a dense univariate polynomial, templated according to the coefficient’s type More...
#include <polynomial.hpp>
Inheritance diagram for Rings::Polynomial< R >:
Public Member Functions | |
| Polynomial () | |
| generates a zero polynomial | |
| Polynomial (const Polynomial< R > &) | |
| copies the coefficients of the given polynomial to this one | |
| Polynomial (const initializer_list< R > &) | |
| initializes coefficients to the ones listed, constant term first | |
| Polynomial (const vector< R > &) | |
| initializes coefficients to the ones listed, constant term first | |
| DEGREE_TYPE | degree () const |
| indicates the polynomial's degree | |
| const R & | coeff (DEGREE_TYPE) const |
| returns the coefficient at the specified degree | |
| const R & | operator() (const R &) const |
| computes the value of the polynomial at the given point | |
| void | set_coeff (DEGREE_TYPE, const R &) |
| sets the value of the coefficient at the given degree | |
| const Polynomial< R > & | operator= (const Ring_Element &) |
| assignment operator may be needed | |
| virtual bool | operator== (const Ring_Element &) const override |
| comparison: other element has same value | |
| virtual bool | operator!= (const Ring_Element &) const override |
| comparison: other element has different value | |
| bool | operator== (const R &) const |
returns true if and only if this is constant and has the same value as the given constant/scalar | |
| const Polynomial< R > & | operator/ (const Polynomial< R > &) const |
quotient from dividing this by the given divisor | |
| const Polynomial< R > & | operator% (const Polynomial< R > &) const |
remainder from dividing this by the given divisor | |
| virtual bool | is_one () const override |
should be True iff element is multiplicative identity | |
| virtual bool | is_zero () const override |
should be True iff element is additive identity | |
| virtual bool | has_inverse () const override |
should be True iff element has a multiplicative inverse | |
| virtual bool | is_cancellable () const override |
should be True iff element can cancel across an equation; e.g., \(ax=ay\Rightarrow x=y\). | |
| virtual Polynomial< R > & | operator+ (const Ring_Element &) const override |
| addition: other element should be of same type, use a cast | |
| virtual Polynomial< R > & | operator- (const Ring_Element &) const override |
| subtraction: other element should be of same type, use a cast | |
| virtual Polynomial< R > & | operator* (const Ring_Element &) const override |
| multiplicationL other element should be of same type, use a cast | |
 Public Member Functions inherited from Rings::Commutative_Ring_Element | |
| virtual bool | is_commutative () const override |
| Duh. | |
Protected Member Functions | |
| void | clear_coeffs () |
| sets all coefficients to zero | |
| void | set_degree (DEGREE_TYPE) |
| sets the degree to the specified value and resizes if necessary | |
| void | verify_degree () |
| verifies that the leading coefficient is zero; if not, decreases degree until either it is or the degree is zero | |
| void | common_division (const Polynomial< R > &) const |
| utility function that obtains both divisor and remainder from division | |
Protected Attributes | |
| DEGREE_TYPE | deg |
| polynomial’s degree | |
| vector< R > | coeffs |
| polynomial’s coefficients | |
Static Protected Attributes | |
| static Polynomial< R > | last_divisor |
| storage for previously used divisor | |
| static Polynomial< R > | last_quotient |
| storage for previously computed quotient | |
| static Polynomial< R > | last_remainder |
| storage for previously computed remainder | |
Related Functions | |
(Note that these are not member functions.) | |
| template<typename R > | |
| ostream & | operator<< (ostream &os, const Polynomial< R > &p) |
| prints a polynomial in customary fashion | |
Detailed Description
template<typename R>
class Rings::Polynomial< R >
a dense univariate polynomial, templated according to the coefficient’s type
The coefficient should descend from Ring_Element.
- Examples:
- test_polynomial.cpp.
The documentation for this class was generated from the following file:
