CoCalc Public Filessj_file.ipynb
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Compute Environment: Ubuntu 20.04 (Default)


In [ ]:


In [1]:
def forloop(n):
if n>0:
sum = 0
for x in range(1,n+1):
sum = sum + x
return sum
else:
return 0

In [2]:
forloop(5)


15
In [6]:
def whileloop(n):
if  n>0:
sum=0
x=1
while x<= n:
sum = sum+x
x=x+1
return sum
else:
return 0


In [7]:
whileloop(5)

15
In [8]:
whileloop(1)

1
In [11]:
i = 1+.044/12
1000*i**30*(1-i**30)/(1-i)

35324.16724932064
In [1]:
x=1+0.03/12
-140000*x**360*(1-x)/(1-x**360)

-590.2456472212258
In [2]:
140000*x**120-590.25*(1-x**120)/(1-x)

106427.12411496
In [3]:
x=1+0.035/12
-106427*x**240*(1-x)/(1-x**240)


-617.2337290578675
In [4]:
106427*x**60-617.23*(1-x**60)/(1-x)

86340.82364340735
In [5]:
x=1+0.04/12
-86340.82*x**180*(1-x)/(1-x**180)


-638.6526204120379
In [8]:
86340.82*x**60-638.65*(1-x)/(1-x**60)/(1-x
)

110617.45808025483
In [10]:
x=1+0.045/12
-110617.45*x**120*(1-x)/(1-x**120)


-1146.4216498758651
In [12]:
110617.45*x**120-1146*(1-x**120)/(1-x)

63.75264899616013
In [ ]:
(1+r/12)**22-86.63*(1-(1+r/12)**22)/(1-(r/12))

In [1]:
x=1+0.16/12
-3000*x**24*(1-x)/(1-x**24)


-146.8893315528303
In [3]:
3000*x**6-146.89*(1-x**6)/(1-x)


2336.89812581878
In [4]:
-2336.90*x**18*(1-x)/(1-x**18)

-146.88918870582367
In [6]:
146.89*x**18-146.89*(1-x**18)/(1-x)

-2779.6529593304626
In [7]:
146.89*18

2644.0199999999995
In [1]:
x=1+0.03/12
-140000*x**360*(1-x)/(1-x**360)

-590.2456472212258
In [6]:
[cube**3 for cube in range(0,11)if cube % 2==0]

[0, 8, 64, 216, 512, 1000]
In [10]:
import numpy as np


In [11]:
x = np.array([0,2,4,6,8,10])


In [12]:
x**3

array([ 0, 8, 64, 216, 512, 1000])
In [37]:
i=[]
def forloop(n):
for i in (n):
if length(n) == 1:
return i
else:
return n[2]


In [9]:
#forloop([7,8,9])

In [39]:
def rec_max(L):
if len(L) == 1:
return L[0]
else:
m = rec_max(L[1:])
if L[0] > m:
return L[0]
else:
return m

In [42]:
rec_max([5,6,7,3,9,3,4])

9
In [64]:
def rec_in(n):
if len(n)==1:
return n[0]
else:

rest= rec_in(n[1:])
r=rest+10
y=n[:-1]
return y


In [65]:
rec_in([2,3,5])

--------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-65-1bf3671e8b60> in <module> ----> 1 rec_in([2,3,5]) <ipython-input-64-eeecef688398> in rec_in(n) 6 7 rest= rec_in(n[1:]) ----> 8 r=rest+10 9 y=n[:-1] 10 return y TypeError: can only concatenate list (not "int") to list 
In [ ]:


def list(j):
if len(j)==0:
return j[0]
else:
k=len(j)
while k>1:
k=len(j)-1
fg=10+j[-1]
return list(j[:-1])


In [163]:

def list(j):
if len(j)==1:
return j[0]
else:

return list(j[:-1])*10+j[-1]


In [164]:
list([6,6,7,3])

6673
In [181]:
def rec_in(x):
if len(x)==1:
return x[0]
else:
n=len(x[:-1])
return x[0]*10**n+rec_in(x[1:])

In [ ]:


In [182]:
rec_in([7,1,5])

715
In [ ]:
p(n)=c*p(n)-1 p(0)=1 c>0

In [ ]:


In [274]:
c=.4
def p(n):
if n == 0:
return 1
else:
return c*p(n-1)


the p(n) sequences converges when c<1

In [275]:
p(0)

1
In [276]:
p(1)

0.4
In [277]:
p(2)

0.16000000000000003
In [278]:
p(3)

0.06400000000000002
In [279]:
p(4)

0.025600000000000008
p(0)= c*1=1
c=1
p(1)=1*1=1
p(2)=1*1=1
p(3)=1*1=1

In [2]:
def sign(x):

if x<0:
return-1
else:

return 1


In [3]:
sign(5)

