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doc///
Key
table
Headline
make a table from a binary function
Usage
table(a, b, f)
table(m, n, f)
Inputs
a:List
b:List
m:ZZ
n:ZZ
f:
a function {\tt f(i,j)} of two variables
Outputs
T:
a table, or list of lists, where $T_{ij}$ is the value
of $f(a_i, b_j)$, OR, if using integer arguments $m$ and $n$,
$T_{ij}=f(i,j)$ for $0\le i < m, 0\le j < n$
Description
Text
The command {\tt table(m, n, f)} is equivalent to
{\tt table(0..(m-1), 0..(n-1), f)}.
Example
t1 = table({1,3,5,7}, {0,1,2,4}, (i,j) -> i^j)
t2 = table(5, 5, (i,j) -> i+j)
Text
Tables can be displayed nicely using @TO netList@.
Example
netList t1
SeeAlso
applyTable
isTable
subtable
"lists and sequences"
///
doc///
Key
applyTable
Headline
apply a function to each element of a table
Usage
applyTable(T, f)
Inputs
T:List
a table (list of lists of the same length)
f:Function
Outputs
A:List
a table of the same shape as $T$, where the function
$f$ has been applied elementwise
Description
Example
t = table({1,3,5,7}, {0,1,2,4}, (i,j) -> i^j);
netList t
netList applyTable(t, i -> 2*i)
netList applyTable(t, isPrime)
SeeAlso
isTable
subtable
table
"lists and sequences"
///
doc ///
Key
subtable
Headline
extract a subtable from a table
Usage
subtable(a, b, T)
Inputs
a:List
of rows to extract
b:List
of columns to extract
Outputs
S:
the subtable of $T$ defined by restricting to rows in the list $a$
and columns in the list $b$
Description
Example
t = table({1,3,5,7}, {0,1,2,4}, (i,j) -> i^j);
netList t
s1 = subtable({0,2}, {1,3}, t);
netList s1
s2 = subtable(toList(0..3), {1}, t);
netList s2
SeeAlso
applyTable
isTable
positions
table
select
"lists and sequences"
///
doc///
Key
isTable
Headline
whether something is a list of lists of equal length
Usage
isTable t
Inputs
t:Thing
Outputs
b:Boolean
whether or not $t$ is a table
Description
Example
isTable {{1,2,3},{4,5,6}}
isTable {{1,2,3},{4,5}}
Caveat
It is intrinsically impossible to represent a $0\times k$ matrix
as a list of lists.
SeeAlso
applyTable
table
subtable
"lists and sequences"
///
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