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>
<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> restart;
<Text-field style="Heading 2" layout="Heading 2">E 11.1. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> diff(1/(x+1),x); LCQqJCksJkkieEc2IiIiIkYoRigiIiMhIiJGKg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 11.2. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn int(1/(x^3+x),x); LCYtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ4R0YoIiIiKiYjRisiIiNGKy1GJDYjLCYqJClGKkYuRitGK0YrRitGKyEiIg==
<Text-field style="Heading 2" layout="Heading 2">E 11.3. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn int(1/(x^2-2),x); LCQqKCMiIiIiIiNGJSlGJkYkRiUtSShhcmN0YW5oRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJCooRiRGJUkieEdGLUYlRidGJUYlRiUhIiI= diff(2^(1/2)/4*ln(x-2^(1/2))-2^(1/2)/4*ln(x+2^(1/2)),x); simplify(%); LCYqKCMiIiIiIiVGJSkiIiMjRiVGKEYlLCZJInhHNiJGJSokRidGJSEiIkYuRiUqKEYkRiVGJ0YlLCZGK0YlRi1GJUYuRi4= KiQsJiokKUkieEc2IiIiIyIiIkYpRighIiJGKg==
<Text-field style="Heading 2" layout="Heading 2">A 11.1. Algoritmus. </Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn SquareFree:=proc(a,x) local i,out,b,c,y,z,w; i:=1; out:=[]; b:=diff(a,x); c:=gcd(a,b); w:=quo(a,c,x); while c<>1 do y:=gcd(w,c); z:=quo(w,y,x); out:=[op(out),z]; i:=i+1; w:=y; c:=quo(c,y,x); od; out:=[op(out),w]; end; Zio2JEkiYUc2IkkieEdGJTYpSSJpR0YlSSRvdXRHRiVJImJHRiVJImNHRiVJInlHRiVJInpHRiVJIndHRiVGJUYlQyk+RigiIiI+Rik3Ij5GKi1JJWRpZmZHJSpwcm90ZWN0ZWRHRiM+RistSSRnY2RHNiRGN0koX3N5c2xpYkdGJTYkRiRGKj5GLi1JJHF1b0dGOzYlRiRGK0YmPyhGJUYxRjFGJTBGK0YxQyg+RiwtRjo2JEYuRis+Ri0tRkA2JUYuRixGJj5GKTckLUkjb3BHRjc2I0YpRi0+RigsJkYoRjFGMUYxPkYuRiw+RistRkA2JUYrRixGJj5GKTckRk1GLkYlRiVGJQ== SquareFree((-12*x^3+9*x+3)/(-12),x); NyQsJkkieEc2IiIiIkYmISIiLCYjRiYiIiNGJkYkRiY= sqrfree(-12*x^3+9*x+3); NyQhIiQ3JDckLCZJInhHNiIiIiJGKSEiIkYpNyQsJkYpRikqJiIiI0YpRidGKUYpRi4= PolynomialDiophant:=proc(a,b,r,x) local y,z,q; gcdex(a,b,x,'y','z'); q:=quo(y*r,b,x); [expand(y*r-q*b),expand(z*r+q*a)] end; Zio2JkkiYUc2IkkiYkdGJUkickdGJUkieEdGJTYlSSJ5R0YlSSJ6R0YlSSJxR0YlRiVGJUMlLUkmZ2NkZXhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2J0YkRiZGKC5GKi5GKz5GLC1JJHF1b0dGMDYlKiZGKiIiIkYnRjtGJkYoNyQtSSdleHBhbmRHRjE2IywmRjpGOyomRixGO0YmRjshIiItRj42IywmKiZGK0Y7RidGO0Y7KiZGLEY7RiRGO0Y7RiVGJUYl PartialFractions1:=proc(r,L,x) local a,b,l,i,c; l:=nops(L); if l<2 then return([[r,L[1]]]) fi; a:=1; for i to l-1 do a:=a*L[i]^i