FirstStepsV2.sagews

reset

<function reset at 0x7fc3ec6bb050>

#Getting help
#with specific command: type the command name, append the question mark. E like solve?
#Example

#solve?
var('x')
solve(x^2+3*x-4==0,x)

x [x == 1, x == -4]

#Help for specific topic
#Example
#search_doc("numerical approximation")

# SageMath as a calculator

15*0.7^3

5.14500000000000

32^15

37778931862957161709568

#Exact and approximate returns
sqrt(8);sqrt(8.0); N(sqrt(8))

2*sqrt(2) 2.82842712474619 2.82842712474619

38/46

19/23

pi; N(pi);pi.n(digits=20)

pi 3.14159265358979 3.1415926535897932385

#Exercise 1 (ws) Evaluate the number e with 15 decimal digits
e;N(e);e.n(digits=15)

e 2.71828182845905 2.71828182845905

#Demo2:Functions and expressions
#Pre-defined functions
N(log(100));log(100,10);val=log(100.,2)

4.60517018598809 2

val;2^val

6.64385618977472 100.000000000000

#Exercise 2 (ws) (a)Evaluate three built-in functions of your choice for inputs of your choice.
# (b) Explain why SageMath refuses to give the result for exp(3) and force it to evaluate the function approximately.
exp(3.0)

20.0855369231877

#Simple user defined functions
f(x)=x^2-3*x+4; f(3)

4

#expr=sin(x)+x^2;expr(1.1); You will see error message. Get used to this. Learn by practicing.

#Demo3: Basic plotting
p=plot(f(x),-2,2,figsize=[4,2],color="lightblue",thickness=3)# Experiment with optional inputs (figsize, thickness, color)
#See http://doc.sagemath.org/html/en/reference/plotting/sage/plot/plot.html for more on 2D plotting

#Saving a plot in a file:
#give a plot a name (say, p ) and type the command
p.save('[file name].png')

#Exercise 3 (ws)
#Remove the pound sign before the command "parametric_plot", and create a parametric plot using the command (choose your favorite color and specify the size of the plot).
#Save the plot in a file with name 'my_first_plot.png'
parametric_plot((cos(x),sin(x)^3),(x,0,2*pi),color="blue",figsize=[5,3 ],thickness=3)

#Declearing variables
var('a b c')

(a, b, c)

#Solving equations exactly
solve(x^2+b*x-5==0,x)

[x == -1/2*b - 1/2*sqrt(b^2 + 20), x == -1/2*b + 1/2*sqrt(b^2 + 20)]

#find_root?

t=var('t')
#Finding roots approximately
find_root(cos(t)-t,0,pi)

0.7390851332151607

# Syntax of user defined function syntax
def char_fcn01(x):
    if x<=0 or x>=1:
        return 0
    else:
        return 1

char_fcn01(0.5);char_fcn(1.5)

1

#Exercise 4. Define a function that finds the minimal element of the list. Test your function on example of your choice.
︠0079d924-025e-4f27-ae82-6b9bb11e2a68︠
#Exercise 5. Experiment with commands in the file sage-quickref-BasicMath.pdf. Include two examples using commands of your choice. Your commands should be different from arithmetic operations and the commands used in this worksheet.
︠8110ea0c-7702-4fc5-86ff-66c95f868d4b︠