# Tables#

Display a rectangular array as a table, either in plain text, LaTeX, or html. See the documentation for table for details and examples.

AUTHORS:

• John H. Palmieri (2012-11)

Bases: SageObject

Display a rectangular array as a table, either in plain text, LaTeX, or html.

INPUT:

• rows (default None) – a list of lists (or list of tuples, etc.), containing the data to be displayed.

• columns (default None) – a list of lists (etc.), containing the data to be displayed, but stored as columns. Set either rows or columns, but not both.

• header_row (default False) – if True, first row is highlighted.

• header_column (default False) – if True, first column is highlighted.

• frame (default False) – if True, put a box around each cell.

• align (default ‘left’) – the alignment of each entry: either ‘left’, ‘center’, or ‘right’

EXAMPLES:

sage: rows = [['a', 'b', 'c'], [100,2,3], [4,5,60]]
sage: table(rows)
a     b   c
100   2   3
4     5   60
sage: latex(table(rows))
\begin{tabular}{lll}
a & b & c \\
$100$ & $2$ & $3$ \\
$4$ & $5$ & $60$ \\
\end{tabular}

>>> from sage.all import *
>>> rows = [['a', 'b', 'c'], [Integer(100),Integer(2),Integer(3)], [Integer(4),Integer(5),Integer(60)]]
>>> table(rows)
a     b   c
100   2   3
4     5   60
>>> latex(table(rows))
\begin{tabular}{lll}
a & b & c \\
$100$ & $2$ & $3$ \\
$4$ & $5$ & $60$ \\
\end{tabular}


If header_row is True, then the first row is highlighted. If header_column is True, then the first column is highlighted. If frame is True, then print a box around every “cell”.

sage: table(rows, header_row=True)
a     b   c
├─────┼───┼────┤
100   2   3
4     5   60
\begin{tabular}{lll}
a & b & c \\ \hline
$100$ & $2$ & $3$ \\
$4$ & $5$ & $60$ \\
\end{tabular}
sage: table(rows=rows, frame=True)
┌─────┬───┬────┐
│ a   | b | c  |
├─────┼───┼────┤
│ 100 | 2 | 3  |
├─────┼───┼────┤
│ 4   | 5 | 60 |
└─────┴───┴────┘
sage: latex(table(rows=rows, frame=True))
\begin{tabular}{|l|l|l|} \hline
a & b & c \\ \hline
$100$ & $2$ & $3$ \\ \hline
$4$ & $5$ & $60$ \\ \hline
\end{tabular}
┌─────╥───┬────┐
│ a   ║ b | c  |
├─────╫───┼────┤
│ 100 ║ 2 | 3  |
├─────╫───┼────┤
│ 4   ║ 5 | 60 |
└─────╨───┴────┘
\begin{tabular}{|l|l|l|} \hline
a & b & c \\ \hline \hline
$100$ & $2$ & $3$ \\ \hline
$4$ & $5$ & $60$ \\ \hline
\end{tabular}
a   │ b   c
100 │ 2   3
4   │ 5   60

>>> from sage.all import *
a     b   c
├─────┼───┼────┤
100   2   3
4     5   60
\begin{tabular}{lll}
a & b & c \\ \hline
$100$ & $2$ & $3$ \\
$4$ & $5$ & $60$ \\
\end{tabular}
>>> table(rows=rows, frame=True)
┌─────┬───┬────┐
│ a   | b | c  |
├─────┼───┼────┤
│ 100 | 2 | 3  |
├─────┼───┼────┤
│ 4   | 5 | 60 |
└─────┴───┴────┘
>>> latex(table(rows=rows, frame=True))
\begin{tabular}{|l|l|l|} \hline
a & b & c \\ \hline
$100$ & $2$ & $3$ \\ \hline
$4$ & $5$ & $60$ \\ \hline
\end{tabular}
┌─────╥───┬────┐
│ a   ║ b | c  |
├─────╫───┼────┤
│ 100 ║ 2 | 3  |
├─────╫───┼────┤
│ 4   ║ 5 | 60 |
└─────╨───┴────┘
\begin{tabular}{|l|l|l|} \hline
a & b & c \\ \hline \hline
$100$ & $2$ & $3$ \\ \hline
$4$ & $5$ & $60$ \\ \hline
\end{tabular}
a   │ b   c
100 │ 2   3
4   │ 5   60


The argument header_row can, instead of being True or False, be the contents of the header row, so that rows consists of the data, while header_row is the header information. The same goes for header_column. Passing lists for both arguments simultaneously is not supported.

sage: table([(x,n(sin(x), digits=2)) for x in [0..3]],                          # needs sage.symbolic
....:       header_row=["$x$", r"$\sin(x)$"], frame=True)
┌─────┬───────────┐
│ $x$ | $\sin(x)$ |
╞═════╪═══════════╡
│ 0   | 0.00      |
├─────┼───────────┤
│ 1   | 0.84      |
├─────┼───────────┤
│ 2   | 0.91      |
├─────┼───────────┤
│ 3   | 0.14      |
└─────┴───────────┘

