PolynomialTraits_d::PseudoDivision

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PolynomialTraits_d::PseudoDivision

Definition

This AdaptableFunctor computes the pseudo division of two polynomials f and g.

Given f and g ≠ 0 this functor computes quotient q and remainder r such that D ⋅ f = g ⋅ q + r and degree(r) < degree(g), where D = leading_coefficient(g)^{max(0, degree(f)-degree(g)+1)}

This functor is useful if the regular division is not available, which is the case if PolynomialTraits_d::Coefficient_type is not a Field. Hence in general it is not possible to invert the leading coefficient of g. Instead f is extended by D allowing integral divisions in the internal computation.

Refines

AdaptableFunctor

Types

typedef void

result_type;

Operations

result_type

fo ( PolynomialTraits_d::Polynomial_d f ,
PolynomialTraits_d::Polynomial_d g ,
PolynomialTraits_d::Polynomial_d & q ,
PolynomialTraits_d::Polynomial_d & r ,
PolynomialTraits_d::Coefficient_type & D )

Computes the pseudo division with respect to the outermost variable x_d-1.