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> restart;
<Text-field style="Heading 2" layout="Heading 2">E 2.1. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> irem(1,1); irem(1,-1); IiIh IiIh irem(18,6); irem(30,6); IiIh IiIh irem(18,-6); irem(30,-6); IiIh IiIh irem(6,-6); irem(-6,6); IiIh IiIh LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.2. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> igcd(18,30); IiIn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.3. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> sign(-6); abs(6); sign(6); abs(6); sign(0); abs(0); ISIi IiIn IiIi IiIn IiIi IiIh igcd(-18,30); -18*30/igcd(-18,30); abs(-18*30)/igcd(-18,30); ilcm(-18,30); IiIn ISMhKg== IiMhKg== IiMhKg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.4. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> abs(-6); abs(6); IiIn IiIn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.5. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> gcd(18,30); 2*18+(-1)*30; (-3)*18+2*30; 7*18+(-4)*30; IiIn IiIn IiIn IiIn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">A 2.1. Algoritmus. </Text-field> Euclid:=proc(a,b,x) local c,d,r,ua,ub,uc; if nargs<3 then c:=abs(a); d:=abs(b); else ua:=lcoeff(collect(a,x),x); if ua<>0 then c:=a/ua fi; ub:=lcoeff(collect(b,x),x); if ub<>0 then d:=b/ub fi; fi; while d<>0 do if nargs<3 then r:=irem(c,d) else r:=rem(c,d,x) fi; c:=d; d:=r; od; if nargs<3 then abs(c); else uc:=lcoeff(collect(c,x),x); if uc<>0 then c/uc else c fi; fi; end; Zio2JUkiYUc2IkkiYkdGJUkieEdGJTYoSSJjR0YlSSJkR0YlSSJyR0YlSSN1YUdGJUkjdWJHRiVJI3VjR0YlRiVGJUMlQCUyJSZuYXJnc0ciIiRDJD5GKS1JJGFic0clKnByb3RlY3RlZEc2I0YkPkYqLUY3NiNGJkMmPkYsLUknbGNvZWZmR0Y4NiQtSShjb2xsZWN0R0YlNiRGJEYnRidAJDBGLCIiIT5GKSomRiQiIiJGLCEiIj5GLS1GQDYkLUZDNiRGJkYnRidAJDBGLUZHPkYqKiZGJkZKRi1GSz8oRiVGSkZKRiUwRipGR0MlQCVGMT5GKy1JJWlyZW1HRjg2JEYpRio+RistSSRyZW1HRiU2JUYpRipGJz5GKUYqPkYqRitAJUYxLUY3NiNGKUMkPkYuLUZANiQtRkM2JEYpRidGJ0AlMEYuRkcqJkYpRkpGLkZLRilGJUYlRiU= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.7. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> debug(Euclid); SSdFdWNsaWRHNiI= Euclid(18,30); {--> enter Euclid, args = 18, 30 IiM9 IiNJ IiM9 IiNJ IiM9 IiM3 IiM9 IiM3 IiIn IiM3 IiIn IiIh IiIn IiIh IiIn <-- exit Euclid (now at top level) = 6} IiIn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">A 2.2. Algoritmus. </Text-field> EEA:=proc(a,b,s,t,x) local c,c1,c2,d,d1,d2,q,r,r1,r2,ua,ub,uc; if nargs<5 then c:=abs(a); d:=abs(b); else ua:=lcoeff(collect(a,x),x); if ua<>0 then c:=a/ua fi; ub:=lcoeff(collect(b,x),x); if ub<>0 then d:=b/ub fi; fi; c1:=1; d1:=0; c2:=0; d2:=1; while d<>0 do if nargs<5 then q:=iquo(c,d) else q:=quo(c,d,x) fi; r:=expand(c-q*d); r1:=expand(c1-q*d1); r2:=expand(c2-q*d2); c:=d; c1:=d1; c2:=d2; d:=r; d1:=r1; d2:=r2; od; if nargs<5 then s:=c1/sign(a)/sign(c); t:=c2/sign(b)/sign(c); abs(c); else uc:=lcoeff(collect(c,x),x); if uc<>0 then if ua<>0 then s:=c1/uc/ua else s:=c1/uc fi; if ub<>0 then t:=c2/uc/ub else s:=c2/uc fi; c/uc; else if ua<>0 then s:=c1/ua else s:=c1 fi; if ub<>0 then t:=c2/ub else s:=c2 fi; c; fi; fi; end; 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.8. