Defactoring: Difference between revisions

Line 612:

==== Wolfram Language implementation ====

This is the furthest progress that was made on SAD defactor before efforts were shifted to column Hermite defactor. This implementation still exhibits problems 2, 3~~, and 4~~; only ~~problem~~ 1 ~~was~~ solved here.

This is the furthest progress that was made on SAD defactor before efforts were shifted to column Hermite defactor. This implementation still exhibits problems 2 and 3; only problems 1 and 4 were solved here. Problem 3 started to be solved, but wasn't quite quashed.

~~sadDefactor~~[m_] := Module[{reduced, linCombs,linCombsDisarmed, maybeDisarmedRow~~, thing~~},

confirmEnfactoredRowReplaced[m_] := Module[{i, enfactoredRowReplaced},

linCombs = linCombsToCheck[m];

enfactoredRowReplaced = True;

linCombsDisarmed = Map[extractGcd, linCombs];

For[i = 1, i <= Length[m], i++,

maybeDisarmedRow = Complement[linCombsDisarmed, linCombs];

If[Apply[GCD, m[[i]]] > 1, enfactoredRowReplaced = False]

];

If[Length[maybeDisarmedRow]==0, m, ~~sadDefactor~~[~~Join[{m[[1]]}~~,{ maybeDisarmedRow~~[[1]]}]~~]]

enfactoredRowReplaced

]</nowiki>

];

handleEnfactored[m_, maybeDisarmedRow_] := Module[{defactored, attemptedReplacementOfEnfactoredRow, i, enfactoredRowReplaced},

For[i = 1, i <= Length[m], i++,

attemptedReplacementOfEnfactoredRow = Prepend[Drop[m, {i}], First[maybeDisarmedRow]];

enfactoredRowReplaced = confirmEnfactoredRowReplaced[attemptedReplacementOfEnfactoredRow];

If[enfactoredRowReplaced, defactored = enhancedSadDefactor[attemptedReplacementOfEnfactoredRow]];

];

defactored

];

enhancedSadDefactor[m_] := Module[{mNoAllZeros, reduced, linCombs, linCombsDisarmed, maybeDisarmedRow},

mNoAllZeros = removeAllZeroRows[m];

linCombs = linCombsToCheck[mNoAllZeros];

linCombsDisarmed = Map[extractGcd, linCombs];

maybeDisarmedRow = Complement[linCombsDisarmed, linCombs];

If[Length[maybeDisarmedRow] == 0, mNoAllZeros, handleEnfactored[mNoAllZeros, maybeDisarmedRow]]

];</nowiki>

=== MADAM defactoring ===

@@ Line 612: / Line 612: @@
 ==== Wolfram Language implementation ====
-This is the furthest progress that was made on SAD defactor before efforts were shifted to column Hermite defactor. This implementation still exhibits problems 2, 3, and 4; only problem 1 was solved here.
+This is the furthest progress that was made on SAD defactor before efforts were shifted to column Hermite defactor. This implementation still exhibits problems 2 and 3; only problems 1 and 4 were solved here. Problem 3 started to be solved, but wasn't quite quashed.
   <nowiki>
-sadDefactor[m_] := Module[{reduced, linCombs,linCombsDisarmed, maybeDisarmedRow, thing},
+confirmEnfactoredRowReplaced[m_] := Module[{i, enfactoredRowReplaced},
-    linCombs = linCombsToCheck[m];
+  enfactoredRowReplaced = True;
-    linCombsDisarmed = Map[extractGcd, linCombs];
+  For[i = 1, i <= Length[m], i++,
-    maybeDisarmedRow = Complement[linCombsDisarmed, linCombs];
+    If[Apply[GCD, m[[i]]] > 1, enfactoredRowReplaced = False]
+  ];
-    If[Length[maybeDisarmedRow]==0, m, sadDefactor[Join[{m[[1]]},{ maybeDisarmedRow[[1]]}]]]
+  enfactoredRowReplaced
-]</nowiki>
+];
+handleEnfactored[m_, maybeDisarmedRow_] := Module[{defactored, attemptedReplacementOfEnfactoredRow, i, enfactoredRowReplaced},
+  For[i = 1, i <= Length[m], i++,
+    attemptedReplacementOfEnfactoredRow = Prepend[Drop[m, {i}], First[maybeDisarmedRow]];
+    enfactoredRowReplaced = confirmEnfactoredRowReplaced[attemptedReplacementOfEnfactoredRow];
+    If[enfactoredRowReplaced, defactored = enhancedSadDefactor[attemptedReplacementOfEnfactoredRow]];
+  ];
+  defactored
+];
+enhancedSadDefactor[m_] := Module[{mNoAllZeros, reduced, linCombs, linCombsDisarmed, maybeDisarmedRow},
+  mNoAllZeros = removeAllZeroRows[m];
+  linCombs = linCombsToCheck[mNoAllZeros];
+  linCombsDisarmed = Map[extractGcd, linCombs];
+  maybeDisarmedRow = Complement[linCombsDisarmed, linCombs];
+  If[Length[maybeDisarmedRow] == 0, mNoAllZeros, handleEnfactored[mNoAllZeros, maybeDisarmedRow]]
+];</nowiki>
 === MADAM defactoring ===

Defactoring: Difference between revisions

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