Interact Functions in the Notebook¶

This module implements an interact() function decorator for the Sage notebook.

AUTHORS:

William Stein (2008-03-02): version 1.0 at Sage/Enthought Days 8 in Texas
Jason Grout (2008-03): discussion and first few prototypes
Jason Grout (2008-05): input_grid control

class sagenb.notebook.interact.ColorInput(var, default_value, label=None, type=None, width=80, **kwargs)¶

Bases: sagenb.notebook.interact.InputBox

render()¶

Render this color input box to HTML.

OUTPUT:

a string - HTML format

EXAMPLES:

sage: sagenb.notebook.interact.ColorInput('c', Color('red')).render()
'...<table>...'

value_js(n)¶

Return JavaScript that evaluates to value of this control. If n is 0, return code for evaluation by the actual color control. If n is 1, return code for the text area that displays the current color.

INPUT:

n - integer, either 0 or 1.

OUTPUT:

a string

EXAMPLES:

sage: C = sagenb.notebook.interact.ColorInput('c', Color('red'))
sage: C.value_js(0)
'color'
sage: C.value_js(1)
'this.value'

class sagenb.notebook.interact.InputBox(var, default_value, label=None, type=None, width=80, **kwargs)¶

Bases: sagenb.notebook.interact.InteractControl

render()¶

Render this control as a string.

OUTPUT:

a string - HTML format

EXAMPLES:

sage: sagenb.notebook.interact.InputBox('theta', 1).render()
'<input type="text" value="1" size=80 onchange="interact(0, '_interact_.update(\'0\', \'theta\', ..., _interact_.standard_b64decode(\''+encode64(this.value)+'\'), globals()); _interact_.recompute(\'0\');')"></input>'

value_js()¶

Return JavaScript string that will give the value of this control element.

OUTPUT:

a string - JavaScript

EXAMPLES:

sage: sagenb.notebook.interact.InputBox('theta', 1).value_js()
'this.value'

class sagenb.notebook.interact.InputGrid(var, rows, columns, default_value=None, label=None, to_value=<function <lambda> at 0x37fd5f0>, width=4)¶

Bases: sagenb.notebook.interact.InteractControl

render()¶

Render this control as a string.

OUTPUT:

string - HTML format

EXAMPLES:

sage: sagenb.notebook.interact.InputGrid('M', 1,2).render()
'<table><tr><td><input type="text" value="None" ...'

value_js()¶

Return JavaScript string that will give the value of this control element.

OUTPUT:

string - JavaScript

EXAMPLES:

sage: sagenb.notebook.interact.InputGrid('M', 2,2).value_js()
" '[['+jQuery(this).parents('table').eq(0).find('tr').map(function(){return jQuery(this).find('input').map(function() {return jQuery(this).val();}).get().join(',');}).get().join('],[')+']]' "

class sagenb.notebook.interact.InteractCanvas(controls, id, layout=None, width=None, **options)¶

cell_id()¶

Returns the ID of the cell that contains this interactive canvas.

OUTPUT:

an integer or a string

EXAMPLES:

sage: B = sagenb.notebook.interact.InputBox('x',2)
sage: sagenb.notebook.interact.InteractCanvas([B], 3).cell_id()
3

controls()¶

Return a list of controls in this canvas.

OUTPUT:

list of controls

Note

Returns a reference to a mutable list.

EXAMPLES:

sage: B = sagenb.notebook.interact.InputBox('x',2)
sage: sagenb.notebook.interact.InteractCanvas([B], 3).controls()
[An InputBox interactive control with x=2 and label 'x']

is_auto_update()¶

Returns True if any change of the values for the controls on this canvas should cause an update. If $auto_update=False$ was not specified in the constructor for this canvas, then this will default to True.

OUTPUT:

a bool

EXAMPLES:

sage: B = sagenb.notebook.interact.InputBox('x',2)
sage: canvas = sagenb.notebook.interact.InteractCanvas([B], 3)
sage: canvas.is_auto_update()
True
sage: canvas = sagenb.notebook.interact.InteractCanvas([B], 3, auto_update=False)
sage: canvas.is_auto_update()
False            

render()¶

Render in text (HTML) the entire interact() canvas.

OUTPUT:

string - HTML format

EXAMPLES:

sage: B = sagenb.notebook.interact.InputBox('x',2)
sage: sagenb.notebook.interact.InteractCanvas([B], 3).render()
'<!--notruncate--><div padding=6 id="div-interact-3"> ...</div>...'

render_controls(side='top')¶

Render in text (HTML) form all the input controls.

OUTPUT:

a string - HTML format

EXAMPLES:

sage: B = sagenb.notebook.interact.InputBox('x',2)
sage: sagenb.notebook.interact.InteractCanvas([B], 3).render_controls()
'<table>...'

render_output()¶

Render in text (HTML) form the output portion of the interact() canvas.

The output contains two special tags, <?TEXT> and <?HTML>, which get replaced at runtime by the text and HTML parts of the output of running the function.

OUTPUT:

a string - HTML format

EXAMPLES:

sage: B = sagenb.notebook.interact.InputBox('x',2)
sage: sagenb.notebook.interact.InteractCanvas([B], 3).render_output()
'<div id="cell-interact...</div>'

wrap_in_outside_frame(inside)¶

Return the entire HTML for the interactive canvas, obtained by wrapping all the inside HTML of the canvas in a div and a table.

