Determines whether a substitution is even or odd. (7 characters)
Author: shiroeExecutions: 20
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Outputs the result of the even/odd check.
Enter one of the digits 1, 2, 3, 4, 5, 6, or 7 into inputs 1, 2, 3, 4, 5, 6, and 7.
Enter distinct digits (no duplicates) into inputs 1, 2, 3, 4, 5, 6, and 7.
Enter one of the digits 1, 2, 3, 4, 5, 6, or 7 into inputs 1, 2, 3, 4, 5, 6, and 7.
Enter distinct digits (no duplicates) into inputs 1, 2, 3, 4, 5, 6, and 7.
| Sign sgn | A string consisting of numbers |
R6 (2024). July 21 (Sun)_Ver. 001
Fixed to 6 digits. Fixed number of digits. Real number calculation mode.
Routine calculation: rumia00.
B>c_near:k
Fixed to 6 digits. Fixed number of digits. Real number calculation mode.
Routine calculation: rumia00.
B>c_near:k
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Here, we consider the permutation of the sequence 1234567.
This determines whether the 7-character permutation σ is even or odd.
If even, sgn(σ) = 1 (one)
If odd, sgn(σ) = -1 (minus one)
Accordingly,
the program outputs 1 or -1 as the result.
A permutation that can be expressed as the product of an even number of transpositions is an even permutation,
while a permutation that can be expressed as the product of an odd number of transpositions is an odd permutation.
If the permutation is even, the parity is determined to be even, and 1 is output.
If the permutation is odd, the parity is determined to be odd, and -1 is output.
Determining whether a permutation is even or odd is sometimes used in the definition of determinants.
In the input field, enter the sequence of numbers (the string of numbers resulting from permuting 1234567) for which you want to check the parity.
In permutation notation, this is often written in the bottom row.
For example, if you want to check the parity of 7651234—which is the result of permuting the numbers 1234567—
enter the following values from top to bottom: Input 1 = 7, Input 2 = 6, Input 3 = 5, Input 4 = 1, Input 5 = 2, Input 6 = 3, and Input 7 = 4.