LinearAlgebra[Modular][IntegerCharacteristicPolynomial] - computation of the characteristic polynomial of an integer matrix using modular methods
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Calling Sequence
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IntegerCharacteristicPolynomial(A, lambda)
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Parameters
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A
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square matrix with integer entries
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lambda
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-
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variable to use for output characteristic polynomial
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Description
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The IntegerCharacteristicPolynomial function computes the characteristic polynomial for a square Matrix with integer entries. This is a programmer level function, and it does not perform argument checking. Thus, argument checking must be handled external to this function.
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Note: The IntegerCharacteristicPolynomial routine uses a probabilistic approach that achieves great gains for structured systems. Information on controlling the probabilistic behavior can be found in EnvProbabilistic.
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This command is part of the LinearAlgebra[Modular] package, so it can be used in the form IntegerCharacteristicPolynomial(..) only after executing the command with(LinearAlgebra[Modular]). However, it can always be used in the form LinearAlgebra[Modular][IntegerCharacteristicPolynomial](..).
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Examples
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This function is provided as a high-efficiency function for computation of characteristic polynomials for larger matrices. For example:
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Speed-up factor:
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