INPUT:

inside - a string; HTML

OUTPUT:

a string - HTML format

EXAMPLES:

sage: B = sagenb.notebook.interact.InputBox('x',2)
sage: sagenb.notebook.interact.InteractCanvas([B], 3).wrap_in_outside_frame('<!--inside-->')
'<!--notruncate--><div padding=6 id="div-interact-3"> ...</div>...'

class sagenb.notebook.interact.InteractControl(var, default_value, label=None)¶

Bases: sagenb.notebook.interact.InteractElement

adapt_number()¶

Return integer index into adapt dictionary of function that is called to adapt the values of this control to Python.

OUTPUT:

an integer

EXAMPLES:

sage: from sagenb.notebook.interact import InteractControl
sage: InteractControl('x', 19/3).adapt_number()       # random -- depends on call order
2

cell_id()¶

Return the ID of the cell that contains this interact() control.

OUTPUT:

an integer or a string

EXAMPLES:

The output below should equal the ID of the current cell:

sage: sagenb.notebook.interact.InteractControl('theta', 1).cell_id()
0

default_value()¶

Return the default value of the variable corresponding to this interact() control.

OUTPUT:

an object

EXAMPLES:

sage: from sagenb.notebook.interact import InteractControl
sage: InteractControl('x', 19/3).default_value()
19/3

html_escaped_default_value()¶

Returns the HTML escaped default value of the variable corresponding to this interact() control. Note that any HTML that uses quotes around this should use double quotes and not single quotes.

OUTPUT:

a string

EXAMPLES:

sage: from sagenb.notebook.interact import InteractControl
sage: InteractControl('x', '"cool"').html_escaped_default_value()
'&quot;cool&quot;'
sage: InteractControl('x',"'cool'").html_escaped_default_value()
"'cool'"
sage: x = var('x')
sage: InteractControl('x', x^2).html_escaped_default_value()
'x^2'

interact(*args)¶

Return a string that when evaluated in JavaScript calls the JavaScript interact() function with appropriate inputs for this control.

This method will check to see if there is a canvas attached to this control and whether or not controls should automatically update the output when their values change. If no canvas is associated with this control, then the control will automatically update.

OUTPUT:

a string - that is meant to be evaluated in JavaScript

EXAMPLES:

sage: sagenb.notebook.interact.InteractControl('x', 1).interact()
"interact(..., '_interact_.update(..., \'x\', ..., _interact_.standard_b64decode(\''+encode64(NULL)+'\'), globals()); _interact_.recompute(\'0\');')"

label()¶

Return the text label of this interact() control.

OUTPUT:

a string

EXAMPLES:

sage: from sagenb.notebook.interact import InteractControl
sage: InteractControl('x', default_value=5, label='the x value').label()
'the x value'        

value_js()¶

JavaScript that when evaluated gives the current value of this control. This should be redefined in a derived class.

OUTPUT:

a string - defaults to ‘NULL’ - this should be redefined.

EXAMPLES:

sage: sagenb.notebook.interact.InteractControl('x', default_value=5).value_js()
'NULL'        

var()¶

Return the name of the variable that this control interacts.

OUTPUT:

a string - name of a variable as a string.

EXAMPLES:

sage: sagenb.notebook.interact.InteractControl('theta', 1).var()
'theta'        

class sagenb.notebook.interact.InteractElement¶

Bases: object

canvas()¶

Returns the InteractCanvas associated to this element. If no canvas has been set (via the set_canvas() method), then raise a ValueError.

EXAMPLES:

sage: from sagenb.notebook.interact import InputBox, InteractCanvas
sage: B = InputBox('x',2)
sage: canvas1 = InteractCanvas([B], 3)
sage: canvas2 = InteractCanvas([B], 3)
sage: B.canvas() is canvas2
True

label()¶

Returns an empty label for this element. This should be overridden for subclasses that need a label.

OUTPUT:

a string

EXAMPLES:

sage: from sagenb.notebook.interact import UpdateButton, InteractElement
sage: b = UpdateButton(1, 'autoupdate')
sage: isinstance(b, InteractElement)
True
sage: b.label()
''

set_canvas(canvas)¶

Sets the InteractCanvas on which this element appears. This method is primarily called in the constructor for InteractCanvas.

EXAMPLES:

sage: from sagenb.notebook.interact import InputBox, InteractCanvas
sage: B = InputBox('x',2)
sage: canvas1 = InteractCanvas([B], 3)
sage: canvas2 = InteractCanvas([B], 3)
sage: B.canvas() is canvas2
True
sage: B.set_canvas(canvas1)
sage: B.canvas() is canvas1
True

class sagenb.notebook.interact.JavascriptCodeButton(label, code)¶

Bases: sagenb.notebook.interact.InteractElement

render()¶

Returns the HTML to display this button.

OUTPUT:

a string - HTML format

EXAMPLES:

sage: b = sagenb.notebook.interact.JavascriptCodeButton('Push me', 'alert("2")')
sage: b.render()
'<input type="button" value="Push me" onclick="alert("2")">\n'

class sagenb.notebook.interact.RangeSlider(var, values, default_position, label=None, display_value=True)¶

Bases: sagenb.notebook.interact.SliderGeneric

default_position()¶

Return the default position (as an integer) of the slider.

OUTPUT:

an integer 2-tuple

EXAMPLES:

sage: sagenb.notebook.interact.RangeSlider('x', [1..5], (2,3), 'alpha').default_position()
(2, 3)

render()¶

Render this control as an HTML string.