od; b:=L[l]^l; c:=PolynomialDiophant(a,b,r,x); [op(PartialFractions1(c[2],L[1..l-1],x)),[c[1],L[l]]]; end; Zio2JUkickc2IkkiTEdGJUkieEdGJTYnSSJhR0YlSSJiR0YlSSJsR0YlSSJpR0YlSSJjR0YlRiVGJUMpPkYrLUklbm9wc0clKnByb3RlY3RlZEc2I0YmQCQyRisiIiNPNyM3JEYkJkYmNiMiIiI+RilGPD8oRixGPEY8LCZGK0Y8RjwhIiJJJXRydWVHRjI+RikqJkYpRjwpJkYmNiNGLEYsRjw+RiopJkYmNiNGK0YrPkYtLUkzUG9seW5vbWlhbERpb3BoYW50R0YlNiZGKUYqRiRGJzckLUkjb3BHRjI2Iy1JMlBhcnRpYWxGcmFjdGlvbnMxR0YlNiUmRi02I0Y2JkYmNiM7RjxGP0YnNyQmRi1GO0ZJRiVGJUYl PartialFractions2:=proc(r,q,e,x) local a,b,l,i,u,v; if e<2 then return([r]) fi; u:=quo(r,q,x,v); [op(PartialFractions2(u,q,e-1,x)),v]; end; Zio2Jkkickc2IkkicUdGJUkiZUdGJUkieEdGJTYoSSJhR0YlSSJiR0YlSSJsR0YlSSJpR0YlSSJ1R0YlSSJ2R0YlRiVGJUMlQCQyRiciIiNPNyNGJD5GLi1JJHF1b0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYmRiRGJkYoRi83JC1JI29wR0Y6NiMtSTJQYXJ0aWFsRnJhY3Rpb25zMkdGJTYmRi5GJiwmRiciIiJGRSEiIkYoRi9GJUYlRiU= PartialFractions:=proc(r,L,x) local i,LL,LLL; LL:=PartialFractions1(r,L,x); LLL:=[]; for i to nops(LL) do LLL:=[op(LLL),[LL[i][2],PartialFractions2(LL[i][1],LL[i][2],i,x)]]; od; end; Zio2JUkickc2IkkiTEdGJUkieEdGJTYlSSJpR0YlSSNMTEdGJUkkTExMR0YlRiVGJUMlPkYqLUkyUGFydGlhbEZyYWN0aW9uczFHRiVGIz5GKzciPyhGKSIiIkYzLUklbm9wc0clKnByb3RlY3RlZEc2I0YqSSV0cnVlR0Y2PkYrNyQtSSNvcEdGNjYjRis3JCYmRio2I0YpNiMiIiMtSTJQYXJ0aWFsRnJhY3Rpb25zMkdGJTYmJkZANiNGM0Y/RilGJ0YlRiVGJQ== HermiteReduction:=proc(p,q,x) local pp,rp,r,qq,ip,i,qi,ri,n,c; pp:=quo(p,q,x); r:=rem(p,q,x); qq:=SquareFree(q,x); r:=PartialFractions(r,qq,x); rp:=0; ip:=0; for i to nops(r) do qi:=r[i][1]; ri:=r[i][2]; n:=i; while n>1 do if ri[n]<>0 then c:=PolynomialDiophant(qi,diff(qi,x),ri[n],x); rp:=rp-c[2]/(n-1)/qi^(n-1); ri[n-1]:=ri[n-1]+c[1]+diff(c[2],x)/(n-1); fi; n:=n-1; od; ip:=ip+ri[1]/qi; od; rp+int(pp,x)+Int(ip,x); end; 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
<Text-field style="Heading 2" layout="Heading 2">E 11.4. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn fp:=441*x^7+780*x^6-2861*x^5+4085*x^4+7695*x^3+3713*x^2-43253*x+24500; LDIqJiIkVCUiIiIpSSJ4RzYiIiIoRiVGJSomIiQheUYlKUYnIiInRiVGJSomIiVoR0YlKUYnIiImRiUhIiIqJiIlJjMlRiUpRiciIiVGJUYlKiYiJSZwKEYlKUYnIiIkRiVGJSomIiU4UEYlKUYnIiIjRiVGJSomIiZgSyVGJUYnRiVGMiImK1gjRiU= fq:=9*x^6+6*x^5-65*x^4+20*x^3+135*x^2-154*x+49; LDAqJiIiKiIiIilJInhHNiIiIidGJUYlKiZGKUYlKUYnIiImRiVGJSomIiNsRiUpRiciIiVGJSEiIiomIiM/RiUpRiciIiRGJUYlKiYiJE4iRiUpRiciIiNGJUYlKiYiJGEiRiVGJ0YlRjEiI1xGJQ== fp:=fp/9; fq:=fq/9; fr:=rem(fp,fq,x); f:=fp/fq; LDIqJiIjXCIiIilJInhHNiIiIihGJUYlKiYjIiRnIyIiJEYlKUYnIiInRiVGJSomIyIlaEciIipGJSlGJyIiJkYlISIiKiYjIiUmMyVGM0YlKUYnIiIlRiVGJSomIiRiKUYlKUYnRi1GJUYlKiYjIiU4UEYzRiUpRiciIiNGJUYlKiYjIiZgSyVGM0YlRidGJUY2IyImK1gjRjNGJQ== LDAqJClJInhHNiIiIiciIiJGKComIyIiIyIiJEYoKUYlIiImRihGKComIyIjbCIiKkYoKUYlIiIlRighIiIqJiMiIz9GMkYoKUYlRixGKEYoKiYiIzpGKClGJUYrRihGKComIyIkYSJGMkYoRiVGKEY1IyIjXEYyRig= LCojIiZhPSMiIioiIiIqJiIkTihGJilJInhHNiIiIiVGJkYmKiYiJFQlRiYpRioiIiNGJkYmKiYjIiZZQyIiIiRGJkYqRiYhIiI= KiYsMiomIiNcIiIiKUkieEc2IiIiKEYmRiYqJiMiJGcjIiIkRiYpRigiIidGJkYmKiYjIiVoRyIiKkYmKUYoIiImRiYhIiIqJiMiJSYzJUY0RiYpRigiIiVGJkYmKiYiJGIpRiYpRihGLkYmRiYqJiMiJThQRjRGJilGKCIiI0YmRiYqJiMiJmBLJUY0RiZGKEYmRjcjIiYrWCNGNEYmRiYsMCokRi9GJkYmKiYjRkRGLkYmRjVGJkYmKiYjIiNsRjRGJkY7RiZGNyomIyIjP0Y0RiZGP0YmRiYqJiIjOkYmRkNGJkYmKiYjIiRhIkY0RiZGKEYmRjcjRiVGNEYmRjc= qq:=SquareFree(fq,x); NyYiIiIsJkkieEc2IkYjIyIiKCIiJEYjRiMsJkYlRiNGIyEiIg== PartialFractions1(fr,qq,x); NyY3JCIiISIiIjckIiQlSCwmSSJ4RzYiRiUjIiIoIiIkRiVGIzckLCgiJCNSRiUqJiIkVCVGJSlGKSIiI0YlRiUqJiIkIykpRiVGKUYlISIiLCZGKUYlRiVGNw== PartialFractions2(392+441*x^2-882*x,x-1,4,x); NyYiIiEiJFQlRiMhI1w= PartialFractions(fr,qq,x); NyY3JCIiIjcjIiIhNyQsJkkieEc2IkYkIyIiKCIiJEYkNyRGJiIkJUg3JEYkNyVGJkYmRiY3JCwmRilGJEYkISIiNyZGJiIkVCVGJiEjXA== convert(f,parfrac,x,sqrfree); LCwqJiIjXCIiIkkieEc2IkYlRiUiI2FGJSomIiRUJUYlKSwmRiZGJUYlISIiIiIjRi1GJSomRiRGJSlGLCIiJUYtRi0qJiIlWUVGJSksJiomIiIkRiVGJkYlRiUiIihGJUYuRi1GJQ== PolynomialDiophant(x+7/3,1,294,x); NyQiIiEiJCVI int(294/(x+7/3)^2,x); LCQqJiIkJUgiIiIsJkkieEc2IkYlIyIiKCIiJEYlISIiRiw= int(441/(x-1)^2-49/(x-1)^4,x); LCYqJiIkVCUiIiIsJkkieEc2IkYlRiUhIiJGKUYpKiYjIiNcIiIkRiUpRiZGLUYpRiU= HermiteReduction(fp,fq,x); LC4qJiIkJUgiIiIsJkkieEc2IkYlIyIiKCIiJEYlISIiRiwqJiMiI1xGK0YlKSwmRidGJUYlRixGK0YsRiUqJiIkVCVGJUYxRixGLComI0YvIiIjRiUpRidGNkYlRiUqJiIjYUYlRidGJUYlLUkkSW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YoNiQiIiFGJ0Yl
<Text-field style="Heading 2" layout="Heading 2">E 11.5. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn gp:=36*x^6+126*x^5+183*x^4+13807/6*x^3-407*x^2-3242/5*x+3044/15;; LDAqJiIjTyIiIilJInhHNiIiIidGJUYlKiYiJEUiRiUpRiciIiZGJUYlKiYiJCQ9RiUpRiciIiVGJUYlKiYjIiYyUSJGKUYlKUYnIiIkRiVGJSomIiQyJUYlKUYnIiIjRiUhIiIqJiMiJVVLRi1GJUYnRiVGOyMiJVdJIiM6RiU= gq:=(x^2+7/6*x+1/3)^2*(x-2/5)^3; KiYpLCgqJClJInhHNiIiIiMiIiJGKiomIyIiKCIiJ0YqRidGKkYqI0YqIiIkRipGKUYqKSwmRidGKiNGKSIiJiEiIkYwRio= g:=gp/gq; KigsMComIiNPIiIiKUkieEc2IiIiJ0YmRiYqJiIkRSJGJilGKCIiJkYmRiYqJiIkJD1GJilGKCIiJUYmRiYqJiMiJjJRIkYqRiYpRigiIiRGJkYmKiYiJDIlRiYpRigiIiNGJiEiIiomIyIlVUtGLkYmRihGJkY8IyIlV0kiIzpGJkYmKSwoKiRGOkYmRiYqJiMiIihGKkYmRihGJkYmI0YmRjdGJkY7RjwpLCZGKEYmI0Y7Ri5GPEY3Rjw= convert(g,parfrac,x,sqrfree); LCwqJiIlcTwiIiIpLCYqJiIiJkYlSSJ4RzYiRiVGJSIiIyEiIkYsRi1GJSomIiU/VkYlKUYnIiIkRi1GJSomIyInYnM9IiM7RiVGJ0YtRiUqKCNGJUY1RiUsJiInRG1NRi0qJiInXTdBRiVGKkYlRi1GJSwoKiYiIidGJSlGKkYsRiVGJSomIiIoRiVGKkYlRiVGLEYlRi1GJSomLCYiJkRxJUYtKiYiJl0nekYlRipGJUYtRiUpRjxGLEYtRiU=
