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Trac #21992.11: Explain p^s-minimal polynomial
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cheuberg committed Jan 2, 2017
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5 changes: 5 additions & 0 deletions src/sage/matrix/matrix_integer_dense.pyx
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Expand Up @@ -5597,6 +5597,11 @@ cdef class Matrix_integer_dense(Matrix_dense): # dense or sparse
integers, the values are the associated `(p^s)`-minimal polynomials
`\nu_s`, `s\in\mathcal{S}`.
For `s\ge 0`, a `(p^s)`-minimal polynomial of
a matrix `B` is a monic polynomial `f\in \mathbb{Z}[X]` of
minimal degree such that all entries of `f(B)` are divisible
by `p^s`.
For `0<t\le \max\mathcal{S}`, a `(p^t)`-minimal polynomial is given by
`\nu_s` where `s=\min\{ r\in\mathcal{S}\mid r\ge t\}`. For
`t>\max\mathcal{S}`, the minimal polynomial of this matrix is also a
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