OUTPUT:

string - HTML format

EXAMPLES:

sage: sagenb.notebook.interact.RangeSlider('x', [1..5], (2,3), 'alpha').render()
'<table>...<div ...var values = ["1","2","3","4","5"];...'

sage: sagenb.notebook.interact.RangeSlider('x', [1..5], (2,3), 'alpha', display_value=False).render()
'<table>...<div ...var values = null;...'

value_js()¶

Return JavaScript string that will give the value of this control element.

OUTPUT:

a string - JavaScript

EXAMPLES:

sage: sagenb.notebook.interact.RangeSlider('x', [1..5], (2,3), 'alpha').value_js()
"pos[0]+' '+pos[1]"

class sagenb.notebook.interact.Selector(var, values, label=None, default=0, nrows=None, ncols=None, width=None, buttons=False)¶

Bases: sagenb.notebook.interact.InteractControl

render()¶

Render this control as a string.

OUTPUT:

a string - HTML format

EXAMPLES:

sage: sagenb.notebook.interact.Selector('x', [1..5]).render()
'<select...</select>'
sage: sagenb.notebook.interact.Selector('x', [1..5], buttons=True).render()
'<table...</table>'

use_buttons()¶

Whether or not to use buttons instead of a drop down menu for this select list.

OUTPUT:

a bool

EXAMPLES:

sage: sagenb.notebook.interact.Selector('x', [1..5]).use_buttons()
False
sage: sagenb.notebook.interact.Selector('x', [1..5], buttons=True).use_buttons()
True        

value_js()¶

Return JavaScript string that will give the value of this control element.

OUTPUT:

a string - JavaScript

EXAMPLES:

sage: sagenb.notebook.interact.Selector('x', [1..5]).value_js()
'this.options[this.selectedIndex].value'
sage: sagenb.notebook.interact.Selector('x', [1..5], buttons=True).value_js()
'this.value'        

class sagenb.notebook.interact.Slider(var, values, default_position, label=None, display_value=True)¶

Bases: sagenb.notebook.interact.SliderGeneric

default_position()¶

Return the default position (as an integer) of the slider.

OUTPUT:

an integer

EXAMPLES:

sage: sagenb.notebook.interact.Slider('x', [1..5], 2, 'alpha').default_position()
2

render()¶

Render this control as an HTML string.

OUTPUT:

a string - HTML format

EXAMPLES:

sage: sagenb.notebook.interact.Slider('x', [1..5], 2, 'alpha').render()
'<table>...<div ...var values = ["1","2","3","4","5"];...'

sage: sagenb.notebook.interact.Slider('x', [1..5], 2, 'alpha', display_value=False).render()
'<table>...<div ...var values = null;...'

value_js()¶

Return JavaScript string that will give the value of this control element.

OUTPUT:

a string - JavaScript

EXAMPLES:

sage: sagenb.notebook.interact.Slider('x', [1..5], 2, 'alpha').value_js()
'position'

class sagenb.notebook.interact.SliderGeneric(var, values, default_value, label=None, display_value=True)¶

Bases: sagenb.notebook.interact.InteractControl

display_value()¶

Returns whether to display the value on the slider.

OUTPUT:

a bool

EXAMPLES:

sagenb.notebook.interact.Slider('x', [1..5], 2, 'alpha').display_value()
True

values()¶

Return list of values the slider acts on.

OUTPUT:

a list

EXAMPLES:

sagenb.notebook.interact.Slider('x', [1..5], 2, 'alpha').values()
[1, 2, 3, 4, 5]

values_js()¶

Returns JavaScript array representation of values or ‘null’ if display_value=False

OUTPUT:

a string

EXAMPLES:

sage: sagenb.notebook.interact.Slider('x', [1..5], 2, 'alpha').values_js()
'["1","2","3","4","5"]'
sage: sagenb.notebook.interact.Slider('x', [1..5], 2, 'alpha', False).values_js()
'null'
sage: sagenb.notebook.interact.Slider('x', [pi..2*pi], 2, 'alpha').values_js()
'["pi","pi + 1","pi + 2","pi + 3"]'

class sagenb.notebook.interact.TextControl(var, data)¶

Bases: sagenb.notebook.interact.InteractControl

render()¶

Render this control as an HTML string.

OUTPUT:

a string - HTML format

EXAMPLES:

sage: sagenb.notebook.interact.TextControl('x', 'something').render()
'<div ...>something</div>'

class sagenb.notebook.interact.UpdateButton(cell_id, var)¶

Bases: sagenb.notebook.interact.JavascriptCodeButton

var()¶

Return the name of the variable that this control interacts.

OUTPUT:

a string - name of a variable as a string.

EXAMPLES:

sage: sagenb.notebook.interact.UpdateButton(1, 'auto_update').var()
'auto_update'

sagenb.notebook.interact.automatic_control(default)¶

Automagically determine the type of control from the default value of the variable.

INPUT:

default - the default value for v given by the function; see the documentation to interact() for details.

