permutation maths

permute.js

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+
+// Utilities for generating sets of coordinates based on 
+// permutations, even permutations and changes of sign.
+// Based on https://www.qfbox.info/epermute
+
+
+function pandita(a) {
+	const n = a.length;
+	for( let k = n - 2; k >= 0; k-- ) {
+		if( a[k] < a[k + 1] ) {
+			for( let l = n - 1; l >= 0; l-- ) {
+				if( a[k] < a[l] ) {
+					const tmp = a[k];
+					a[k] = a[l];
+					a[l] = tmp;
+					const revtail = a.slice(k + 1);
+					revtail.reverse();
+					for( let i = 0; i < revtail.length; i++ ) {
+						a[k + 1 + i] = revtail[i];
+					}
+					return Math.floor(revtail.length / 2) + 1;
+				}
+			}
+			console.log("Shouldn't get here");
+			process.exit();
+		}
+	}
+	return false;
+}
+
+function permutations(a) {
+	a.sort();
+	const ps = [ [...a] ];
+	while( pandita(a) ) {
+		ps.push([...a]);
+	}
+	return ps;
+}
+
+function permutations_even(a) {
+	a.sort();
+	let parity = 'even';
+	const ps = [ [...a] ];
+	let running = true;
+	while( running ) {
+		const s = pandita(a);
+		if( s ) {
+			if( parity === 'even' ) {
+				if( s % 2 === 1 ) {
+					parity = 'odd';
+				}
+			} else {
+				if( s % 2 === 1 ) {
+					parity = 'even';
+				}
+			}
+			if( parity === 'even' ) {
+				ps.push([...a]);
+			}
+		} else {
+			running = false;
+		}
+	}
+	return ps;
+}
+
+