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83 lines
3.2 KiB
Python
83 lines
3.2 KiB
Python
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# https://www.chilimath.com/lessons/advanced-algebra/cramers-rule-with-two-variables
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# https://en.wikipedia.org/wiki/Cramer%27s_rule
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def cramers_rule_2x2(equation1: list[int], equation2: list[int]) -> str:
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"""
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Solves the system of linear equation in 2 variables.
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:param: equation1: list of 3 numbers
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:param: equation2: list of 3 numbers
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:return: String of result
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input format : [a1, b1, d1], [a2, b2, d2]
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determinant = [[a1, b1], [a2, b2]]
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determinant_x = [[d1, b1], [d2, b2]]
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determinant_y = [[a1, d1], [a2, d2]]
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>>> cramers_rule_2x2([2, 3, 0], [5, 1, 0])
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'Trivial solution. (Consistent system) x = 0 and y = 0'
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>>> cramers_rule_2x2([0, 4, 50], [2, 0, 26])
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'Non-Trivial Solution (Consistent system) x = 13.0, y = 12.5'
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>>> cramers_rule_2x2([11, 2, 30], [1, 0, 4])
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'Non-Trivial Solution (Consistent system) x = 4.0, y = -7.0'
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>>> cramers_rule_2x2([4, 7, 1], [1, 2, 0])
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'Non-Trivial Solution (Consistent system) x = 2.0, y = -1.0'
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>>> cramers_rule_2x2([1, 2, 3], [2, 4, 6])
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Traceback (most recent call last):
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...
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ValueError: Infinite solutions. (Consistent system)
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>>> cramers_rule_2x2([1, 2, 3], [2, 4, 7])
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Traceback (most recent call last):
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...
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ValueError: No solution. (Inconsistent system)
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>>> cramers_rule_2x2([1, 2, 3], [11, 22])
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Traceback (most recent call last):
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...
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ValueError: Please enter a valid equation.
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>>> cramers_rule_2x2([0, 1, 6], [0, 0, 3])
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Traceback (most recent call last):
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...
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ValueError: No solution. (Inconsistent system)
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>>> cramers_rule_2x2([0, 0, 6], [0, 0, 3])
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Traceback (most recent call last):
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...
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ValueError: Both a & b of two equations can't be zero.
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>>> cramers_rule_2x2([1, 2, 3], [1, 2, 3])
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Traceback (most recent call last):
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...
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ValueError: Infinite solutions. (Consistent system)
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>>> cramers_rule_2x2([0, 4, 50], [0, 3, 99])
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Traceback (most recent call last):
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...
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ValueError: No solution. (Inconsistent system)
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"""
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# Check if the input is valid
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if not len(equation1) == len(equation2) == 3:
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raise ValueError("Please enter a valid equation.")
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if equation1[0] == equation1[1] == equation2[0] == equation2[1] == 0:
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raise ValueError("Both a & b of two equations can't be zero.")
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# Extract the coefficients
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a1, b1, c1 = equation1
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a2, b2, c2 = equation2
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# Calculate the determinants of the matrices
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determinant = a1 * b2 - a2 * b1
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determinant_x = c1 * b2 - c2 * b1
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determinant_y = a1 * c2 - a2 * c1
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# Check if the system of linear equations has a solution (using Cramer's rule)
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if determinant == 0:
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if determinant_x == determinant_y == 0:
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raise ValueError("Infinite solutions. (Consistent system)")
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else:
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raise ValueError("No solution. (Inconsistent system)")
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else:
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if determinant_x == determinant_y == 0:
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return "Trivial solution. (Consistent system) x = 0 and y = 0"
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else:
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x = determinant_x / determinant
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y = determinant_y / determinant
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return f"Non-Trivial Solution (Consistent system) x = {x}, y = {y}"
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