OUTPUT:

an interact() control

EXAMPLES:

sage: sagenb.notebook.interact.automatic_control('')
Interact input box labeled None with default value ''
sage: sagenb.notebook.interact.automatic_control(15)
Interact input box labeled None with default value 15
sage: sagenb.notebook.interact.automatic_control(('start', 15))
Interact input box labeled 'start' with default value 15
sage: sagenb.notebook.interact.automatic_control((1,250))
Slider: None [1.0--|1.0|---250.0]
sage: sagenb.notebook.interact.automatic_control(('alpha', (1,250)))
Slider: alpha [1.0--|1.0|---250.0]
sage: sagenb.notebook.interact.automatic_control((2,(0,250)))
Slider: None [0.0--|2.00400801603|---250.0]
sage: sagenb.notebook.interact.automatic_control(('alpha label', (2,(0,250))))
Slider: alpha label [0.0--|2.00400801603|---250.0]
sage: sagenb.notebook.interact.automatic_control((2, ('alpha label',(0,250))))
Slider: alpha label [0.0--|2.00400801603|---250.0]
sage: C = sagenb.notebook.interact.automatic_control((1,52, 5)); C
Slider: None [1--|1|---52]
sage: C.values()
[1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 52]
sage: sagenb.notebook.interact.automatic_control((17, (1,100,5)))
Slider: None [1--|16|---100]
sage: sagenb.notebook.interact.automatic_control([1..4])
Button bar with 4 buttons
sage: sagenb.notebook.interact.automatic_control([1..100])
Drop down menu with 100 options
sage: sagenb.notebook.interact.automatic_control((1..100))
Slider: None [1--|1|---100]
sage: sagenb.notebook.interact.automatic_control((5, (1..100)))
Slider: None [1--|5|---100]
sage: sagenb.notebook.interact.automatic_control(matrix(2,2))
Interact 2 x 2 input grid control labeled None with default value [0, 0, 0, 0]

class sagenb.notebook.interact.checkbox(default=True, label=None)¶: Bases: sagenb.notebook.interact.input_box

class sagenb.notebook.interact.color_selector(default=(0, 0, 1), label=None, widget='farbtastic', hide_box=False)¶

Bases: sagenb.notebook.interact.input_box

hide_box()¶

Return whether to hide the input box associated with this color selector.

OUTPUT:

a boolean

EXAMPLES:

sage: color_selector().hide_box()
False
sage: color_selector('green', hide_box=True, widget='jpicker').hide_box()
True
sage: color_selector((0.75,0.5,0.25)).hide_box()
False

widget()¶

Return the name of the HTML widget for this color selector.

OUTPUT:

a string; the widget’s name

EXAMPLES:

sage: color_selector().widget()
'farbtastic'
sage: color_selector('#abcdef', hide_box=True, widget='jpicker').widget()
'jpicker'
sage: color_selector(widget='colorpicker').widget()
'colorpicker'
sage: color_selector(default=Color(0,0.5,0.25)).widget()
'farbtastic'

class sagenb.notebook.interact.control(label=None)¶

label()¶

Return the label of this control.

OUTPUT:

a string

EXAMPLES:

sage: sagenb.notebook.interact.control('a control').label()
'a control'
sage: selector([1,2,7], 'alpha').label()
'alpha'

set_label(label)¶

Set the label of this control.

INPUT:

label - a string

EXAMPLES:

sage: C = sagenb.notebook.interact.control('a control')
sage: C.set_label('sage'); C
Interative control 'sage' (abstract base class)

sagenb.notebook.interact.html(s)¶

Print the input string s in a form that tells the notebook to display it in the HTML portion of the output. This function has no return value.

INPUT:

s - a string

EXAMPLES:

sage: sagenb.notebook.interact.html('hello')
<html>hello</html>    

sagenb.notebook.interact.html_color_selector(id, change, input_change, default='000000', widget='farbtastic', hide_box=False)¶

Return HTML representation of a jQuery color selector.

INPUT:

id - an integer or string; an identifier (e.g., cell ID) for this selector
change - a string; JavaScript code to execute when the color selector changes.
default - a string (default: '000000'); default color as a 6-character HTML hexadecimal string.
widget - a string (default: ‘farbtastic’); the color selector widget to use; other choices are ‘jpicker’ and ‘colorpicker’
hide_box - a boolean (default: False); whether to hide the input box associated with the color selector widget

OUTPUT:

a string - HTML that creates the slider.

EXAMPLES:

sage: sagenb.notebook.interact.html_color_selector(0, 'alert("changed")', '', default='0afcac')
'...<table>...farbtastic...'
sage: sagenb.notebook.interact.html_color_selector(99, 'console.log(color);', '', default='fedcba', widget='jpicker', hide_box=True)
'...<table>...jpicker...'

sagenb.notebook.interact.html_rangeslider(id, values, callback, steps, default_l=0, default_r=1, margin=0)¶

Return the HTML representation of a jQuery range slider.

INPUT:

id - a string; the DOM ID of the slider (better be unique)
values - a string; ‘null’ or JavaScript string containing array of values on slider
callback - a string; JavaScript that is executed whenever the slider is done moving
steps - an integer; number of steps from minimum to maximum value
default_l - an integer (default: 0); the default position of the left edge of the slider
default_r - an integer (default: 1); the default position of the right edge of the slider
margin - an integer (default: 0); size of margin to insert around the slider

OUTPUT:

a string - HTML format

EXAMPLES:

We create a jQuery range slider. If you do the following in the notebook you should obtain a slider that when moved pops up a window showing its current position:

sage: from sagenb.notebook.interact import html_rangeslider, html
sage: html(html_rangeslider('slider-007', 'null', 'alert(pos[0]+", "+pos[1])', steps=5, default_l=2, default_r=3, margin=5))
<html>...</html>

sagenb.notebook.interact.html_slider(id, values, callback, steps, default=0, margin=0)¶

Return the HTML representation of a jQuery slider.

