\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Polynomial

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PolynomialTraits_d::Substitute Concept Reference
Concepts

## Definition

This `Functor` substitutes all variables of a given multivariate `PolynomialTraits_d::Polynomial_d` by the values given in the iterator range, where begin refers the value for the innermost variable.

Refines:

  Assignable

  CopyConstructible

  DefaultConstructible

Types

Note that the `result_type` is the coercion type of the value type of the given iterator range and `PolynomialTraits_d::Innermost_coefficient_type`. In particular `std::iterator_traits<Input_iterator>::value_type` must be `ExplicitInteroperable` with `PolynomialTraits_d::Innermost_coefficient_type`. Hence, it can not be provided as a public type in advance.

See Also
  `Polynomial_d`
  `PolynomialTraits_d`
  `PolynomialTraits_d::SubstituteHomogeneous`
  `CGAL::Coercion_traits`

## Operations
template<class Input_iterator >
result_type | operator() (PolynomialTraits_d::Polynomial_d p, Input_iterator begin, Input_iterator end)
| Substitutes each variable of \( p\) by the values given in the iterator range, where begin refers to the innermost variable \( x_0\). More...

## Member Function Documentation

template<class Input_iterator >

result_type PolynomialTraits_d::Substitute::operator() | ( | PolynomialTraits_d::Polynomial_d | p,
|  | Input_iterator | begin,
|  | Input_iterator | end
| ) |  |

Substitutes each variable of \( p\) by the values given in the iterator range, where begin refers to the innermost variable \( x_0\).

Precondition
  (`end-begin` == `PolynomialTraits_d::d`)