Gapplet
Given polynomials f and d in Q[X], we determine the matrix of multiplication by f in Q[X]/(d) with respect to the basis 1, X, ..., Xn-1, where n = deg(d).
Input d, e.g., X^5-3*X-1 |
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Input f, e.g., X-2 |
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Compute the matrix of the linear transformation g -> fg on Q[X]/dQ[X] as well as its determinant |
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The determinant is nonzero if and only if f is invertible mod d. The polynomial f, occurs in vector form as the first column vector of the matrix. |
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