INPUT:

id - a string; the DOM ID of the slider (better be unique)
values - a string; ‘null’ or JavaScript string containing array of values on slider
callback - a string; JavaScript that is executed whenever the slider is done moving
steps - an integer; number of steps from minimum to maximum value
default - an integer (default: 0); the default position of the slider
margin - an integer (default: 0); size of margin to insert around the slider

OUTPUT:

a string - HTML format

EXAMPLES:

We create a jQuery HTML slider. If you do the following in the notebook you should obtain a slider that when moved pops up a window showing its current position:

sage: from sagenb.notebook.interact import html_slider, html
sage: html(html_slider('slider-007', 'null', 'alert(position)', steps=5, default=2, margin=5))
<html>...</html>

class sagenb.notebook.interact.input_box(default=None, label=None, type=None, width=80, **kwargs)¶

Bases: sagenb.notebook.interact.control

default()¶

Return the default value of this input box.

OUTPUT:

an object

EXAMPLES:

sage: input_box('2+2', 'Expression').default()
'2+2'
sage: input_box(x^2 + 1, 'Expression').default()
x^2 + 1
sage: checkbox(True, "Points").default()
True

render(var)¶

Return rendering of this input box as an InputBox to be used for an interact() canvas. Basically this specializes this input to be used for a specific function and variable.

INPUT:

var - a string (variable; one of the variable names input to f)

OUTPUT:

an InputBox instance

EXAMPLES:

sage: input_box("2+2", 'Exp').render('x')
An InputBox interactive control with x='2+2' and label 'Exp'        

type()¶

Return the type that elements of this input box are coerced to or None if they are not coerced (they have whatever type they evaluate to).

OUTPUT:

a type

EXAMPLES:

sage: input_box("2+2", 'expression', type=int).type()
<type 'int'>
sage: input_box("2+2", 'expression').type() is None
True

class sagenb.notebook.interact.input_grid(nrows, ncols, default=None, label=None, to_value=<function <lambda> at 0x37ff398>, width=4)¶

Bases: sagenb.notebook.interact.control

default()¶

Return the default value of this input grid.

OUTPUT:

an object

EXAMPLES:

sage: input_grid(2,2, default=1).default()
1

render(var)¶

Return rendering of this input grid as an InputGrid to be used for an interact() canvas. Basically this specializes this input to be used for a specific function and variable.

INPUT:

var - a string (variable; one of the variable names input to f)

OUTPUT:

an InputGrid instance.

EXAMPLES:

sage: input_grid(2,2).render('x')
A 2 x 2 InputGrid interactive control with x=[[None, None], [None, None]] and label 'x'

sagenb.notebook.interact.interact(*args, **kwds)¶

Use interact as a decorator to create interactive Sage notebook cells with sliders, text boxes, radio buttons, check boxes, and color selectors. Simply put @interact on the line before a function definition in a cell by itself, and choose appropriate defaults for the variable names to determine the types of controls (see tables below).

INPUT:

f - a Python function
layout (optional) - a dictionary with keys ‘top’, ‘bottom’, ‘left’, ‘right’ and values lists of rows of control variable names. Controls are laid out according to this pattern. If layout is not a dictionary, it is assumed to be the ‘top’ value. If layout is None, then all controls are assigned separate rows in the top value.

EXAMPLES:

In each example below we use a single underscore for the function name. You can use any name you want; it does not have to be an underscore.

We create an interact control with two inputs, a text input for the variable a and a y slider that runs through the range of integers from $0$ to $19$ .

sage: @interact
... def _(a=5, y=(0..20)): print a + y
...
<html>...

sage: @interact(layout=[['a','b'],['d']])
... def _(a=x^2, b=(0..20), c=100, d=x+1): print a+b+c+d
...
<html>...

sage: @interact(layout={'top': [['a', 'b']], 'left': [['c']], 'bottom': [['d']]})
... def _(a=x^2, b=(0..20), c=100, d=x+1): print a+b+c+d
...
<html>...

Draw a plot interacting with the “continuous” variable a. By default continuous variables have exactly 50 possibilities.

sage: @interact
... def _(a=(0,2)):
...     show(plot(sin(x*(1+a*x)), (x,0,6)), figsize=4)
<html>...

Interact a variable in steps of 1 (we also use an unnamed function):

sage: @interact
... def _(n=(10,100,1)):
...     show(factor(x^n - 1))
<html>...

Interact two variables:

sage: @interact
... def _(a=(1,4), b=(0,10)):
...     show(plot(sin(a*x+b), (x,0,6)), figsize=3)
<html>...

Place a block of text among the controls:

sage: @interact
... def _(t1=text_control("Factors an integer."), n="1"):
...     print factor(Integer(n))   
<html>...

You do not have to use interact as a decorators; you can also simply write interact(f) where f is any Python function that you have defined, though this is frowned upon. E.g., f can also be a library function as long as it is written in Python:

sage: interact(matrix)   # put ZZ, 2,2,[1..4] in boxes...
<html>...

If your the time to evaluate your function takes awhile, you may not want to have it reevaluated every time the inputs change. In order to prevent this, you can add a keyword auto_update=False to your function to prevent it from updating whenever the values are changed. This will cause a button labeled ‘Update’ to appear which you can click on to re-evaluate your function.

sage: @interact
... def _(n=(10,100,1), auto_update=False):
...     show(factor(x^n - 1))
<html>...