>>> from sage.all import *
>>> table([(x,n(sin(x), digits=Integer(2))) for x in (ellipsis_range(Integer(0),Ellipsis,Integer(3)))],                          # needs sage.symbolic
...       header_row=["$x$", r"$\sin(x)$"], frame=True)
┌─────┬───────────┐
│ $x$ | $\sin(x)$ |
╞═════╪═══════════╡
│ 0   | 0.00      |
├─────┼───────────┤
│ 1   | 0.84      |
├─────┼───────────┤
│ 2   | 0.91      |
├─────┼───────────┤
│ 3   | 0.14      |
└─────┴───────────┘


You can create the transpose of this table in several ways, for example, “by hand,” that is, changing the data defining the table:

sage: table(rows=[[x for x in [0..3]],                                          # needs sage.symbolic
....:             [n(sin(x), digits=2) for x in [0..3]]],
....:       header_column=['$x$', r'$\sin(x)$'], frame=True)
┌───────────╥──────┬──────┬──────┬──────┐
│ $x$       ║ 0    | 1    | 2    | 3    |
├───────────╫──────┼──────┼──────┼──────┤
│ $\sin(x)$ ║ 0.00 | 0.84 | 0.91 | 0.14 |
└───────────╨──────┴──────┴──────┴──────┘

>>> from sage.all import *
>>> table(rows=[[x for x in (ellipsis_range(Integer(0),Ellipsis,Integer(3)))],                                          # needs sage.symbolic
...             [n(sin(x), digits=Integer(2)) for x in (ellipsis_range(Integer(0),Ellipsis,Integer(3)))]],
...       header_column=['$x$', r'$\sin(x)$'], frame=True)
┌───────────╥──────┬──────┬──────┬──────┐
│ $x$       ║ 0    | 1    | 2    | 3    |
├───────────╫──────┼──────┼──────┼──────┤
│ $\sin(x)$ ║ 0.00 | 0.84 | 0.91 | 0.14 |
└───────────╨──────┴──────┴──────┴──────┘


or by passing the original data as the columns of the table and using header_column instead of header_row:

sage: table(columns=[(x, n(sin(x), digits=2)) for x in [0..3]],                 # needs sage.symbolic
....:       header_column=['$x$', r'$\sin(x)$'], frame=True)
┌───────────╥──────┬──────┬──────┬──────┐
│ $x$       ║ 0    | 1    | 2    | 3    |
├───────────╫──────┼──────┼──────┼──────┤
│ $\sin(x)$ ║ 0.00 | 0.84 | 0.91 | 0.14 |
└───────────╨──────┴──────┴──────┴──────┘

>>> from sage.all import *
>>> table(columns=[(x, n(sin(x), digits=Integer(2))) for x in (ellipsis_range(Integer(0),Ellipsis,Integer(3)))],                 # needs sage.symbolic
...       header_column=['$x$', r'$\sin(x)$'], frame=True)
┌───────────╥──────┬──────┬──────┬──────┐
│ $x$       ║ 0    | 1    | 2    | 3    |
├───────────╫──────┼──────┼──────┼──────┤
│ $\sin(x)$ ║ 0.00 | 0.84 | 0.91 | 0.14 |
└───────────╨──────┴──────┴──────┴──────┘


or by taking the transpose() of the original table:

sage: table(rows=[(x, n(sin(x), digits=2)) for x in [0..3]],                    # needs sage.symbolic
....:       header_row=['$x$', r'$\sin(x)$'], frame=True).transpose()
┌───────────╥──────┬──────┬──────┬──────┐
│ $x$       ║ 0    | 1    | 2    | 3    |
├───────────╫──────┼──────┼──────┼──────┤
│ $\sin(x)$ ║ 0.00 | 0.84 | 0.91 | 0.14 |
└───────────╨──────┴──────┴──────┴──────┘

>>> from sage.all import *
>>> table(rows=[(x, n(sin(x), digits=Integer(2))) for x in (ellipsis_range(Integer(0),Ellipsis,Integer(3)))],                    # needs sage.symbolic
...       header_row=['$x$', r'$\sin(x)$'], frame=True).transpose()
┌───────────╥──────┬──────┬──────┬──────┐
│ $x$       ║ 0    | 1    | 2    | 3    |
├───────────╫──────┼──────┼──────┼──────┤
│ $\sin(x)$ ║ 0.00 | 0.84 | 0.91 | 0.14 |
└───────────╨──────┴──────┴──────┴──────┘


