Fix thread-safety (ConcurrentHashMap) and typos

src/core/config/Settings.java

@@ -113,7 +113,10 @@ private Settings(){}
 	public static boolean cacheDerivatives = true;
 
 	/**
-	 * Denotes whether or not to cache Legrende polynomials
+	 * Denotes whether or not to cache Legendre polynomials.
+	 * <p><b>Note:</b> The field name "cacheLegrendePolynomials" contains a historical typo
+	 * (correct spelling: "cacheLegendrePolynomials"). The name is kept unchanged for
+	 * API and configuration file compatibility.
 	 */
 	public static boolean cacheLegrendePolynomials = true;
 

src/core/functions/GeneralFunction.java

@@ -19,6 +19,7 @@
 
 import java.util.Collections;
 import java.util.HashMap;
+import java.util.concurrent.ConcurrentHashMap;
 import java.util.Iterator;
 import java.util.Map;
 import java.util.function.Function;
@@ -52,9 +53,13 @@ public abstract class GeneralFunction implements Evaluable, Differentiable, Simp
 	};
 
 	/**
-	 * Caches derivatives with the key corresponding to the {@code varID} of the derivative
+	 * Caches derivatives with the key corresponding to the {@code varID} of the derivative.
+	 * <p><b>Thread-Safety:</b> Using {@link java.util.concurrent.ConcurrentHashMap} to allow
+	 * concurrent get() and put() operations without explicit locking. Required for parallel
+	 * Jacobian construction (e.g. {@code IntStream.parallel()} in CMDSolver).
+	 * A plain {@code HashMap} would cause race conditions under concurrent access.
 	 */
-	protected final Map<String, GeneralFunction> derivatives = new HashMap<>();
+	protected final Map<String, GeneralFunction> derivatives = new ConcurrentHashMap<>();
 
 	/**
 	 * Returns a String representation of this {@link GeneralFunction}

src/core/tools/functiongenerators/LegrendePolynomial.java

@@ -10,16 +10,25 @@
 
 import java.util.HashMap;
 import java.util.Map;
+import java.util.concurrent.ConcurrentHashMap;
 
 import static java.lang.Math.*;
 import static core.tools.MiscTools.*;
 
 /**
- * The methods in {@link LegrendePolynomial} deal with <a href="https://en.wikipedia.org/wiki/Legendre_polynomials">Legrende Polynomials</a>.
+ * The methods in {@link LegrendePolynomial} deal with
+ * <a href="https://en.wikipedia.org/wiki/Legendre_polynomials">Legendre Polynomials</a>.
+ * <p><b>Note:</b> The class name "LegrendePolynomial" contains a historical typo
+ * (correct spelling: "LegendrePolynomial"). The name is kept unchanged for API compatibility.
 */
 public class LegrendePolynomial {
 
-	private static final Map<Integer, GeneralFunction> cache = new HashMap<>();
+	/**
+	 * Thread-safe cache using ConcurrentHashMap.
+	 * A plain HashMap would cause race conditions under concurrent access
+	 * (multiple threads calling makeLegrendePolynomial() simultaneously).
+	 */
+	private static final Map<Integer, GeneralFunction> cache = new ConcurrentHashMap<>();
 	private static final String defaultVariable = "\\var";
 
 	private static GeneralFunction makeLegrendePolynomial(int n) {

src/parsing/LatexReplacer.java

@@ -33,7 +33,7 @@ private LatexReplacer(){}
 			put(Pattern.compile("\\\\epsilon"		+ "(?![\\w.'[^\\x00-\\x7F]])"), "ϵ");
 			put(Pattern.compile("\\\\varepsilon"	+ "(?![\\w.'[^\\x00-\\x7F]])"), "ε");
 			put(Pattern.compile("\\\\Zeta"			+ "(?![\\w.'[^\\x00-\\x7F]])"), "Ζ");
-			put(Pattern.compile("\\\\zeto"			+ "(?![\\w.'[^\\x00-\\x7F]])"), "ζ");
+			put(Pattern.compile("\\\\zeta"			+ "(?![\\w.'[^\\x00-\\x7F]])"), "ζ"); // Fix: was "\\zeto" (typo)
 			put(Pattern.compile("\\\\Eta"			+ "(?![\\w.'[^\\x00-\\x7F]])"), "Η");
 			put(Pattern.compile("\\\\eta"			+ "(?![\\w.'[^\\x00-\\x7F]])"), "η");
 			put(Pattern.compile("\\\\Theta"			+ "(?![\\w.'[^\\x00-\\x7F]])"), "Θ");