Diszkrét matematika III gyakorlat
Linkek:
5.1(a),
5.1(b),
5.1(c),
5.1(d),
5.3(b),
5.3(c)
Euklideszi algoritmus egész számokkal
%display latex
a = 44
b = 34
while b!=0:
a, b = b, a%b
a
Ha már nem emlékszel erre, itt egy részletesebb magyarázat.
Euklideszi algoritmus polinomokkal
%display latex
R.<x> = PolynomialRing(QQ)
a = x*(x+1)*(x+12)*(x+13)
b = x*(x+1)*(x+14)
while b!=0:
a, b = b, a%b
a
Írjuk ki részletesen a lépéseket:
%display latex
R.<x> = PolynomialRing(QQ)
f = x*(x+1)*(x+12)*(x+13)
g = x*(x+1)*(x+14)
def eukl(f,g):
while g!=0:
q, r = f.quo_rem(g)
pretty_print("osztandó: \t", f)
pretty_print("osztó: \t", g)
pretty_print("hányados: \t", q)
pretty_print("maradék: \t", r)
pretty_print("---------------------------")
f, g = g, r
pretty_print("lnko: \t", f)
eukl(f,g)
5.1(a) feladat
R.<x> = PolynomialRing(QQ)
f = 2*x^4 - 3*x^3 - 2*x^2 + 2*x - 1
g = 2*x^3 - x^2 - 4*x - 1
eukl(f,g)
#g/gcd(f,g)
5.1(b) feladat
#5.1(b)
R.<x> = PolynomialRing(QQ)
f = -x^4 - 4*x^3 + 34*x^2 + 76*x - 105
g = x^4 + 6*x^3 - 6*x^2 + 6*x - 7
eukl(f,g)
5.1(c) feladat
R.<x> = PolynomialRing(GF(13))
f = x^8 - 1
g = x^6 - 1
eukl(f,g)
5.1(d) feladat
R.<x> = PolynomialRing(GF(5))
f = 4*x^4 + 2*x^3 + x^2 + x + 2
g = 2*x^4 + 3*x^2 + 1
eukl(f,g)
5.3(b) feladat
R.<x> = PolynomialRing(GF(2))
f = x^5 + x^4 + x^3 + 1
g = x^4 + 1
eukl(f,g)
5.3(c) feladat
R.<x> = PolynomialRing(GF(5))
f = x^4 + x^3 + x + 1
g = x^3 + 2*x^2 + 2*x + 1
eukl(f,g)
Üres cellák