<Text-field style="Heading 2" layout="Heading 2">A 11.2. Algoritmus. </Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn HorowitzReduction:=proc(p,q,x) local pop,pp,d,b,m,n,a,aa,c,cc,r,i,j,e,s; pop:=quo(p,q,x); pp:=rem(p,q,x); d:=gcd(q,diff(q,x)); b:=quo(q,d,x); m:=degree(b); n:=degree(d); aa:=sum(a[i]*x^i,i=0..m-1); cc:=sum(c[i]*x^i,i=0..n-1); r:=expand(b*diff(cc,x)-cc*quo(b*diff(d,x),d,x)+d*aa); for i from 0 to m+n-1 do e[i]:=coeff(pp,x,i)=coeff(r,x,i); od; s:=solve([e[j]$j=0..m+n-1],[a[j]$j=0..m-1,c[j]$j=0..n-1]); aa:=sum(a[j]*x^j,j=0..m-1); aa:=subs(op(s),aa); cc:=sum(c[j]*x^j,j=0..n-1); cc:=subs(op(s),cc); cc/d+Int(pop,x)+Int(aa/b,x); end; 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
<Text-field style="Heading 2" layout="Heading 2">E 11.6. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn debug(HorowitzReduction); HorowitzReduction(fp,fq,x); STJIb3Jvd2l0elJlZHVjdGlvbkc2Ig== {--> enter HorowitzReduction, args = 49*x^7+260/3*x^6-2861/9*x^5+4085/9*x^4+855*x^3+3713/9*x^2-43253/9*x+24500/9, x^6+2/3*x^5-65/9*x^4+20/9*x^3+15*x^2-154/9*x+49/9, x LCYqJiIjXCIiIkkieEc2IkYlRiUiI2FGJQ== LCojIiZhPSMiIioiIiIqJiIkTihGJilJInhHNiIiIiVGJkYmKiYiJFQlRiYpRioiIiNGJkYmKiYjIiZZQyIiIiRGJkYqRiYhIiI= LCwjIiIoIiIkISIiKiYiIiciIiJJInhHNiJGKUYpKiYiIiVGKSlGKiIiI0YpRiYqJiNGL0YlRikpRipGJUYpRiYqJClGKkYtRilGKQ== LCgqJClJInhHNiIiIiMiIiJGKComIyIiJSIiJEYoRiVGKEYoIyIiKEYsISIi IiIj IiIl LCYmSSJhRzYiNiMiIiEiIiIqJiZGJDYjRihGKEkieEdGJUYoRig= LComSSJjRzYiNiMiIiEiIiIqJiZGJDYjRihGKEkieEdGJUYoRigqJiZGJDYjIiIjRigpRixGMEYoRigqJiZGJDYjIiIkRigpRixGNUYoRig= LEwqKCMiIzUiIiQiIiImSSJjRzYiNiMiIiNGJylJInhHRipGLEYnISIiKiYjIiIoRiZGJyZJImFHRio2IyIiIUYnRi8qKEYxRicmRjQ2I0YnRidGLkYnRi8qKCMiIzlGJkYnJkYpRjlGJ0YuRidGLyooRixGJyZGKTYjRiZGJylGLkYmRidGLyooRjtGJ0YoRidGLkYnRi8qKEYyRidGP0YnRi1GJ0YvKihGJkYnRi1GJ0Y9RidGLyooRixGJ0ZBRidGKEYnRi8qJilGLiIiJUYnRj9GJ0YvKihGSEYnJkYpRjVGJ0YuRidGLyooIiInRidGLkYnRjNGJ0YnKihGTEYnRjhGJ0YtRidGJyooRkhGJ0YtRidGM0YnRi8qKEZIRidGQUYnRjhGJ0YvKigjRixGJkYnRkFGJ0YzRidGLyooRlFGJ0ZHRidGOEYnRi8qJkZHRidGM0YnRicqJilGLiIiJkYnRjhGJ0YnKiZGTEYnRkpGJ0YvKiZGMUYnRj1GJ0Yv LyMiJmE9IyIiKiwoKiYjIiIoIiIkIiIiJkkiYUc2IjYjIiIhRishIiIqJiIiJ0YrJkkiY0dGLkYvRitGMSomRihGKyZGNTYjRitGK0Yx