Interact Functions in the Notebook¶
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, height=1, **kwargs)[source]¶ Bases:
sagenb.notebook.interact.InputBox
-
render
()[source]¶ Render this color input box to HTML.
OUTPUT:
- a string - HTML format
EXAMPLES:
sage: sagenb.notebook.interact.ColorInput('c', Color('red')).render() '...table...color...'
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value_js
(n)[source]¶ Return JavaScript that evaluates to value of this control. If
n
is 0, return code for evaluation by the actual color control. Ifn
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'
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-
class
sagenb.notebook.interact.
InputBox
(var, default_value, label=None, type=None, width=80, height=1, **kwargs)[source]¶
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class
sagenb.notebook.interact.
InputGrid
(var, rows, columns, default_value=None, label=None, to_value=<function <lambda>>, width=4)[source]¶
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class
sagenb.notebook.interact.
InteractCanvas
(controls, id, layout=None, width=None, **options)[source]¶ Bases:
object
-
cell_id
()[source]¶ 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: B = sagenb.notebook.interact.InputBox('x',2) sage: C = sagenb.notebook.interact.InteractCanvas([B], 3); C Interactive canvas in cell 3 with 1 controls sage: C.cell_id() 3
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controls
()[source]¶ 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']
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is_auto_update
()[source]¶ 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
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render
()[source]¶ 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...interact...table...x...'
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render_controls
(side='top')[source]¶ 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...x...input...2...'
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render_output
()[source]¶ 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...interact...3...'
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wrap_in_outside_frame
(inside)[source]¶ 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...interact...table...inside...'
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-
class
sagenb.notebook.interact.
InteractControl
(var, default_value, label=None)[source]¶ Bases:
sagenb.notebook.interact.InteractElement
-
adapt_number
()[source]¶ 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
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cell_id
()[source]¶ 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
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default_value
()[source]¶ 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
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html_escaped_default_value
()[source]¶ 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() '"cool"' sage: InteractControl('x',"'cool'").html_escaped_default_value() "'cool'" sage: x = var('x') sage: InteractControl('x', x^2).html_escaped_default_value() 'x^2'
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interact
(*args)[source]¶ 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...x...1..."
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label
()[source]¶ 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'
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-
class
sagenb.notebook.interact.
InteractElement
[source]¶ Bases:
object
-
canvas
()[source]¶ Returns the
InteractCanvas
associated to this element. If no canvas has been set (via theset_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
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label
()[source]¶ 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() ''
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set_canvas
(canvas)[source]¶ Sets the
InteractCanvas
on which this element appears. This method is primarily called in the constructor forInteractCanvas
.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
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-
class
sagenb.notebook.interact.
RangeSlider
(var, values, default_position, label=None, display_value=True)[source]¶ Bases:
sagenb.notebook.interact.SliderGeneric
-
default_position
()[source]¶ 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)
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render
()[source]¶ 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...slider...["1","2","3","4","5"]...range...' sage: sagenb.notebook.interact.RangeSlider('x', [1..5], (2,3), 'alpha', display_value=False).render() '...table...slider...null...range...
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-
class
sagenb.notebook.interact.
Selector
(var, values, label=None, default=0, nrows=None, ncols=None, width=None, buttons=False)[source]¶ Bases:
sagenb.notebook.interact.InteractControl
-
render
()[source]¶ Render this control as a string.
OUTPUT:
- a string - HTML format
EXAMPLES:
sage: sagenb.notebook.interact.Selector('x', [1..5]).render() '...select...x...' sage: sagenb.notebook.interact.Selector('x', [1..5], buttons=True).render() '...table...button...x...'
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
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value_js
()[source]¶ 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'
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class
sagenb.notebook.interact.
Slider
(var, values, default_position, label=None, display_value=True)[source]¶ Bases:
sagenb.notebook.interact.SliderGeneric
-
default_position
()[source]¶ 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
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render
()[source]¶ 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...slider...["1","2","3","4","5"]...' sage: sagenb.notebook.interact.Slider('x', [1..5], 2, 'alpha', display_value=False).render() '...table...slider...null...'
