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# gbSnapshot -- the Gröbner basis matrix as so far computed

## Synopsis

• Usage:
gbSnapshot M
• Inputs:
• Outputs:
• , the Gröbner basis as so far computed

## Description

This routine is useful to be able to obtain partial results from a partially computed Gröbner basis. Little computation is done (although a minimalization, auto-reduction and sort is performed).
 i1 : R = ZZ/101[a..d] o1 = R o1 : PolynomialRing i2 : I = intersect((ideal(a,b,c^3-d^3))^2,ideal(a^2-c^2,b^2-d^2)) 2 2 2 2 2 3 3 3 3 3 2 o2 = ideal (b c - a d , a b*c - b*c - b d + b*d , a c - a*c - a*b d + ------------------------------------------------------------------------ 3 4 2 2 3 2 2 2 2 2 3 2 4 2 2 a*d , b - b d , a*b - a*b*d , a b - a d , a b - a*b*c , a - a c , ------------------------------------------------------------------------ 2 4 6 2 3 3 3 2 4 6 a c - c - 2a c*d + 2c d + b d - d ) o2 : Ideal of R i3 : gb(I, BasisElementLimit=>5) o3 = GroebnerBasis[status: BasisElementLimit; all S-pairs handled up to degree 5] o3 : GroebnerBasis i4 : gbSnapshot I o4 = | b2c2-a2d2 a2bc-bc3-b3d+bd3 a3c-ac3-ab2d+ad3 b4-b2d2 ab3-abd2 a2b2-a2d2 ------------------------------------------------------------------------ a3b-abc2 a4-a2c2 a2c4-c6-2a2cd3+2c3d3+b2d4-d6 | 1 9 o4 : Matrix R <-- R i5 : gb(I, BasisElementLimit=>10) o5 = GroebnerBasis[status: done; S-pairs encountered up to degree 6] o5 : GroebnerBasis i6 : gbSnapshot I o6 = | b2c2-a2d2 a2bc-bc3-b3d+bd3 a3c-ac3-ab2d+ad3 b4-b2d2 ab3-abd2 a2b2-a2d2 ------------------------------------------------------------------------ a3b-abc2 a4-a2c2 a2c4-c6-2a2cd3+2c3d3+b2d4-d6 | 1 9 o6 : Matrix R <-- R i7 : gens gb I o7 = | b2c2-a2d2 a2bc-bc3-b3d+bd3 a3c-ac3-ab2d+ad3 b4-b2d2 ab3-abd2 a2b2-a2d2 ------------------------------------------------------------------------ a3b-abc2 a4-a2c2 a2c4-c6-2a2cd3+2c3d3+b2d4-d6 | 1 9 o7 : Matrix R <-- R

• gb -- compute a Gröbner basis
• gbTrace -- provide tracing output during various computations in the engine.
• gbRemove -- remove Gröbner basis

## Ways to use gbSnapshot :

• gbSnapshot(Ideal)
• gbSnapshot(Matrix)
• gbSnapshot(Module)

## For the programmer

The object gbSnapshot is .