Merge pull request #49 from SageMathOER-CCC/boolean

Boolean

source/boolean-algebra/ch-boolean-algebra.ptx

@@ -0,0 +1,14 @@
+<?xml version="1.0" encoding="UTF-8"?>
+
+<chapter xml:id="ch-boolean-algebra" xmlns:xi="http://www.w3.org/2001/XInclude">
+  <title>Boolean Algebra</title>
+
+  <introduction>
+    <p> Boolean algebra introduction paragraph here </p>
+  </introduction>
+
+  <!-- include sections -->
+  <xi:include href="sec-boolean-definition.ptx" />
+
+
+</chapter>

source/boolean-algebra/sec-boolean-definition.ptx

@@ -0,0 +1,55 @@
+<section xml:id="sec-boolean-definition" xmlns:xi="http://www.w3.org/2001/XInclude">
+    <title>Definition</title>
+    <p>
+        Boolean algebra is a branch of algebra that deals with variables that can take two values: true or false. This form of algebra is foundational in fields such as digital electronics and computer science where binary systems are prevalent.
+    </p>
+    <p>
+        In SageMath, Boolean algebra can be manipulated through various built-in functions designed for handling Boolean variables and expressions.
+    </p>
+    <sage>
+        <input>
+            B = BooleanPolynomialRing(3, 'x')
+            f = B('x0 + x1 * x2')
+            show(f)
+        </input>
+        <output>
+            # Outputs the Boolean expression in polynomial form
+        </output>
+    </sage>
+    <p>
+        A common structure analyzed in Boolean algebra is the lattice. Below, we show how to work with a divisor lattice, which is a specific type of lattice useful in various mathematical computations.
+    </p>
+    <sage>
+        <input>
+            p = Posets.DivisorLattice(20)
+            p.show()
+        </input>
+        <output>
+            # This will display the lattice structure for divisors of the number 20.
+        </output>
+    </sage>
+    <p>
+        The following Sage cell checks whether the divisor lattice is distributive. A distributive lattice is one where the operations of join and meet distribute over each other.
+    </p>
+    <sage>
+        <input>
+            p = Posets.DivisorLattice(20)
+            p.is_distributive(certificate='True')
+        </input>
+        <output>
+            # Returns True if the lattice is distributive, along with a certificate if applicable.
+        </output>
+    </sage>
+    <p>
+        Another important property in Boolean algebra is the complemented lattice. A complemented lattice is one where every element has a complement in the lattice.
+    </p>
+    <sage>
+        <input>
+            p = Posets.DivisorLattice(20)
+            p.is_complemented(certificate='True')
+        </input>
+        <output>
+            # Returns True if the lattice is complemented, along with a certificate if applicable.
+        </output>
+    </sage>
+</section>

source/lattices/sec-definition.ptx

@@ -1,5 +1,6 @@
 <section xml:id="sec-definition" xmlns:xi="http://www.w3.org/2001/XInclude">
-            <title>Definition</title>
+    <subsection xml:id="definition">        
+    <title>Definition</title>
             <p>
                 A lattice is defined as a partially ordered set (poset) in which any two elements have a least upper bound (also known as join) and greatest lower bound (also known as meet). 
             </p>
@@ -44,8 +45,10 @@
                 <output>
                     # This will check if the poset is a lattice.
                 </output>
-            </sage>
-
+            </sage>                
+          </subsection>    
+
+
         <subsection xml:id="join">
             <title>Join</title>
             <p>

source/main.ptx

@@ -21,6 +21,7 @@
     <xi:include href="./graph-theory/ch-graph-theory.ptx" />
     <xi:include href="./trees/ch-trees.ptx" />
     <xi:include href="./lattices/ch-lattices.ptx" /> 
+    <xi:include href="./boolean-algebra/ch-boolean-algebra.ptx" />
     <!-- Include backmatter -->
     <xi:include href="./backmatter.ptx" />