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Diffstat (limited to 'Qwen2.5-Eval/evaluation/latex2sympy/sandbox')
8 files changed, 364 insertions, 0 deletions
diff --git a/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/linalg_equations.py b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/linalg_equations.py new file mode 100755 index 0000000..fa65ba7 --- /dev/null +++ b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/linalg_equations.py @@ -0,0 +1,10 @@ +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)) diff --git a/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/linalg_span.py b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/linalg_span.py new file mode 100755 index 0000000..2839139 --- /dev/null +++ b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/linalg_span.py @@ -0,0 +1,19 @@ +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)) diff --git a/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/matrix.py b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/matrix.py new file mode 100755 index 0000000..9aed3c2 --- /dev/null +++ b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/matrix.py @@ -0,0 +1,46 @@ +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)) diff --git a/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/matrix_placeholders.py b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/matrix_placeholders.py new file mode 100755 index 0000000..79cb672 --- /dev/null +++ b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/matrix_placeholders.py @@ -0,0 +1,65 @@ +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 =============') diff --git a/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/sandbox.py b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/sandbox.py new file mode 100755 index 0000000..2c41100 --- /dev/null +++ b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/sandbox.py @@ -0,0 +1,23 @@ +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('-----------------------------------------------------') diff --git a/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/sandbox_equality.py b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/sandbox_equality.py new file mode 100755 index 0000000..5e3f444 --- /dev/null +++ b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/sandbox_equality.py @@ -0,0 +1,75 @@ +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('-----------------------------------------------------') diff --git a/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/sectan.py b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/sectan.py new file mode 100755 index 0000000..0e0c7aa --- /dev/null +++ b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/sectan.py @@ -0,0 +1,51 @@ +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)) diff --git a/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/vector.py b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/vector.py new file mode 100755 index 0000000..5b48aee --- /dev/null +++ b/Qwen2.5-Eval/evaluation/latex2sympy/sandbox/vector.py @@ -0,0 +1,75 @@ +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)) |