Sz\303\241m\303\255t\303\263g\303\251pes sz\303\241melm\303\251let J\303\241rai Antal Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">1. A pr\303\255mek eloszl\303\241sa, szit\303\241l\303\241s</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">2. Egyszer\305\261 faktoriz\303\241l\303\241si m\303\263dszerek</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">3. Egyszer\305\261 pr\303\255mtesztel\303\251si m\303\263dszerek</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 1" layout="Heading 1">4. Lucas-sorozatok</Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">5. Alkalmaz\303\241sok </Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">6. Sz\303\241mok \303\251s polinomok</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">7. Gyors Fourier-transzform\303\241ci\303\263</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">8. Elliptikus f\303\274ggv\303\251nyek</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">9. Sz\303\241mol\303\241s elliptikus g\303\266rb\303\251ken</Font></Text-field> restart;
<Text-field style="Heading 2" layout="Heading 2">9.1. Elliptikus <Font encoding="UTF-8">g\303\266rb\303\251k.</Font></Text-field> # # This routine randomly choose an elliptic "curve" modulo n, # where gcd(n,6)=1. The coordinates x,y are choosen # randomly, the parameter a too, and b is calculated. # The list [x,y,a,b] is given back or a divisor d of n. # ellrand:=proc(n) local x,y,a,b,r,d,f; r:=rand(n); d:=0; while d=0 do x:=r(n); y:=r(n); a:=r(n); b:=y^2-x^3-a*x mod n; d:=4*a^3+27*b^2 mod n; gcd(d,n); od; if %<n and %>1 then return % fi; [x,y,a,b]; end; Zio2I0kibkc2IjYpSSJ4R0YlSSJ5R0YlSSJhR0YlSSJiR0YlSSJyR0YlSSJkR0YlSSJmR0YlRiVGJUMnPkYrLUklcmFuZEdGJUYjPkYsIiIhPyhGJSIiIkY1RiUvRixGM0MoPkYnLUYrRiM+RihGOT5GKUY5PkYqLUkkbW9kR0YlNiQsKCokKUYoIiIjRjVGNSokKUYnIiIkRjUhIiIqJkYpRjVGJ0Y1RkdGJD5GLC1GPjYkLCYqJiIiJUY1KUYpRkZGNUY1KiYiI0ZGNSlGKkZDRjVGNUYkLUkkZ2NkR0YlNiRGLEYkQCQzMkkiJUdGJUYkMkY1RllPRlk3JkYnRihGKUYqRiVGJUYl ellrand(97); ellrand(97); ellrand(97); ellrand(97); ellrand(97); NyYiIiYiI2UiI1YiIzw= NyYiI1AiI28iI0UiI2E= NyYiIyYqIiM7IiMqKSIjYQ== NyYiI0wiIzwiI14iIzk= NyYiI2IiI1UiIyMpIiNa
<Text-field style="Heading 2" layout="Heading 2">9.2. Hasse t<Font encoding="UTF-8">\303\251</Font>tele.</Text-field> # # This brute force procedure calculate the number of points # on an elliptic curve modulo p>3, a prime. The curve # parameters are a, b. # ellcount:=proc(a,b,p) local x,c; c:=1; for x from 0 to p-1 do c:=c+numtheory[jacobi](x^3+a*x+b,p)+1; od; c; end; Zio2JUkiYUc2IkkiYkdGJUkicEdGJTYkSSJ4R0YlSSJjR0YlRiVGJUMlPkYqIiIiPyhGKSIiIUYtLCZGJ0YtRi0hIiJJJXRydWVHJSpwcm90ZWN0ZWRHPkYqLChGKkYtLSZJKm51bXRoZW9yeUdGJTYjSSdqYWNvYmlHRiU2JCwoKiQpRikiIiRGLUYtKiZGJEYtRilGLUYtRiZGLUYnRi1GLUYtRipGJUYlRiU= ellrand(97); ellcount(%[3],%[4],97); ellrand(97); ellcount(%[3],%[4],97); ellrand(97); ellcount(%[3],%[4],97); ellrand(97); ellcount(%[3],%[4],97); ellrand(97); ellcount(%[3],%[4],97); NyYiI2YiIyMqIiM4IiIl IiMpKQ== NyYiI1wiI1kiIigiI1I= IiQ6Ig== NyYiI1giI1YiIikiIyop IiQ3Ig== NyYiI3ciI2UiIzoiI1I= IiQwIg== NyYiIiEiI3AiI3ciIik= IiMoKg==
<Text-field style="Heading 2" layout="Heading 2">9.3. Gyakorlat.</Text-field> with(plots); 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 implicitplot(y^2=x^3-10*x+10,x=-5..10,y=-20..20,numpoints=10000); 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<Text-field style="Heading 2" layout="Heading 2">9.4. Gyakorlat.</Text-field> # # Doubling on an elliptic "curve" modulo n, where gcd(n,6)=1. # P is the point to double and a, b are the parameters. # The return value is the double of the point P or # a divisor d of n. # elldou:=proc(P,a,b,n) local l,d; if P[3]=0 then return P fi; if P[2]=0 then return [0,1,0] fi; d:=igcdex(2*P[2],n,'l'); if 1<d and d<n then return d fi; l:=(3*P[1]^2+a)*l mod n; l^2-2*P[1] mod n; [%,l*(P[1]-%)-P[2] mod n,1]; end; Zio2JkkiUEc2IkkiYUdGJUkiYkdGJUkibkdGJTYkSSJsR0YlSSJkR0YlRiVGJUMpQCQvJkYkNiMiIiQiIiFPRiRAJC8mRiQ2IyIiI0YyTzclRjIiIiJGMj5GKy1JJ2lnY2RleEdGJTYlLCQqJkY4RjtGNkY7RjtGKC5GKkAkMzJGO0YrMkYrRihPRis+RiotSSRtb2RHRiU2JComLCYqJkYxRjspJkYkNiNGO0Y4RjtGO0YmRjtGO0YqRjtGKC1GSjYkLCYqJClGKkY4RjtGOyomRjhGO0ZQRjshIiJGKDclSSIlR0YlLUZKNiQsJiomRipGOywmRlBGO0ZaRlhGO0Y7RjZGWEYoRjtGJUYlRiU= # # Addition on an elliptic "curve" modulo n, where gcd(n,6)=1. # P and Q are the points to add and a,b are the parameters. # The return value is the sum of the points or a divisor d of n. # elladd:=proc(P,Q,a,b,n) local l,d; if P[3]=0 then return Q fi; if Q[3]=0 then return P fi; if P=Q then return elldou(P,a,b,n) fi; if P[1]=Q[1] then return [0,1,0] fi; d:=igcdex(P[1]-Q[1],n,'l'); if 1<d and d<n then return d fi; l:=(P[2]-Q[2])*l mod n; l^2-P[1]-Q[1] mod n; [%,l*(P[1]-%)-P[2] mod n,1]; end; Zio2J0kiUEc2IkkiUUdGJUkiYUdGJUkiYkdGJUkibkdGJTYkSSJsR0YlSSJkR0YlRiVGJUMrQCQvJkYkNiMiIiQiIiFPRiZAJC8mRiZGMUYzT0YkQCQvRiRGJk8tSSdlbGxkb3VHRiU2JkYkRidGKEYpQCQvJkYkNiMiIiImRiZGQk83JUYzRkNGMz5GLC1JJ2lnY2RleEdGJTYlLCZGQUZDRkQhIiJGKS5GK0AkMzJGQ0YsMkYsRilPRiw+RistSSRtb2RHRiU2JComLCYmRiQ2IyIiI0ZDJkYmRlpGTEZDRitGQ0YpLUZVNiQsKCokKUYrRmVuRkNGQ0ZBRkxGREZMRik3JUkiJUdGJS1GVTYkLCYqJkYrRkMsJkZBRkNGXW9GTEZDRkNGWUZMRilGQ0YlRiVGJQ== n:= 97; P:=[59,92,1]; a:=13; b:=4; IiMoKg== NyUiI2YiIyMqIiIi IiM4 IiIl elldou(P,a,b,n); elldou(%,a,b,n); elldou(%,a,b,n); NyUiIyEpIiNnIiIi NyUiI3giI2YiIiI= NyUiI24iI0giIiI= elladd(P,P,a,b,n); elladd(%,P,a,b,n); elladd(%,P,a,b,n); elladd(%,P,a,b,n); NyUiIyEpIiNnIiIi NyUiI24iI28iIiI= NyUiI3giI2YiIiI= NyUiIyIqIiMnKiIiIg==
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">10. Faktoriz\303\241l\303\241s elliptikus g\303\266rb\303\251kkel</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">11. Pr\303\255mteszt elliptikus g\303\266rb\303\251kkel</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">12. Polinomfaktoriz\303\241l\303\241s</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1">13. Az AKS-teszt</Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">14. A szita m\303\263dszerek alapjai</Font></Text-field>
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