如何将整数数组及三维整数数组转换为SymPy有理矩阵？

I'll walk you through exactly how to turn your 3D integer array into a SymPy matrix of rational numbers using the Rational and Matrix classes you mentioned. Let's break this down with your example input.

Step 1: Understand the Input Structure #

Your input array [[[2, 1], [1, 3], [3, 2]], [[4, 3], [5, 2], [0, 1]]] is structured as:

• 2 outer sublists (each will become a row in the final matrix)
• Each outer sublist contains 3 integer pairs, where each pair [a, b] translates to the rational number a/b

Step 2: Import Required SymPy Tools #

First, make sure SymPy is installed, then import the classes we need:

from sympy import Rational, Matrix

Step 3: Convert Pairs to Rational Numbers #

We'll iterate through the 3D array, convert each integer pair to a Rational object, and collect them into a flat list. A list comprehension makes this concise:

# Your input 3D array
input_array = [[[2, 1], [1, 3], [3, 2]], [[4, 3], [5, 2], [0, 1]]]

# Convert each [numerator, denominator] pair to a SymPy Rational
rational_elements = [Rational(num, den) for row in input_array for num, den in row]

Step 4: Build the SymPy Matrix #

Pass the flat list of Rational elements to Matrix, specifying the shape (2 rows, 3 columns) to match your input's structure:

# Create a 2x3 matrix from the rational values
rational_matrix = Matrix(2, 3, rational_elements)

# Print the result
print(rational_matrix)

Step 5: Check the Output #

When you run this code, you'll get exactly the matrix you're expecting:

Matrix([
[2, 1/3, 3/2],
[4/3, 5/2, 0]])

Key Notes #

• Using Rational guarantees exact fractional representation (no floating-point inaccuracies), which is critical for SymPy's symbolic math capabilities.
• If your input size varies, you can calculate the matrix shape dynamically instead of hardcoding it (e.g., num_rows = len(input_array), num_cols = len(input_array[0])).
• Double-check that all denominators are non-zero—SymPy will throw an error if you try to create a Rational with a denominator of 0.

内容的提问来源于stack exchange，提问作者LOL