William Stein wrote: > On Sat, 17 Nov 2007 09:29:27 -0800, Jason Grout <[EMAIL PROTECTED]> wrote: [snip]
> > I'm pretty excited about this! I think it would be extremely amazingly > useful if you could make up some more examples like this one > > sage: a = Slider(1,10) > sage: plot(sin(a()*x),-3,3) > > and explain what they would do. Also, if we could make it more like > > sage: a = Slider([1..10]) > > i.e., have a discrete range as input, then doing caching would be easier. Here are a few more examples. You can look at the Manipulate help page at http://reference.wolfram.com/mathematica/ref/Manipulate.html for examples of the Mathematica command. Slider(list) creates a slider on the list. For example, Slider([1..10,step=.01]) creates a slider that goes from 1 to 10 on the list. Slider([0,pi/3,pi/2,2*pi/3,pi]) creates a slider that takes on values of pi (note that these are symbolic values, rather than numeric values). Slider([sin,cos,tan]) creates a slider that changes the function Examples: sage: a=Slider([1..10,step=.01]) sage: sin(a()) # outputs the sin of the slider. sage: a=Slider([0,pi/3,pi/2,2*pi/3,pi]) sage: sin(a()) # outputs the sin of various fractions of pi. sage: b=Slider([sin,cos,tan]) sage: (b())(a()) # Two sliders, the first selects the function and the second selects the fraction of pi. sage: a=Slider([1..10]) sage: a()! # Compute the factorial of the selected number. PlaneSlider(list,list) selects from the cartesian product of the lists. This can be used to select a point on a plane. The control presents a small rectangle with a dot in it. You drag the dot to select a different point. sage: a=PlaneSlider([1..10],[1,10]) # a grid sage: some_function_that_takes_a_point(a()) # what function would take a list of two elements? Checkbox() returns true or false. sage: showtangent = Checkbox() sage: point=Slider([0..3,step=.1]) sage: p=plot(sin(x),0,3) # the following command shows the tangent line at the x-value given by the point slider if the tangent checkbox is checked. sage: if(showtangent): (p+plot(sin(point())+cos(point())*(x-point()),0,3)).show() else: p.show() Buttons(list) makes a list of buttons, only one of which can be selected. We could also make a RadioButton(list) widget. sage: a=Buttons([sin,cos,tan]) sage: plot((a())(x),0,3).show() # Shows the selected function Textbox() makes a user textbox. Hmmm, we should probably make an optional validation function for this one! sage: a=Textbox(default="sin") sage: plot(eval(a())(x),0,3).show() # plots the function entered into the text box. ColorChooser() makes a color chooser. sage: a=ColorChooser(default="blue") sage: plot(sin(x),0,3,color=a()).show() # I don't know how to set the color of a plot! >> Performance might be a problem. In that case, we could eventually have >> some command that would cache the output of the expression for different >> widget values so the update would be faster. > > Performance without caching would be a major problem. Performance with > caching could be excellent. E.g., in the above example we could autoload > all 10 images, so that no communication with sage at all would be required, > and scrolling would be instant. > > Please please post several examples of what you imagine doing with this, > which is the perfect first step. Try to include examples that involve > all the different controls that mathematica supports. These aren't all of the controls in Mathematica (I think there's a menu control, for example). It also doesn't touch on the "Dynamic" command which is much more powerful. Here are some more references from Mathematica: http://reference.wolfram.com/mathematica/tutorial/IntroductionToManipulate.html http://reference.wolfram.com/mathematica/tutorial/IntroductionToDynamic.html to be continued... -Jason --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
