,745,5,97,0,0,745,753,5,99,0,0,746,747,5,
92,0,0,747,748,5,116,0,0,748,749,5,102,0,0,749,750,5,114,0,0,750,
751,5,97,0,0,751,753,5,99,0,0,752,735,1,0,0,0,752,740,1,0,0,0,752,
746,1,0,0,0,753,136,1,0,0,0,754,755,5,92,0,0,755,756,5,98,0,0,756,
757,5,105,0,0,757,758,5,110,0,0,758,759,5,111,0,0,759,760,5,109,
0,0,760,138,1,0,0,0,761,762,5,92,0,0,762,763,5,100,0,0,763,764,5,
98,0,0,764,765,5,105,0,0,765,766,5,110,0,0,766,767,5,111,0,0,767,
768,5,109,0,0,768,140,1,0,0,0,769,770,5,92,0,0,770,771,5,116,0,0,
771,772,5,98,0,0,772,773,5,105,0,0,773,774,5,110,0,0,774,775,5,111,
0,0,775,776,5,109,0,0,776,142,1,0,0,0,777,778,5,92,0,0,778,779,5,
109,0,0,779,780,5,97,0,0,780,781,5,116,0,0,781,782,5,104,0,0,782,
783,5,105,0,0,783,784,5,116,0,0,784,144,1,0,0,0,785,786,5,95,0,0,
786,146,1,0,0,0,787,788,5,94,0,0,788,148,1,0,0,0,789,790,5,58,0,
0,790,150,1,0,0,0,791,792,7,0,0,0,792,152,1,0,0,0,793,797,5,100,
0,0,794,796,3,151,75,0,795,794,1,0,0,0,796,799,1,0,0,0,797,798,1,
0,0,0,797,795,1,0,0,0,798,807,1,0,0,0,799,797,1,0,0,0,800,808,7,
1,0,0,801,803,5,92,0,0,802,804,7,1,0,0,803,802,1,0,0,0,804,805,1,
0,0,0,805,803,1,0,0,0,805,806,1,0,0,0,806,808,1,0,0,0,807,800,1,
0,0,0,807,801,1,0,0,0,808,154,1,0,0,0,809,810,7,1,0,0,810,156,1,
0,0,0,811,812,7,2,0,0,812,158,1,0,0,0,813,817,5,38,0,0,814,816,3,
151,75,0,815,814,1,0,0,0,816,819,1,0,0,0,817,818,1,0,0,0,817,815,
1,0,0,0,818,821,1,0,0,0,819,817,1,0,0,0,820,813,1,0,0,0,820,821,
1,0,0,0,821,822,1,0,0,0,822,834,5,61,0,0,823,831,5,61,0,0,824,826,
3,151,75,0,825,824,1,0,0,0,826,829,1,0,0,0,827,828,1,0,0,0,827,825,
1,0,0,0,828,830,1,0,0,0,829,827,1,0,0,0,830,832,5,38,0,0,831,827,
1,0,0,0,831,832,1,0,0,0,832,834,1,0,0,0,833,820,1,0,0,0,833,823,
1,0,0,0,834,160,1,0,0,0,835,836,5,92,0,0,836,837,5,110,0,0,837,838,
5,101,0,0,838,839,5,113,0,0,839,162,1,0,0,0,840,841,5,60,0,0,841,
164,1,0,0,0,842,843,5,92,0,0,843,844,5,108,0,0,844,845,5,101,0,0,
845,852,5,113,0,0,846,847,5,92,0,0,847,848,5,108,0,0,848,852,5,101,
0,0,849,852,3,167,83,0,850,852,3,169,84,0,851,842,1,0,0,0,851,846,
1,0,0,0,851,849,1,0,0,0,851,850,1,0,0,0,852,166,1,0,0,0,853,854,
5,92,0,0,854,855,5,108,0,0,855,856,5,101,0,0,856,857,5,113,0,0,857,
858,5,113,0,0,858,168,1,0,0,0,859,860,5,92,0,0,860,861,5,108,0,0,
861,862,5,101,0,0,862,863,5,113,0,0,863,864,5,115,0,0,864,865,5,
108,0,0,865,866,5,97,0,0,866,867,5,110,0,0,867,868,5,116,0,0,868,
170,1,0,0,0,869,870,5,62,0,0,870,172,1,0,0,0,871,872,5,92,0,0,872,
873,5,103,0,0,873,874,5,101,0,0,874,881,5,113,0,0,875,876,5,92,0,
0,876,877,5,103,0,0,877,881,5,101,0,0,878,881,3,175,87,0,879,881,
3,177,88,0,880,871,1,0,0,0,880,875,1,0,0,0,880,878,1,0,0,0,880,879,
1,0,0,0,881,174,1,0,0,0,882,883,5,92,0,0,883,884,5,103,0,0,884,885,
5,101,0,0,885,886,5,113,0,0,886,887,5,113,0,0,887,176,1,0,0,0,888,
889,5,92,0,0,889,890,5,103,0,0,890,891,5,101,0,0,891,892,5,113,0,
0,892,893,5,115,0,0,893,894,5,108,0,0,894,895,5,97,0,0,895,896,5,
110,0,0,896,897,5,116,0,0,897,178,1,0,0,0,898,899,5,33,0,0,899,180,
1,0,0,0,900,902,5,39,0,0,901,900,1,0,0,0,902,903,1,0,0,0,903,901,
1,0,0,0,903,904,1,0,0,0,904,182,1,0,0,0,905,907,5,92,0,0,906,908,