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-
class
sagenb.notebook.interact.
SliderGeneric
(var, values, default_value, label=None, display_value=True)[source]¶ Bases:
sagenb.notebook.interact.InteractControl
-
display_value
()[source]¶ 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
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values
()[source]¶ 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]
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values_js
()[source]¶ 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"]'
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-
sagenb.notebook.interact.
automatic_control
(default)[source]¶ Automagically determine the type of control from the default value of the variable.
INPUT:
default
- the default value forv
given by the function; see the documentation tointeract()
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]
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class
sagenb.notebook.interact.
color_selector
(default=(0, 0, 1), label=None, widget='colorpicker', hide_box=False)[source]¶ Bases:
sagenb.notebook.interact.input_box
-
hide_box
()[source]¶ 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
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widget
()[source]¶ Return the name of the HTML widget for this color selector.
OUTPUT:
- a string; the widget’s name
EXAMPLES:
sage: color_selector().widget() 'colorpicker' sage: color_selector('#abcdef', hide_box=True, widget='farbtastic').widget() 'farbtastic' sage: color_selector(widget='jpicker').widget() 'jpicker' sage: color_selector(default=Color(0,0.5,0.25)).widget() 'colorpicker'
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-
class
sagenb.notebook.interact.
control
(label=None)[source]¶
-
sagenb.notebook.interact.
html
(s)[source]¶ 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>
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sagenb.notebook.interact.
html_color_selector
(id, change, input_change, default='000000', widget='colorpicker', hide_box=False)[source]¶ Return HTML representation of a jQuery color selector.
INPUT:
id
- an integer or string; an identifier (e.g., cell ID) for this selectorchange
- 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: ‘colorpicker’); the color selector widget to use; choices are ‘colorpicker’, ‘farbtastic’ and ‘jpicker’ (currently broken)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>...colorpicker...' sage: sagenb.notebook.interact.html_color_selector(99, 'console.log(color);', '', default='fedcba', widget='farbtastic', hide_box=True) '...<table>...farbtastic...'
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sagenb.notebook.interact.
html_rangeslider
(id, values, callback, steps, default_l=0, default_r=1, margin=0)[source]¶ 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 slidercallback
- a string; JavaScript that is executed whenever the slider is done movingsteps
- an integer; number of steps from minimum to maximum valuedefault_l
- an integer (default: 0); the default position of the left edge of the sliderdefault_r
- an integer (default: 1); the default position of the right edge of the slidermargin
- 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>...slider...range...</html>
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sagenb.notebook.interact.
html_slider
(id, values, callback, steps, default=0, margin=0)[source]¶ 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 slidercallback
- a string; JavaScript that is executed whenever the slider is done movingsteps
- an integer; number of steps from minimum to maximum valuedefault
- an integer (default: 0); the default position of the slidermargin
- 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>...slider...</html>
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class
sagenb.notebook.interact.
input_box
(default=None, label=None, type=None, width=80, height=1, **kwargs)[source]¶ Bases:
sagenb.notebook.interact.control
-
default
()[source]¶ 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
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render
(var)[source]¶ Return rendering of this input box as an
InputBox
to be used for aninteract()
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 tof
)
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
()[source]¶ 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
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-
class
sagenb.notebook.interact.
input_grid
(nrows, ncols, default=None, label=None, to_value=<function <lambda>>, width=4)[source]¶ Bases:
sagenb.notebook.interact.control
-
default
()[source]¶ Return the default value of this input grid.
OUTPUT:
- an object
EXAMPLES:
sage: input_grid(2,2, default=1).default() 1
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render
(var)[source]¶ Return rendering of this input grid as an
InputGrid
to be used for aninteract()
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 tof
)
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'
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-
sagenb.notebook.interact.
interact
(*args, **kwds)[source]¶ 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 functionlayout
(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. Iflayout
is not a dictionary, it is assumed to be the ‘top’ value. Iflayout
is None, then all controls are assigned separate rows in thetop
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 ay
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>...
