[[Biojava:Cookbook:Alphabets:CrossProduct|CrossProductAlphabets]] are used to represent groups of [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/Symbol.html Symbols] as a single Symbol. This is very useful for treating things like codons as single [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/Symbol.html Symbols]. Sometimes however, you might want to covert the [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/Symbol.html Symbols] back into their component [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/Symbol.html Symbols]. The following recipe demonstrates how this can be done.

The [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/Symbol.html Symbols] from a [[Biojava:Cookbook:Alphabets:CrossProduct|CrossProductAlphabet]] are implementations of the [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/AtomicSymbol.html AtomicSymbol] interface. The prefix 'Atomic' suggests that the [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/Symbol.html Symbols] cannot be divided so one might ask, 'how can an indivisible Symbol be divided into it's component parts?'. The full definition of the [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/AtomicSymbol.html AtomicSymbol] is that it cannot be divided into a simpler Symbol that is still part of the same [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/Alphabet.html Alphabet]. The component parts of an [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/AtomicSymbol.html AtomicSymbol] from a [[Biojava:Cookbook:Alphabets:CrossProduct|CrossProductAlphabet]] are not members of the same [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/Alphabet.html Alphabet] so the 'Atomic' definition still stands. A [[wp:codon|codon]] would be from the (DNA x DNA x DNA) Alphabet whereas the components of the [[wp:codon|codon]] [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/Symbol.html Symbol] are from the DNA alphabet.

Contrast this with the definition of a [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/BasisSymbol.html BasisSymbol]. A [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/BasisSymbol.html BasisSymbol] can be validly divided into components that are still part of the same [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/Alphabet.html Alphabet]. In this way a [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/BasisSymbol.html BasisSymbol] can be ambiguous. For further discussion of [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/BasisSymbol.html BasisSymbol] follow this [http://www.biojava.org/docs/api1.8/org/biojava/bio/symbol/BasisSymbol.html link].