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Model: nv-community/Nemotron-Cascade-8B
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2026-04-24 22:32:56 +08:00
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10
evaluation/eval/tools/latex2sympy/sandbox/linalg_equations.py Normal file
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from latex2sympy import process_sympy
import sys
sys.path.append("..")
# latex = "2\\begin{pmatrix}1&1&1\\\\0&1&1\\\\0&0&1\\end{pmatrix}\\begin{pmatrix}1&1&1\\\\0&1&1\\\\0&0&1\\end{pmatrix}"
latex = "\\frac{a^{2} \\left(3 \\pi - 4 \\sin{\\left(\\pi \\right)} + \\frac{\\sin{\\left(2 \\pi \\right)}}{2}\\right)}{2}"
math = process_sympy(latex)
print(type(math))
print("latex: %s to math: %s" % (latex, math))

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evaluation/eval/tools/latex2sympy/sandbox/linalg_span.py Normal file
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from latex2sympy import process_sympy
import sys
sys.path.append("..")
latex = "\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix}"
math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, math))
latex = "\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix},\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix}"
math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, math))
latex = "[\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix},\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix}]"
math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, math))
latex = "\\left\\{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix},\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix}\\right\\}"
math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, math))

46
evaluation/eval/tools/latex2sympy/sandbox/matrix.py Normal file
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from latex2sympy import process_sympy
from sympy import *
import sys
sys.path.append("..")
theta = Symbol('theta', real=True)
latex = "\\begin{matrix}1&2\\\\3&4\\end{matrix}"
math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, math))
latex = "\\begin{matrix}1&2\\\\3&4\\\\5&6\\end{matrix}"
math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, math))
latex = "\\begin{matrix}1&2&3\\\\4&5&6\\\\7&8&9\\end{matrix}"
math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, math))
latex = "\\begin{matrix}x^1&x^2&x^3\\\\y^1&y^2&y^3\\\\z^1&z^2&z^3\\end{matrix}"
math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, math))
latex = "\\begin{matrix}x\\\\y\\end{matrix}"
math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, math))
latex = "2\\cdot\\begin{matrix}x\\\\y\\end{matrix}"
math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, math))
latex = "2\\cdot\\begin{matrix}x\\\\y\\end{matrix} + \\begin{matrix}2\\\\3\\end{matrix}"
math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, math))
latex = "-2\\begin{matrix}1&2\\\\3&4\\end{matrix}"
math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, math))
latex = "2\\cdot\\theta\\begin{matrix}x\\\\y\\end{matrix} + \\begin{matrix}2\\\\3\\end{matrix}"
math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, math))
latex = "\\theta\\begin{matrix}1\\\\3\\end{matrix} - \\begin{matrix}-1\\\\2\\end{matrix}"
math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, math))

65
evaluation/eval/tools/latex2sympy/sandbox/matrix_placeholders.py Normal file
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from latex2sympy import process_sympy
from sympy import *
import sys
import hashlib
import time
sys.path.append("..")
M = Matrix([[1, 2], [3, 4]])
v = Matrix([1, 2])
# sub settings
sub_settings_symbols = {}
sub_settings_symbols[Symbol('M' + hashlib.md5('M'.encode()).hexdigest(), real=True)] = M
sub_settings_symbols[Symbol('v' + hashlib.md5('v'.encode()).hexdigest(), real=True)] = v
# one parameters
latex = "\\begin{matrix}1&2\\\\3&4\\end{matrix}\\cdot[!v!]"
equation_sympy_check = MatMul(M, Symbol('v' + hashlib.md5('v'.encode()).hexdigest(), real=True))
equation_sympy_subs_check = MatMul(M, v)
# placeholders
equation_sympy = process_sympy(latex)
print('latex = %s' % latex)
print('equation_sympy = %s' % equation_sympy)
print('equation_sympy_check = %s' % equation_sympy_check)
print('equation_sympy = %s' % (srepr(equation_sympy)))
equation_sympy_subs = equation_sympy.subs(sub_settings_symbols, evaluate=False)
print('equation_sympy_subs = %s' % equation_sympy_subs)
print('equation_sympy_subs_check = %s' % equation_sympy_subs_check)
# two parameters
# sub settings
print('')
print('============== Two Parameters -> M*v = Matrix*Vector =============')
sub_settings_symbols = {}
sub_settings_symbols[Symbol('M' + hashlib.md5('M'.encode()).hexdigest(), commutative=False)] = M
sub_settings_symbols[Symbol('v' + hashlib.md5('v'.encode()).hexdigest(), commutative=False)] = v
latex = "[!M!]\\cdot[!v!]"
math_check = Mul(Symbol('M' + hashlib.md5('M'.encode()).hexdigest(), commutative=False), Symbol('v' + hashlib.md5('v'.encode()).hexdigest(), commutative=False))
# placeholders
equation_sympy = process_sympy(latex)
print(latex)
print(math_check)
print(equation_sympy)
print(srepr(equation_sympy))
# performance
t0 = time.time()
# process_sympy and substitute at the same time
# Only needed for linalg input
placeholder_values = {'M': M, 'v': v}
equation_sympy_subs = process_sympy(latex, variable_values=placeholder_values)
t1 = time.time()
print('equation with substituted placeholders = %s' % (str(equation_sympy_subs)))
print('time to process to sympy with placeholders = %s s' % (t1 - t0))
print('')
print('============== Two Parameters -> M*v = Matrix*Vector =============')

23
evaluation/eval/tools/latex2sympy/sandbox/sandbox.py Normal file
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from sympy import *
from latex2sympy import process_sympy
# latex = '\\variable{a}^{\\variable{b}}'
# variables = {'a': process_sympy('658.95998'), 'b': process_sympy('185083.8060')}
# c_ans_expr = process_sympy(latex, variables)
# print(c_ans_expr)
# print(srepr(c_ans_expr))
# c_ans = c_ans_expr.doit(deep=False).evalf(chop=True)
# print(c_ans)
# print(srepr(c_ans))
# numeric_responses = ['1', '1.0', '-1', '-1.0', '.5', '-.5', '3x10^3', '3E3', '3,000x10^{-3}', '0.5E-1', '\\frac{1}{3}', '(5\\times 3)^3', '\\sin(1)']
# for latex in numeric_responses:
# parsed = process_sympy(latex)
# print('latex: ', latex)
# print('sympy: ', parsed)
# print('is_number: ', parsed.is_number)
# print('is_Number: ', parsed.is_Number)
# print('srepr: ', srepr(parsed))
# print('-----------------------------------------------------')

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evaluation/eval/tools/latex2sympy/sandbox/sandbox_equality.py Normal file
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from sympy import *
from latex2sympy import process_sympy
#
# Equality Testing
#
answer_sets = [
{
'correct_answer': '(x-y)(x+2y)',
'student_answers': [
'x^2+xy-2y^2',
'(x-y)(x+2y)',
'(x+2y)(x-y)',
'(2\\times y+x)(-y+x)',
'(y\\cdot 2+x)(-y+x)'
]
},
{
'correct_answer': '2\\pi \\variable{r}^2',
'student_answers': [
'2\\pi \\variable{r}^2',
'\\pi 2\\variable{r}^2',
'2\\times \\pi \\times \\variable{r}^2',
'2\\pi \\variable{r} \\times \\variable{r}'
]
},
{
'correct_answer': '2x - 3y',
'student_answers': [
'-3y + 2x'
]
},
{
'correct_answer': 'x\\times x',
'student_answers': [
'x\\times x',
'x\\cdot x',
'x^2',
'(\\sqrt{x})^{4}'
]
},
{
'correct_answer': '23e^{-1\\times \\sqrt{t^2}}',
'student_answers': [
'23e^{-t}'
]
},
{
'correct_answer': 'a=x^2+1',
'student_answers': [
'x^2+1=a'
]
}
]
for answer_set in answer_sets:
correct_answer = answer_set['correct_answer']
correct_answer_parsed = process_sympy(answer_set['correct_answer'])
for student_answer in answer_set['student_answers']:
student_answer_parsed = process_sympy(student_answer)
print('correct_answer (c): ', correct_answer, correct_answer_parsed)
print('student_answer (a): ', student_answer, student_answer_parsed)
print('')
print('Expression Tree (srepr(c) == srepr(a)) =>', srepr(correct_answer_parsed) == srepr(student_answer_parsed))
print('srepr(c) =>', srepr(correct_answer_parsed))
print('srepr(a) =>', srepr(student_answer_parsed))
print('')
# print('Structural (c == a) =>', correct_answer_parsed == student_answer_parsed)
print('Symbolic (simplify(c - s) == 0) =>', simplify(correct_answer_parsed - student_answer_parsed) == 0)
print('simplified =>', simplify(correct_answer_parsed - student_answer_parsed))
print('')
print('Numeric Substitution (c.equals(s)) =>', correct_answer_parsed.equals(student_answer_parsed))
print('-----------------------------------------------------')