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
, andcolor_selector
. There is also a text control (see the defaults below).u = input_box(default=None, label=None, type=None)
- input box with givendefault
; usetype=str
to get input as an arbitrary stringu = slider(vmin, vmax=None, step_size=1, default=None, label=None)
- slider with given list of possible values;vmin
can be a listu = range_slider(vmin, vmax=None, step_size=1, default=None, label=None)
- range slider with given list of possible values;vmin
can be a listu = checkbox(default=True, label=None)
- a checkboxu = selector(values, label=None, nrows=None, ncols=None, buttons=False)
- a dropdown menu or buttons (get buttons ifnrows
,ncols
, orbuttons
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='colorpicker', hide_box=False)
- a color selector with a possibly hidden input box; thewidget
can also be'farbtastic'
or'jpicker'
(currently not working properly)u = text_control(value='')
- a block of text
You can also create a color selector by setting the default value for an
input_box
toColor(...)
.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 betweenu
andv
by just writingx=(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 fieldu = element
- input_box withdefault=element
, if element not below.u = (umin,umax)
- continuous slider (really 100 steps)u = (umin,umax,du)
- slider with step sizedu
u = list
- buttons iflen(list)
at most 5; otherwise, drop downu = iterator
(e.g. a generator) - a slider (up to 10000 steps)u = bool
- a checkboxu = Color('blue')
- a color selector; returnsColor
objectu = (default, v)
-v
as above, with givendefault
valueu = (label, v)
-v
as above, with givenlabel
(a string)u = matrix
- aninput_grid
withto_value
set tomatrix.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 signaturef(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 theglobal
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 variablexyz
. 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 and hide the input box:
sage: @interact ....: def _(color=color_selector((1,0,1), label='', 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 variesp
the data does not randomly change. We do this by simply caching the results for eachn
in a dictionary.:sage: data = {} sage: @interact ....: def _(n=(500,(100,5000,1)), p=(1,(0.1,10))): ....: n = int(n) ....: if n not in data: ....: 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)[source]¶ Given an iterator v, return first n elements it produces as a list.
INPUT:
v
- an iteratorn
- 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
()[source]¶ 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)[source]¶ Bases:
sagenb.notebook.interact.slider_generic
-
default_index
[source]¶ File: /build/sage-notebook/src/sagenb-1.1.2/sagenb/notebook/interact.py (starting at line 3404)
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)[source]¶ 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)[source]¶ Evaluates the
interact()
function associated to the cellcell_id
. This typically gets called after a call toupdate()
.INPUT:
cell_id
- a string or an integer; the ID of aninteract()
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
()[source]¶ 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)[source]¶ Bases:
sagenb.notebook.interact.control
-
default
()[source]¶ 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)[source]¶ Return rendering of this button as a
Selector
instance to be used for aninteract()
canvas.INPUT:
var
- a string (variable; one of the variable names input tof
)
OUTPUT:
- a
Selector
instance
EXAMPLES:
sage: selector([1..5]).render('alpha') Selector with 5 options for variable 'alpha'
-
-
class
sagenb.notebook.interact.
slider
(vmin, vmax=None, step_size=None, default=None, label=None, display_value=True)[source]¶ Bases:
sagenb.notebook.interact.slider_generic
-
default_index
[source]¶ File: /build/sage-notebook/src/sagenb-1.1.2/sagenb/notebook/interact.py (starting at line 3286)
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)[source]¶ 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)[source]¶ Bases:
sagenb.notebook.interact.control
-
display_value
()[source]¶ 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
[source]¶ File: /build/sage-notebook/src/sagenb-1.1.2/sagenb/notebook/interact.py (starting at line 3149)
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='')[source]¶ Bases:
sagenb.notebook.interact.control
-
render
(var)[source]¶ Return rendering of the text field
INPUT:
var
- a string (variable; one of the variable names input tof
)
OUTPUT:
- a
TextControl
instance
-
-
sagenb.notebook.interact.
update
(cell_id, var, adapt, value, globs)[source]¶ 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 aninteract()
cellvar
- an object; a variable associated to that celladapt
- in integer; the number of the adapt functionvalue
- an object; new value of the controlglobs
- 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__