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> debug(EEA); SSRFRUFHNiI= EEA(18,30,'s','t'); {--> enter EEA, args = 18, 30, s, t IiM9 IiNJ IiIi IiIh IiIh IiIi IiIh IiM9 IiIi IiIh IiNJ IiIh IiIi IiM9 IiIi IiIh IiIi IiM3 ISIi IiIi IiM9 IiIi IiIh IiM3 ISIi IiIi IiIi IiIn IiIj ISIi IiM3 ISIi IiIi IiIn IiIj ISIi IiIj IiIh ISIm IiIk IiIn IiIj ISIi IiIh ISIm IiIk IiIj ISIi IiIn <-- exit EEA (now at top level) = 6} IiIn s; t; IiIj ISIi LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.9. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.10. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.11. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> a:=3*x^3+x^2+x+5; b:=5*x^2-3*x+1; LCoqJiIiJCIiIilJInhHNiJGJEYlRiUqJClGJyIiI0YlRiVGJ0YlIiImRiU= LCgqJiIiJiIiIilJInhHNiIiIiNGJUYlKiYiIiRGJUYnRiUhIiJGJUYl q1:=3/5*x; r1:=expand(a-q1*b); LCQqJiMiIiQiIiYiIiJJInhHNiJGJ0Yn LCgqJiMiIzkiIiYiIiIpSSJ4RzYiIiIjRidGJyomI0YrRiZGJ0YpRidGJ0YmRic= q2:=14/25; r2:=expand(r1-q2*b); IyIjOSIjRA== LCYqJiMiI18iI0QiIiJJInhHNiJGJ0YnIyIkNiJGJkYn q:=q1+q2; r:=r2; a=expand(q*b+r); LCYqJiMiIiQiIiYiIiJJInhHNiJGJ0YnIyIjOSIjREYn LCYqJiMiI18iI0QiIiJJInhHNiJGJ0YnIyIkNiJGJkYn LywqKiYiIiQiIiIpSSJ4RzYiRiVGJkYmKiQpRigiIiNGJkYmRihGJiIiJkYmRiM= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.12. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.13. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.14. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> a:=48*x^3-84*x^2+42*x-36; b:=-4*x^3-10*x^2+44*x-30; LCoqJiIjWyIiIilJInhHNiIiIiRGJUYlKiYiIyUpRiUpRiciIiNGJSEiIiomIiNVRiVGJ0YlRiUiI09GLg== LCoqJiIiJSIiIilJInhHNiIiIiRGJSEiIiomIiM1RiUpRiciIiNGJUYqKiYiI1dGJUYnRiVGJSIjSUYq Euclid(a,b,x); {--> enter Euclid, args = 48*x^3-84*x^2+42*x-36, -4*x^3-10*x^2+44*x-30, x IiNb LCoqJClJInhHNiIiIiQiIiJGKComIyIiKCIiJUYoKUYlIiIjRighIiIqJiNGKyIiKUYoRiVGKEYoI0YnRixGLw== ISIl LCoqJClJInhHNiIiIiQiIiJGKComIyIiJiIiI0YoKUYlRixGKEYoKiYiIzZGKEYlRighIiIjIiM6RixGKA== LCgjIiNMIiIlISIiKiYjIiM8RiUiIiIpSSJ4RzYiIiIjRipGJiomIyIjJioiIilGKkYsRipGKg== LCoqJClJInhHNiIiIiQiIiJGKComIyIiJiIiI0YoKUYlRixGKEYoKiYiIzZGKEYlRighIiIjIiM6RixGKA== LCgjIiNMIiIlISIiKiYjIiM8RiUiIiIpSSJ4RzYiIiIjRipGJiomIyIjJioiIilGKkYsRipGKg== LCYjIiUwOyIkeSYhIiIqJiMiJE4mIiQqRyIiIkkieEc2IkYrRis= LCgjIiNMIiIlISIiKiYjIiM8RiUiIiIpSSJ4RzYiIiIjRipGJiomIyIjJioiIilGKkYsRipGKg== LCYjIiUwOyIkeSYhIiIqJiMiJE4mIiQqRyIiIkkieEc2IkYrRis= IiIh LCYjIiUwOyIkeSYhIiIqJiMiJE4mIiQqRyIiIkkieEc2IkYrRis= IiIh IyIkTiYiJCpH LCYjIiIkIiIjISIiSSJ4RzYiIiIi <-- exit Euclid (now at top level) = -3/2+x} LCYjIiIkIiIjISIiSSJ4RzYiIiIi LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.15. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> EEA(a,b,'s','t',x); {--> enter EEA, args = 48*x^3-84*x^2+42*x-36, -4*x^3-10*x^2+44*x-30, s, t, x IiNb LCoqJClJInhHNiIiIiQiIiJGKComIyIiKCIiJUYoKUYlIiIjRighIiIqJiNGKyIiKUYoRiVGKEYoI0YnRixGLw== ISIl LCoqJClJInhHNiIiIiQiIiJGKComIyIiJiIiI0YoKUYlRixGKEYoKiYiIzZGKEYlRighIiIjIiM6RixGKA== IiIi IiIh IiIh IiIi IiIi LCgjIiNMIiIlISIiKiYjIiM8RiUiIiIpSSJ4RzYiIiIjRipGJiomIyIjJioiIilGKkYsRipGKg== IiIi ISIi LCoqJClJInhHNiIiIiQiIiJGKComIyIiJiIiI0YoKUYlRixGKEYoKiYiIzZGKEYlRighIiIjIiM6RixGKA== IiIh