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7.10.4.6 lpGBPres2Poly
Procedure from libraryfreegb.lib (see freegb_lib).
- Usage:
- lpGBPres2Poly(p,G); poly p, ideal G
- Assume:
- L is a valid Groebner presentation like the result of lpDivision
- Return:
- poly
- Note:
- assembles p = \sum_(i,j) l_(ij) g_i r_(ij) + NF(p,I) = \sum_(i) L[2][i][2] I[L[2][i][1]] L[2][i][3] + L[1]
LIB "freegb.lib"; ring r = 0,(x,y),dp; ring R = freeAlgebra(r, 4); ideal I = x*x + y*y - 1; // 2D sphere ideal J = twostd(I); // compute a two-sided Groebner basis J; // it is finite and nice ==> J[1]=x*x+y*y-1 ==> J[2]=y*y*x-x*y*y poly h = x*x*y-y*x*x+x*y; list L = lpDivision(h,J); L[1]; // what means that the normal form (or the remainder) of h wrt J is x*y ==> x*y lpGBPres2Poly(L,J); // we see, that it is equal to h from above ==> -y*x*x+x*x*y+x*y |