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doc ///
Key
tally
(tally, VisibleList)
(tally, String)
Headline
tally the elements of a list, sequence, array, or string
Usage
y = tally x
Inputs
x:{VisibleList,String}
Outputs
y:Tally
Description
Text
It produces a hash table (multiset) @TT "y"@ which tallies the frequencies
of the occurrences of items in the list or string @TT "x"@, i.e.,
@TT "y_i"@ is the number of times @TT "i"@ appears in @TT "x"@, or is
@TT "0"@ if @TT "i"@ doesn't appear in the list or string.
Example
y = tally {1,2,3,a,b,1,2,a,1,2,{a,b},{a,b},a}
y_2
y_5
y_{a,b}
tally "Hello, world!"
SeeAlso
Tally
///
document {
Key => Tally,
Headline => "the class of all tally results",
TT "Tally", " -- a class designed to hold tally results, i.e., multisets.",
SeeAlso => { Set },
Subnodes => {
TO (symbol +, Tally, Tally),
TO (symbol -, Tally, Tally),
}
}
document {
Key => VirtualTally,
"The only difference between this class and ", TO "Tally", " is that this class allows negative numbers.",
EXAMPLE lines ///
x = tally {a,b,b,c,c,c}
y = tally {a,a,a,b,b,c}
x' = new VirtualTally from x
y' = new VirtualTally from y
x-y
x'-y'
///,
Subnodes => {
TO Tally,
TO BettiTally,
TO (symbol **, VirtualTally, VirtualTally),
TO (symbol ^**, VirtualTally, ZZ),
TO (symbol +, VirtualTally, VirtualTally),
TO (symbol -, VirtualTally, VirtualTally),
TO (symbol -, VirtualTally),
TO (symbol _, VirtualTally, Thing),
TO (product, VirtualTally),
TO (sum, VirtualTally),
}
}
document {
Key => (symbol **, VirtualTally, VirtualTally),
Headline => "Cartesian product of tallies",
TT "x ** y", " -- produces the Cartesian product of two tallies.",
PARA{},
"One of the arguments may be a ", TO "Set", ".",
PARA{},
EXAMPLE {
"x = tally {a,a,b}",
"y = tally {1,2,2,2}",
"x ** y",
},
SeeAlso => {"Tally", "tally"}
}
-- TODO
document {
Key => (symbol -, VirtualTally, VirtualTally),
}
document {
Key => (symbol +, VirtualTally, VirtualTally),
Headline => "union of tallies",
TT "x + y", " -- produces the union of two tallies.",
PARA{},
"One of the arguments may be a ", TO "Set", ".",
PARA{},
EXAMPLE {
"x = tally {a,b,b,c,c,c,d,d,d}",
"y = tally {a,a,a,b,b,c,d}",
"x' = new VirtualTally from x",
"y' = new VirtualTally from y",
"z' = y' - x'",
"z' + x'",
"z' + y'",
},
}
document {
Key => (symbol -, VirtualTally),
Headline => "negation of a virtual tally",
TT "-x", " -- the negation of ", TT "x",
PARA{},
EXAMPLE {
"x = tally {a,b,b,c,c,d,d,d}",
"x' = new VirtualTally from x",
"- x'",
},
}
document {
Key => (symbol +, Tally, Tally),
Headline => "union of tallies",
TT "x + y", " -- produces the union of two tallies.",
PARA{},
"One of the arguments may be a ", TO "Set", ".",
PARA{},
EXAMPLE {
"x = tally {a,a,a,b,b,c}",
"y = tally {b,c,c,d,d,d}",
"x + y",
},
SeeAlso => {"Tally", "tally"}
}
document {
Key => (symbol -, Tally, Tally),
Headline => "difference of tallies",
Usage => "x - y",
Inputs => { "x", "y" },
Outputs => { { "the difference of the two tallies" } },
"The count associated to an item ", TT "i", " in the result is the difference of the counts in
", TT "x", " and in ", TT "y", " if it's positive, otherwise, zero.",
EXAMPLE "tally {a,a,b,c} - tally {c,d,d}",
SeeAlso => "Tally"
}
document {
Key => (symbol ^**, VirtualTally, ZZ),
Headline => "Cartesian power of sets and tallies",
Usage => "B = A^**n",
Inputs => { "A", "n" },
Outputs => {"B" => { "the tally of ", TT "n", "-tuples of elements from ", TT "A" }},
"If ", TT "A", " is ", ofClass Set, ", then so is ", TT "B", ".",
EXAMPLE lines ///
A = set {1,2}
A^**3
A = tally {1,1,2}
A^**3
///,
SeeAlso => {Set, (symbol**,Set,Set)}
}
document {
Key => (symbol _, VirtualTally, Thing),
Headline => "get a count from a tally",
Usage => "t_x",
Inputs => {
"t","x"
},
Outputs => {
ZZ => {"the number of times ", TT "x", " is counted by ", TT "t"}
},
EXAMPLE lines ///
t = tally apply(1..10000, i -> # factor i)
t_5
t_6
///,
SeeAlso => {Tally}
}
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