LyMhJllDIiIiJCwsKiYjIiIoRiUiIiImSSJhRzYiNiNGKkYqISIiKiYjIiM5RiVGKiZJImNHRi1GLkYqRi8qJkYxRiomRjQ2IyIiI0YqRi8qJiIiJUYqJkY0NiMiIiFGKkYvKiYiIidGKiZGLEY8RipGKg== LyIkVCUsLComIyIjNSIiJCIiIiZJImNHNiI2IyIiI0YpISIiKiYiIihGKSZGKzYjRihGKUYvKiZGKEYpJkYrNiNGKUYpRi8qJiIiJ0YpJkkiYUdGLEY2RilGKSomIiIlRikmRjo2IyIiIUYpRi8= LyIiISwqKiYiIiMiIiImSSJjRzYiNiMiIiRGJyEiIiomRiZGJyZGKTYjRiZGJ0YtKiYiIiVGJyZJImFHRio2I0YnRidGLSomI0YmRixGJyZGNDYjRiNGJ0Yt LyIkTigsKCZJImNHNiI2IyIiJCEiIiomIyIiI0YpIiIiJkkiYUdGJzYjRi5GLkYqJkYwNiMiIiFGLg== LyIiISZJImFHNiI2IyIiIg== NyM3KC8mSSJhRzYiNiMiIiFGKS8mRiY2IyIiIkYpLyZJImNHRidGKCMhJXNpIiIqLyZGMEYsIyIlYUEiIiQvJkYwNiMiIiMiJE4oLyZGMDYjRjghJE4o LCYmSSJhRzYiNiMiIiEiIiIqJiZGJDYjRihGKEkieEdGJUYoRig= IiIh LComSSJjRzYiNiMiIiEiIiIqJiZGJDYjRihGKEkieEdGJUYoRigqJiZGJDYjIiIjRigpRixGMEYoRigqJiZGJDYjIiIkRigpRixGNUYoRig= LCojIiVzaSIiKiEiIiomIyIlYUEiIiQiIiJJInhHNiJGK0YrKiYiJE4oRispRiwiIiNGK0YrKiZGL0YrKUYsRipGK0Ym LCgqJiwqIyIlc2kiIiohIiIqJiMiJWFBIiIkIiIiSSJ4RzYiRi1GLSomIiROKEYtKUYuIiIjRi1GLSomRjFGLSlGLkYsRi1GKEYtLCwjIiIoRixGKComIiInRi1GLkYtRi0qJiIiJUYtRjJGLUYoKiYjRjNGLEYtRjVGLUYoKiQpRi5GPEYtRi1GKEYtLUkkSW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YvNiQsJiomIiNcRi1GLkYtRi0iI2FGLUYuRi0tRkI2JCIiIUYuRi0= <-- exit HorowitzReduction (now at top level) = (-6272/9+2254/3*x+735*x^2-735*x^3)/(-7/3+6*x-4*x^2-2/3*x^3+x^4)+Int(49*x+54, x)+Int(0, x)} LCgqJiwqIyIlc2kiIiohIiIqJiMiJWFBIiIkIiIiSSJ4RzYiRi1GLSomIiROKEYtKUYuIiIjRi1GLSomRjFGLSlGLkYsRi1GKEYtLCwjIiIoRixGKComIiInRi1GLkYtRi0qJiIiJUYtRjJGLUYoKiYjRjNGLEYtRjVGLUYoKiQpRi5GPEYtRi1GKEYtLUkkSW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YvNiQsJiomIiNcRi1GLkYtRi0iI2FGLUYuRi0tRkI2JCIiIUYuRi0=
<Text-field style="Heading 2" layout="Heading 2">E 11.7. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn debug(HorowitzReduction); HorowitzReduction(gp,gq,x); STJIb3Jvd2l0elJlZHVjdGlvbkc2Ig== {--> enter HorowitzReduction, args = 36*x^6+126*x^5+183*x^4+13807/6*x^3-407*x^2-3242/5*x+3044/15, (x^2+7/6*x+1/3)^2*(x-2/5)^3, x IiIh LDAqJiIjTyIiIilJInhHNiIiIidGJUYlKiYiJEUiRiUpRiciIiZGJUYlKiYiJCQ9RiUpRiciIiVGJUYlKiYjIiYyUSJGKUYlKUYnIiIkRiVGJSomIiQyJUYlKUYnIiIjRiUhIiIqJiMiJVVLRi1GJUYnRiVGOyMiJVdJIiM6RiU= KiYsKCokKUkieEc2IiIiIyIiIkYpKiYjIiIoIiInRilGJkYpRikjRikiIiRGKUYpKSwmRiZGKSNGKCIiJiEiIkYoRik= LCoqJClJInhHNiIiIiQiIiJGKComIyIjQiIjSUYoKUYlIiIjRihGKComI0YuIiM6RihGJUYoISIiRjBGMg== IiIk IiIl