7,1,0,0,907,906,1,0,0,0,908,909,1,0,0,0,909,907,1,0,0,0,909,910,
1,0,0,0,910,184,1,0,0,0,22,0,192,208,223,240,276,380,503,520,752,
797,805,807,817,820,827,831,833,851,880,903,909,1,6,0,0
]
class LaTeXLexer(Lexer):
atn = ATNDeserializer().deserialize(serializedATN())
decisionsToDFA = [ DFA(ds, i) for i, ds in enumerate(atn.decisionToState) ]
T__0 = 1
T__1 = 2
WS = 3
THINSPACE = 4
MEDSPACE = 5
THICKSPACE = 6
QUAD = 7
QQUAD = 8
NEGTHINSPACE = 9
NEGMEDSPACE = 10
NEGTHICKSPACE = 11
CMD_LEFT = 12
CMD_RIGHT = 13
IGNORE = 14
ADD = 15
SUB = 16
MUL = 17
DIV = 18
L_PAREN = 19
R_PAREN = 20
L_BRACE = 21
R_BRACE = 22
L_BRACE_LITERAL = 23
R_BRACE_LITERAL = 24
L_BRACKET = 25
R_BRACKET = 26
BAR = 27
R_BAR = 28
L_BAR = 29
L_ANGLE = 30
R_ANGLE = 31
FUNC_LIM = 32
LIM_APPROACH_SYM = 33
FUNC_INT = 34
FUNC_SUM = 35
FUNC_PROD = 36
FUNC_EXP = 37
FUNC_LOG = 38
FUNC_LG = 39
FUNC_LN = 40
FUNC_SIN = 41
FUNC_COS = 42
FUNC_TAN = 43
FUNC_CSC = 44
FUNC_SEC = 45
FUNC_COT = 46
FUNC_ARCSIN = 47
FUNC_ARCCOS = 48
FUNC_ARCTAN = 49
FUNC_ARCCSC = 50
FUNC_ARCSEC = 51
FUNC_ARCCOT = 52
FUNC_SINH = 53
FUNC_COSH = 54
FUNC_TANH = 55
FUNC_ARSINH = 56
FUNC_ARCOSH = 57
FUNC_ARTANH = 58
L_FLOOR = 59
R_FLOOR = 60
L_CEIL = 61
R_CEIL = 62
FUNC_SQRT = 63
FUNC_OVERLINE = 64
CMD_TIMES = 65
CMD_CDOT = 66
CMD_DIV = 67
CMD_FRAC = 68
CMD_BINOM = 69
CMD_DBINOM = 70
CMD_TBINOM = 71
CMD_MATHIT = 72
UNDERSCORE = 73
CARET = 74
COLON = 75
DIFFERENTIAL = 76
LETTER = 77
DIGIT = 78
EQUAL = 79
NEQ = 80
LT = 81
LTE = 82
LTE_Q = 83
LTE_S = 84
GT = 85
GTE = 86
GTE_Q = 87
GTE_S = 88
BANG = 89
SINGLE_QUOTES = 90
SYMBOL = 91
channelNames = [ u"DEFAULT_TOKEN_CHANNEL", u"HIDDEN" ]
modeNames = [ "DEFAULT_MODE" ]
literalNames = [ "<INVALID>",
"','", "'.'", "'\\quad'", "'\\qquad'", "'\\negmedspace'", "'\\negthickspace'",
"'\\left'", "'\\right'", "'+'", "'-'", "'*'", "'/'", "'('",
"')'", "'{'", "'}'", "'\\{'", "'\\}'", "'['", "']'", "'|'",
"'\\right|'", "'\\left|'", "'\\langle'", "'\\rangle'", "'\\lim'",
"'\\sum'", "'\\prod'", "'\\exp'", "'\\log'", "'\\lg'", "'\\ln'",
"'\\sin'", "'\\cos'", "'\\tan'", "'\\csc'", "'\\sec'", "'\\cot'",
"'\\arcsin'", "'\\arccos'", "'\\arctan'", "'\\arccsc'", "'\\arcsec'",
"'\\arccot'", "'\\sinh'", "'\\cosh'", "'\\tanh'", "'\\arsinh'",
"'\\arcosh'", "'\\artanh'", "'\\lfloor'", "'\\rfloor'", "'\\lceil'",
"'\\rceil'", "'\\sqrt'", "'\\overline'", "'\\times'", "'\\cdot'",
"'\\div'", "'\\binom'", "'\\dbinom'", "'\\tbinom'", "'\\mathit'",
"'_'", "'^'", "':'", "'\\neq'", "'<'", "'\\leqq'", "'\\leqslant'",
"'>'", "'\\geqq'", "'\\geqslant'", "'!'" ]
symbolicNames = [ "<INVALID>",
"WS", "THINSPACE", "MEDSPACE", "THICKSPACE", "QUAD", "QQUAD",
"NEGTHINSPACE", "NEGMEDSPACE", "NEGTHICKSPACE", "CMD_LEFT",
"CMD_RIGHT", "IGNORE", "ADD", "SUB", "MUL", "DIV", "L_PAREN",
"R_PAREN", "L_BRACE", "R_BRACE", "L_BRACE_LITERAL", "R_BRACE_LITERAL",
"L_BRACKET", "R_BRACKET", "BAR", "R_BAR", "L_BAR", "L_ANGLE",
"R_ANGLE", "FUNC_LIM", "LIM_APPROACH_SYM", "FUNC_INT", "FUNC_SUM",
"FUNC_PROD", "FUNC_EXP", "FUNC_LOG", "FUNC_LG", "FUNC_LN", "FUNC_SIN",
"FUNC_COS", "FUNC_TAN", "FUNC_CSC", "FUNC_SEC", "FUNC_COT",
"FUNC_ARCSIN", "FUNC_ARCCOS", "FUNC_ARCTAN", "FUNC_ARCCSC",
"FUNC_ARCSEC", "FUNC_ARCCOT", "FUNC_SINH", "FUNC_COSH", "FUNC_TANH",
"FUNC_ARSINH", "FUNC_ARCOSH", "FUNC_ARTANH", "L_FLOOR", "R_FLOOR",
"L_CEIL", "R_CEIL", "FUNC_SQRT", "FUNC_OVERLINE", "CMD_TIMES",
"CMD_CDOT", "CMD_DIV", "CMD_FRAC", "CMD_BINOM", "CMD_DBINOM",
"CMD_TBINOM", "CMD_MATHIT", "UNDERSCORE", "CARET", "COLON",
"DIFFERENTIAL", "LETTER", "DIGIT", "EQUAL", "NEQ", "LT", "LTE",
"LTE_Q", "LTE_S", "GT", "GTE", "GTE_Q", "GTE_S", "BANG", "SINGLE_QUOTES",
"SYMBOL" ]
ruleNames = [ "T__0", "T__1", "WS", "THINSPACE", "MEDSPACE", "THICKSPACE",
"QUAD", "QQUAD", "NEGTHINSPACE", "NEGMEDSPACE", "NEGTHICKSPACE",
"CMD_LEFT", "CMD_RIGHT", "IGNORE", "ADD", "SUB", "MUL",
"DIV", "L_PAREN", "R_PAREN", "L_BRACE", "R_BRACE", "L_BRACE_LITERAL",
"R_BRACE_LITERAL", "L_BRACKET", "R_BRACKET", "BAR", "R_BAR",
"L_BAR", "L_ANGLE", "R_ANGLE", "FUNC_LIM", "LIM_APPROACH_SYM",
"FUNC_INT", "FUNC_SUM", "FUNC_PROD", "FUNC_EXP", "FUNC_LOG",
"FUNC_LG", "FUNC_LN", "FUNC_SIN", "FUNC_COS", "FUNC_TAN",
"FUNC_CSC", "FUNC_SEC", "FUNC_COT", "FUNC_ARCSIN", "FUNC_ARCCOS",
"FUNC_ARCTAN", "FUNC_ARCCSC", "FUNC_ARCSEC", "FUNC_ARCCOT",
"FUNC_SINH", "FUNC_COSH", "FUNC_TANH", "FUNC_ARSINH",
"FUNC_ARCOSH", "FUNC_ARTANH", "L_FLOOR", "R_FLOOR", "L_CEIL",
"R_CEIL", "FUNC_SQRT", "FUNC_OVERLINE", "CMD_TIMES", "CMD_CDOT",
"CMD_DIV", "CMD_FRAC", "CMD_BINOM", "CMD_DBINOM", "CMD_TBINOM",
"CMD_MATHIT", "UNDERSCORE", "CARET", "COLON", "WS_CHAR",
"DIFFERENTIAL", "LETTER", "DIGIT", "EQUAL", "NEQ", "LT",
"LTE", "LTE_Q", "LTE_S", "GT", "GTE", "GTE_Q", "GTE_S",
"BANG", "SINGLE_QUOTES", "SYMBOL" ]
grammarFileName = "LaTeX.g4"
def __init__(self, input=None, output:TextIO = sys.stdout):
super().__init__(input, output)
self.checkVersion("4.11.1")
self._interp = LexerATNSimulator(self, self.atn, self.decisionsToDFA, PredictionContextCache())
self._actions = None
self._predicates = None

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import os
import subprocess
import glob
from sympy.utilities.misc import debug
here = os.path.dirname(__file__)
grammar_file = os.path.abspath(os.path.join(here, "LaTeX.g4"))
dir_latex_antlr = os.path.join(here, "_antlr")
header = '''\
# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
#
# Generated from ../LaTeX.g4, derived from latex2sympy
# latex2sympy is licensed under the MIT license
# https://github.com/augustt198/latex2sympy/blob/master/LICENSE.txt
#
# Generated with antlr4
# antlr4 is licensed under the BSD-3-Clause License
# https://github.com/antlr/antlr4/blob/master/LICENSE.txt
'''
def check_antlr_version():
debug("Checking antlr4 version...")
try:
debug(subprocess.check_output(["antlr4"])
.decode('utf-8').split("\n")[0])
return True
except (subprocess.CalledProcessError, FileNotFoundError):
debug("The 'antlr4' command line tool is not installed, "
"or not on your PATH.\n"
"> Please refer to the README.md file for more information.")
return False
def build_parser(output_dir=dir_latex_antlr):
check_antlr_version()
debug("Updating ANTLR-generated code in {}".format(output_dir))
if not os.path.exists(output_dir):
os.makedirs(output_dir)
with open(os.path.join(output_dir, "__init__.py"), "w+") as fp:
fp.write(header)
args = [
"antlr4",
grammar_file,
"-o", output_dir,
# for now, not generating these as latex2sympy did not use them
"-no-visitor",
"-no-listener",
]
debug("Running code generation...\n\t$ {}".format(" ".join(args)))
subprocess.check_output(args, cwd=output_dir)
debug("Applying headers, removing unnecessary files and renaming...")
# Handle case insensitive file systems. If the files are already
# generated, they will be written to latex* but LaTeX*.* won't match them.
for path in (glob.glob(os.path.join(output_dir, "LaTeX*.*")) or
glob.glob(os.path.join(output_dir, "latex*.*"))):
# Remove files ending in .interp or .tokens as they are not needed.
if not path.endswith(".py"):
os.unlink(path)
continue
new_path = os.path.join(output_dir, os.path.basename(path).lower())
with open(path, 'r') as f:
lines = [line.rstrip() + '\n' for line in f.readlines()]
os.unlink(path)
with open(new_path, "w") as out_file:
offset = 0
while lines[offset].startswith('#'):
offset += 1
out_file.write(header)
out_file.writelines(lines[offset:])
debug("\t{}".format(new_path))
return True
if __name__ == "__main__":
build_parser()

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# Ported from latex2sympy by @augustt198
# https://github.com/augustt198/latex2sympy
# See license in LICENSE.txt
from importlib.metadata import version
import sympy
from sympy.external import import_module
from sympy.printing.str import StrPrinter
from sympy.physics.quantum.state import Bra, Ket
from .errors import LaTeXParsingError
LaTeXParser = LaTeXLexer = MathErrorListener = None
try:
LaTeXParser = import_module('sympy.parsing.latex._antlr.latexparser',
import_kwargs={'fromlist': ['LaTeXParser']}).LaTeXParser
LaTeXLexer = import_module('sympy.parsing.latex._antlr.latexlexer',
import_kwargs={'fromlist': ['LaTeXLexer']}).LaTeXLexer
except Exception:
pass
ErrorListener = import_module('antlr4.error.ErrorListener',
warn_not_installed=True,
import_kwargs={'fromlist': ['ErrorListener']}
)
if ErrorListener:
class MathErrorListener(ErrorListener.ErrorListener): # type:ignore # noqa:F811
def __init__(self, src):
super(ErrorListener.ErrorListener, self).__init__()
self.src = src
def syntaxError(self, recog, symbol, line, col, msg, e):
fmt = "%s\n%s\n%s"
marker = "~" * col + "^"
if msg.startswith("missing"):
err = fmt % (msg, self.src, marker)
elif msg.startswith("no viable"):
err = fmt % ("I expected something else here", self.src, marker)
elif msg.startswith("mismatched"):
names = LaTeXParser.literalNames
expected = [
names[i] for i in e.getExpectedTokens() if i < len(names)
]
if len(expected) < 10:
expected = " ".join(expected)
err = (fmt % ("I expected one of these: " + expected, self.src,
marker))
else:
err = (fmt % ("I expected something else here", self.src,
marker))
else:
err = fmt % ("I don't understand this", self.src, marker)
raise LaTeXParsingError(err)
def parse_latex(sympy, strict=False):
antlr4 = import_module('antlr4')
if None in [antlr4, MathErrorListener] or \
not version('antlr4-python3-runtime').startswith('4.11'):
raise ImportError("LaTeX parsing requires the antlr4 Python package,"
" provided by pip (antlr4-python3-runtime) or"
" conda (antlr-python-runtime), version 4.11")
sympy = sympy.strip()
matherror = MathErrorListener(sympy)
stream = antlr4.InputStream(sympy)
lex = LaTeXLexer(stream)
lex.removeErrorListeners()
lex.addErrorListener(matherror)
tokens = antlr4.CommonTokenStream(lex)
parser = LaTeXParser(tokens)
# remove default console error listener
parser.removeErrorListeners()
parser.addErrorListener(matherror)
relation = parser.math().relation()
if strict and (relation.start.start != 0 or relation.stop.stop != len(sympy) - 1):
raise LaTeXParsingError("Invalid LaTeX")
expr = convert_relation(relation)
return expr
def convert_relation(rel):
if rel.expr():
return convert_expr(rel.expr())
lh = convert_relation(rel.relation(0))
rh = convert_relation(rel.relation(1))
if rel.LT():
return sympy.StrictLessThan(lh, rh)
elif rel.LTE():
return sympy.LessThan(lh, rh)
elif rel.GT():
return sympy.StrictGreaterThan(lh, rh)
elif rel.GTE():
return sympy.GreaterThan(lh, rh)
elif rel.EQUAL():
return sympy.Eq(lh, rh)
elif rel.NEQ():
return sympy.Ne(lh, rh)
def convert_expr(expr):
return convert_add(expr.additive())
def convert_add(add):
if add.ADD():
lh = convert_add(add.additive(0))
rh = convert_add(add.additive(1))
return sympy.Add(lh, rh, evaluate=False)
elif add.SUB():
lh = convert_add(add.additive(0))
rh = convert_add(add.additive(1))
if hasattr(rh, "is_Atom") and rh.is_Atom:
return sympy.Add(lh, -1 * rh, evaluate=False)
return sympy.Add(lh, sympy.Mul(-1, rh, evaluate=False), evaluate=False)
else:
return convert_mp(add.mp())
def convert_mp(mp):
if hasattr(mp, 'mp'):
mp_left = mp.mp(0)
mp_right = mp.mp(1)
else:
mp_left = mp.mp_nofunc(0)
mp_right = mp.mp_nofunc(1)
if mp.MUL() or mp.CMD_TIMES() or mp.CMD_CDOT():
lh = convert_mp(mp_left)
rh = convert_mp(mp_right)
return sympy.Mul(lh, rh, evaluate=False)
elif mp.DIV() or mp.CMD_DIV() or mp.COLON():
lh = convert_mp(mp_left)
rh = convert_mp(mp_right)
return sympy.Mul(lh, sympy.Pow(rh, -1, evaluate=False), evaluate=False)
else:
if hasattr(mp, 'unary'):
return convert_unary(mp.unary())
else:
return convert_unary(mp.unary_nofunc())
def convert_unary(unary):
if hasattr(unary, 'unary'):
nested_unary = unary.unary()
else:
nested_unary = unary.unary_nofunc()
if hasattr(unary, 'postfix_nofunc'):
first = unary.postfix()
tail = unary.postfix_nofunc()
postfix = [first] + tail
else:
postfix = unary.postfix()
if unary.ADD():
return convert_unary(nested_unary)
elif unary.SUB():
numabs = convert_unary(nested_unary)
# Use Integer(-n) instead of Mul(-1, n)
return -numabs
elif postfix:
return convert_postfix_list(postfix)
def convert_postfix_list(arr, i=0):
if i >= len(arr):
raise LaTeXParsingError("Index out of bounds")
res = convert_postfix(arr[i])
if isinstance(res, sympy.Expr):
if i == len(arr) - 1:
return res # nothing to multiply by
else:
if i > 0:
left = convert_postfix(arr[i - 1])
right = convert_postfix(arr[i + 1])
if isinstance(left, sympy.Expr) and isinstance(
right, sympy.Expr):
left_syms = convert_postfix(arr[i - 1]).atoms(sympy.Symbol)
right_syms = convert_postfix(arr[i + 1]).atoms(
sympy.Symbol)
