Tensor inheritance (#115)

* Updated inheritance of tensors.

- All ring tensors now inherit from their equivalent semiring tensors.
- All field tensors now inherit from their equivalent ring tensors.
- Added tests for Complex64 numbers.

* Added Tests

- Removed redundant transpose classes.

* Fixed Javadoc.

* Remove duplicated code.

* Added tests.

- Fixed bugs that caused failing tests.

* Added tests.

- Fixed bugs that caused failing tests.

* Added tests.

- Fixed bugs which failing tests.

* Fix for norms.

- Updated and fixed matrix and vector norms
- Changes to norms are reflected in the Condition.java for computing condition numbers.

* Added balancing decomposition

* Small fixes.

docs/flag4j/org/flag4j/linalg/operations/dense/real/RealDenseMatrixMultTranspose.html

@@ -86,7 +86,7 @@
 <h1 title="Class RealDenseMatrixMultTranspose" class="title">Class RealDenseMatrixMultTranspose</h1>
 </div>
 <div class="inheritance" title="Inheritance Tree"><a href="https://docs.oracle.com/en/java/javase/22/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">java.lang.Object</a>
-<div class="inheritance">org.flag4j.linalg.ops.dense.real.RealDenseMatrixMultTranspose</div>
+<div class="inheritance">org.flag4j.linalg.ops.dense.real.RealDenseMatMultTranspose</div>
 </div>
 <section class="class-description" id="class-description">
 <div class="horizontal-scroll">

docs/flag4j/org/flag4j/linalg/operations/dense/real/RealDenseMatrixMultiplication.html

@@ -86,7 +86,7 @@
 <h1 title="Class RealDenseMatrixMultiplication" class="title">Class RealDenseMatrixMultiplication</h1>
 </div>
 <div class="inheritance" title="Inheritance Tree"><a href="https://docs.oracle.com/en/java/javase/22/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">java.lang.Object</a>
-<div class="inheritance">org.flag4j.linalg.ops.dense.real.RealDenseMatrixMultiplication</div>
+<div class="inheritance">org.flag4j.linalg.ops.dense.real.RealDenseMatMult</div>
 </div>
 <section class="class-description" id="class-description">
 <div class="horizontal-scroll">

docs/flag4j/org/flag4j/linalg/operations/dense_sparse/csr/field_ops/DenseCsrFieldMatMult.html

@@ -86,7 +86,7 @@
 <h1 title="Class DenseCsrFieldMatMult" class="title">Class DenseCsrFieldMatMult</h1>
 </div>
 <div class="inheritance" title="Inheritance Tree"><a href="https://docs.oracle.com/en/java/javase/22/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">java.lang.Object</a>
-<div class="inheritance">org.flag4j.linalg.ops.dense_sparse.csr.field_ops.DenseCsrFieldMatMult</div>
+<div class="inheritance">org.flag4j.linalg.ops.dense_sparse.csr.semiring_ops.DenseCsrSemiringMatMult</div>
 </div>
 <section class="class-description" id="class-description">
 <div class="horizontal-scroll">

docs/flag4j/org/flag4j/linalg/operations/sparse/coo/field_ops/CooFieldNorms.html

@@ -86,7 +86,7 @@
 <h1 title="Class CooFieldNorms" class="title">Class CooFieldNorms</h1>
 </div>
 <div class="inheritance" title="Inheritance Tree"><a href="https://docs.oracle.com/en/java/javase/22/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">java.lang.Object</a>
-<div class="inheritance">org.flag4j.linalg.ops.sparse.coo.field_ops.CooFieldNorms</div>
+<div class="inheritance">org.flag4j.linalg.ops.sparse.coo.ring_ops.CooRingNorms</div>
 </div>
 <section class="class-description" id="class-description">
 <div class="horizontal-scroll">

docs/flag4j/org/flag4j/linalg/operations/sparse/coo/real/RealSparseMatrixGetSet.html

@@ -86,7 +86,7 @@
 <h1 title="Class RealSparseMatrixGetSet" class="title">Class RealSparseMatrixGetSet</h1>
 </div>
 <div class="inheritance" title="Inheritance Tree"><a href="https://docs.oracle.com/en/java/javase/22/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">java.lang.Object</a>
-<div class="inheritance">org.flag4j.linalg.ops.sparse.coo.real.RealSparseMatrixGetSet</div>
+<div class="inheritance">org.flag4j.linalg.ops.sparse.coo.real.RealCooMatrixGetSet</div>
 </div>
 <section class="class-description" id="class-description">
 <div class="horizontal-scroll">

docs/flag4j/org/flag4j/linalg/operations/sparse/csr/field_ops/CsrFieldEquals.html

@@ -86,7 +86,7 @@
 <h1 title="Class CsrFieldEquals" class="title">Class CsrFieldEquals</h1>
 </div>
 <div class="inheritance" title="Inheritance Tree"><a href="https://docs.oracle.com/en/java/javase/22/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">java.lang.Object</a>
-<div class="inheritance">org.flag4j.linalg.ops.sparse.csr.field_ops.CsrFieldEquals</div>
+<div class="inheritance">org.flag4j.linalg.ops.sparse.csr.ring_ops.CsrRingProperties</div>
 </div>
 <section class="class-description" id="class-description">
 <div class="horizontal-scroll">

docs/flag4j/org/flag4j/linalg/ops/dense/real/RealDenseMatrixMultTranspose.html

@@ -86,7 +86,7 @@
 <h1 title="Class RealDenseMatrixMultTranspose" class="title">Class RealDenseMatrixMultTranspose</h1>
 </div>
 <div class="inheritance" title="Inheritance Tree"><a href="https://docs.oracle.com/en/java/javase/23/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">java.lang.Object</a>
-<div class="inheritance">org.flag4j.linalg.ops.dense.real.RealDenseMatrixMultTranspose</div>
+<div class="inheritance">org.flag4j.linalg.ops.dense.real.RealDenseMatMultTranspose</div>
 </div>
 <section class="class-description" id="class-description">
 <div class="horizontal-scroll">

docs/flag4j/org/flag4j/linalg/ops/dense/real/RealDenseMatrixMultiplication.html

@@ -94,7 +94,7 @@
 <h1 title="Class RealDenseMatrixMultiplication" class="title">Class RealDenseMatrixMultiplication</h1>
 </div>
 <div class="inheritance" title="Inheritance Tree"><a href="https://docs.oracle.com/en/java/javase/23/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">java.lang.Object</a>
-<div class="inheritance">org.flag4j.linalg.ops.dense.real.RealDenseMatrixMultiplication</div>
+<div class="inheritance">org.flag4j.linalg.ops.dense.real.RealDenseMatMult</div>
 </div>
 <section class="class-description" id="class-description">
 <div class="horizontal-scroll">

docs/flag4j/org/flag4j/linalg/ops/dense_sparse/csr/field_ops/DenseCsrFieldMatMult.html

@@ -85,7 +85,7 @@
 <h1 title="Class DenseCsrFieldMatMult" class="title">Class DenseCsrFieldMatMult</h1>
 </div>
 <div class="inheritance" title="Inheritance Tree"><a href="https://docs.oracle.com/en/java/javase/23/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">java.lang.Object</a>
-<div class="inheritance">org.flag4j.linalg.ops.dense_sparse.csr.field_ops.DenseCsrFieldMatMult</div>
+<div class="inheritance">org.flag4j.linalg.ops.dense_sparse.csr.semiring_ops.DenseCsrSemiringMatMult</div>
 </div>
 <section class="class-description" id="class-description">
 <div class="horizontal-scroll">

docs/flag4j/org/flag4j/linalg/ops/sparse/coo/field_ops/CooFieldNorms.html

@@ -85,7 +85,7 @@
 <h1 title="Class CooFieldNorms" class="title">Class CooFieldNorms</h1>
 </div>
 <div class="inheritance" title="Inheritance Tree"><a href="https://docs.oracle.com/en/java/javase/23/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">java.lang.Object</a>
-<div class="inheritance">org.flag4j.linalg.ops.sparse.coo.field_ops.CooFieldNorms</div>
+<div class="inheritance">org.flag4j.linalg.ops.sparse.coo.ring_ops.CooRingNorms</div>
 </div>
 <section class="class-description" id="class-description">
 <div class="horizontal-scroll">

docs/flag4j/org/flag4j/linalg/ops/sparse/coo/real/RealSparseMatrixGetSet.html

@@ -104,7 +104,7 @@
 <h1 title="Class RealSparseMatrixGetSet" class="title">Class RealSparseMatrixGetSet</h1>
 </div>
 <div class="inheritance" title="Inheritance Tree"><a href="https://docs.oracle.com/en/java/javase/23/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">java.lang.Object</a>
-<div class="inheritance">org.flag4j.linalg.ops.sparse.coo.real.RealSparseMatrixGetSet</div>
+<div class="inheritance">org.flag4j.linalg.ops.sparse.coo.real.RealCooMatrixGetSet</div>
 </div>
 <section class="class-description" id="class-description">
 <div class="horizontal-scroll">

