Definition in file bound.h.
Go to the source code of this file.
Classes | |
| struct | NISP |
| Negative Inverse Sum bound for positive roots. More... | |
| struct | NISN |
| Negative Inverse Sum bound for negative roots. More... | |
| struct | Cauchy |
| Cauchy bound. More... | |
| struct | abs_max< T > |
Functions | |
| template<typename POLY, typename M, typename T> | |
| T | bound (const POLY &p, const M &mth, type::As< T >) |
| Prototype function, Computes an upper bound for the real roots. | |
| template<typename FT, typename POLY> | |
| FT | bound (const POLY &p, Cauchy) |
| Computes the Cauchy root bound. | |
| template<typename FT, typename POLY> | |
| FT | max_bound (const POLY &p, Cauchy) |
| template<typename FT, typename POLY> | |
| FT | min_bound (const POLY &p, Cauchy) |
| template<typename FT, typename POLY> | |
| FT | bound (const POLY &p, NISP) |
| Computes the "Negative Inverse Sum" bound for the positive roots. | |
| template<typename FT, typename POLY> | |
| FT | bound (const POLY &p, NISN) |
| Computes the "Negative Inverse Sum" bound for the negative roots. | |
| FT bound | ( | const POLY & | p, | |
| NISN | ||||
| ) |
| FT bound | ( | const POLY & | p, | |
| NISP | ||||
| ) |
| FT bound | ( | const POLY & | p, | |
| Cauchy | ||||
| ) |
Computes the Cauchy root bound.
| p | Univariate polynomials | |
| Cauchy | The method that we use | |
| FT | type of the result. |
p is in the monomial basis is of the form
![\[ p(x) = a_{0} + a_{1} x+ \cdots + a_{d}\, x^d, \]](form_504.png)
the Cauchy bound on the modul of the roots of 
is
![\[ 1 + max{|a_{0}|,...,|a_{d-1}|}/|a_{d}| \]](form_505.png)
Definition at line 85 of file bound.h.
References let::convert(), UPOLDAR::lcoeff(), abs_max< T >::max, and DEBUG::print().
| T bound | ( | const POLY & | p, | |
| const M & | mth, | |||
| type::As< T > | ||||
| ) |
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