| Lagrange Interpolation binary function based on the results, the definition of a ternary function Lagrange interpolation nodes only solvable group proposed conicoid full intersection and on the quadratic surface Lagrange interpolation nodes solvable groups basic concepts studied solvable quadratic surface interpolation node group some basic theory and topology. On this basis, given the structure of binary spatial interpolation polynomial solvable only a superposition constructor point group. Finally, the effectiveness of the algorithm is given.Theorem1.3 Let be { }1nd i iQ=A = of(3)nP an interpolation nodes solvable group, do a quadratic surface, it does not by any point of A. Take any one time n +k on the interpolation nodes q( X) =0 solvable groups(3)()n kB I q+?, AUBmust constitute the(3)n kP+ interpolation space solvable group of nodes.This theorem can be interpreted as construction interpolation nodes solvable group added conicoid law.Theorem1.5 Set quadratic algebraic surfaces q( X) =0 and q( X) =0 ample space algebraic curves intersect C =s( p, q).On the surface of q( X) =0,not only through the curve C =s( p, q) Select the n surface of a sub-group of the interpolation nodes solvable( )( )3nA ?I q( n 3k -3), whichever one office of C =s( p, q) at the same time curve n +m interpolation solvable group of nodes(3)()n mB I C+?, There AUB surfaces must be made q( X) =0 order interpolation nodes on n +m solvable groups.This theorem can be interpreted as the algebraic structure along the junction surface interpolation solvable group added conicoid law.Theorem1.6 Quadratic algebraic surfaces q( X) =0 and q( X) =0 ample space algebraic curves intersect C =s( p, q). r( X) =0 and C =s( p, q) intersect exactly at eight distinct points, denoted { }81i iQ=A =, Assuming Point Group ( )( )(3)3nB ?I C n 3m +k -,B IA =f,then ( )( )3n lB A I C+U?.This theorem can be interpreted as the space of algebraic curves constructed along the interpolation nodes solvable group added conicoid law. |
