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I want to import data out of a string field in my shapefile to a new field for labeling.

The string field contains river names and codes and I just want to display the text i.e river names

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could you post an example of the river names and codes? – dango Jul 19 '12 at 10:41

In field calculator you can use this python function under the Show Codeblock option:

def removeNumbers(oldfield, newfield):
  newfield = ''.join([letter for letter in oldfield if not letter.isdigit()])
  return newfield

removeNumbers(!StringNumber!, !NoNumber!)
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This question, and its first answer, appear to have been written at a time prior to the Python Parser becoming available for writing Label Expressions.

In this case I think the expression (untested) would be:

def FindLabel ( [StringNumber] ):
  S = ''.join([letter for letter in [StringNumber] if not letter.isdigit()])
  return S
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