<> <> <> <<>> DIRECTORY Rope, Basics, IO, MathExpr, AlgebraClasses, Variables, VariableSequences, DistribPolys; PolynomialSignatures: CEDAR DEFINITIONS ~ BEGIN <> Signature: TYPE = AlgebraClasses.Object; SignatureData: TYPE = LIST OF PolynomialSignatureEntry; PolynomialSignatureEntryRec: TYPE = RECORD[ signature: Signature, clustersWithThisSignature: LIST OF Clusters.Cluster -- each of which has this signature ]; <> <> MakePolynomialSignature: PROC; <> DisambiguatePolynomialSignature: PROC; <> <> <<1. Select some basis polynomial F (in any dimension) that is not currently a signature polynomial. Initialize newTable _ NIL;>> <<2. For each current table entry E, create between 1 and 3 new table entries by calling RefinePolynomialSignatureEntryByPolynomial[E, F], add to newTable.>> <<3. Set table _ newTable;>> <> RefinePolynomialSignatureEntryByPolynomial: PROC [E: PolynomialSignatureEntry, F: Polynomial] RETURNS [LIST OF PolynomialSignatureEntry]; <> RefineClusterByPolynomial: PROC [C: Cluster, (i, j): RefToBasisElement] RETURNS [negativeSign, zeroSign, positiveSign: Cluster]; <> GetCellSignAtBasisElement: PROC [c: Cell, (i, j): RefToBasisElement] RETURNS [Sign]; <= i space, (i, j) is a reference to (jth element of i-dimensional basis), looks into stack file for rep cell e of i-space cluster containing i-space cell d induced by c (how do we know in what file to find that cluster?), and returns jth element of e's basis signature>> <<>> ExtractSolutionSignatures: PROC [T: PolynomialSignature] RETURNS [solutionSignatures, dontOccur: LIST OF Signature]; <> SimplifySignatures: PROC [LIST OF Signature] RETURNS [LIST OF Signature]; <> SignaturesToFormula: PROC [LIST OF Signature] RETURNS [Formula]; <> <<>> MakeSolutionFormula: PROC; <> <> DisambiguatePolynomialSignature: PROC [inTable: QET.PolynomialSignature] RETURNS [outTable: QET.PolynomialSignature]; <> <> <> <<1. Select some polynomial P from the basis of some (proper) induced cad, such that P is not an element of outTable.polynomials (use hashing).>> <<2. Augment the secondarySignature's of all cells of all regions of this entry by sign(P).>> <<3. For each region of this entry, form the subgraph it induces, and construct signed components in this subgraph wrt secondarySignature.>> <<4. Collect the cumulative data: if the sign(s) of P on all newly formed components which are contained in the solution set differ from the sign(s) of P on all newly formed components which are external to the solution set, then we have succeeded in disambiguating this entry with P.>> <<5. Delete this entry, and create two new appropriate unambiguous entries, with appropriately augmented signatures.>> <<6. For all unambiguous entries, augment their signatures with "don't care" in the P position, and augment appropriately (i.e. with the correct P sign) the secondarySignature's of all constituent cells of all entry regions.>> <<7. For each ambiguous entry, carry out steps 2,3,4, and see if we have succeeding in disambiguating that entry with P. If so, then carry out step 5 for this entry. If not, then split this entry into up to three or more (each of which may be ambiguous or unambiguous, but at least one of which must be ambiguous if we are here) entries, corresponding to splitting each of the prior entry regions into up to three or more new regions by the sign of P.>> SimplifySignatureSeq: PROC [QET.SignatureSeq] RETURNS [QET.SignatureSeq]; <> <> SignatureSeqToFormula: PROC [QET.SignatureSeq] RETURNS [QFF.QFFormula]; <> END.