In either plain text or LaTeX, entries in tables can be aligned to the left (default), center, or right:

sage: table(rows, align='left')
a     b   c
100   2   3
4     5   60
sage: table(rows, align='center')
a    b   c
100   2   3
4    5   60
sage: table(rows, align='right', frame=True)
┌─────┬───┬────┐
│   a | b |  c |
├─────┼───┼────┤
│ 100 | 2 |  3 |
├─────┼───┼────┤
│   4 | 5 | 60 |
└─────┴───┴────┘

>>> from sage.all import *
>>> table(rows, align='left')
a     b   c
100   2   3
4     5   60
>>> table(rows, align='center')
a    b   c
100   2   3
4    5   60
>>> table(rows, align='right', frame=True)
┌─────┬───┬────┐
│   a | b |  c |
├─────┼───┼────┤
│ 100 | 2 |  3 |
├─────┼───┼────┤
│   4 | 5 | 60 |
└─────┴───┴────┘


To generate HTML you should use html(table(...)):

sage: # needs sage.symbolic
sage: data = [["$x$", r"$\sin(x)$"]] + [(x, n(sin(x), digits=2))
....:                                   for x in [0..3]]
sage: output = html(table(data, header_row=True, frame=True))
sage: type(output)
<class 'sage.misc.html.HtmlFragment'>
sage: print(output)
<div class="notruncate">
<table border="1" class="table_form">
<tbody>
<tr>
<th style="text-align:left">$$x$$</th>
<th style="text-align:left">$$\sin(x)$$</th>
</tr>
<tr class ="row-a">
<td style="text-align:left">$$0$$</td>
<td style="text-align:left">$$0.00$$</td>
</tr>
<tr class ="row-b">
<td style="text-align:left">$$1$$</td>
<td style="text-align:left">$$0.84$$</td>
</tr>
<tr class ="row-a">
<td style="text-align:left">$$2$$</td>
<td style="text-align:left">$$0.91$$</td>
</tr>
<tr class ="row-b">
<td style="text-align:left">$$3$$</td>
<td style="text-align:left">$$0.14$$</td>
</tr>
</tbody>
</table>
</div>

>>> from sage.all import *
>>> # needs sage.symbolic
>>> data = [["$x$", r"$\sin(x)$"]] + [(x, n(sin(x), digits=Integer(2)))
...                                   for x in (ellipsis_range(Integer(0),Ellipsis,Integer(3)))]
>>> output = html(table(data, header_row=True, frame=True))
>>> type(output)
<class 'sage.misc.html.HtmlFragment'>
>>> print(output)
<div class="notruncate">
<table border="1" class="table_form">
<tbody>
<tr>
<th style="text-align:left">$$x$$</th>
<th style="text-align:left">$$\sin(x)$$</th>
</tr>
<tr class ="row-a">
<td style="text-align:left">$$0$$</td>
<td style="text-align:left">$$0.00$$</td>
</tr>
<tr class ="row-b">
<td style="text-align:left">$$1$$</td>
<td style="text-align:left">$$0.84$$</td>
</tr>
<tr class ="row-a">
<td style="text-align:left">$$2$$</td>
<td style="text-align:left">$$0.91$$</td>
</tr>
<tr class ="row-b">
<td style="text-align:left">$$3$$</td>
<td style="text-align:left">$$0.14$$</td>
</tr>
</tbody>
</table>
</div>


It is an error to specify both rows and columns:

sage: table(rows=[[1,2,3], [4,5,6]], columns=[[0,0,0], [0,0,1024]])
Traceback (most recent call last):
...
ValueError: do not set both 'rows' and 'columns' when defining a table

sage: table(columns=[[0,0,0], [0,0,1024]])
0 0
0 0
0 1024

>>> from sage.all import *
>>> table(rows=[[Integer(1),Integer(2),Integer(3)], [Integer(4),Integer(5),Integer(6)]], columns=[[Integer(0),Integer(0),Integer(0)], [Integer(0),Integer(0),Integer(1024)]])
Traceback (most recent call last):
...
ValueError: do not set both 'rows' and 'columns' when defining a table

>>> table(columns=[[Integer(0),Integer(0),Integer(0)], [Integer(0),Integer(0),Integer(1024)]])
0 0
0 0
0 1024


Note that if rows is just a list or tuple, not nested, then it is treated as a single row:

sage: table([1,2,3])
1   2   3

>>> from sage.all import *
>>> table([Integer(1),Integer(2),Integer(3)])
1   2   3


Also, if you pass a non-rectangular array, the longer rows or columns get truncated:

sage: table([[1,2,3,7,12], [4,5]])
1   2
4   5
sage: table(columns=[[1,2,3], [4,5,6,7]])
1   4
2   5
3   6

>>> from sage.all import *
>>> table([[Integer(1),Integer(2),Integer(3),Integer(7),Integer(12)], [Integer(4),Integer(5)]])
1   2
4   5
>>> table(columns=[[Integer(1),Integer(2),Integer(3)], [Integer(4),Integer(5),Integer(6),Integer(7)]])
1   4
2   5
3   6

_rich_repr_(display_manager, **kwds)[source]#

Rich Output Magic Method

See sage.repl.rich_output for details.

