def show_ducci_sequence(L):
w = max([len(str(i)) for i in L]) + 2
for i in ducci_sequence(L):
equal_spacing(i, w)
#show_ducci_sequence([52,999,78,967,25,7])
def long_multiplication_steps(A,B):
# Get the digits
dA = [int(i) for i in str(A)]
dB = [int(i) for i in str(B)]
# Go through the digits of each number backward doing single digit
# multiplication
rows = []
for sh,b in enumerate(reversed(dB)):
R = [0]*(len(dA)+len(dB))
for pos,a in enumerate(reversed(dA)):
# Store the results of the multiplication in a row
R[-(sh+pos)-1] = a*b
rows.append(R)
# Deep copy of rows
R = [rows[i].copy() for i in range(len(rows))]
# Calculate the addition
out = ""
carry = 0
C = []
while len(rows[0]) > 0:
C.append(carry)
s = carry
for row in rows:
s += row.pop()
carry = s // 10
digit = s%10
out = str(digit) + out
equal_spacing(reversed([" Carries"]+C),3)
equal_spacing_grid(R,3)
print()
equal_spacing(out,3)
return int(out)
from Combinatorics import stirling_numbers_1, stirling_numbers_2
from GeneralUtils import equal_spacing
print("Stirling Numbers of the First Kind")
for i in range(8):
L = []
for j in range(i + 1):
L.append(stirling_numbers_1(i, j))
equal_spacing(L, 5, 'left')
print("\nStirling Numbers of the Second Kind")
for i in range(8):
L = []
for j in range(i + 1):
L.append(stirling_numbers_2(i, j))
equal_spacing(L, 4, 'left')
from Computation import addition_chain
from GeneralUtils import equal_spacing
for i in range(1,50):
equal_spacing(addition_chain(i),3,'center')
a, b = 620, 380
print(
"The greatest common denominator of two natural numbers is the largest number that is a factor of both."
)
print(f"The GCD of the set {a} and {b} is {gcd(a,b)}")
print(
"\nCalculating the GCD can be done reasonably quickly using the Euclidean Algorithm."
)
a, b = 629, 777
print(
f"\nThis algorithm procedes by subtracting the smaller number from the larger until the numbers are equal. Here we find the GCD of {a} and {b}.\n"
)
equal_spacing([a, b], 5, 'left')
while a != b:
if a > b:
a = a - b
else:
b = b - a
equal_spacing([a, b], 5, 'left')
print(f"\nSo the their greatest common denominator is {gcd(a,b)}")
print(
"\nThere are slightly more efficient methods of calculation available today."
)
S = [5610, 24871, 1683]
print("\nWe can also find the GCD of a set of numbers")
def show_pascals_triangle(n,w=5):
triangle = pascals_triangle(n)
for ctr,row in enumerate(triangle):
equal_spacing(row,w,'left')