IiIi LCgjIiNMIiIlISIiKiYjIiM8RiUiIiIpSSJ4RzYiIiIjRipGJiomIyIjJioiIilGKkYsRipGKg== IiIi ISIi LCYqJiMiIiUiIzwiIiJJInhHNiJGJyEiIiMiJGckIiQqR0Yq LCYjIiUwOyIkeSYhIiIqJiMiJE4mIiQqRyIiIkkieEc2IkYrRis= LCYjIiRnJCIkKkciIiIqJiMiIiUiIzxGJkkieEc2IkYmRiY= LCYjIiNyIiQqRyEiIiomIyIiJSIjPCIiIkkieEc2IkYrRiY= LCgjIiNMIiIlISIiKiYjIiM8RiUiIiIpSSJ4RzYiIiIjRipGJiomIyIjJioiIilGKkYsRipGKg== IiIi ISIi LCYjIiUwOyIkeSYhIiIqJiMiJE4mIiQqRyIiIkkieEc2IkYrRis= LCYjIiRnJCIkKkciIiIqJiMiIiUiIzxGJkkieEc2IkYmRiY= LCYjIiNyIiQqRyEiIiomIyIiJSIjPCIiIkkieEc2IkYrRiY= LCYqJiMiJThcIiVTQCIiIkkieEc2IkYnISIiIyIlekoiJXE1Ric= IiIh LCgjIiQqRyIkMiIhIiIqJiMiJWM2IiROJiIiIkkieEc2IkYrRisqJiNGJEYqRispRiwiIiNGK0Yr LCgjIiQqRyIlcTUhIiIqJiNGJCIlU0AiIiJJInhHNiJGKkYqKiYjRiQiJE4mRiopRisiIiNGKkYm LCYjIiUwOyIkeSYhIiIqJiMiJE4mIiQqRyIiIkkieEc2IkYrRis= LCYjIiRnJCIkKkciIiIqJiMiIiUiIzxGJkkieEc2IkYmRiY= LCYjIiNyIiQqRyEiIiomIyIiJSIjPCIiIkkieEc2IkYrRiY= IiIh LCgjIiQqRyIkMiIhIiIqJiMiJWM2IiROJiIiIkkieEc2IkYrRisqJiNGJEYqRispRiwiIiNGK0Yr LCgjIiQqRyIlcTUhIiIqJiNGJCIlU0AiIiJJInhHNiJGKkYqKiYjRiQiJE4mRiopRisiIiNGKkYm IyIkTiYiJCpH LCYjIiIkIiQ5IyIiIiomIyIjPCIlP2tGJkkieEc2IkYmRiY= LCYjIiNyIiVTQCIiIiomIyIjPCIkTiZGJkkieEc2IkYmRiY= LCYjIiIkIiIjISIiSSJ4RzYiIiIi <-- exit EEA (now at top level) = -3/2+x} LCYjIiIkIiIjISIiSSJ4RzYiIiIi s; t; expand(s*a+t*b); LCYjIiIkIiQ5IyIiIiomIyIjPCIlP2tGJkkieEc2IkYmRiY= LCYjIiNyIiVTQCIiIiomIyIjPCIkTiZGJkkieEc2IkYmRiY= LCYjIiIkIiIjISIiSSJ4RzYiIiIi LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.16. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> p:=5*x^3*y^2-x^2*y^4-3*x^2*y^2+7*x*y^2+2*x*y-2*x+4*y^4+5; LDIqKCIiJiIiIilJInhHNiIiIiRGJSlJInlHRigiIiNGJUYlKiYpRidGLEYlKUYrIiIlRiUhIiIqKEYpRiVGLkYlRipGJUYxKigiIihGJUYnRiVGKkYlRiUqKEYsRiVGJ0YlRitGJUYlKiZGLEYlRidGJUYxKiZGMEYlRi9GJUYlRiRGJQ== sort(p,[y,x],plex); LDIqJilJInlHNiIiIiUiIiIpSSJ4R0YmIiIjRighIiIqJkYnRihGJEYoRigqKCIiJkYoKUYlRitGKClGKiIiJEYoRigqKEYyRihGMEYoRilGKEYsKigiIihGKEYwRihGKkYoRigqKEYrRihGJUYoRipGKEYoKiZGK0YoRipGKEYsRi9GKA== sort(p,[x,y],plex); LDIqKCIiJiIiIilJInhHNiIiIiRGJSlJInlHRigiIiNGJUYlKiYpRidGLEYlKUYrIiIlRiUhIiIqKEYpRiVGLkYlRipGJUYxKigiIihGJUYnRiVGKkYlRiUqKEYsRiVGJ0YlRitGJUYlKiZGLEYlRidGJUYxKiZGMEYlRi9GJUYlRiRGJQ== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.17. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> collect(p,[x,y]); LCwqKCIiJiIiIilJInhHNiIiIiRGJSlJInlHRigiIiNGJUYlKiYsJiokKUYrIiIlRiUhIiIqJkYpRiVGKkYlRjJGJSlGJ0YsRiVGJSomLCgqJkYsRiVGK0YlRiVGLEYyKiYiIihGJUYqRiVGJUYlRidGJUYlKiZGMUYlRjBGJUYlRiRGJQ== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.18. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> p:=collect(p,[x,y],`distributed`); lcoeff(p,[x,y],'t'); t; LDIqKCIiJiIiIilJInhHNiIiIiRGJSlJInlHRigiIiNGJUYlKiYpRidGLEYlKUYrIiIlRiUhIiIqKEYpRiVGLkYlRipGJUYxKigiIihGJUYnRiVGKkYlRiUqKEYsRiVGJ0YlRitGJUYlKiZGLEYlRidGJUYxKiZGMEYlRi9GJUYlRiRGJQ== IiIm KiYpSSJ4RzYiIiIkIiIiKUkieUdGJSIiI0Yn convert(t,list); map(x->op(2,x),%); NyQqJClJInhHNiIiIiQiIiIqJClJInlHRiYiIiNGKA== NyQiIiQiIiM= degree(p,{x,y}); IiIn degree(p,x); IiIk degree(p,y); IiIl LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.19. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> a=expand((1)*(2)*(3)*(2*x-3)*(4*x^2-x+2)); b=expand((-1)*(2)*(2*x-3)*(x-1)*(x+5)); LywqKiYiI1siIiIpSSJ4RzYiIiIkRiZGJiomIiMlKUYmKUYoIiIjRiYhIiIqJiIjVUYmRihGJkYmIiNPRi9GIw== LywqKiYiIiUiIiIpSSJ4RzYiIiIkRiYhIiIqJiIjNUYmKUYoIiIjRiZGKyomIiNXRiZGKEYmRiYiI0lGK0Yj expand((2)*(2*x-3)); LCYiIichIiIqJiIiJSIiIkkieEc2IkYnRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.20. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> a=expand((48)*(x-3/2)*(x^2-1/4*x+1/2)); b=expand((-4)*(x-3/2)*(x-1)*(x+5)); LywqKiYiI1siIiIpSSJ4RzYiIiIkRiZGJiomIiMlKUYmKUYoIiIjRiYhIiIqJiIjVUYmRihGJkYmIiNPRi9GIw== LywqKiYiIiUiIiIpSSJ4RzYiIiIkRiYhIiIqJiIjNUYmKUYoIiIjRiZGKyomIiNXRiZGKEYmRiYiI0lGK0Yj x-3/2; LCYjIiIkIiIjISIiSSJ4RzYiIiIi LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.21. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> u:=proc(p,L,typ) local pp,uu; pp:=expand(p); pp:=collect(pp,L,`distributed`); uu:=lcoeff(pp,L); if uu=0 then return 1 fi; if typ='integer' then return sign(uu) fi; uu; end; Zio2JUkicEc2IkkiTEdGJUkkdHlwR0YlNiRJI3BwR0YlSSN1dUdGJUYlRiVDKD5GKS1JJ2V4cGFuZEclKnByb3RlY3RlZEc2I0YkPkYpLUkoY29sbGVjdEc2JEYvSShfc3lzbGliR0YlNiVGKUYmSSxkaXN0cmlidXRlZEdGJT5GKi1JJ2xjb2VmZkdGLzYkRilGJkAkL0YqIiIhTyIiIkAkL0YnLkkoaW50ZWdlckdGL08tSSVzaWduR0YvNiNGKkYqRiVGJUYl cont:=proc(p,L,typ) local pp,uu,cL; if nops(L)=1 and typ<>'integer' then return 1 fi; uu:=u(p,L,typ); pp:=simplify(p/uu); pp:=collect(pp,L[1]); cL:=coeffs(pp,L[1]); if nops(L)=1 then return igcd(cL) fi; GCD([cL],L[2..nops(L)],typ); end; Zio2JUkicEc2IkkiTEdGJUkkdHlwR0YlNiVJI3BwR0YlSSN1dUdGJUkjY0xHRiVGJUYlQylAJDMvLUklbm9wc0clKnByb3RlY3RlZEc2I0YmIiIiMEYnLkkoaW50ZWdlckdGMk9GND5GKi1JInVHRiVGIz5GKS1JKXNpbXBsaWZ5R0YlNiMqJkYkRjRGKiEiIj5GKS1JKGNvbGxlY3RHNiRGMkkoX3N5c2xpYkdGJTYkRikmRiY2I0Y0PkYrLUknY29lZmZzR0YyRkdAJEYvTy1JJWlnY2RHRjI2I0YrLUkkR0NER0YlNiU3I0YrJkYmNiM7IiIjRjBGJ0YlRiVGJQ== pp:=proc(p,L,typ) local uu,pp,c; uu:=u(p,L,typ); pp:=simplify(p/uu); c:=cont(pp,L,typ); if c=0 then 0 else simplify(pp/c) fi; end; Zio2JUkicEc2IkkiTEdGJUkkdHlwR0YlNiVJI3V1R0YlSSNwcEdGJUkiY0dGJUYlRiVDJj5GKS1JInVHRiVGIz5GKi1JKXNpbXBsaWZ5R0YlNiMqJkYkIiIiRikhIiI+RistSSVjb250R0YlNiVGKkYmRidAJS9GKyIiIUY9LUYyNiMqJkYqRjVGK0Y2RiVGJUYl a; LCoqJiIjWyIiIilJInhHNiIiIiRGJUYlKiYiIyUpRiUpRiciIiNGJSEiIiomIiNVRiVGJ0YlRiUiI09GLg== u(a,[x],'integer'); IiIi cont(a,[x],'integer'); IiIn pp(a,[x],'integer'); LCoqJiIiKSIiIilJInhHNiIiIiRGJUYlKiYiIzlGJSlGJyIiI0YlISIiKiYiIihGJUYnRiVGJSIiJ0Yu u(a,[x],'rational'); IiNb cont(a,[x],'rational'); IiIi pp(a,[x],'rational'); LCoqJClJInhHNiIiIiQiIiJGKComIyIiKCIiJUYoKUYlIiIjRighIiIqJiNGKyIiKUYoRiVGKEYoI0YnRixGLw== b; LCoqJiIiJSIiIilJInhHNiIiIiRGJSEiIiomIiM1RiUpRiciIiNGJUYqKiYiI1dGJUYnRiVGJSIjSUYq u(b,[x],'integer'); ISIi cont(b,[x],'integer'); IiIj pp(b,[x],'integer'); LCoqJiIiIyIiIilJInhHNiIiIiRGJUYlKiYiIiZGJSlGJ0YkRiVGJSomIiNBRiVGJ0YlISIiIiM6RiU= u(b,[x],'rational'); ISIl cont(b,[x],'rational'); IiIi pp(b,[x],'rational'); LCoqJClJInhHNiIiIiQiIiJGKComIyIiJiIiI0YoKUYlRixGKEYoKiYiIzZGKEYlRighIiIjIiM6RixGKA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">A 2.3. Algoritmus. </Text-field> pseudodiv:=proc(a,b,x,q,r) local l,beta,qq,aa,bb; aa:=collect(expand(a),x); bb:=collect(expand(b),x); l:=degree(aa,x)-degree(bb,x)+1; q:=0; if