LCgmSSJhRzYiNiMiIiEiIiIqJiZGJDYjRihGKEkieEdGJUYoRigqJiZGJDYjIiIjRigpRixGMEYoRig= LComSSJjRzYiNiMiIiEiIiIqJiZGJDYjRihGKEkieEdGJUYoRigqJiZGJDYjIiIjRigpRixGMEYoRigqJiZGJDYjIiIkRigpRixGNUYoRig= LGhuKigiIiQiIiIpSSJ4RzYiRiRGJSZJImNHRig2I0YlRiUhIiIqKCIiI0YlKUYnIiIlRiUmRio2I0YuRiVGLComKUYnIiImRiUmRio2I0YkRiVGLCooIyIjSCIjOkYlKUYnRi5GJUYpRiVGLCooIyIiKCIiJ0YlRiZGJUYxRiVGLCooI0YuRjVGJUYvRiVGNkYlRiwqKEYwRiUmRio2IyIiIUYlRjxGJUYsKigjIiNGIiM1RiVGREYlRidGJUYsKiZGL0YlJkkiYUdGKEZFRiVGJSomRjRGJSZGTUYrRiVGJSomKUYnRkBGJSZGTUYyRiVGJSooIyIjNiIjSUYlRiZGJUZMRiVGJSooRlRGJUYvRiVGT0YlRiUqKEZURiVGNEYlRlJGJUYlKigjRlUiI0RGJUY8RiVGTEYlRiwqKEZaRiVGJkYlRk9GJUYsKihGWkYlRi9GJUZSRiVGLCooI0YuRmVuRiVGJ0YlRkxGJUYsKihGaW5GJUZPRiVGPEYlRiwqKEZpbkYlRlJGJUYmRiVGLComI0YwIiN2RiVGTEYlRiUqKEZdb0YlRk9GJUYnRiVGJSooRl1vRiVGUkYlRjxGJUYlKigjRiVGJEYlRilGJUYnRiVGLCooI0Y/RjtGJUYxRiVGPEYlRiwqKCNGJEY1RiVGNkYlRiZGJUYsKigjRjBGO0YlRjFGJUYnRiVGLCooRkJGJUY2RiVGPEYlRiwqJiNGJUY1RiVGREYlRiwqJiNGLkY7RiVGKUYlRiw= LyMiJVdJIiM6LCgqJiMiIiUiI3YiIiImSSJhRzYiNiMiIiFGK0YrKiYjRisiIiZGKyZJImNHRi5GL0YrISIiKiYjIiIjRiVGKyZGNTYjRitGK0Y2 LyMhJVVLIiImLCwqJiMiI0YiIzUiIiImSSJjRzYiNiMiIiFGKyEiIiomIyIiIyIjREYrJkkiYUdGLkYvRitGMSomIyIiJSIjdkYrJkY3NiNGK0YrRisqJiNGKyIiJEYrJkYtRj1GK0YxKiYjRjoiIzpGKyZGLTYjRjRGK0Yx LyEkMiUsMComIyIjSCIjOiIiIiZJImNHNiI2I0YpRikhIiIqJiIiJUYpJkYrNiMiIiFGKUYuKiYjIiM2IiNERikmSSJhR0YsRjJGKUYuKiYjIiIjRjdGKSZGOUYtRilGLiomI0YwIiN2RikmRjk2I0Y8RilGKSomIyIiKEYoRikmRitGQkYpRi4qJiNGPCIiJkYpJkYrNiMiIiRGKUYu LyMiJjJRIiIiJywuKiYiIiQiIiImSSJjRzYiNiNGKUYpISIiKiYjIiIoRiVGKSZGKzYjIiIjRilGLiomIyIjNiIjSUYpJkkiYUdGLDYjIiIhRilGKSomI0Y3IiNERikmRjpGLUYpRi4qJiNGNEY/RikmRjpGM0YpRi4qJiNGKCIiJkYpJkYrNiNGKEYpRi4= LyIkJD0sLComIiIjIiIiJkkiY0c2IjYjRiZGJyEiIiomI0YmIiImRicmRik2IyIiJEYnRiwmSSJhR0YqNiMiIiFGJyomIyIjNiIjSUYnJkY0NiNGJ0YnRicqJiNGOSIjREYnJkY0RitGJ0Ys LyIkRSIsKCZJImNHNiI2IyIiJCEiIiZJImFHRic2IyIiIkYuKiYjIiM2IiNJRi4mRiw2IyIiI0YuRi4= LyIjTyZJImFHNiI2IyIiIw== NyM3KS8mSSJhRzYiNiMiIiEjIiVcTiIiIy8mRiY2IyIiIiIlbjYvJkYmNiNGLCIjTy8mSSJjR0YnRigjIiVVciIjRC8mRjhGLyMhJj01JEY7LyZGOEY0IyImWiZSIiNdLyZGODYjIiIkIyIlcl8iIiY= LCgmSSJhRzYiNiMiIiEiIiIqJiZGJDYjRihGKEkieEdGJUYoRigqJiZGJDYjIiIjRigpRixGMEYoRig= LCgjIiVcTiIiIyIiIiomIiVuNkYmSSJ4RzYiRiZGJiomIiNPRiYpRilGJUYmRiY= LComSSJjRzYiNiMiIiEiIiIqJiZGJDYjRihGKEkieEdGJUYoRigqJiZGJDYjIiIjRigpRixGMEYoRigqJiZGJDYjIiIkRigpRixGNUYoRig= LCojIiVVciIjRCIiIiomIyImPTUkRiVGJkkieEc2IkYmISIiKiYjIiZaJlIiI11GJilGKiIiI0YmRiYqJiMiJXJfIiImRiYpRioiIiRGJkYm LCgqKCwqIyIlVXIiI0QiIiIqJiMiJj01JEYnRihJInhHNiJGKCEiIiomIyImWiZSIiNdRigpRiwiIiNGKEYoKiYjIiVyXyIiJkYoKUYsIiIkRihGKEYoLCgqJEYzRihGKComIyIiKCIiJ0YoRixGKEYoI0YoRjpGKEYuKSwmRixGKCNGNEY4Ri5GNEYuRigtSSRJbnRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRi02JCIiIUYsRigtRkY2JComLCgjIiVcTkY0RigqJiIlbjZGKEYsRihGKComIiNPRihGM0YoRihGKCwqKiRGOUYoRigqJiMiI0IiI0lGKEYzRihGKComI0Y0IiM6RihGLEYoRi5GZ25GLkYuRixGKA== <-- exit HorowitzReduction (now at top level) = (7142/25-31018/25*x+39547/50*x^2+5271/5*x^3)/((x^2+7/6*x+1/3)*(x-2/5)^2)+Int(0, x)+Int((3549/2+1167*x+36*x^2)/(x^3+23/30*x^2-2/15*x-2/15), x)} LCgqKCwqIyIlVXIiI0QiIiIqJiMiJj01JEYnRihJInhHNiJGKCEiIiomIyImWiZSIiNdRigpRiwiIiNGKEYoKiYjIiVyXyIiJkYoKUYsIiIkRihGKEYoLCgqJEYzRihGKComIyIiKCIiJ0YoRixGKEYoI0YoRjpGKEYuKSwmRixGKCNGNEY4Ri5GNEYuRigtSSRJbnRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRi02JCIiIUYsRigtRkY2JComLCgjIiVcTkY0RigqJiIlbjZGKEYsRihGKComIiNPRihGM0YoRihGKCwqKiRGOUYoRigqJiMiI0IiI0lGKEYzRihGKComI0Y0IiM6RihGLEYoRi5GZ25GLkYuRixGKA==
<Text-field style="Heading 2" layout="Heading 2">A 11.3. Algoritmus. </Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 11.8. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn a:=1; b:=x^3+x; resultant(a-z*diff(b,x),b,x); IiIi LCYqJClJInhHNiIiIiQiIiJGKEYlRig= KiYsJiIiIkYkSSJ6RzYiISIiRiQpLCYqJiIiI0YkRiVGJEYkRiRGJEYrRiQ= gcd(a-1*diff(b,x),b); gcd(a+1/2*diff(b,x),b); SSJ4RzYi LCYqJClJInhHNiIiIiMiIiJGKEYoRig=
<Text-field style="Heading 2" layout="Heading 2">E 11.9. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn a:=1; b:=x^2-2; resultant(a-z*diff(b,x),b,x); IiIi LCYqJClJInhHNiIiIiMiIiJGKEYnISIi LCYqJiIiKSIiIilJInpHNiIiIiNGJSEiIkYlRiU= alpha:=2^(1/2)/4; gcd(a+alpha*diff(b,x),b); gcd(a-alpha*diff(b,x),b); LCQqJiMiIiIiIiVGJSkiIiMjRiVGKEYlRiU= LCYqJCkiIiMjIiIiRiVGJ0YnSSJ4RzYiRic= LCYqJCkiIiMjIiIiRiVGJyEiIkkieEc2IkYn
<Text-field style="Heading 2" layout="Heading 2">E 11.10. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn a:=36*x^2+1167*x+3549/2; b:=x^3+23/30*x^2-2/15*x-2/15; resultant(a-z*diff(b,x),b,x); LCgqJiIjTyIiIilJInhHNiIiIiNGJUYlKiYiJW42RiVGJ0YlRiUjIiVcTkYpRiU= LCoqJClJInhHNiIiIiQiIiJGKComIyIjQiIjSUYoKUYlIiIjRihGKComI0YuIiM6RihGJUYoISIiRjBGMg== LCoqJiMiIzsiJEQnIiIiKUkiekc2IiIiJEYnRicqJiMiJHcmRiZGJylGKSIiI0YnISIiKiYjIik0PygzI0YlRidGKUYnRjEiKyt6PElGRic= factor(%); LCQqKiMiIiIiJisrIkYlLCYqJiIjO0YlSSJ6RzYiRiVGJSImXnUkISIiRiUsJkYqRiUiJSshKUYlRiUsJkYoRiUiJkQ2KkYtRiVGJQ== gcd(a+8000*diff(b,x),b); gcd(a-91125/16*diff(b,x),b); gcd(a-37451/16*diff(b,x),b); LCYjIiIiIiIjRiRJInhHNiJGJA== LCYjIiIjIiIkIiIiSSJ4RzYiRiY= LCYjIiIjIiImISIiSSJ4RzYiIiIi