DEFAULTS:

Defaults for the variables of the input function determine interactive controls. The standard controls are input_box, slider, range_slider, checkbox, selector, input_grid, and color_selector. There is also a text control (see the defaults below).

u = input_box(default=None, label=None, type=None) - input box with given default; use type=str to get input as an arbitrary string
u = slider(vmin, vmax=None, step_size=1, default=None, label=None) - slider with given list of possible values; vmin can be a list
u = range_slider(vmin, vmax=None, step_size=1, default=None, label=None) - range slider with given list of possible values; vmin can be a list
u = checkbox(default=True, label=None) - a checkbox
u = selector(values, label=None, nrows=None, ncols=None, buttons=False) - a dropdown menu or buttons (get buttons if nrows, ncols, or buttons is set, otherwise a dropdown menu)
u = input_grid(nrows, ncols, default=None, label=None, to_value=lambda x:x, width=4) - an editable grid of objects (a matrix or array)
u = color_selector(default=(0,0,1), label=None, widget='farbtastic', hide_box=False) - a color selector with a possibly hidden input box; the widget can also be 'jpicker' or 'colorpicker'
u = text_control(value='') - a block of text

You can also create a color selector by setting the default value for an input_box to Color(...).

There are also some convenient defaults that allow you to make controls automatically without having to explicitly specify them. E.g., you can make x a continuous slider of values between u and v by just writing x=(u,v) in the argument list of your function. These are all just convenient shortcuts for creating the controls listed above.

u - blank input_box field
u = element - input_box with default=element, if element not below.
u = (umin,umax) - continuous slider (really $100$ steps)
u = (umin,umax,du) - slider with step size du
u = list - buttons if len(list) at most $5$ ; otherwise, drop down
u = generator - a slider (up to $10000$ steps)
u = bool - a checkbox
u = Color('blue') - a color selector; returns Color object
u = (default, v) - v as above, with given default value
u = (label, v) - v as above, with given label (a string)
u = matrix - an input_grid with to_value set to matrix.parent() and default values given by the matrix

Note

Suppose you would like to make an interactive with a default RGB color of (1,0,0), so the function would have signature f(color=(1,0,0)). Unfortunately, the above shortcuts reinterpret the (1,0,0) as a discrete slider with step size 0 between 1 and 0. Instead you should do the following:

sage: @interact
... def _(v = input_box((1,0,0))):
...       show(plot(sin,color=v))
<html>...

An alternative:

sage: @interact
... def _(c = color_selector((1, 0, 0))):
...       show(plot(sin, color = c))
<html>...

MORE EXAMPLES:

We give an input box that allows one to enter completely arbitrary strings:

sage: @interact
... def _(a=input_box('sage', label="Enter your name", type=str)):
...        print "Hello there %s"%a.capitalize()
<html>...

The scope of variables that you control via interact() are local to the scope of the function being interacted with. However, by using the global Python keyword, you can still modify global variables as follows:

sage: xyz = 10
sage: @interact
... def _(a=('xyz',5)):
...       global xyz
...       xyz = a
<html>...

If you enter the above you obtain an interact() canvas. Entering values in the box changes the global variable xyz. Here’s a example with several controls:

sage: @interact
... def _(title=["A Plot Demo", "Something silly", "something tricky"], a=input_box(sin(x*sin(x*sin(x))), 'function'),
...     clr = Color('red'), thickness=[1..30], zoom=(1,0.95,..,0.1), plot_points=(200..2000)):
...     html('<h1 align=center>%s</h1>'%title)
...     print plot_points
...     show(plot(a, -zoom*pi,zoom*pi, color=clr, thickness=thickness, plot_points=plot_points))
<html>...

For a more compact color control, use an empty label, a different widget ('colorpicker' or 'jpicker'), and hide the input box:

sage: @interact
... def _(color=color_selector((1,0,1), label='', widget='colorpicker', hide_box=True)):
...     show(plot(x/(8/7+sin(x)), (x,-50,50), fill=True, fillcolor=color))
<html>...

We give defaults and name the variables:

sage: @interact
... def _(a=('first', (1,4)), b=(0,10)):
...       show(plot(sin(a*x+sin(b*x)), (x,0,6)), figsize=3)
<html>...

Another example involving labels, defaults, and the slider command:

sage: @interact
... def _(a = slider(1, 4, default=2, label='Multiplier'),
...       b = slider(0, 10, default=0, label='Phase Variable')):
...     show(plot(sin(a*x+b), (x,0,6)), figsize=4)
<html>...

An example where the range slider control is useful:

sage: @interact
... def _(b = range_slider(-20, 20, 1, default=(-19,3), label='Range')):
...     plot(sin(x)/x, b[0], b[1]).show(xmin=b[0],xmax=b[1])
<html>...

An example using checkboxes, obtained by making the default values bools:

sage: @interact
... def _(axes=('Show axes', True), square=False):
...       show(plot(sin, -5,5), axes=axes, aspect_ratio = (1 if square else None))
<html>...

An example generating a random walk that uses a checkbox control to determine whether points are placed at each step:

sage: @interact
... def foo(pts = checkbox(True, "points"), n = (50,(10..100))):
...       s = 0; v = [(0,0)]
...       for i in range(n): 
...            s += random() - 0.5
...            v.append((i, s))
...       L = line(v, rgbcolor='#4a8de2')
...       if pts: L += points(v, pointsize=20, rgbcolor='black')
...       show(L)
<html>...