# if the left and right sides contain no variables and the
# symbol in between is 'x', treat as multiplication.
if not (left_syms or right_syms) and str(res) == 'x':
return convert_postfix_list(arr, i + 1)
# multiply by next
return sympy.Mul(
res, convert_postfix_list(arr, i + 1), evaluate=False)
else: # must be derivative
wrt = res[0]
if i == len(arr) - 1:
raise LaTeXParsingError("Expected expression for derivative")
else:
expr = convert_postfix_list(arr, i + 1)
return sympy.Derivative(expr, wrt)
def do_subs(expr, at):
if at.expr():
at_expr = convert_expr(at.expr())
syms = at_expr.atoms(sympy.Symbol)
if len(syms) == 0:
return expr
elif len(syms) > 0:
sym = next(iter(syms))
return expr.subs(sym, at_expr)
elif at.equality():
lh = convert_expr(at.equality().expr(0))
rh = convert_expr(at.equality().expr(1))
return expr.subs(lh, rh)
def convert_postfix(postfix):
if hasattr(postfix, 'exp'):
exp_nested = postfix.exp()
else:
exp_nested = postfix.exp_nofunc()
exp = convert_exp(exp_nested)
for op in postfix.postfix_op():
if op.BANG():
if isinstance(exp, list):
raise LaTeXParsingError("Cannot apply postfix to derivative")
exp = sympy.factorial(exp, evaluate=False)
elif op.eval_at():
ev = op.eval_at()
at_b = None
at_a = None
if ev.eval_at_sup():
at_b = do_subs(exp, ev.eval_at_sup())
if ev.eval_at_sub():
at_a = do_subs(exp, ev.eval_at_sub())
if at_b is not None and at_a is not None:
exp = sympy.Add(at_b, -1 * at_a, evaluate=False)
elif at_b is not None:
exp = at_b
elif at_a is not None:
exp = at_a
return exp
def convert_exp(exp):
if hasattr(exp, 'exp'):
exp_nested = exp.exp()
else:
exp_nested = exp.exp_nofunc()
if exp_nested:
base = convert_exp(exp_nested)
if isinstance(base, list):
raise LaTeXParsingError("Cannot raise derivative to power")
if exp.atom():
exponent = convert_atom(exp.atom())
elif exp.expr():
exponent = convert_expr(exp.expr())
return sympy.Pow(base, exponent, evaluate=False)
else:
if hasattr(exp, 'comp'):
return convert_comp(exp.comp())
else:
return convert_comp(exp.comp_nofunc())
def convert_comp(comp):
if comp.group():
return convert_expr(comp.group().expr())
elif comp.abs_group():
return sympy.Abs(convert_expr(comp.abs_group().expr()), evaluate=False)
elif comp.atom():
return convert_atom(comp.atom())
elif comp.floor():
return convert_floor(comp.floor())
elif comp.ceil():
return convert_ceil(comp.ceil())
elif comp.func():
return convert_func(comp.func())
def convert_atom(atom):
if atom.LETTER():
sname = atom.LETTER().getText()
if atom.subexpr():
if atom.subexpr().expr(): # subscript is expr
subscript = convert_expr(atom.subexpr().expr())
else: # subscript is atom
subscript = convert_atom(atom.subexpr().atom())
sname += '_{' + StrPrinter().doprint(subscript) + '}'
if atom.SINGLE_QUOTES():
sname += atom.SINGLE_QUOTES().getText() # put after subscript for easy identify
return sympy.Symbol(sname)
elif atom.SYMBOL():
s = atom.SYMBOL().getText()[1:]
if s == "infty":
return sympy.oo
else:
if atom.subexpr():
subscript = None
if atom.subexpr().expr(): # subscript is expr
subscript = convert_expr(atom.subexpr().expr())
else: # subscript is atom
subscript = convert_atom(atom.subexpr().atom())
subscriptName = StrPrinter().doprint(subscript)
s += '_{' + subscriptName + '}'
return sympy.Symbol(s)
elif atom.number():
s = atom.number().getText().replace(",", "")
return sympy.Number(s)
elif atom.DIFFERENTIAL():
var = get_differential_var(atom.DIFFERENTIAL())
return sympy.Symbol('d' + var.name)
elif atom.mathit():
text = rule2text(atom.mathit().mathit_text())
return sympy.Symbol(text)
elif atom.frac():
return convert_frac(atom.frac())
elif atom.binom():
return convert_binom(atom.binom())
elif atom.bra():
val = convert_expr(atom.bra().expr())
return Bra(val)
elif atom.ket():
val = convert_expr(atom.ket().expr())
return Ket(val)
def rule2text(ctx):
stream = ctx.start.getInputStream()
# starting index of starting token
startIdx = ctx.start.start
