LinearAlgebra[Generic][BerkowitzAlgorithm] - apply the Berkowitz algorithm to a square Matrix
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Calling Sequence
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BerkowitzAlgorithm[R](A)
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Parameters
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R
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a table or module, the domain of computation
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A
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square Matrix of values in R
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Description
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Given an n x n Matrix A of values from a commutative ring R, BerkowitzAlgorithm[R](A) returns a Vector V of dimension n+1 of values in R with the coefficients of the characteristic polynomial of A.
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The characteristic polynomial is the polynomial V[1]*x^n + V[2]*x^(n-1) + ... + V[n]*x + V[n+1].
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The Berkowitz algorithm does O(n^4) multiplications and additions in R.
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The (indexed) parameter R, which specifies the domain of computation, a commutative ring, must be a Maple table/module which has the following values/exports:
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R[`0`] : a constant for the zero of the ring R
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R[`1`] : a constant for the (multiplicative) identity of R
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R[`+`] : a procedure for adding elements of R (nary)
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R[`-`] : a procedure for negating and subtracting elements of R (unary and binary)
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R[`*`] : a procedure for multiplying elements of R (binary and commutative)
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R[`=`] : a boolean procedure for testing if two elements of R are equal
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Examples
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Download Help Document
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