Singular Manual: lpGBPres2Poly

| #### 7.10.4.6 lpGBPres2Poly Procedure from library `freegb.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] Example:
    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

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