You can rotate and zoom into 3-D graphics while interacting with a variable:

sage: @interact
... def _(a=(0,1)):
...     x,y = var('x,y')
...     show(plot3d(sin(x*cos(y*a)), (x,0,5), (y,0,5)), figsize=4)
<html>...

A random polygon:

sage: pts = [(random(), random()) for _ in xrange(20)]
sage: @interact
... def _(n = (4..len(pts)), c=Color('purple') ):
...     G = points(pts[:n],pointsize=60) + polygon(pts[:n], rgbcolor=c)
...     show(G, figsize=5, xmin=0, ymin=0)
<html>...

Two “sinks” displayed simultaneously via a contour plot and a 3-D interactive plot:

sage: @interact
... def _(q1=(-1,(-3,3)), q2=(-2,(-3,3))):
...     x,y = var('x,y')
...     f = q1/sqrt((x+1)^2 + y^2) + q2/sqrt((x-1)^2+(y+0.5)^2)
...     C = contour_plot(f, (-2,2), (-2,2), plot_points=30, contours=15, cmap='cool')
...     show(C, figsize=3, aspect_ratio=1)
...     show(plot3d(f, (x,-2,2), (y,-2,2)), figsize=4)        
<html>...

This is similar to above, but you can select the color map from a dropdown menu:

sage: @interact
... def _(q1=(-1,(-3,3)), q2=(-2,(-3,3)), 
...    cmap=['autumn', 'bone', 'cool', 'copper', 'gray', 'hot', 'hsv',
...          'jet', 'pink', 'prism', 'spring', 'summer', 'winter']):
...     x,y = var('x,y')
...     f = q1/sqrt((x+1)^2 + y^2) + q2/sqrt((x-1)^2+(y+0.5)^2)
...     C = contour_plot(f, (x,-2,2), (y,-2,2), plot_points=30, contours=15, cmap=cmap)
...     show(C, figsize=3, aspect_ratio=1)
<html>...

A quadratic roots etch-a-sketch:

sage: v = []
sage: html('<h2>Quadratic Root Etch-a-sketch</h2>')
<html>...<h2>Quadratic Root Etch-a-sketch</h2>...</html>
sage: @interact
... def _(a=[-10..10], b=[-10..10], c=[-10..10]):
...       f = a*x^2 + b*x + c == 0; show(f)
...       soln = solve(a*x^2 + b*x + c == 0, x)[0].rhs()
...       show(soln)
...       P = tuple(CDF(soln))
...       v.append(P)
...       show(line(v, rgbcolor='purple') + point(P, pointsize=200))    
<html>...

In the following example, we only generate data for a given n once, so that as one varies p the data does not randomly change. We do this by simply caching the results for each n in a dictionary.:

sage: data = {}
sage: @interact
... def _(n=(500,(100,5000,1)), p=(1,(0.1,10))):
...     n = int(n)
...     if not data.has_key(n):
...         data[n] = [(random(), random()) for _ in xrange(n)]
...     show(points([(x^p,y^p) for x,y in data[n]], rgbcolor='black'), xmin=0, ymin=0, axes=False)
<html>...

A conchoid:

sage: @interact
... def _(k=(1.2,(1.1,2)), k_2=(1.2,(1.1,2)), a=(1.5,(1.1,2))):
...     u, v = var('u,v')
...     f = (k^u*(1+cos(v))*cos(u), k^u*(1+cos(v))*sin(u), k^u*sin(v)-a*k_2^u)
...     show(parametric_plot3d(f, (u,0,6*pi), (v,0,2*pi), plot_points=[40,40], texture=(0,0.5,0)))
<html>...

An input grid:

sage: @interact
... def _(A=matrix(QQ,3,3,range(9)), v=matrix(QQ,3,1,range(3))):
...     try:
...         x = A\v
...         html('$$%s %s = %s$$'%(latex(A), latex(x), latex(v)))
...     except:
...         html('There is no solution to $$%s x=%s$$'%(latex(A), latex(v)))
<html>...

sagenb.notebook.interact.list_of_first_n(v, n)¶

Given an iterator v, return first n elements it produces as a list.

INPUT:

v - an iterator
n - an integer

OUTPUT:

a list

EXAMPLES:

sage: from itertools import takewhile
sage: p100 = takewhile(lambda x: x < 100, Primes())
sage: sagenb.notebook.interact.list_of_first_n(p100, 10)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
sage: sagenb.notebook.interact.list_of_first_n((1..5), 10)
[1, 2, 3, 4, 5]
sage: sagenb.notebook.interact.list_of_first_n(QQ, 10)
[0, 1, -1, 1/2, -1/2, 2, -2, 1/3, -1/3, 3]

sagenb.notebook.interact.new_adapt_number()¶

Return an integer, always counting up, and starting with 0. This is used for saving the adapt methods for controls. An adapt method is just a function that coerces data into some object, e.g., makes sure the control always produces int’s.

OUTPUT:

an integer

EXAMPLES:

sage: sagenb.notebook.interact.new_adapt_number()   # random output -- depends on when called
1    

class sagenb.notebook.interact.range_slider(vmin, vmax=None, step_size=None, default=None, label=None, display_value=True)¶

Bases: sagenb.notebook.interact.slider_generic

default_index()¶

Return default index into the list of values.