<Text-field style="Heading 2" layout="Heading 2">E 11.11. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn a:=7*x^13+10*x^8+4*x^7-7*x^6-4*x^3-4*x^2+3*x+3; b:=x^14-2*x^8-2*x^7-2*x^4-4*x^3-x^2+2*x+1; resultant(a-z*diff(b,x),b,x); LDIqJiIiKCIiIilJInhHNiIiIzhGJUYlKiYiIzVGJSlGJyIiKUYlRiUqJiIiJUYlKUYnRiRGJUYlKiZGJEYlKUYnIiInRiUhIiIqJkYvRiUpRiciIiRGJUY0KiZGL0YlKUYnIiIjRiVGNComRjdGJUYnRiVGJUY3RiU= LDIqJClJInhHNiIiIzkiIiJGKComIiIjRigpRiUiIilGKCEiIiomRipGKClGJSIiKEYoRi0qJkYqRigpRiUiIiVGKEYtKiZGM0YoKUYlIiIkRihGLSokKUYlRipGKEYtKiZGKkYoRiVGKEYoRihGKA== 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 factor(%); LCQqJiIwR3g4LXU1WCIiIiIpLCgqJiIiJUYlKUkiekc2IiIiI0YlRiUqJkYpRiVGK0YlISIiRiVGLyIiKEYlRi8= alpha:=(1+2^(1/2))/2; gcd(a-alpha*diff(b,x),b); gcd(a-(1-alpha)*diff(b,x),b); LCYjIiIiIiIjRiQqJkYjRiQpRiVGI0YkRiQ= LCwqJClJInhHNiIiIigiIiJGKComKSIiIyNGKEYrRigpRiVGK0YoISIiRiVGLiomRipGKEYlRihGLkYoRi4= LCwqJClJInhHNiIiIigiIiJGKComKSIiIyNGKEYrRigpRiVGK0YoRihGJSEiIiomRipGKEYlRihGKEYoRi4=
<Text-field style="Heading 2" layout="Heading 2">A 11.4. Algoritmus. </Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 11.12. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn a:=6*x^5+6*x^4-8*x^3-18*x^2+8*x+8; b:=x^6-5*x^4-8*x^3-2*x^2+2*x+1; resultant(a-z*diff(b,x),b,x); LC4qJiIiJyIiIilJInhHNiIiIiZGJUYlKiZGJEYlKUYnIiIlRiVGJSomIiIpRiUpRiciIiRGJSEiIiomIiM9RiUpRiciIiNGJUYxKiZGLkYlRidGJUYlRi5GJQ== LC4qJClJInhHNiIiIiciIiJGKComIiImRigpRiUiIiVGKCEiIiomIiIpRigpRiUiIiRGKEYtKiYiIiNGKClGJUYzRihGLSomRjNGKEYlRihGKEYoRig= LDAqJiIoW0tYIiIiIilJInpHNiIiIidGJSEiIiomIigpWz4oKUYlKUYnIiImRiVGJSomRixGJSlGJyIiJUYlRioqJiIpbz5EQkYlKUYnIiIkRiVGKiomIil3KlF1IkYlKUYnIiIjRiVGJSomIilfeihbJEYlRidGJUYlIiklKWZpNkYl factor(%); LCQqJiIoW0tYIiIiIiksKCokKUkiekc2IiIiI0YlRiUqJkYsRiVGKkYlISIiRixGLiIiJEYlRi4=
<Text-field style="Heading 2" layout="Heading 2">E 11.13. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn a:=2*x^5-19*x^4+60*x^3-159*x^2+50*x+11; b:=x^6-13*x^5+58*x^4-85*x^3-66*x^2-17*x+1; resultant(a-z*diff(b,x),b,x); LC4qJiIiIyIiIilJInhHNiIiIiZGJUYlKiYiIz5GJSlGJyIiJUYlISIiKiYiI2dGJSlGJyIiJEYlRiUqJiIkZiJGJSlGJ0YkRiVGLiomIiNdRiVGJ0YlRiUiIzZGJQ== LDAqJClJInhHNiIiIiciIiJGKComIiM4RigpRiUiIiZGKCEiIiomIiNlRigpRiUiIiVGKEYoKiYiIyYpRigpRiUiIiRGKEYtKiYiI21GKClGJSIiI0YoRi0qJiIjPEYoRiVGKEYtRihGKA== LC4qJiIwKyFHZGsyLD4iIiIpSSJ6RzYiIiInRiUhIiIqJiIwK2dYIkg6LVFGJSlGJyIiJkYlRiUqJiIwK1M9UEhLcSZGJSlGJyIiJUYlRioqJkYkRiUpRiciIiNGJUYlKiZGLEYlRidGJUYqRiRGKg== factor(%); LCQqJiIwKyFHZGsyLD4iIiIpLCoqJClJInpHNiIiIiRGJUYlKiQpRioiIiNGJSEiIkYqRiVGJUYlRi9GJUYw
<Text-field style="Heading 1" layout="Heading 1">12. A Risch-algoritmus.</Text-field>
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn