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StringTools

  

LexOrder

  

perform lexicographical order comparison of strings

  

ShortLexOrder

  

perform short lexicographical order comparison of strings

  

RevLexOrder

  

perform reverse lexicographical order comparison of strings

  

ShortRevLexOrder

  

perform short reverse lexicographical order comparison of strings

  

LeftRecursivePathOrder

  

perform left recursive path order comparison of strings

  

RightRecursivePathOrder

  

perform right recursive path order comparison of strings

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

LexOrder( s1, s2 )

ShortLexOrder( s1, s2 )

RevLexOrder( s1, s2 )

ShortRevLexOrder( s1, s2 )

LeftRecursivePathOrder( s1, s2 )

RightRecursivePathOrder( s1, s2 )

Parameters

s1, s2

-

Maple strings

Description

• 

These six procedures implement various order relations on strings, extended from the numeric order on character code points.

• 

Each procedure takes two strings s1 and s2 as arguments, and returns one of the values 1,0,1, according to the following table.

String Order

Return Value

 

 

s1 precedes s2

-1

s1 is identical to s2

0

s1 follows s2

1

• 

The LexOrder(s1, s2) command implements simple lexicographic (dictionary) ordering of strings.

• 

The RevLexOrder(s1, s2) command implements the reverse lexicographic order, which is equivalent to the lexicographic order on the reversed strings.

• 

The ShortLexOrder(s1, s2) and ShortRevLexOrder(s1, s2) commands are similar, but apply the respective ordering relation only to strings of equal length. Strings are first compared according to their lengths, with shorter strings preceeding longer strings. The short variants are important because they are translation-invariant: ShortLexOrderu,v = ShortLexOrdercatu,w,catv,w, ShortLexOrderu,v = ShortLexOrdercatw,u,catw,v, ShortRevLexOrderu,v = ShortRevLexOrdercatu,w,catv,w and ShortRevLexOrderu,v = ShortRevLexOrdercatw,u,catw,v,

• 

The left and right recursive path orders are also translation invariant, and are computed by the LeftRecursivePathOrder(s1, s2) and RightRecursivePathOrder(s1, s2) commands, respectively.

• 

The left and right recursive path orders, manifest in the LeftRecursivePathOrder(s1, s2) and RightRecursivePathOrder(s1, s2) commands and are defined for two strings s and t, as follows. Characters (strings with length equal to 1) compare according to the numeric order of the corresponding code points.

  

String s precedes string t in the left recursive path order if one among the following holds: (1) s1&equals;t1 and s1..2 precedes t1..2; (2) t1<s1 and s1..2 precedes t; or (3) s1<t1 and s precedes t1..2.

  

String s precedes string t in the right recursive path order if one among the following holds: (1) s1&equals;t1 and s2..1 precedes t2..1; (2) t1<s1 and s2..1 precedes t; or (3) s1<t1 and s precedes t2..1.

Examples

withStringTools&colon;

LexOrderabc&comma;abd

1

(1)

LexOrderabd&comma;abcd

1

(2)

ShortLexOrderabd&comma;abcd

1

(3)

RevLexOrderbcd&comma;abd

1

(4)

RevLexOrderbcd&comma;bd

1

(5)

ShortRevLexOrderaba&comma;abc

1

(6)

ShortRevLexOrderabc&comma;abc

0

(7)

LeftRecursivePathOrderabc&comma;abcc

1

(8)

RightRecursivePathOrderabc&comma;acc

1

(9)

See Also

lexorder

string

StringTools

StringTools[Compare]

 


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