InnerNumericEigenPackage(K, F, Par)

numeigen.spad line 1 [edit on github]

• K: Field

• F: Field

• Par: Join(Field, OrderedRing)

This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.

charpol: Matrix K -> SparseUnivariatePolynomial K

charpol(m) computes the characteristic polynomial of a matrix m with entries in K.

innerEigenvectors: (Matrix K, Par, SparseUnivariatePolynomial K -> Factored SparseUnivariatePolynomial K) -> List Record(outval: F, outmult: Integer, outvect: List Matrix F)

innerEigenvectors(m, eps, factor) computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix m. The parameter eps determines the type of the output, factor is the univariate factorizer used to reduce the characteristic polynomial into irreducible factors.

solve1: (SparseUnivariatePolynomial K, Par) -> List F

solve1(pol, eps) finds the roots of the univariate polynomial polynomial pol to precision eps. If K is Fraction Integer then only the real roots are returned, if K is Complex Fraction Integer then all roots are found.