onLine => [
repCell: Cell, -- representative cell
signatures: LIST OF QESignatureStructure.Signature, -- (see below)
truthValue: BOOL, -- result of formula evalution (e.g. at repCell sample point, or at signature), or determination of containment in solution set
constituentCells: LIST OF Cell,
AdjacencyFile -- intracluster adjacencies (11/87 - why do we need this?)
];
We can be keeping track of signatures of several different polynomial sequences simultaneously for a cluster, e.g. r-variate input polynomials, and basis polynomials in r and lower dimensions. Comparing names of signature Structures should enable us to keep them straight.
When we construct initial clusters in i-space, signature polynomials will be be complete factors, i.e. all irreducible factors, of i-variate input polynomials. We get the signs of factors which are not i-variate basis polys (which we get from cells) by making this cells signature polys union of baseCluster signature polys and i-variate basis.
Rule: signature polynomials are elements of i-variate basis for some i. However nothing assumed about the order in which they occur in the PolynomialSequenceFile.
Rule: a cluster's set or signature polynomials is as large as possible, i.e. is the largest collection of basis polynomials that is invariant on the constituent cells of this cluster. Thus for example, when we are not doing any pasting of clusters as we extend our cad, i.e. clusters just have one constituent cell, i.e. "original" cad algorithm, then signature polys in dimension i should be collection of all i and lower dimensional basis polynomials.
Note: to get a cluster's rep cell sample point, you have to look in the stack file containing the rep cell. Assert: there will always exist a stack file containing any cluster's rep cell.