# stopping index of stopping token
stopIdx = ctx.stop.stop
return stream.getText(startIdx, stopIdx)
def convert_frac(frac):
diff_op = False
partial_op = False
if frac.lower and frac.upper:
lower_itv = frac.lower.getSourceInterval()
lower_itv_len = lower_itv[1] - lower_itv[0] + 1
if (frac.lower.start == frac.lower.stop
and frac.lower.start.type == LaTeXLexer.DIFFERENTIAL):
wrt = get_differential_var_str(frac.lower.start.text)
diff_op = True
elif (lower_itv_len == 2 and frac.lower.start.type == LaTeXLexer.SYMBOL
and frac.lower.start.text == '\\partial'
and (frac.lower.stop.type == LaTeXLexer.LETTER
or frac.lower.stop.type == LaTeXLexer.SYMBOL)):
partial_op = True
wrt = frac.lower.stop.text
if frac.lower.stop.type == LaTeXLexer.SYMBOL:
wrt = wrt[1:]
if diff_op or partial_op:
wrt = sympy.Symbol(wrt)
if (diff_op and frac.upper.start == frac.upper.stop
and frac.upper.start.type == LaTeXLexer.LETTER
and frac.upper.start.text == 'd'):
return [wrt]
elif (partial_op and frac.upper.start == frac.upper.stop
and frac.upper.start.type == LaTeXLexer.SYMBOL
and frac.upper.start.text == '\\partial'):
return [wrt]
upper_text = rule2text(frac.upper)
expr_top = None
if diff_op and upper_text.startswith('d'):
expr_top = parse_latex(upper_text[1:])
elif partial_op and frac.upper.start.text == '\\partial':
expr_top = parse_latex(upper_text[len('\\partial'):])
if expr_top:
return sympy.Derivative(expr_top, wrt)
if frac.upper:
expr_top = convert_expr(frac.upper)
else:
expr_top = sympy.Number(frac.upperd.text)
if frac.lower:
expr_bot = convert_expr(frac.lower)
else:
expr_bot = sympy.Number(frac.lowerd.text)
inverse_denom = sympy.Pow(expr_bot, -1, evaluate=False)
if expr_top == 1:
return inverse_denom
else:
return sympy.Mul(expr_top, inverse_denom, evaluate=False)
def convert_binom(binom):
expr_n = convert_expr(binom.n)
expr_k = convert_expr(binom.k)
return sympy.binomial(expr_n, expr_k, evaluate=False)
def convert_floor(floor):
val = convert_expr(floor.val)
return sympy.floor(val, evaluate=False)
def convert_ceil(ceil):
val = convert_expr(ceil.val)
return sympy.ceiling(val, evaluate=False)
def convert_func(func):
if func.func_normal():
if func.L_PAREN(): # function called with parenthesis
arg = convert_func_arg(func.func_arg())
else:
arg = convert_func_arg(func.func_arg_noparens())
name = func.func_normal().start.text[1:]
# change arc<trig> -> a<trig>
if name in [
"arcsin", "arccos", "arctan", "arccsc", "arcsec", "arccot"
]:
name = "a" + name[3:]
expr = getattr(sympy.functions, name)(arg, evaluate=False)
if name in ["arsinh", "arcosh", "artanh"]:
name = "a" + name[2:]
expr = getattr(sympy.functions, name)(arg, evaluate=False)
if name == "exp":
expr = sympy.exp(arg, evaluate=False)
if name in ("log", "lg", "ln"):
if func.subexpr():
if func.subexpr().expr():
base = convert_expr(func.subexpr().expr())
else:
base = convert_atom(func.subexpr().atom())
elif name == "lg": # ISO 80000-2:2019
base = 10
elif name in ("ln", "log"): # SymPy's latex printer prints ln as log by default
base = sympy.E
expr = sympy.log(arg, base, evaluate=False)
func_pow = None
should_pow = True
if func.supexpr():
if func.supexpr().expr():
func_pow = convert_expr(func.supexpr().expr())
else:
func_pow = convert_atom(func.supexpr().atom())
if name in [
"sin", "cos", "tan", "csc", "sec", "cot", "sinh", "cosh",
"tanh"
]:
if func_pow == -1:
name = "a" + name
should_pow = False
expr = getattr(sympy.functions, name)(arg, evaluate=False)
if func_pow and should_pow:
expr = sympy.Pow(expr, func_pow, evaluate=False)
return expr
elif func.LETTER() or func.SYMBOL():
if func.LETTER():
fname = func.LETTER().getText()
elif func.SYMBOL():
fname = func.SYMBOL().getText()[1:]
fname = str(fname) # can't be unicode
if func.subexpr():
if func.subexpr().expr(): # subscript is expr
subscript = convert_expr(func.subexpr().expr())
else: # subscript is atom