l<=0 then r:=aa; return fi; beta:=lcoeff(bb,x); aa:=collect(expand(aa*beta^l),x); while degree(aa,x)>=degree(bb,x) do l:=degree(aa,x)-degree(bb,x); qq:=lcoeff(aa,x)/beta; q:=q+qq; aa:=collect(expand(aa-qq*x^l*bb),x); od; r:=aa; end; Zio2J0kiYUc2IkkiYkdGJUkieEdGJUkicUdGJUkickdGJTYnSSJsR0YlSSViZXRhR0YlSSNxcUdGJUkjYWFHRiVJI2JiR0YlRiVGJUMrPkYuLUkoY29sbGVjdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLUknZXhwYW5kR0Y1NiNGJEYnPkYvLUYzNiQtRjk2I0YmRic+RissKC1JJ2RlZ3JlZUdGNTYkRi5GJyIiIi1GQzYkRi9GJyEiIkZFRkU+RigiIiFAJDFGK0ZKQyQ+RilGLk9GJT5GLC1JJ2xjb2VmZkdGNUZHPkYuLUYzNiQtRjk2IyomRi5GRSlGLEYrRkVGJz8oRiVGRUZFRiUxRkZGQkMmPkYrLCZGQkZFRkZGSD5GLSomLUZSRkRGRUYsRkg+RigsJkYoRkVGLUZFPkYuLUYzNiQtRjk2IywmRi5GRSooRi1GRSlGJ0YrRkVGL0ZFRkhGJ0ZORiVGJUYl PrimitiveEuclidean:=proc(a,b,L,typ) local c,d,r,q,gamma; c:=pp(a,L,typ); d:=pp(b,L,typ); while d<>0 do pseudodiv(c,d,L[1],'q','r'); c:=d; d:=pp(r,L,typ); od; if nops(L)=1 then if typ='integer' then gamma:=igcd(cont(a,L,typ),cont(b,L,typ)); else gamma:=1 fi; else gamma:=PrimitiveEuclidean(cont(a,L,typ),cont(b,L,typ),L[2..nops(L)],typ); fi; gamma*c; end; Zio2JkkiYUc2IkkiYkdGJUkiTEdGJUkkdHlwR0YlNidJImNHRiVJImRHRiVJInJHRiVJInFHRiVJJmdhbW1hRyUqcHJvdGVjdGVkR0YlRiVDJz5GKi1JI3BwR0YlNiVGJEYnRig+RistRjM2JUYmRidGKD8oRiUiIiJGOUYlMEYrIiIhQyUtSSpwc2V1ZG9kaXZHRiU2J0YqRismRic2I0Y5LkYtLkYsPkYqRis+RistRjM2JUYsRidGKEAlLy1JJW5vcHNHRi82I0YnRjlAJS9GKC5JKGludGVnZXJHRi8+Ri4tSSVpZ2NkR0YvNiQtSSVjb250R0YlRjQtRlZGNz5GLkY5PkYuLUkzUHJpbWl0aXZlRXVjbGlkZWFuR0YlNiZGVUZXJkYnNiM7IiIjRkpGKComRi5GOUYqRjlGJUYlRiU= GCD:=proc(P,L,typ) if nops(P)=0 then return 0 fi; if nops(P)=1 then return expand(P[1]/u(P[1],L,typ)) fi; if nops(P)=2 then PrimitiveEuclidean(op(P),L,typ) else GCD([PrimitiveEuclidean(P[1],P[2],L,typ),op(P[3..nops(P)])],L,typ) fi; end; Zio2JUkiUEc2IkkiTEdGJUkkdHlwR0YlRiVGJUYlQyVAJC8tSSVub3BzRyUqcHJvdGVjdGVkRzYjRiQiIiFPRi9AJC9GKyIiIk8tSSdleHBhbmRHRi02IyomJkYkNiNGM0YzLUkidUdGJTYlRjlGJkYnISIiQCUvRisiIiMtSTNQcmltaXRpdmVFdWNsaWRlYW5HRiU2JS1JI29wR0YtRi5GJkYnLUkkR0NER0YlNiU3JC1GQzYmRjkmRiQ2I0ZBRiZGJy1GRjYjJkYkNiM7IiIkRitGJkYnRiVGJUYl LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.22. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> debug(PrimitiveEuclidean); STNQcmltaXRpdmVFdWNsaWRlYW5HNiI= PrimitiveEuclidean(a,b,[x],'integer'); {--> enter PrimitiveEuclidean, args = 48*x^3-84*x^2+42*x-36, -4*x^3-10*x^2+44*x-30, [x], integer LCoqJiIiKSIiIilJInhHNiIiIiRGJUYlKiYiIzlGJSlGJyIiI0YlISIiKiYiIihGJUYnRiVGJSIiJ0Yu LCoqJiIiIyIiIilJInhHNiIiIiRGJUYlKiYiIiZGJSlGJ0YkRiVGJSomIiNBRiVGJ0YlISIiIiM6RiU= LCgiJEsiISIiKiYiI28iIiIpSSJ4RzYiIiIjRidGJComIiQhPkYnRilGJ0Yn LCoqJiIiIyIiIilJInhHNiIiIiRGJUYlKiYiIiZGJSlGJ0YkRiVGJSomIiNBRiVGJ0YlISIiIiM6RiU= LCgiI20iIiIqJiIjTUYkKUkieEc2IiIiI0YkRiQqJiIjJipGJEYoRiQhIiI= LCYiJT9rISIiKiYiJSFHJSIiIkkieEc2IkYnRic= LCgiI20iIiIqJiIjTUYkKUkieEc2IiIiI0YkRiQqJiIjJipGJEYoRiQhIiI= LCYiIiQhIiIqJiIiIyIiIkkieEc2IkYnRic= IiIh LCYiIiQhIiIqJiIiIyIiIkkieEc2IkYnRic= IiIh IiIj LCYiIichIiIqJiIiJSIiIkkieEc2IkYnRic= <-- exit PrimitiveEuclidean (now at top level) = -6+4*x} LCYiIichIiIqJiIiJSIiIkkieEc2IkYnRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.23. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> aa:=-30*x^3*y+90*x^2*y^2+15*x^2-60*x*y+45*y^2; bb:=100*x^2*y-140*x^2-250*x*y^2+350*x*y-150*y^3+210*y^2; LCwqKCIjSSIiIilJInhHNiIiIiRGJUkieUdGKEYlISIiKigiIyEqRiUpRiciIiNGJSlGKkYvRiVGJSomIiM6RiVGLkYlRiUqKCIjZ0YlRidGJUYqRiVGKyomIiNYRiVGMEYlRiU= LC4qKCIkKyIiIiIpSSJ4RzYiIiIjRiVJInlHRihGJUYlKiYiJFMiRiVGJkYlISIiKigiJF0jRiVGJ0YlKUYqRilGJUYtKigiJF0kRiVGJ0YlRipGJUYlKiYiJF0iRiUpRioiIiRGJUYtKiYiJDUjRiVGMEYlRiU= aa:=collect(aa,[x,y]); LCoqKCIjSSIiIilJInhHNiIiIiRGJUkieUdGKEYlISIiKiYsJiomIiMhKkYlKUYqIiIjRiVGJSIjOkYlRiUpRidGMUYlRiUqKCIjZ0YlRidGJUYqRiVGKyomIiNYRiVGMEYlRiU= bb:=collect(bb,[x,y]); LCoqJiwmKiYiJCsiIiIiSSJ5RzYiRidGJyIkUyIhIiJGJylJInhHRikiIiNGJ0YnKiYsJiomIiRdI0YnKUYoRi5GJ0YrKiYiJF0kRidGKEYnRidGJ0YtRidGJyomIiRdIkYnKUYoIiIkRidGKyomIiQ1I0YnRjNGJ0Yn coeffs(aa,x); NiYsJComIiNYIiIiKUkieUc2IiIiI0YmRiYsJComIiNnRiZGKEYmISIiLCQqJiIjSUYmRihGJkYuLCYqJiIjISpGJkYnRiZGJiIjOkYm coeffs(bb,x); NiUsJiomIiRdIiIiIilJInlHNiIiIiRGJiEiIiomIiQ1I0YmKUYoIiIjRiZGJiwmKiYiJF0jRiZGLkYmRisqJiIkXSRGJkYoRiZGJiwmKiYiJCsiRiZGKEYmRiYiJFMiRis= debug(GCD): GCD([%%%],[y],'integer'); {--> enter GCD, args = [45*y^2, -60*y, -30*y, 90*y^2+15], [y], integer {--> enter PrimitiveEuclidean, args = 45*y^2, -60*y, [y], integer KiQpSSJ5RzYiIiIjIiIi SSJ5RzYi IiIh SSJ5RzYi IiIh IiM6 LCQqJiIjOiIiIkkieUc2IkYlRiU= <-- exit PrimitiveEuclidean (now in GCD) = 15*y} {--> enter GCD, args = [15*y, -30*y, 90*y^2+15], [y], integer {--> enter PrimitiveEuclidean, args = 15*y, -30*y, [y], integer SSJ5RzYi SSJ5RzYi IiIh SSJ5RzYi IiIh IiM6 LCQqJiIjOiIiIkkieUc2IkYlRiU= <-- exit PrimitiveEuclidean (now in GCD) = 15*y} {--> enter GCD, args = [15*y, 90*y^2+15], [y], integer {--> enter PrimitiveEuclidean, args = 15*y, 90*y^2+15, [y], integer SSJ5RzYi LCYqJiIiJyIiIilJInlHNiIiIiNGJUYlRiVGJQ== LCYqJiIiJyIiIilJInlHNiIiIiNGJUYlRiVGJQ== SSJ5RzYi IiIi SSJ5RzYi IiIi IiIh IiIi IiIh IiM6 IiM6 <-- exit PrimitiveEuclidean (now in GCD) = 15} IiM6 <-- exit GCD (now in GCD) = 15} IiM6 <-- exit GCD (now in GCD) = 15} IiM6 <-- exit GCD (now at top level) = 15} IiM6 GCD([%%%],[y],'integer'); {--> enter GCD, args = [-150*y^3+210*y^2, -250*y^2+350*y, 100*y-140], [y], integer {--> enter PrimitiveEuclidean, args = -150*y^3+210*y^2, -250*y^2+350*y, [y], integer LCYqJiIiJiIiIilJInlHNiIiIiRGJUYlKiYiIihGJSlGJyIiI0YlISIi LCYqJiIiJiIiIilJInlHNiIiIiNGJUYlKiYiIihGJUYnRiUhIiI= IiIh LCYqJiIiJiIiIilJInlHNiIiIiNGJUYlKiYiIihGJUYnRiUhIiI= IiIh IiM1 LCYqJiIjXSIiIilJInlHNiIiIiNGJUYlKiYiI3FGJUYnRiUhIiI= <-- exit PrimitiveEuclidean (now in GCD) = 50*y^2-70*y} {--> enter GCD, args = [50*y^2-70*y, 100*y-140], [y], integer {--> enter PrimitiveEuclidean, args = 50*y^2-70*y, 100*y-140, [y], integer LCYqJiIiJiIiIilJInlHNiIiIiNGJUYlKiYiIihGJUYnRiUhIiI= LCYqJiIiJiIiIkkieUc2IkYlRiUiIighIiI= IiIh LCYqJiIiJiIiIkkieUc2IkYlRiUiIighIiI= IiIh IiM1 LCYqJiIjXSIiIkkieUc2IkYlRiUiI3EhIiI= <-- exit PrimitiveEuclidean (now in GCD) = 50*y-70} LCYqJiIjXSIiIkkieUc2IkYlRiUiI3EhIiI= <-- exit GCD (now in GCD) = 50*y-70} LCYqJiIjXSIiIkkieUc2IkYlRiUiI3EhIiI= <-- exit GCD (now at top level) = 50*y-70} LCYqJiIjXSIiIkkieUc2IkYlRiUiI3EhIiI= undebug(GCD); SSRHQ0RHNiI= pp(aa,[x,y],'integer'); {--> enter