Determinant and permanent: Difference between revisions
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More efficient algorithms for the determinant are known: [[LU decomposition]], see for example [[wp:LU decomposition#Computing the determinant]]. Efficient methods for calculating the permanent are not known. |
More efficient algorithms for the determinant are known: [[LU decomposition]], see for example [[wp:LU decomposition#Computing the determinant]]. Efficient methods for calculating the permanent are not known. |
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=={{header|J}}== |
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Given the example matrix: |
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<lang J> i. 5 5 |
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0 1 2 3 4 |
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5 6 7 8 9 |
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10 11 12 13 14 |
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15 16 17 18 19 |
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20 21 22 23 24</lang> |
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It's determinant is 0. When we use IEEE floating point, we only get an approximation of this result: |
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<lang J> -/ .* i. 5 5 |
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_1.30277e_44</lang> |
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If we use exact (rational) arithmetic, we get a precise result: |
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<lang J> -/ .* i. 5 5x |
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0</lang> |
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The permanent does not have this problem in this example (the matrix contains no negative values and permanent does not use subtraction): |
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<lang J> +/ .* i. 5 5x |
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6778800</lang> |
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=={{header|PARI/GP}}== |
=={{header|PARI/GP}}== |
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