1
In [5]:
def psum(n):
a=0

for v in range(1,n+1):
a=a+v**2
return a


In [6]:
psum(5)


55

Plot f(x) = x^3-x+1 on the interval [-2,2]

In [1]:
import numpy as np
import matplotlib.pyplot as plt


In [1]:
x = np.linspace(-2,2,100)
y = x**3+1
plt.xlabel('x')
plt.ylabel('y')


--------------------------------------------------------------------------- NameError Traceback (most recent call last) <ipython-input-1-c97b7dc2d9fb> in <module> ----> 1 x = np.linspace(-2,2,100) 2 y = x**3+1 3 plt.xlabel('x') 4 plt.ylabel('y') NameError: name 'np' is not defined 
In [5]:
plt.plot(x,y)

[<matplotlib.lines.Line2D at 0x7f1efb9d3df0>]
In [6]:
def rec_in(n):
if len(n)==1:
return n[0]
else:

rest= rec_in(n[1:])
r=rest+10
y=n[:-1]
return y

In [8]:
rec_max([5,6,7,3,9,3,4])

--------------------------------------------------------------------------- NameError Traceback (most recent call last) <ipython-input-8-84bca8af7d8c> in <module> ----> 1 rec_max([5,6,7,3,9,3,4]) NameError: name 'rec_max' is not defined 
In [ ]:


In [13]:
def quad_tan(a,b,c):
x = [-10+i/1000*20 for i in range(1001)]
yquad = [a*n*n+b*n+c for n in x]
ytan = [b*n+c for n in x]
plt.plot(x,ytan,color='red')
plt.show()

In [14]:
def has_3(arr):
for n in arr:
if n == 3:
return 1
return -1

In [18]:

has_3([1,2,3,3,4])

1
In [19]:
20000*(1+0.082/12)**(48)/((1-(1+0.082/12)**(48))/(-0.082/12))

490.1382323808438
In [20]:
quad_tan(3,2,1)

In [21]:
def line_intersect(m1,b1,m2,b2):
x = [-10+i/1000*20 for i in range(1001)]
yline1 = [m1*n+b1 for n in x]
yline2 = [m2*n+b2 for n in x]
X = (b2-b1)/(m1-m2)
Y = m1*X+b1
plt.plot(x,yline1,color='blue')
plt.plot(x,yline2,color='red')
plt.scatter(X,Y,color='black',s=40)
plt.show()

In [ ]:


In [ ]:


In [22]:
line_intersect(3,2,-3,4)

In [23]:

def min_cost(n):
if n*10.99 > 100:
print(100)
else:
print(n*10.99)


In [24]:
min_cost(9)

98.91
In [26]:
for n in range(501):
for m in range(501):
if n*n-7*m*m == 1:
print(n)

1 8 127
In [ ]:
for n in range(501):


In [13]:
[odd for odd in range(0,51)if odd%2==1]

[1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]
In [7]:

t=3*a*x**(3-1)+2*b*x**(2-1)+1*c*x+d(0)


In [8]:
cube_deriv(3,-2,0,5)

--------------------------------------------------------------------------- NameError Traceback (most recent call last) <ipython-input-8-1a2e8871728c> in <module> ----> 1 cube_deriv(3,-2,0,5) <ipython-input-7-56e8ca8586bd> in cube_deriv(a, b, c, d) 1 def cube_deriv(a,b,c,d): ----> 2 y = a*x**3+b*x**2+c*x+d 3 t=3*a*x**(3-1)+2*b*x**(2-1)+1*c*x+d(0) 4 prin(t) NameError: name 'x' is not defined 
In [1]:
import numpy as np

In [3]:
np.random.randint(0,2,size=100)

array([0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0])
In [2]:
import numpy as np
import matplotlib .pyplot as plt

In [3]:
def bisection(a,b,c,e):
c = (a+b)/2
while c-a > e:
if f(c)==0:
return c
elif f(a)*f(c)>0:
a=c
else:
b=c
x= (a+b)/2
return c


In [ ]:
zero=heads
one=tails

In [14]:
coin_f=np.random.randint(0,2,size=10)

In [15]:
coin_f

array([0, 1, 1, 0, 1, 0, 0, 1, 0, 1])
In [40]:
def filp(n):
for i in range(100):
coin_f=np.random.randint(0,2,size=n)
list=[]
f_st=0
for coin in coin_f:
if coin ==1:
f_st +=1
else:
if f_st>=4:
list.append(f_st)
f_st =0
return list


In [44]:
filp(10)

[]
In [42]:


--------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-42-d85ea1407ed1> in <module> ----> 1 np.mean([filp(10) for i in range(100)]) <__array_function__ internals> in mean(*args, **kwargs) /usr/local/lib/python3.8/dist-packages/numpy/core/fromnumeric.py in mean(a, axis, dtype, out, keepdims) 3370 return mean(axis=axis, dtype=dtype, out=out, **kwargs) 3371 -> 3372 return _methods._mean(a, axis=axis, dtype=dtype, 3373 out=out, **kwargs) 3374 /usr/local/lib/python3.8/dist-packages/numpy/core/_methods.py in _mean(a, axis, dtype, out, keepdims) 170 ret = ret.dtype.type(ret / rcount) 171 else: --> 172 ret = ret / rcount 173 174 return ret TypeError: unsupported operand type(s) for /: 'list' and 'int' 
In [70]:
for i in range(100):
coin_f=np.random.randint(0,2,size=10)
list=[]
f_st=0
for coin in range(100):

if coin ==1:
f_st +=1
else:

if f_st==4:

list.append(f_st)
f_st=0


In [71]:
list

[]
In [85]:
def flip(n):
list=[]
for i in range(n):
coin_f=np.random.randint(0,2,size=10)
return list.append(coin_f)


In [86]:
flip(100)


In [74]:
coin_f=np.random.randint(0,2,size=10)

In [90]:

for i in range(100):
coin_f=np.random.randint(0,2,size=10)
print(coin_f)

[1 0 1 0 0 0 1 1 0 0] [0 1 0 0 0 0 1 1 1 1] [1 0 1 0 1 0 0 0 0 1] [1 0 1 0 0 1 0 1 1 1] [0 0 1 1 0 0 0 1 0 0] [0 1 0 0 1 1 1 1 1 0] [0 1 1 0 1 1 1 0 1 0] [0 1 0 0 0 0 0 0 1 1] [1 1 0 0 1 1 1 1 1 1] [0 0 1 1 1 1 1 0 0 0] [0 0 0 0 0 1 1 1 1 0] [0 1 0 1 1 1 0 0 1 0] [0 0 1 1 1 1 0 1 0 0] [1 0 1 1 1 1 0 1 1 1] [0 1 1 1 1 1 0 0 0 1] [1 0 0 1 0 1 1 0 1 1] [1 0 0 0 0 1 1 0 0 1] [1 1 0 0 1 0 1 0 0 1] [0 1 0 0 1 0 0 1 1 0] [0 1 1 0 1 0 0 1 0 1] [1 0 0 1 0 1 1 0 0 0] [0 1 1 0 0 1 0 1 0 0] [0 1 0 1 0 1 1 0 0 1] [1 0 1 1 0 0 0 1 0 0] [1 0 1 0 1 1 0 0 0 1] [1 0 0 1 0 0 0 0 0 0] [0 1 1 0 1 1 0 1 1 1] [0 0 0 1 1 0 1 1 0 1] [0 1 1 0 0 0 1 1 0 1] [0 1 1 0 0 0 1 0 0 0] [0 1 0 1 0 0 0 1 0 1] [0 1 1 0 1 1 1 1 1 0] [1 0 1 1 0 0 1 0 0 1] [1 0 0 1 1 0 1 0 0 0] [1 0 1 1 0 0 1 0 1 1] [0 1 1 1 0 0 1 1 1 1] [0 0 0 1 1 1 0 0 0 0] [1 1 1 1 1 0 1 0 0 1] [0 0 1 0 0 1 1 1 0 1] [1 1 0 0 1 1 0 0 0 0] [0 0 1 0 0 0 1 0 1 1] [0 0 0 1 0 1 0 1 0 0] [1 0 0 1 0 0 0 1 0 1] [1 1 1 1 0 1 1 0 0 0] [1 0 1 1 0 1 1 0 1 0] [0 1 1 0 1 0 1 0 1 1] [0 1 0 0 0 0 1 0 0 1] [0 0 1 1 0 1 1 1 1 0] [0 1 1 1 1 1 1 0 0 1] [1 1 1 0 0 1 1 1 1 1] [0 1 1 0 0 1 1 0 1 0] [0 1 1 1 1 1 0 1 1 1] [0 0 1 0 0 0 0 1 0 0] [1 0 0 1 0 1 1 1 0 1] [1 1 0 1 0 1 0 1 1 1] [1 1 1 1 0 1 0 1 1 1] [0 0 0 0 1 0 1 0 0 1] [0 1 1 0 1 0 1 0 0 1] [1 0 1 0 0 1 0 1 1 1] [1 0 0 1 1 1 0 1 1 0] [1 1 1 0 1 1 0 0 1 0] [0 0 1 1 0 1 0 1 0 1] [0 0 1 0 1 0 0 0 1 1] [0 1 0 1 0 1 1 0 0 0] [1 1 1 0 1 0 0 1 1 0] [0 0 1 1 0 0 1 1 0 1] [0 0 0 1 0 0 1 1 0 1] [0 0 0 1 0 1 1 1 0 0] [0 0 1 1 1 0 0 0 1 0] [0 0 0 0 1 0 0 1 1 0] [0 0 0 0 1 1 1 1 0 1] [1 0 0 1 1 1 0 0 1 0] [1 1 0 1 1 0 1 0 1 0] [1 0 0 0 0 0 1 1 0 0] [1 1 0 1 0 0 1 1 1 0] [0 1 0 1 0 0 0 0 0 1] [1 1 1 1 1 0 0 1 1 0] [0 1 0 0 1 1 1 0 0 1] [1 1 0 1 1 1 1 0 0 1] [0 1 1 0 0 0 1 0 0 0] [0 0 1 0 1 1 1 1 1 1] [0 0 0 0 1 1 0 0 0 0] [0 1 1 1 0 1 1 0 0 1] [0 1 1 1 1 0 0 1 0 1] [0 0 1 0 1 0 1 0 0 1] [0 0 0 0 0 1 0 1 0 1] [1 0 0 0 0 0 0 0 1 1] [1 0 1 1 1 1 1 1 1 0] [0 1 1 0 1 1 0 0 1 1] [1 0 0 1 1 1 0 0 1 1] [0 0 0 0 0 0 0 0 1 1] [1 1 1 1 0 0 1 1 0 0] [0 1 0 1 1 0 0 1 1 0] [0 0 0 1 0 0 1 0 0 1] [1 0 1 0 0 0 0 1 1 0] [1 1 0 1 0 0 0 1 0 1] [0 0 0 1 1 0 0 1 0 0] [1 1 0 0 1 1 1 0 0 0] [1 1 1 0 1 0 0 1 0 0] [0 1 1 0 0 1 0 0 0 1]
In [1]:
def dyn_fib(n):
fib_list =[0 for i in range(n+1)]
fib_list[0]=0
fib_list[1]=1
for i in range(2,n+1):
fib_list[i]=fib_list[i-1]+fib_list[i-2]
return fib_list[-1]


