初始化项目，由ModelHub XC社区提供模型

Model: nv-community/Nemotron-Cascade-8B
Source: Original Platform

evaluation/eval/tools/latex2sympy/sandbox/vector.py

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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))