EXAMPLES:

sage: from sage.repl.rich_output import get_display_manager
sage: dm = get_display_manager()
sage: t = table([1, 2, 3])
sage: t._rich_repr_(dm)    # the doctest backend does not support html

>>> from sage.all import *
>>> from sage.repl.rich_output import get_display_manager
>>> dm = get_display_manager()
>>> t = table([Integer(1), Integer(2), Integer(3)])
>>> t._rich_repr_(dm)    # the doctest backend does not support html

options(**kwds)[source]#

With no arguments, return the dictionary of options for this table. With arguments, modify options.

INPUT:

• header_row – if True, first row is highlighted.

• header_column – if True, first column is highlighted.

• frame – if True, put a box around each cell.

• align – the alignment of each entry: either ‘left’, ‘center’, or ‘right’

EXAMPLES:

sage: T = table([['a', 'b', 'c'], [1,2,3]])
sage: T.options()['align'], T.options()['frame']
('left', False)
sage: T.options(align='right', frame=True)
sage: T.options()['align'], T.options()['frame']
('right', True)

>>> from sage.all import *
>>> T = table([['a', 'b', 'c'], [Integer(1),Integer(2),Integer(3)]])
>>> T.options()['align'], T.options()['frame']
('left', False)
>>> T.options(align='right', frame=True)
>>> T.options()['align'], T.options()['frame']
('right', True)


Note that when first initializing a table, header_row or header_column can be a list. In this case, during the initialization process, the header is merged with the rest of the data, so changing the header option later using table.options(...) doesn’t affect the contents of the table, just whether the row or column is highlighted. When using this options() method, no merging of data occurs, so here header_row and header_column should just be True or False, not a list.

sage: T = table([[1,2,3], [4,5,6]], header_row=['a', 'b', 'c'], frame=True)
sage: T
┌───┬───┬───┐
│ a | b | c |
╞═══╪═══╪═══╡
│ 1 | 2 | 3 |
├───┼───┼───┤
│ 4 | 5 | 6 |
└───┴───┴───┘
sage: T
┌───┬───┬───┐
│ a | b | c |
├───┼───┼───┤
│ 1 | 2 | 3 |
├───┼───┼───┤
│ 4 | 5 | 6 |
└───┴───┴───┘

>>> from sage.all import *
>>> T = table([[Integer(1),Integer(2),Integer(3)], [Integer(4),Integer(5),Integer(6)]], header_row=['a', 'b', 'c'], frame=True)
>>> T
┌───┬───┬───┐
│ a | b | c |
╞═══╪═══╪═══╡
│ 1 | 2 | 3 |
├───┼───┼───┤
│ 4 | 5 | 6 |
└───┴───┴───┘
>>> T
┌───┬───┬───┐
│ a | b | c |
├───┼───┼───┤
│ 1 | 2 | 3 |
├───┼───┼───┤
│ 4 | 5 | 6 |
└───┴───┴───┘


If you do specify a list for header_row, an error is raised:

sage: T.options(header_row=['x', 'y', 'z'])
Traceback (most recent call last):
...
TypeError: header_row should be either True or False.

>>> from sage.all import *
Traceback (most recent call last):
...
TypeError: header_row should be either True or False.

transpose()[source]#

Return a table which is the transpose of this one: rows and columns have been interchanged. Several of the properties of the original table are preserved: whether a frame is present and any alignment setting. On the other hand, header rows are converted to header columns, and vice versa.

EXAMPLES:

sage: T = table([[1,2,3], [4,5,6]])
sage: T.transpose()
1   4
2   5
3   6
sage: T = table([[1,2,3], [4,5,6]], header_row=['x', 'y', 'z'], frame=True)
sage: T.transpose()
┌───╥───┬───┐
│ x ║ 1 | 4 |
├───╫───┼───┤
│ y ║ 2 | 5 |
├───╫───┼───┤
│ z ║ 3 | 6 |
└───╨───┴───┘

>>> from sage.all import *
>>> T = table([[Integer(1),Integer(2),Integer(3)], [Integer(4),Integer(5),Integer(6)]])
>>> T.transpose()
1   4
2   5
3   6
>>> T = table([[Integer(1),Integer(2),Integer(3)], [Integer(4),Integer(5),Integer(6)]], header_row=['x', 'y', 'z'], frame=True)
>>> T.transpose()
┌───╥───┬───┐
│ x ║ 1 | 4 |
├───╫───┼───┤
│ y ║ 2 | 5 |
├───╫───┼───┤
│ z ║ 3 | 6 |
└───╨───┴───┘