subscript = convert_atom(func.subexpr().atom())
subscriptName = StrPrinter().doprint(subscript)
fname += '_{' + subscriptName + '}'
if func.SINGLE_QUOTES():
fname += func.SINGLE_QUOTES().getText()
input_args = func.args()
output_args = []
while input_args.args(): # handle multiple arguments to function
output_args.append(convert_expr(input_args.expr()))
input_args = input_args.args()
output_args.append(convert_expr(input_args.expr()))
return sympy.Function(fname)(*output_args)
elif func.FUNC_INT():
return handle_integral(func)
elif func.FUNC_SQRT():
expr = convert_expr(func.base)
if func.root:
r = convert_expr(func.root)
return sympy.root(expr, r, evaluate=False)
else:
return sympy.sqrt(expr, evaluate=False)
elif func.FUNC_OVERLINE():
expr = convert_expr(func.base)
return sympy.conjugate(expr, evaluate=False)
elif func.FUNC_SUM():
return handle_sum_or_prod(func, "summation")
elif func.FUNC_PROD():
return handle_sum_or_prod(func, "product")
elif func.FUNC_LIM():
return handle_limit(func)
def convert_func_arg(arg):
if hasattr(arg, 'expr'):
return convert_expr(arg.expr())
else:
return convert_mp(arg.mp_nofunc())
def handle_integral(func):
if func.additive():
integrand = convert_add(func.additive())
elif func.frac():
integrand = convert_frac(func.frac())
else:
integrand = 1
int_var = None
if func.DIFFERENTIAL():
int_var = get_differential_var(func.DIFFERENTIAL())
else:
for sym in integrand.atoms(sympy.Symbol):
s = str(sym)
if len(s) > 1 and s[0] == 'd':
if s[1] == '\\':
int_var = sympy.Symbol(s[2:])
else:
int_var = sympy.Symbol(s[1:])
int_sym = sym
if int_var:
integrand = integrand.subs(int_sym, 1)
else:
# Assume dx by default
int_var = sympy.Symbol('x')
if func.subexpr():
if func.subexpr().atom():
lower = convert_atom(func.subexpr().atom())
else:
lower = convert_expr(func.subexpr().expr())
if func.supexpr().atom():
upper = convert_atom(func.supexpr().atom())
else:
upper = convert_expr(func.supexpr().expr())
return sympy.Integral(integrand, (int_var, lower, upper))
else:
return sympy.Integral(integrand, int_var)
def handle_sum_or_prod(func, name):
val = convert_mp(func.mp())
iter_var = convert_expr(func.subeq().equality().expr(0))
start = convert_expr(func.subeq().equality().expr(1))
if func.supexpr().expr(): # ^{expr}
end = convert_expr(func.supexpr().expr())
else: # ^atom
end = convert_atom(func.supexpr().atom())
if name == "summation":
return sympy.Sum(val, (iter_var, start, end))
elif name == "product":
return sympy.Product(val, (iter_var, start, end))
def handle_limit(func):
sub = func.limit_sub()
if sub.LETTER():
var = sympy.Symbol(sub.LETTER().getText())
elif sub.SYMBOL():
var = sympy.Symbol(sub.SYMBOL().getText()[1:])
else:
var = sympy.Symbol('x')
if sub.SUB():
direction = "-"
elif sub.ADD():
direction = "+"
else:
direction = "+-"
approaching = convert_expr(sub.expr())
content = convert_mp(func.mp())
return sympy.Limit(content, var, approaching, direction)
def get_differential_var(d):
text = get_differential_var_str(d.getText())
return sympy.Symbol(text)
def get_differential_var_str(text):
for i in range(1, len(text)):
c = text[i]
if not (c == " " or c == "\r" or c == "\n" or c == "\t"):
idx = i
break
text = text[idx:]
if text[0] == "\\":
text = text[1:]
return text

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rl/Lib/site-packages/sympy/parsing/latex/errors.py Normal file
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class LaTeXParsingError(Exception):
pass

2
rl/Lib/site-packages/sympy/parsing/latex/lark/__init__.py Normal file
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from .latex_parser import parse_latex_lark, LarkLaTeXParser # noqa
from .transformer import TransformToSymPyExpr # noqa

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rl/Lib/site-packages/sympy/parsing/latex/lark/__pycache__/__init__.cpython-312.pyc Normal file
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