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evaluation/eval/tools/latex2sympy/sandbox/sectan.py Normal file
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from sympy import *
import sys
sys.path.append("..")
# # x^2\cdot \left(3\cdot \tan \left([!a!]\cdot x+[!c!]\right)+[!a!]\cdot x\left(\sec \left([!a!]\cdot x+[!c!]\right)\right)^2\right)
# latex1 = "x^2\\cdot \\left(3\\cdot \\tan \\left(2\\cdot x+5\\right)+2\\cdot x\\left(\\sec \\left(2\\cdot x+5\\right)\\right)^2\\right)"
# math1 = process_sympy(latex1)
# print("latex: %s to math: %s" %(latex1,math1))
#
# latex2 = "x^2\\cdot \\left(3\\cdot \\tan \\left(2\\cdot x+5\\right)+2\\cdot x\\left(\\sec \\left(2\\cdot x+5\\right)^2\\right)\\right)"
# math2 = process_sympy(latex2)
# print("latex: %s to math: %s" %(latex2,math2))
#
# latex3 = "x^2\\cdot \\left(3\\cdot \\tan \\left(2\\cdot x+5\\right)+2\\cdot x\\left(1+\\tan \\left(2\\cdot x+5\\right)^2\\right)\\right)"
# math3 = process_sympy(latex3)
# print("latex: %s to math: %s" %(latex3,math3))
#
# print(simplify(math1 - math2))
# print(simplify(math1 - math3))
#
# latex1 = "\\sec^2(2\\cdot x+5)"
# math1 = process_sympy(latex1)
# print("latex: %s to math: %s" %(latex1,math1))
#
# latex2 = "1+\\tan^2(2\\cdot x+5)"
# math2 = process_sympy(latex2)
# print("latex: %s to math: %s" %(latex2,math2))
# print(simplify(math1 - math2))
x = Symbol('x', real=True)
y = Symbol('y', real=True)
# BUG: 1 + tan^2(x+1) should be == sec^2(x+1) but isnt
lhs = (1 + (tan(x + 1))**2)
rhs = (sec(x + 1))**2
eq = lhs - rhs
print(simplify(lhs))
print(simplify(rhs))
print(simplify(eq))
print(simplify(lhs) == simplify(rhs))
# 1 + tan^2(x) == sec^2(x) but isnt
lhs = (1 + (tan(x))**2)
rhs = (sec(x))**2
eq = lhs - rhs
print(simplify(lhs))
print(simplify(rhs))
print(simplify(eq))
print(simplify(lhs) == simplify(rhs))

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evaluation/eval/tools/latex2sympy/sandbox/vector.py Normal file
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import numpy as np
from sympy import *
import sys
sys.path.append("..")
# row column matrix = vector
v = [1, 2, 3]
# single column matrix = vector
m = Matrix([1, 2, 3])
print(m[:, 0])
# a three row and 2 column matrix
m = Matrix([[1, 2], [3, 4], [5, 6]])
print(m[:, 0])
# determinant of lin indp system != 0
m = Matrix([[1, 1], [1, 2]])
print(m.det())
# determinant of lin dep system = 0
m = Matrix([[1, 1], [2, 2]])
print(m.det())
# determinant of lin dep system = 0
x = Symbol('x')
y = Symbol('y')
m = Matrix([[x, y], [x, y]])
print(m.det())
# Reduced Row-Echelon Form
_, ind = m.rref()
print(len(ind))
# determinant of lin dep system != 0
m = Matrix([[x, y], [y, x]])
print(m.det())
# Reduced Row-Echelon Form
_, ind = m.rref()
print(len(ind))
# determinant of lin dep system != 0
# Reduced Row-Echelon Form
m = Matrix([[x, x, y], [y, y, y]])
_, ind = m.rref()
# Reduced Row-Echelon Form
print(len(ind))
#==================#
#===== Numpy ======#
#==================#
# http://kitchingroup.cheme.cmu.edu/blog/2013/03/01/Determining-linear-independence-of-a-set-of-vectors/
# Lin Indp of set of numerical vectors
TOLERANCE = 1e-14
v1 = [6, 0, 3, 1, 4, 2]
v2 = [0, -1, 2, 7, 0, 5]
v3 = [12, 3, 0, -19, 8, -11]
A = np.row_stack([v1, v2, v3])
U, s, V = np.linalg.svd(A)
print(s)
print(np.sum(s > TOLERANCE))
v1 = [1, 1]
v2 = [4, 4]
A = np.row_stack([v1, v2])
U, s, V = np.linalg.svd(A)
print(s)
print(np.sum(s > TOLERANCE))
latex = "\\begin{matrix}1&2\\\\3&4\\end{matrix}"
# math = process_sympy(latex)
print("latex: %s to math: %s" % (latex, 1))