docs/flag4j/org/flag4j/linalg/ops/sparse/csr/field_ops/CsrFieldEquals.html

@@ -84,7 +84,7 @@
 <h1 title="Class CsrFieldEquals" class="title">Class CsrFieldEquals</h1>
 </div>
 <div class="inheritance" title="Inheritance Tree"><a href="https://docs.oracle.com/en/java/javase/23/docs/api/java.base/java/lang/Object.html" title="class or interface in java.lang" class="external-link">java.lang.Object</a>
-<div class="inheritance">org.flag4j.linalg.ops.sparse.csr.field_ops.CsrFieldEquals</div>
+<div class="inheritance">org.flag4j.linalg.ops.sparse.csr.ring_ops.CsrRingProperties</div>
 </div>
 <section class="class-description" id="class-description">
 <div class="horizontal-scroll">

src/main/java/module-info.java

@@ -3,6 +3,7 @@
  */
 module flag4j {
     requires java.logging;
+    requires java.desktop;
 
     // Abstract algebra stuff.
     exports org.flag4j.algebraic_structures;
@@ -67,14 +68,12 @@
     exports org.flag4j.linalg.ops.sparse;
 
     exports org.flag4j.linalg.ops.sparse.coo;
-    exports org.flag4j.linalg.ops.sparse.coo.field_ops;
     exports org.flag4j.linalg.ops.sparse.coo.real;
     exports org.flag4j.linalg.ops.sparse.coo.real_complex;
     exports org.flag4j.linalg.ops.sparse.coo.ring_ops;
     exports org.flag4j.linalg.ops.sparse.coo.semiring_ops;
 
     exports org.flag4j.linalg.ops.sparse.csr;
-    exports org.flag4j.linalg.ops.sparse.csr.field_ops;
     exports org.flag4j.linalg.ops.sparse.csr.real;
     exports org.flag4j.linalg.ops.sparse.csr.real_complex;
     // ------------------------------------------------------------------------
@@ -85,4 +84,7 @@
     // Utilities
     exports org.flag4j.util;
     exports org.flag4j.util.exceptions;
+    exports org.flag4j.linalg.ops.sparse.csr.ring_ops;
+    exports org.flag4j.linalg.ops.dense_sparse.csr.semiring_ops;
+    exports org.flag4j.linalg.decompositions.balance;
 }

src/main/java/org/flag4j/algebraic_structures/Complex128.java

@@ -1,7 +1,7 @@
 /*
  * MIT License
  *
- * Copyright (c) 2024. Jacob Watters
+ * Copyright (c) 2024-2025. Jacob Watters
  *
  * Permission is hereby granted, free of charge, to any person obtaining a copy
  * of this software and associated documentation files (the "Software"), to deal
@@ -350,7 +350,7 @@ public Complex128 mult(Complex128 b) {
      */
     @Override
     public boolean isZero() {
-        return equals(ZERO);
+        return re == 0.0 && im == 0.0;
     }
 
 
@@ -363,7 +363,7 @@ public boolean isZero() {
      */
     @Override
     public boolean isOne() {
-        return equals(ONE);
+        return re == 1.0 && im == 0.0;
     }
 
 
@@ -398,6 +398,7 @@ public Complex128 getOne() {
      * @param b Second element in product.
      * @return The product of this field element and {@code b}.
      */
+    @Override
     public Complex128 mult(double b) {
         return new Complex128(re*b, im*b);
     }

src/main/java/org/flag4j/algebraic_structures/Complex64.java

@@ -180,6 +180,15 @@ public Complex64(String num) {
     }
 
 
+    /**
+     * Checks if this complex has zero imaginary part and real part equal to a double.
+     * @return True if {@code this.re == b && this.im == 0}. False otherwise.
+     */
+    public boolean equals(float b) {
+        return this.re == b && this.im == 0;
+    }
+
+
     /**
      * Checks if an object is equal to this Field element.
      * @param b Object to compare to this Field element.
@@ -502,18 +511,6 @@ public Complex64 conj() {
     }
 
 
-    /**
-     * Compute a raised to the power of b. This method wraps {@link Math#pow(double, double)}
-     * and returns a {@link Complex64}.
-     * @param a The base.
-     * @param b The exponent.
-     * @return a raised to the power of b.
-     */
-    public static Complex64 pow(float a, float b) {
-        return new Complex64((float) Math.pow(a, b));
-    }
-
-
     /**
      * Compute a raised to the power of b.
      * and returns a {@link Complex64}.

src/main/java/org/flag4j/algebraic_structures/Field.java

@@ -169,7 +169,7 @@ default T mult(double b) {
      */
     default T div(double b) {
         throw new UnsupportedOperationException("Division with primitive doubles is not supported for this field: "
-                + getClass() + ".");
+                + getClass().getName() + ".");
     }
 
 

src/main/java/org/flag4j/algebraic_structures/Ring.java

@@ -105,7 +105,7 @@ public interface Ring<T extends Ring<T>> extends Semiring<T> {
      * @param b Second ring element in difference.
      * @return The difference of this ring element and {@code b}.
      */
-    public T sub(T b);
+    T sub(T b);
 
 
     /**
@@ -115,7 +115,7 @@ public interface Ring<T extends Ring<T>> extends Semiring<T> {
      *
      * @return The additive inverse for this ring element.
      */
-    public T addInv();
+    T addInv();
 
 
     /**
@@ -133,8 +133,9 @@ default double abs() {
      * Computes the magnitude of this ring element.
      * @return The magnitude of this ring element.
      */
-    default public double mag() {
-        throw new UnsupportedOperationException("Magnitude/absolute value is not defined for this ring: " + getClass() + ".");
+    default double mag() {
+        throw new UnsupportedOperationException("Magnitude/absolute value is not defined for this algebraic object: "
+                + getClass().getName() + ".");
     }
 
 
@@ -143,7 +144,8 @@ default public double mag() {
      * @return The conjugation of this ring's element.
      * @implNote The default implementation of this method simply returns this rings element.
      */
-    public default T conj() {
-        throw new UnsupportedOperationException("Magnitude/absolute value is not defined for this ring: " + getClass() + ".");
+    default T conj() {
+        throw new UnsupportedOperationException("Conjugation is not defined for this algebraic object: "
+                + getClass().getName() + ".");
     }
 }

src/main/java/org/flag4j/arrays/SmartMatrix.java

@@ -26,7 +26,6 @@
 
 import org.flag4j.algebraic_structures.Complex128;
 import org.flag4j.algebraic_structures.Field;
-import org.flag4j.algebraic_structures.RealFloat64;
 import org.flag4j.algebraic_structures.Semiring;
 import org.flag4j.arrays.backend.MatrixMixin;
 import org.flag4j.arrays.backend.smart_visitors.*;
@@ -394,45 +393,4 @@ public int hashCode() {
     public String toString() {
         return "SmartMatrix type: " + this.matrix.getClass().getSimpleName() + "\n" + matrix.toString();
     }
-
-
-    // TODO: TESTING
-    public static void main(String[] args) {
-        var realDense = new Matrix(new double[][]{
-                {1, 2, 3},
-                {4, 5, 6},
-                {7, 8, 9}
-        });
-
-        var complexDense = new CMatrix(new Complex128[][]{
-                {new Complex128(1.46, 12.6), new Complex128(-2, 1),new Complex128(0, 4)},
-                {new Complex128(2), new Complex128(2.1, 3),new Complex128(-1, 3)},
-                {new Complex128(1, 1), new Complex128(12, 5),new Complex128(0, -2)}
-        });
-
-        var fieldDense = new FieldMatrix<>(new Complex128[][]{
-                {new Complex128(1.46, 12.6), new Complex128(-2, 1),new Complex128(0, 4)},
-                {new Complex128(2), new Complex128(2.1, 3),new Complex128(-1, 3)},
-                {new Complex128(1, 1), new Complex128(12, 5),new Complex128(0, -2)}
-        });
-
-        var fieldDense2 = new FieldMatrix<>(new RealFloat64[][]{
-                {new RealFloat64(1.5566), new RealFloat64(-9.3), new RealFloat64(0)},
-                {new RealFloat64(1), new RealFloat64(-2), new RealFloat64(400.1)},
-                {new RealFloat64(2), new RealFloat64(0.84), new RealFloat64(8e9)}
-        });
-
-        SmartMatrix a = new SmartMatrix(realDense);
-        SmartMatrix b = new SmartMatrix(complexDense);
-        SmartMatrix c = new SmartMatrix(fieldDense);
-        SmartMatrix d = new SmartMatrix(fieldDense2);
-
-        double trace = a.tr(Double.class);
-
-        System.out.println("a:\n" + a + "\n");
-        System.out.println("b:\n" + b + "\n");
-        System.out.println("a + b:\n" + a.add(b) + "\n");
-        System.out.println("c + c:\n" + d.add(d) + "\n");
-        System.out.println();
-    }
 }