Informatics1-2019/HW7
A MathWikiből
(Változatok közti eltérés)
(Új oldal, tartalma: „= Sage= 6 points The exercises should be done via a sage function: def nameofthefunction(input): ... ... return ... == Relative primes == 3 points W…”) |
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− | 2019.12. | + | 2019.12.16 23:59 |
A lap jelenlegi, 2019. december 10., 13:38-kori változata
Tartalomjegyzék |
Sage
6 points
The exercises should be done via a sage function:
def nameofthefunction(input): ... ... return ...
Relative primes
3 points
Write a function called relativeprimes with a positive integer as input. The output should be a univariate polynomial such that:
- its variable is x
- every coefficient is 1
- only the powers of x should be in the polynomial where exponent less than n and relative prime to n.
Example:
>>> relativeprimes(9) x^8 + x^7 + x^5 + x^4 + x^2 + x
Use list comprehension and sum
Pythagorean primes
3 points
Find Pythagorean triplets where:
- every term is a positive integer
- they are in a descending order
- the sum of the squares of the last two is the square of the first one
- at least on of the three is a prime
Define a function called pythagorean with one input (n) and return all such triplets up to n.
Example:
def pythagorean(n): ... ... pythagorean(100)
[(5, 4, 3), (13, 12, 5), (17, 15, 8), (29, 21, 20), (25, 24, 7), (37, 35, 12), (41, 40, 9), (53, 45, 28), (73, 55, 48), (61, 60, 11), (97, 72, 65), (89, 80, 39), (85, 84, 13)]
Handing in
Send the code of the functions in the email!
Deadline
2019.12.16 23:59