lab3.ipynb

Kernel: SageMath 9.1

Lab 3 Using Lists and Loops

Example 1: Plotting lists of points using list_plot()

# height over time

height=[61, 62, 66, 68, 70]
ages = [10, 12, 14, 16, 17]

list_plot(height)

# plot list of pairs of points

pairs = [(10, 61), (12, 62), (14, 66), (16, 68), (17, 70)]
list_plot(pairs, size=50, color='green', axes_labels=["ages [yr]", "height [in]"], title="My height over time")

pairs = list(zip(ages, height)) # replacement for typing the above.
list_plot(pairs, size=50, color='green', axes_labels=["ages [yr]", "height [in]"], title="My height over time")

# Convert inches to m

height

# create an empty list to hold the metric heights
metric_heights = []

# repeatedly, for each item in the list height...
for h in height:
    # convert height to meters
    h_meters = h*0.0254

    # append converted height to metric list
    metric_heights.append(h_meters)

# display converted time series.
list_plot(list(zip(ages, metric_heights)), size=50, color='green', axes_labels=["ages [yr]", "height [m]"], title="My height over time")

Example 2: Processing lists of data using for loops

Example 3: editing a trajectory

Pre-created lists xlist and ylist:

times = list(srange(0, 2*pi, 0.1))
xlist = [cos(t) for t in times]
ylist = [sin(t) for t in times]
print("xlist = {}...".format(xlist[:5]))
print("ylist = {}...".format(ylist[:5]))

xlist = [1, 0.995004165278026, 0.980066577841242, 0.955336489125606, 0.921060994002885]...
ylist = [0, 0.0998334166468282, 0.198669330795061, 0.295520206661340, 0.389418342308651]...

old_circle = list_plot(list(zip(xlist, ylist)), aspect_ratio=1)
show(old_circle)

new_cos_list = []
for x in xlist:
    new_cos_list.append(2*x)
new_cos_list

new_sin_list = []
for y in ylist:
    new_sin_list.append(2*y)
new_sin_list

new_circle = list_plot(list(zip(new_cos_list, new_sin_list)), aspect_ratio=1, color='red', plotjoined=True)

# overlay both:
new_circle + old_circle