Lab01_slides_v2.ipynb

Kernel: SageMath (stable)

Week 01

LS30A LAB 1B/1D

TA: Hao Lee

LA: Evelyn Malamut

About TA

• Name: Hao Lee

• Major:

Making Iron Man Suit (Robotics)

• What I look like?

*Fig. 1: Different versions of Hao (in case any unexpected transformation happens)

About Class

OH:

• Mon. 10 AM - 11 AM

• Tue. 1 PM - 2 PM

Location: TBA

Login to CoCalc!!

What is CoCalc

• A platform to use SAGE

• Online system, no environment setup is needed!

Why use SAGE?

• Simplified version of Python

• More math-friendly

Example (You don't need to know this)

How to plot sin(t)?

In python

import numpy as np
from matplotlib import pyplot as plt
t = np.linspace(0,10,100)
plt.plot(t,np.sin(t))

[<matplotlib.lines.Line2D object at 0x7f018fed28d0>]

In CoCalc (SAGE)

plot(sin(x),(x,0,10))

SAGE is much simplier

How to use CoCalc?

Mach Operations

• Plus: +

• Minus: -

• Multiply: *

• Division: /

• Things need to be evaluate first: (put it inside the parentheses)

100/3

100/3

Shortcut Commands!

• Shift + Enter (Run this cell!)

• Alt + Enter (Run this cell and create an empty cell!)

Fractions and Decimal Numbers

The default display format is fraction, but sometimes we prefer decimal numbers (easier to compare)

Just put a dot next to the number!

print(2./3)
print(2/3.)
print(2./3.)

0.666666666666667
0.666666666666667
0.666666666666667

Variables

Assign/Save Values

a = 5

"=" has different meaning in programming, it means "assigning the value on the right to the variable on the left"

#Question:
a = 4
a = a+1
# what is a?

print(a)

5

Functions

"Tasks we can do it again and again!!!"

Syntax of a Function:

function_name(inputs)

Build-in Functions

print(sqrt(3.))
print(log(10.))

1.73205080756888
2.30258509299405

Self-defined Functions

Consider define a function:

$$output = 10^{input_1}+input_2$$

def my_function(input1,input2):
    result = 10^input1+input2
    return result

Nothing is process in the above function definition!

If you want to use it, you need to Call the function.

my_function(2,4)

104

Plot the Data

Sometimes we prefer to visualize the data

e.g., plot $$x^3+2x+1$$

fig = plot(function,(x,x_min,x_max),options)

options are really "optional", you can leave it blank but still plot

p = plot(x^3+2*x+1,(x,-5,5))
show(p)

p = plot(x^3+2*x+1,(x,-5,5),color='red')
show(p)

Plots can interacts with you!!

@interact
def interact_plot(m=(0,5)):
    p1 = plot(x^3+m*x+1,(x,-5,5))
    p2 = plot(m*x^2,(x,-5,5),color='red')
    show(p1+p2,ymax=100,ymin=-100)