In [2]:
dyn_fib(4)

3

The lightbulb problem Suppose that a company sells lightbulbs in packages of size 1, 2, 6, and 8. If a customer orders 30 bulbs, what is the least number of packages (of any size) that can be used to put this order together?

In [1]:
def bulb(n):
L = [0 for i in range(n)]

L[0] = 1 # 1 bulb
L[1] = 1 # 2 bulbs
L[2] = 2 # 3 bulbs
L[3] = 2 # 4 bulbs
L[4] = 3 # 5 bulbs
L[5] = 1 # 6 bulbs
L[6] = 2 # 7 bulbs
L[7] = 1 # 8 bulbs
for i in range(8,n):
L[i] = 1 + min(L[i-1],L[i-2],L[i-6],L[i-8])
print(L)
return L[n-1]


In [2]:
bulb(30)

[1, 1, 2, 2, 3, 1, 2, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 4, 4, 5, 4, 5, 4]
4

Suppose that a company sells computer chips in packages of size 1, 5, and 8. Find the least number of packages that can be used to order 20 chips.

In [5]:
def chips(n):
L = [0 for i in range(n)]

L[0] = 1 # 1 chip
L[1] = 2 # 2 chips
L[2] = 3 # 3 chips
L[3] = 4 # 4 chips
L[4] = 1 # 5 chips
L[5] = 2 # 6 chips
L[6] = 3 # 7 chips
L[7] = 1 # 8 chips
for i in range(8,n):
L[i] = 1 + min(L[i-1],L[i-5],L[i-8])
print(L)
return L[n-1]

In [6]:
chips(20)

[1, 2, 3, 4, 1, 2, 3, 1, 2, 2, 3, 4, 2, 3, 3, 2, 3, 3, 4, 4]
4
In [6]:
j=[60]
a=[140]
for i in range(5):
j_n=j[-1]
a_n=a[-1]
j_time=0.05*j_n+0.65*a_n-52
a_time=0.45*j_n+0.69*a_n+72
j.append(j_time)
a.append(a_time)

In [3]:
import numpy as np
import random

In [29]:
listt=[]
stat=0
def spin():
if total < 100 and total >85:
return 1
else:
return 0
#print(num1,num2,total)
for i in range(100):
num1= random.randrange(0,101,5)
num2= random.randrange (0,101,5)
total=num1+num2
listt.append(spin())
for u in listt:
stat=stat+u
length=len(listt)
print(listt,stat,length)
print(stat/length)


[1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 7 100 0.07
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