OUTPUT:

an integer 2-tuple

EXAMPLES:

sage: range_slider(2, 5, 1/2, (3,4), 'alpha').default_index()
(2, 4)

render(var)¶

Render the interact() control for the given function and variable.

INPUT:

var - string; variable name

OUTPUT:

a RangeSlider instance

EXAMPLES:

sage: S = range_slider(0, 10, 1, default=(3,7), label='theta'); S
Range Slider: theta [0--|3==7|---10]
sage: S.render('x')
Range Slider Interact Control: theta [0--|3==7|---10]

sage: range_slider(2, 5, 2/7, (3,4), 'alpha').render('x')
Range Slider Interact Control: alpha [2--|20/7==4|---5]

sagenb.notebook.interact.recompute(cell_id)¶

Evaluates the interact() function associated to the cell cell_id. This typically gets called after a call to update().

INPUT:

cell_id - a string or an integer; the ID of an interact() cell

EXAMPLES:

The following outputs __SAGE_INTERACT_RESTART__ to indicate that not all the state of the interact() canvas has been set up yet (this setup happens when JavaScript calls certain functions):

sage: sagenb.notebook.interact.recompute(10)
__SAGE_INTERACT_RESTART__         

sagenb.notebook.interact.reset_state()¶

Reset the interact() state of this sage process.

EXAMPLES:

sage: sagenb.notebook.interact.state  # random output
{1: {'function': <function g at 0x72aaab0>, 'variables': {'m': 3, 'n': 5}, 'adapt': {1: <bound method Slider._adaptor of Slider Interact Control: n [1--|1|---10].>, 2: <bound method Slider._adaptor of Slider Interact Control: m [1--|1|---10].>}}}
sage: from sagenb.notebook.interact import reset_state
sage: reset_state()
sage: sagenb.notebook.interact.state
{}    

class sagenb.notebook.interact.selector(values, label=None, default=None, nrows=None, ncols=None, width=None, buttons=False)¶

Bases: sagenb.notebook.interact.control

default()¶

Return the default choice for this control.

OUTPUT:

an integer, with 0 corresponding to the first choice.

EXAMPLES:

sage: selector([1,2,7], default=2).default()
1        

render(var)¶

Return rendering of this button as a Selector instance to be used for an interact() canvas.

INPUT:

var - a string (variable; one of the variable names input to f)

OUTPUT:

a Selector instance

EXAMPLES:

sage: selector([1..5]).render('alpha') 
Selector with 5 options for variable 'alpha'

values()¶

Return the list of values or (val, lbl) pairs that this selector can take on.

OUTPUT:

a list

EXAMPLES:

sage: selector([1..5]).values()    
[1, 2, 3, 4, 5]
sage: selector([(5,'fifth'), (8,'eight')]).values()
[(5, 'fifth'), (8, 'eight')]

class sagenb.notebook.interact.slider(vmin, vmax=None, step_size=None, default=None, label=None, display_value=True)¶

Bases: sagenb.notebook.interact.slider_generic

default_index()¶

Return default index into the list of values.

OUTPUT:

an integer

EXAMPLES:

sage: slider(2, 5, 1/2, 3, 'alpha').default_index()
2

render(var)¶

Render the interact() control for the given function and variable.

INPUT:

var - a string; variable name

OUTPUT:

a Slider instance

EXAMPLES:

sage: S = slider(0, 10, 1, default=3, label='theta'); S
Slider: theta [0--|3|---10]
sage: S.render('x')
Slider Interact Control: theta [0--|3|---10]

sage: slider(2, 5, 2/7, 3, 'alpha').render('x')
Slider Interact Control: alpha [2--|20/7|---5]

class sagenb.notebook.interact.slider_generic(vmin, vmax=None, step_size=None, label=None, display_value=True)¶

Bases: sagenb.notebook.interact.control

display_value()¶

Returns whether to display the value on the slider.

OUTPUT:

a bool

EXAMPLES:

sagenb.notebook.interact.slider_generic(1,10,1/2).display_value()
True

values()¶

Returns list of values that this slider takes on, in order.

OUTPUT:

a list

Note

This is a reference to a mutable list.

EXAMPLES:

sage: sagenb.notebook.interact.slider(1,10,1/2).values()
[1, 3/2, 2, 5/2, 3, 7/2, 4, 9/2, 5, 11/2, 6, 13/2, 7, 15/2, 8, 17/2, 9, 19/2, 10]

class sagenb.notebook.interact.text_control(value='')¶

Bases: sagenb.notebook.interact.control

render(var)¶

Return rendering of the text field

INPUT:

var - a string (variable; one of the variable names input to f)

OUTPUT:

a TextControl instance

sagenb.notebook.interact.update(cell_id, var, adapt, value, globs)¶

Called when updating the positions of an interactive control. Note that this just causes the values of the variables to be updated; it does not reevaluate the function with the new values.

INPUT:

cell_id - an integer or string; the ID of an interact() cell
var - an object; a variable associated to that cell
adapt - in integer; the number of the adapt function
value - an object; new value of the control
globs - global variables.

EXAMPLES:

The following outputs __SAGE_INTERACT_RESTART__ to indicate that not all the state of the interact() canvas has been set up yet (this setup happens when JavaScript calls certain functions):

sage: sagenb.notebook.interact.update(0, 'a', 0, '5', globals())
__SAGE_INTERACT_RESTART__         

Interact Functions in the Notebook¶

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