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== Is a variant normalized? ==
== Is a variant normalized? ==
In order to detect if a variant is normalized, we first prove the following lemma.
A variant is normalized if and only if it is parsimonious and left aligned.
== Lemma ==
In order to detect if a variant is normalized, we first prove the following lemma (1).
Each allele ends with the same nucleotide if and only if it is not left aligned or not right parsimonious.
Each allele ends with the same nucleotide if and only if it is not left aligned or not right parsimonious.
Suppose a variant is not right parsimonious, then for sure, all the alleles have length greater than one and by definition, the right most nucleotide is the same for all alleles and may be removed.
Suppose a variant is not right parsimonious, then for sure, all the alleles have length greater than one and by definition, the right most nucleotide is the same for all alleles and may be removed.
== Corollary ==
A variant is normalized if and only if
1. it is has no superfluous nucleotides on the left side and
2. each allele do not end with the same type of nucleotide.
Proof:
*A variant is normalized if and only if it is parsimonious and left aligned.
*A variant is normalized if and only if it is left parsimonious and right parsimonious and left aligned.
*A variant is normalized if and only if it is has no superfluous nucleotides on the left side and right parsimonious and left aligned. (definition of left parsimony)
*A variant is normalized if and only if it is has no superfluous nucleotides on the left side and each allele do not end with the same type of nucleotide. (lemma 1)
= Algorithm for Normalization =
= Algorithm for Normalization =
