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Hello friends and welcome to the tutorial on 'Using SAGE to teach'.

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At the end of this tutorial, you will be able to,

 Use @interact  feature of SAGE for better demonstration.

 Share, publish and edit SAGE worksheets for collaborative learning.

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Before beginning this tutorial,we would suggest you to complete the tutorial on "Getting started with Sage" and "Getting started with Symbolics."

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Let us start by looking at a typical example of demonstrating a damped oscillation.

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So you can type t=var('t') ,then next line you can type p1=plot (e raised to minus (-t)into sin of (2 into t),(t,0,15))

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then third line you can type show(p1)

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Now let us reduce the damping factor by half

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so for that you have to type t=var('t')

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then p1=plot(e raised to (-t by 2) * sin(2 into t),(t,0,15))

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then third line you can type show(p1)

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Now, if we want to reduce the damping factor even more, we would be using e charat to (-t by 3).

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We can observe that every time we have to change, all we do is change something very small and re-evaluate the cell.

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This process can be simplified, using the  @interact  feature of SAGE.

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So you can type  @interact  ,then def plot_damped(n-1):

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Then, t=var('t')

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p1=plot (e raised to(-t/n) * sin(2*t),(t,0,20))

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then type show(p1)

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We can see that the function is evaluated and the plot is shown.

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We can also see that there is a field to enter the value of n  and it is currently set to  1 .

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Let us change it to 2 and hit enter.

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So you type 2 and hit enter.

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We see that the new plot with reduced damping factor is shown.

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Similarly we can change  n to any desired value and hit enter and the function will be evaluated.

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This is a very handy tool while demonstrating or teaching.

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Pause the video here, try out the following exercise and resume the video.

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'Plot the sine curve and vary its frequency using the @interact feature.

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Now, switch to your worksheet for solution.

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You can type @interact

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then def sine_plot(n=1):

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then x=var('x')

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then p2=plot (sin(n*x),(x,0,2*pi))

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then finally you can type show(p2)

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So often we would want to vary a parameter over range instead of taking it as an input from the user.

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For instance we would not want the user to give  n as 0 for the damping oscillation we discussed.

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In such cases we use a range of values as the default argument.

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at the rate interact

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should be typed in the worksheet so in the worksheet you can type

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@interact then def plot underscore damped(n=(1..10)):

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then next line you can type t=var('t')

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then p1=plot(e raised to (-t/n) * sin(2*t)),(t,0,20))

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then you can type show(p1)

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Now we had seen an error

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So the error that we have rectified is after sin(2*t) we have accidentally placed an extra bracket.

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So we get similar plot but the only difference is the input widget.

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Here it is a slider unlike an input field.

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We can see that the slider is moved, the function is evaluated and plotted accordingly.

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Pause the video here,and try out the following exercise and resume the video.

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Take a string as input from user and circular shift it to the left and vary the shift length using a slider.

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For this problem, again we will use the  @interact  feature of sage.

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We shall first assign a string say 'MADAM' to a variable and then shift the alphabets one by one.

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So we can type @interact

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def str_shift(s="MADAM", shift=(0..8)) colon

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then you can type shift_len=shift modulus len(s)

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then chars=list(s)

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then shifted_chars=chars[shift_len:]+chars[: shift_len]

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then print "Actual String:",s

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then print "Shifted String:", "".join(shifted_chars)

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As we move the slider, we see that shifting is taking place.

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Sometimes we want the user to have only a given set of options.

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We use a list of items as the default argument in such situations.

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So we can type @interact

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then def str_shift(s="STRING",shift=(0..8), direction=["Left","Right"]):

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then next line shift_len=shift modulus len(s)

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then chars=list(s)

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if direction=="Right" colon

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then shifted_chars=chars[-shift_len colon]+chars[colon -shift_len]

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else colon shifted_chars=chars[shift_len colon]+chars[colon shift_len]

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then type print "Actual String:",s

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then print "Shifted String:", ""

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then dot join(shifted_chars)

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We can see that buttons are displayed which enables us to select from a given set of options.

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We see that, as we select left or right button, the shifting takes place appropriately.

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Thus, we have learnt how to use the  @interact  feature of SAGE for better demonstration.

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Now we shall look at how to use SAGE worksheets for collaborative learning.

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The first feature we shall see is the  publish  feature.

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Open a worksheet and in the top right, we can see a button called publish

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Click on that and we get a confirmation page with an option for re-publishing.

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For now lets forget that option and simply publish by clicking  yes .

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The worksheet is now published.

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Now lets sign out and go to the sage notebook home.

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We see link to browse published worksheets.

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Lets click on it and we can see the worksheet.

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This does not require login and anyone can view the worksheet.

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Alternatively, if one wants to edit the sheet, there is a link on top left corner that enables the user to download a copy of the sheet onto their home.

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This way they can edit a copy of the worksheet.

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We have learnt how to publish the worksheets to enable users to edit a copy.

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Next, we shall look at how to enable users to edit the actual worksheet itself.

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Let us open the worksheet and we see a link called share  on the top right corner of the worksheet.

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Click the link and we get a box where we can type the usernames of users whom we want to share the worksheet with.

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We can even specify multiple users by separating their names using commas.

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Once we have shared the worksheet, the worksheet appears on the home of shared users.

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This brings us to the end of this tutorial.

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In this tutorial, we have learnt to,

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Use interactive features of SAGE using @interact .

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then publishing our work.

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then edit a copy of one of the published worksheets.

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then share the worksheets with fellow users.

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Here are some self assessment questions for you to solve

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1. Which default argument, when used with @interact gives a slider starting at 0 and ending in 10.

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options are (0..11)

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then range(0, 11)

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Then [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]  separated by comma

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then in brackets (0..10)

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2. What is the input widget resulted by using n = [2, 4, 5, 9]\ in the default arguments along with @interact.

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options are input field,  set of buttons, slider, None

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Now we will look at the answers,

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1.The default argument, used with @interact  which gives a slider starting at 0 and ending in 10 is (0..10).

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2. The input widget resulted by using  n = [2, 4, 5, 9]  in the default arguments along with  @interact  will be a set of buttons that is the second one.

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Hope you have enjoyed this tutorial and found it useful.

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Thank you!