Komputeralgebrai algoritmusok J\303\241rai Antal Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak.
<Text-field style="Heading 1" layout="Heading 1">1. T<Font encoding="UTF-8">\303\266rt\303\251</Font>net</Text-field>
<Text-field style="Heading 1" layout="Heading 1">2. Algebrai alapok</Text-field>
<Text-field style="Heading 1" layout="Heading 1">3. Norm<Font encoding="UTF-8">\303\241</Font>l form<Font encoding="UTF-8">\303\241</Font>k, reprezent<Font encoding="UTF-8">\303\241ci\303\263</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1">4. Aritmetika</Text-field>
<Text-field style="Heading 1" layout="Heading 1">5. K<Font encoding="UTF-8">\303\255</Font>nai marad<Font encoding="UTF-8">\303\251</Font>kol<Font encoding="UTF-8">\303\241</Font>s</Text-field> restart;
<Text-field style="Heading 2" layout="Heading 2">E 5.1. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.2. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> a:=-30*x^3*y+90*x^2*y^2+15*x^2-60*x*y+45*y^2; LCwqKCIjSSIiIilJInhHNiIiIiRGJUkieUdGKEYlISIiKigiIyEqRiUpRiciIiNGJSlGKkYvRiVGJSomIiM6RiVGLkYlRiUqKCIjZ0YlRidGJUYqRiVGKyomIiNYRiVGMEYlRiU= collect(a,[x,y],`distributed`); LCwqKCIjSSIiIilJInhHNiIiIiRGJUkieUdGKEYlISIiKigiIyEqRiUpRiciIiNGJSlGKkYvRiVGJSomIiM6RiVGLkYlRiUqKCIjZ0YlRidGJUYqRiVGKyomIiNYRiVGMEYlRiU= collect(a,x); LCoqKCIjSSIiIilJInhHNiIiIiRGJUkieUdGKEYlISIiKiYsJiomIiMhKkYlKUYqIiIjRiVGJSIjOkYlRiUpRidGMUYlRiUqKCIjZ0YlRidGJUYqRiVGKyomIiNYRiVGMEYlRiU= collect(a,y); LCgqJiwmKiYiIyEqIiIiKUkieEc2IiIiI0YnRiciI1hGJ0YnKUkieUdGKkYrRidGJyomLCYqJiIjSUYnKUYpIiIkRichIiIqJiIjZ0YnRilGJ0Y1RidGLkYnRicqJiIjOkYnRihGJ0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.3. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> 3/1; IiIk LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.4. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> [i$i=-8..8]; map(x->x mod 6,%); NzMhIikhIighIichIiYhIiUhIiQhIiMhIiIiIiEiIiIiIiMiIiQiIiUiIiYiIiciIigiIik= NzMiIiUiIiYiIiEiIiIiIiMiIiRGI0YkRiVGJkYnRihGI0YkRiVGJkYn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.5. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> subs(x=5,a); subs(y=2,a); LCgqJiIlXVMiIiJJInlHNiJGJSEiIiomIiUmSCNGJSlGJiIiI0YlRiUiJHYkRiU= LCoqJiIjZyIiIilJInhHNiIiIiRGJSEiIiomIiR2JEYlKUYnIiIjRiVGJSomIiQ/IkYlRidGJUYqIiQhPUYl LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.6. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> a:=3*x^2*y^2-x^2*y+5*x^2+x*y^2-3*x*y; b:=2*x*y+7*x+y^2-2; LCwqKCIiJCIiIilJInhHNiIiIiNGJSlJInlHRihGKUYlRiUqJkYmRiVGK0YlISIiKiYiIiZGJUYmRiVGJSomRidGJUYqRiVGJSooRiRGJUYnRiVGK0YlRi0= LCoqKCIiIyIiIkkieEc2IkYlSSJ5R0YnRiVGJSomIiIoRiVGJkYlRiUqJClGKEYkRiVGJUYkISIi a mod 5; b mod 5; LCoqKCIiJCIiIilJInhHNiIiIiNGJSlJInlHRihGKUYlRiUqKCIiJUYlRiZGJUYrRiVGJSomRidGJUYqRiVGJSooRilGJUYnRiVGK0YlRiU= LCoqKCIiIyIiIkkieEc2IkYlSSJ5R0YnRiVGJSomRiRGJUYmRiVGJSokKUYoRiRGJUYlIiIkRiU= a mod 7; b mod 7; LCwqKCIiJCIiIilJInhHNiIiIiNGJSlJInlHRihGKUYlRiUqKCIiJ0YlRiZGJUYrRiVGJSomIiImRiVGJkYlRiUqJkYnRiVGKkYlRiUqKCIiJUYlRidGJUYrRiVGJQ== LCgqKCIiIyIiIkkieEc2IkYlSSJ5R0YnRiVGJSokKUYoRiRGJUYlIiImRiU= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.7. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> a:=7*x+5; b:=2*x-3; c:=expand(a*b); LCYqJiIiKCIiIkkieEc2IkYlRiUiIiZGJQ== LCYqJiIiIyIiIkkieEc2IkYlRiUiIiQhIiI= LCgqJiIjOSIiIilJInhHNiIiIiNGJUYlKiYiIzZGJUYnRiUhIiIiIzpGLA== subs(x=0,a) mod 5; subs(x=0,b) mod 5; subs(x=0,c) mod 5; IiIh IiIj IiIh subs(x=1,a) mod 5; subs(x=1,b) mod 5; subs(x=1,c) mod 5; IiIj IiIl IiIk subs(x=2,a) mod 5; subs(x=2,b) mod 5; subs(x=2,c) mod 5; IiIl IiIi IiIl subs(x=0,a) mod 7; subs(x=0,b) mod 7; subs(x=0,c) mod 7; IiIm IiIl IiIn subs(x=1,a) mod 7; subs(x=1,b) mod 7; subs(x=1,c) mod 7; IiIm IiIn IiIj subs(x=2,a) mod 7; subs(x=2,b) mod 7; subs(x=2,c) mod 7; IiIm IiIi IiIm c mod 7; c mod 5; LCYqJiIiJCIiIkkieEc2IkYlRiUiIidGJQ== LCYqJiIiJSIiIilJInhHNiIiIiNGJUYlKiZGJEYlRidGJUYl LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.8. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> m*i$i=-infinity..infinity; LUkiJEclKnByb3RlY3RlZEc2JComSSJtRzYiIiIiSSJpR0YoRikvRio7LCRJKWluZmluaXR5R0YkISIiRi4= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.9. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> p:=5*x+2; p*d; LCYqJiIiJiIiIkkieEc2IkYlRiUiIiNGJQ== KiYsJiomIiImIiIiSSJ4RzYiRiZGJiIiI0YmRiZJImRHRihGJg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.10. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> p1:=x; p2:=y; SSJ4RzYi SSJ5RzYi p1*a1+p2*a2; LCYqJkkieEc2IiIiIkkjYTFHRiVGJkYmKiZJInlHRiVGJkkjYTJHRiVGJkYm LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.11. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> [i$i=-8..8]; map(x->x mod 6,%); NzMhIikhIighIichIiYhIiUhIiQhIiMhIiIiIiEiIiIiIiMiIiQiIiUiIiYiIiciIigiIik= NzMiIiUiIiYiIiEiIiIiIiMiIiRGI0YkRiVGJkYnRihGI0YkRiVGJkYn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.12. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> p:=x^2+1; LCYqJClJInhHNiIiIiMiIiJGKEYoRig= a:=x^2+8*x+4; rem(a,p,x); b:=2*x^2+8*x+5; rem(b,p,x); LCgqJClJInhHNiIiIiMiIiJGKComIiIpRihGJUYoRigiIiVGKA== LCYiIiQiIiIqJiIiKUYkSSJ4RzYiRiRGJA== LCgqJiIiIyIiIilJInhHNiJGJEYlRiUqJiIiKUYlRidGJUYlIiImRiU= LCYiIiQiIiIqJiIiKUYkSSJ4RzYiRiRGJA== p:=x-2; rem(a,p,x); subs(x=2,a); rem(b,p,x); subs(x=2,b); LCZJInhHNiIiIiIiIiMhIiI= IiND IiND IiNI IiNI LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.13. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> a:=-30*x^3*y+90*x^2*y^2+15*x^2-60*x*y+45*y^2; a mod 7; subs(y=3,a); LCwqKCIjSSIiIilJInhHNiIiIiRGJUkieUdGKEYlISIiKigiIyEqRiUpRiciIiNGJSlGKkYvRiVGJSomIiM6RiVGLkYlRiUqKCIjZ0YlRidGJUYqRiVGKyomIiNYRiVGMEYlRiU= LCwqKCIiJiIiIilJInhHNiIiIiRGJUkieUdGKEYlRiUqKCIiJ0YlKUYnIiIjRiUpRipGLkYlRiUqJEYtRiVGJSooRilGJUYnRiVGKkYlRiUqJkYpRiVGL0YlRiU= LCoqJiIjISoiIiIpSSJ4RzYiIiIkRiUhIiIqJiIkRClGJSlGJyIiI0YlRiUqJiIkIT1GJUYnRiVGKiIkMCVGJQ== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.14. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> m0:=3; m1:=5; m:=m0*m1; 11=2+3*3; -4=-1+(-1)*3; IiIk IiIm IiM6 LyIjNkYj LyEiJUYj LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">A 5.1. Algoritmus. </Text-field> IntegerCRA:=proc(M,U) local G,N,n,i,j,t; n:=nops(M)-1; G:=[0$i=1..n]; N:=[0$i=0..n]; for j to n do t:=M[1] mod M[j+1]; for i to j-1 do t:=t*M[i+1] mod M[j+1]; od; G[j]:=1/t mod M[j+1]; od; N[1]:=U[1]; for j to n do t:=N[j]; for i from j-2 to 0 by -1 do t:=t*M[i+1]+N[i+1] mod M[j+1]; od; N[j+1]:=(U[j+1]-t)*G[j] mod M[j+1]; od; t:=N[n+1]; for j from n-1 to 0 by -1 do t:=t*M[j+1]+N[j+1]; od; t; end; Zio2JEkiTUc2IkkiVUdGJTYoSSJHR0YlSSJOR0YlSSJuR0YlSSJpR0YlSSJqR0YlSSJ0R0YlRiVGJUMrPkYqLCYtSSVub3BzRyUqcHJvdGVjdGVkRzYjRiQiIiJGNSEiIj5GKDcjLUkiJEdGMzYkIiIhL0YrO0Y1Rio+Rik3Iy1GOjYkRjwvRis7RjxGKj8oRixGNUY1RipJJXRydWVHRjNDJT5GLS1JJG1vZEdGJTYkJkYkNiNGNSZGJDYjLCZGLEY1RjVGNT8oRitGNUY1LCZGLEY1RjVGNkZGPkYtLUZKNiQqJkYtRjUmRiQ2IywmRitGNUY1RjVGNUZOPiZGKDYjRiwtRko2JCokRi1GNkZOPiZGKUZNJkYmRk0/KEYsRjVGNUYqRkZDJT5GLSZGKUZmbj8oRissJkYsRjUiIiNGNkY2RjxGRj5GLS1GSjYkLCZGVkY1JkYpRlhGNUZOPiZGKUZPLUZKNiQqJiwmJkYmRk9GNUYtRjZGNUZlbkY1Rk4+Ri0mRik2IywmRipGNUY1RjU/KEYsLCZGKkY1RjVGNkY2RjxGRj5GLSwmKiZGLUY1Rk5GNUY1RmpvRjVGLUYlRiVGJQ== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.15. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> `mod`:=mods; debug(IntegerCRA); IntegerCRA([99,97,95],[49,-21,-30]); SSVtb2RzRyUqcHJvdGVjdGVkRw== SStJbnRlZ2VyQ1JBRzYi {--> enter IntegerCRA, args = [99, 97, 95], [49, -21, -30] IiIj NyQiIiFGIw== NyUiIiFGI0Yj IiIj ISNb IiIl IiIp IiM3 IiNc IiNc ISNO ISNO IiIl ISNH ISNH ISVeRg== IScrQkY= IScrQkY= <-- exit IntegerCRA (now at top level) = 272300} IScrQkY= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">A 5.2. Algoritmus. </Text-field> NewtonInterp:=proc(a,u,x,p) local i,j,t,n,G,N; n:=nops(a)-1; G:=[0$i=1..n]; N:=[0$i=0..n]; for j to n do t:=a[j+1]-a[1] mod p; for i to j-1 do t:=t*(a[j+1]-a[i+1]) mod p; od; G[j]:=1/t mod p; od; N[1]:=u[1]; for j to n do t:=N[j]; for i from j-2 to 0 by -1 do t:=t*(a[j+1]-a[i+1])+N[i+1] mod p; od; N[j+1]:=(u[j+1]-t)*G[j] mod p; od; t:=N[n+1]; for j from n-1 to 0 by -1 do t:=t*(x-a[j+1])+N[j+1] mod p; od; t; end; 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.16. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> u0:=NewtonInterp([0,1],[-21,-30],y,97); LCYqJiIiKiIiIkkieUc2IkYlISIiIiNARig= u1:=NewtonInterp([0,1],[20,17],y,97); LCYqJiIiJCIiIkkieUc2IkYlISIiIiM/RiU= u2:=NewtonInterp([0,1],[-36,-31],y,97); LCYqJiIiJiIiIkkieUc2IkYlRiUiI08hIiI= u:=NewtonInterp([0,1,2],[u0,u1,u2],x,97); expand(u); LCgqJiwoKiZJInlHNiIiIiIsJkkieEdGJ0YoRighIiJGKEYoKiYiIidGKEYmRihGKCIjVEYoRihGKkYoRigqJiIiKkYoRiZGKEYrIiNARis= LCwqJilJInhHNiIiIiMiIiJJInlHRiZGKEYoKigiIiZGKEYlRihGKUYoRigqJiIjVEYoRiVGKEYoKiYiIipGKEYpRighIiIiI0BGMA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 5.17. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> a:=7*x+5; b:=2*x-3; c:=expand(a*b); LCYqJiIiKCIiIkkieEc2IkYlRiUiIiZGJQ== LCYqJiIiIyIiIkkieEc2IkYlRiUiIiQhIiI= LCgqJiIjOSIiIilJInhHNiIiIiNGJUYlKiYiIzZGJUYnRiUhIiIiIzpGLA== c5:=expand(NewtonInterp([0,1,2],[0,-2,-1],x,5)) mod 5; LCYqJClJInhHNiIiIiMiIiIhIiJGJUYp c7:=expand(NewtonInterp([0,1,2],[-1,2,-2],x,7)) mod 7; LCYqJiIiJCIiIkkieEc2IkYlRiVGJSEiIg== c3:=expand(NewtonInterp([0,1,-1],[0,0,1],x,3)) mod 3; LCYqJClJInhHNiIiIiMiIiIhIiJGJUYo expand(IntegerCRA([5,7,3],[-x^2-x,3*x-1,-x^2+x])) mod 105; {--> enter IntegerCRA, args = [5, 7, 3], [-x^2-x, 3*x-1, -x^2+x] IiIj NyQiIiFGIw== NyUiIiFGI0Yj ISIj IiIk ISIi ISIi ISIi LCYqJClJInhHNiIiIiMiIiIhIiJGJUYp LCYqJClJInhHNiIiIiMiIiIhIiJGJUYp LCgqJiIiIyIiIkkieEc2IkYlISIiIiIkRigqJkYpRiUpRiZGJEYlRiU= LCgqJiIiIyIiIkkieEc2IkYlISIiIiIkRigqJkYpRiUpRiZGJEYlRiU= LCYqJClJInhHNiIiIiMiIiIhIiJGJUYo IiIh IiIh LCgqJiIiIyIiIkkieEc2IkYlISIiIiIkRigqJkYpRiUpRiZGJEYlRiU= LCgqJiIjOSIiIilJInhHNiIiIiNGJUYlKiYiIzZGJUYnRiUhIiIiIzpGLA== LCgqJiIjOSIiIilJInhHNiIiIiNGJUYlKiYiIzZGJUYnRiUhIiIiIzpGLA== <-- exit IntegerCRA (now at top level) = 14*x^2-11*x-15} LCgqJiIjOSIiIilJInhHNiIiIiNGJUYlKiYiIzZGJUYnRiUhIiIiIzpGLA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 1" layout="Heading 1">6. Newton-iter<Font encoding="UTF-8">\303\241</Font>ci<Font encoding="UTF-8">\303\263</Font>, Hensel-felemel<Font encoding="UTF-8">\303\251</Font>s</Text-field>
<Text-field style="Heading 1" layout="Heading 1">7. Legnagyobb k<Font encoding="UTF-8">\303\266</Font>z<Font encoding="UTF-8">\303\266</Font>s oszt<Font encoding="UTF-8">\303\263</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1">8. Faktoriz<Font encoding="UTF-8">\303\241</Font>l<Font encoding="UTF-8">\303\241</Font>s</Text-field>
<Text-field style="Heading 1" layout="Heading 1">9. Egyenletrendszerek</Text-field>
<Text-field style="Heading 1" layout="Heading 1">10. Gr<Font encoding="UTF-8">\303\266bner-b\303\241zisok</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1">11. Racion<Font encoding="UTF-8">\303\241</Font>lis t<Font encoding="UTF-8">\303\266</Font>rtf<Font encoding="UTF-8">\303\274</Font>ggv<Font encoding="UTF-8">\303\251</Font>nyek integr<Font encoding="UTF-8">\303\241</Font>l<Font encoding="UTF-8">\303\241</Font>sa</Text-field>
<Text-field style="Heading 1" layout="Heading 1">12. A Risch-algoritmus.</Text-field>
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn