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initial version of algebraic kernel for quadrics

This commit is contained in:
Eric Berberich 2007-03-27 15:18:57 +00:00
parent df609d3f19
commit 338cbd0ef6
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Quadrical_kernel_3/doc_tex/Quadrical_kernel_3_ref/AlgebraicKernelForQuadrics.tex Normal file
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\begin{ccRefConcept}{AlgebraicKernelForQuadrics}
\ccDefinition
The \ccc{AlgebraicKernelForQuadrics} concept is meant to provide the
quadrical kernel with all the algebraic functionalities required for the
manipulation of quadrics and (arcs of) intersection curves
defined by quadrics in 3D.
\ccHasModels
%\ccc{Algebraic_kernel_for_quadrics_2_3}
\ccTypes
A model of \ccc{AlgebraicKernelForQuadrics} is supposed to provide
\ccNestedType{Coefficient}{A model of \ccc{IntegralDomain}. }
%\ccNestedType{RT}{A model of \ccc{RingNumberType}. }%In addition, the
%class \ccc{Root_of_traits_2<RT>} must be defined and provide a nested
%type \ccc{Type} which must be the same as \ccc{Root_of_2} and a
%function \ccc{make_root_of_2(RT,RT,RT,int)} whose return type is
%\ccc{Type}.}
%\ccGlue
%\ccNestedType{FT}{A model of \ccc{FieldNumberType}\ccc{<RT>}.}
%\footnote{concept template...?}
%\ccNestedType{Polynomial_1_3}{A model of
%\ccc{AlgebraicKernelForQuadrics::Polynomial_1_3}, for trivariate polynomials
%of degree up to~1.}
%\ccGlue
\ccNestedType{Polynomial_2_3}{A model of
\ccc{AlgebraicKernelForQuadrics::Polynomial_2_3}, for trivariate polynomials
of degree up to~2.}
\ccNestedType{Root_of_8_1}{A model of
\ccc{RootOf_8_1}, for algebraic numbers
of degreee at most 8}
\ccGlue
\ccNestedType{Root_of_8_3}{A model of
\ccc{AlgebraicKernelForQuadric::Root_of_8_3}, for
solutions of systems of three models of
\ccc{AlgebraicKernelForQuadrics::Polynomial_2_3}.}
\ccNestedType{Construct_polynomial_2_3}{A model of
\ccc{AlgebraicKernelForQuadrics::ConstructPolynomial_2_3}.}
\ccNestedType{Compare_x}{A model of the concept
\ccc{AlgebraicKernelForQuadrics::CompareX}.}
\ccGlue
\ccNestedType{Compare_y}{A model of the concept
\ccc{AlgebraicKernelForQuadrics::CompareY}.}
\ccGlue
\ccNestedType{Compare_z}{A model of the concept
\ccc{AlgebraicKernelForQuadrics::CompareZ}.}
\ccGlue
\ccNestedType{Compare_xy}{A model of the concept
\ccc{AlgebraicKernelForQuadrics::CompareXY}.}
\ccGlue
\ccNestedType{Compare_xyz}{A model of the concept
\ccc{AlgebraicKernelForQuadrics::CompareXYZ}.}
\ccNestedType{Sign_at}{A model of the concept \ccc{AlgebraicKernelForQuadrics::SignAt}.}
\ccNestedType{X_critical_points}{A model of the concept
\ccc{AlgebraicKernelForQuadrics::XCriticalPoints}.}
\ccGlue
\ccNestedType{Y_critical_points}{A model of the concept
\ccc{AlgebraicKernelForQuadrics::YCriticalPoints}.}
\ccGlue
\ccNestedType{Z_critical_points}{A model of the concept
\ccc{AlgebraicKernelForQuadrics::ZCriticalPoints}.}
\ccNestedType{Solve}{A model of the concept \ccc{AlgebraicKernelForQuadrics::Solve}. It computes the roots of trivariate polynomial equations. The polynomials need to be square-free and coprime.}
\ccSeeAlso
\ccRefIdfierPage{QuadricalKernel_3}
\end{ccRefConcept}