PrimitiveEuclidean, args = -45*y^2, 60*y, [y], integer KiQpSSJ5RzYiIiIjIiIi SSJ5RzYi IiIh SSJ5RzYi IiIh IiM6 LCQqJiIjOiIiIkkieUc2IkYlRiU= <-- exit PrimitiveEuclidean (now in GCD) = 15*y} {--> enter PrimitiveEuclidean, args = 15*y, 30*y, [y], integer SSJ5RzYi SSJ5RzYi IiIh SSJ5RzYi IiIh IiM6 LCQqJiIjOiIiIkkieUc2IkYlRiU= <-- exit PrimitiveEuclidean (now in GCD) = 15*y} {--> enter PrimitiveEuclidean, args = 15*y, -90*y^2-15, [y], integer SSJ5RzYi LCYqJiIiJyIiIilJInlHNiIiIiNGJUYlRiVGJQ== LCYqJiIiJyIiIilJInlHNiIiIiNGJUYlRiVGJQ== SSJ5RzYi IiIi SSJ5RzYi IiIi IiIh IiIi IiIh IiM6 IiM6 <-- exit PrimitiveEuclidean (now in GCD) = 15} LCwqKCIiIyIiIilJInhHNiIiIiRGJUkieUdGKEYlRiUqKCIiJ0YlKUYnRiRGJSlGKkYkRiUhIiIqJEYtRiVGLyooIiIlRiVGJ0YlRipGJUYlKiZGKUYlRi5GJUYv pp(bb,[x,y],'integer'); {--> enter PrimitiveEuclidean, args = -150*y^3+210*y^2, -250*y^2+350*y, [y], integer LCYqJiIiJiIiIilJInlHNiIiIiRGJUYlKiYiIihGJSlGJyIiI0YlISIi LCYqJiIiJiIiIilJInlHNiIiIiNGJUYlKiYiIihGJUYnRiUhIiI= IiIh LCYqJiIiJiIiIilJInlHNiIiIiNGJUYlKiYiIihGJUYnRiUhIiI= IiIh IiM1 LCYqJiIjXSIiIilJInlHNiIiIiNGJUYlKiYiI3FGJUYnRiUhIiI= <-- exit PrimitiveEuclidean (now in GCD) = 50*y^2-70*y} {--> enter PrimitiveEuclidean, args = 50*y^2-70*y, 100*y-140, [y], integer LCYqJiIiJiIiIilJInlHNiIiIiNGJUYlKiYiIihGJUYnRiUhIiI= LCYqJiIiJiIiIkkieUc2IkYlRiUiIighIiI= IiIh LCYqJiIiJiIiIkkieUc2IkYlRiUiIighIiI= IiIh IiM1 LCYqJiIjXSIiIkkieUc2IkYlRiUiI3EhIiI= <-- exit PrimitiveEuclidean (now in GCD) = 50*y-70} LCgqJiIiJCIiIilJInlHNiIiIiNGJSEiIiooIiImRiVJInhHRihGJUYnRiVGKiomRilGJSlGLUYpRiVGJQ== PrimitiveEuclidean(aa,bb,[x,y],'integer'); {--> enter PrimitiveEuclidean, args = -30*x^3*y+(90*y^2+15)*x^2-60*x*y+45*y^2, (100*y-140)*x^2+(-250*y^2+350*y)*x-150*y^3+210*y^2, [x, y], integer {--> enter PrimitiveEuclidean, args = -45*y^2, 60*y, [y], integer KiQpSSJ5RzYiIiIjIiIi SSJ5RzYi IiIh SSJ5RzYi IiIh IiM6 LCQqJiIjOiIiIkkieUc2IkYlRiU= <-- exit PrimitiveEuclidean (now in GCD) = 15*y} {--> enter PrimitiveEuclidean, args = 15*y, 30*y, [y], integer SSJ5RzYi SSJ5RzYi IiIh SSJ5RzYi IiIh IiM6 LCQqJiIjOiIiIkkieUc2IkYlRiU= <-- exit PrimitiveEuclidean (now in GCD) = 15*y} {--> enter PrimitiveEuclidean, args = 15*y, -90*y^2-15, [y], integer SSJ5RzYi LCYqJiIiJyIiIilJInlHNiIiIiNGJUYlRiVGJQ== LCYqJiIiJyIiIilJInlHNiIiIiNGJUYlRiVGJQ== SSJ5RzYi IiIi SSJ5RzYi IiIi IiIh IiIi IiIh IiM6 IiM6 <-- exit PrimitiveEuclidean (now in GCD) = 15} LCwqKCIiIyIiIilJInhHNiIiIiRGJUkieUdGKEYlRiUqKCIiJ0YlKUYnRiRGJSlGKkYkRiUhIiIqJEYtRiVGLyooIiIlRiVGJ0YlRipGJUYlKiZGKUYlRi5GJUYv {--> enter PrimitiveEuclidean, args = -150*y^3+210*y^2, -250*y^2+350*y, [y], integer LCYqJiIiJiIiIilJInlHNiIiIiRGJUYlKiYiIihGJSlGJyIiI0YlISIi LCYqJiIiJiIiIilJInlHNiIiIiNGJUYlKiYiIihGJUYnRiUhIiI= IiIh LCYqJiIiJiIiIilJInlHNiIiIiNGJUYlKiYiIihGJUYnRiUhIiI= IiIh IiM1 LCYqJiIjXSIiIilJInlHNiIiIiNGJUYlKiYiI3FGJUYnRiUhIiI= <-- exit PrimitiveEuclidean (now in GCD) = 50*y^2-70*y} {--> enter PrimitiveEuclidean, args = 50*y^2-70*y, 100*y-140, [y], integer LCYqJiIiJiIiIilJInlHNiIiIiNGJUYlKiYiIihGJUYnRiUhIiI= LCYqJiIiJiIiIkkieUc2IkYlRiUiIighIiI= IiIh LCYqJiIiJiIiIkkieUc2IkYlRiUiIighIiI= IiIh IiM1 LCYqJiIjXSIiIkkieUc2IkYlRiUiI3EhIiI= <-- exit PrimitiveEuclidean (now in GCD) = 50*y-70} LCgqJiIiJCIiIilJInlHNiIiIiNGJSEiIiooIiImRiVJInhHRihGJUYnRiVGKiomRilGJSlGLUYpRiVGJQ== LCgqJiwmKiYiIiMiIiIpSSJ5RzYiIiIkRidGJyomIiInRidGKUYnRidGJ0kieEdGKkYnRicqJiIjPUYnKUYpRiZGJyEiIiomRi1GJylGKSIiJUYnRjI= LCgqJiIiJCIiIilJInlHNiIiIiNGJSEiIiooIiImRiVJInhHRihGJUYnRiVGKiomRilGJSlGLUYpRiVGJQ== {--> enter PrimitiveEuclidean, args = -18*y^2-6*y^4, 2*y^3+6*y, [y], integer LCYqJiIiJCIiIilJInlHNiIiIiNGJUYlKiQpRiciIiVGJUYl LCYqJClJInlHNiIiIiQiIiJGKComRidGKEYlRihGKA== IiIh LCYqJClJInlHNiIiIiQiIiJGKComRidGKEYlRihGKA== IiIh IiIj LCYqJiIiIyIiIilJInlHNiIiIiRGJUYlKiYiIidGJUYnRiVGJQ== <-- exit PrimitiveEuclidean (now in GCD) = 2*y^3+6*y} LCYqJiIiJCIiIkkieUc2IkYlISIiSSJ4R0YnRiU= IiIh LCYqJiIiJCIiIkkieUc2IkYlISIiSSJ4R0YnRiU= IiIh {--> enter PrimitiveEuclidean, args = -45*y^2, 60*y, [y], integer KiQpSSJ5RzYiIiIjIiIi SSJ5RzYi IiIh SSJ5RzYi IiIh IiM6 LCQqJiIjOiIiIkkieUc2IkYlRiU= <-- exit PrimitiveEuclidean (now in GCD) = 15*y} {--> enter PrimitiveEuclidean, args = 15*y, 30*y, [y], integer SSJ5RzYi SSJ5RzYi IiIh SSJ5RzYi IiIh IiM6 LCQqJiIjOiIiIkkieUc2IkYlRiU= <-- exit PrimitiveEuclidean (now in GCD) = 15*y} {--> enter PrimitiveEuclidean, args = 15*y, -90*y^2-15, [y], integer SSJ5RzYi LCYqJiIiJyIiIilJInlHNiIiIiNGJUYlRiVGJQ== LCYqJiIiJyIiIilJInlHNiIiIiNGJUYlRiVGJQ== SSJ5RzYi IiIi SSJ5RzYi IiIi IiIh IiIi IiIh IiM6 IiM6 <-- exit PrimitiveEuclidean (now in GCD) = 15} {--> enter PrimitiveEuclidean, args = -150*y^3+210*y^2, -250*y^2+350*y, [y], integer LCYqJiIiJiIiIilJInlHNiIiIiRGJUYlKiYiIihGJSlGJyIiI0YlISIi LCYqJiIiJiIiIilJInlHNiIiIiNGJUYlKiYiIihGJUYnRiUhIiI= IiIh LCYqJiIiJiIiIilJInlHNiIiIiNGJUYlKiYiIihGJUYnRiUhIiI= IiIh IiM1 LCYqJiIjXSIiIilJInlHNiIiIiNGJUYlKiYiI3FGJUYnRiUhIiI= <-- exit PrimitiveEuclidean (now in GCD) = 50*y^2-70*y} {--> enter PrimitiveEuclidean, args = 50*y^2-70*y, 100*y-140, [y], integer LCYqJiIiJiIiIilJInlHNiIiIiNGJUYlKiYiIihGJUYnRiUhIiI= LCYqJiIiJiIiIkkieUc2IkYlRiUiIighIiI= IiIh LCYqJiIiJiIiIkkieUc2IkYlRiUiIighIiI= IiIh IiM1 LCYqJiIjXSIiIkkieUc2IkYlRiUiI3EhIiI= <-- exit PrimitiveEuclidean (now in GCD) = 50*y-70} {--> enter PrimitiveEuclidean, args = 15, 50*y-70, [y], integer IiIi LCYqJiIiJiIiIkkieUc2IkYlRiUiIighIiI= LCYqJiIiJiIiIkkieUc2IkYlRiUiIighIiI= IiIi IiIh IiIi IiIh IiIm IiIm <-- exit PrimitiveEuclidean (now in PrimitiveEuclidean) = 5} IiIm LCYqJiIjOiIiIkkieUc2IkYlISIiKiYiIiZGJUkieEdGJ0YlRiU= <-- exit PrimitiveEuclidean (now at top level) = -15*y+5*x} LCYqJiIjOiIiIkkieUc2IkYlISIiKiYiIiZGJUkieEdGJ0YlRiU= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.24. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> PrimitiveEuclidean(a,b,[x],'rational'); {--> enter PrimitiveEuclidean, args = 48*x^3-84*x^2+42*x-36, -4*x^3-10*x^2+44*x-30, [x], rational LCoqJClJInhHNiIiIiQiIiJGKComIyIiKCIiJUYoKUYlIiIjRighIiIqJiNGKyIiKUYoRiVGKEYoI0YnRixGLw== LCoqJClJInhHNiIiIiQiIiJGKComIyIiJiIiI0YoKUYlRixGKEYoKiYiIzZGKEYlRighIiIjIiM6RixGKA== LCgjIiNMIiIlISIiKiYjIiM8RiUiIiIpSSJ4RzYiIiIjRipGJiomIyIjJioiIilGKkYsRipGKg== LCoqJClJInhHNiIiIiQiIiJGKComIyIiJiIiI0YoKUYlRixGKEYoKiYiIzZGKEYlRighIiIjIiM6RixGKA== LCgjIiNMIiM8IiIiKiQpSSJ4RzYiIiIjRiZGJiomIyIjJioiI01GJkYpRiYhIiI= LCYjIiUwOyIkeSYhIiIqJiMiJE4mIiQqRyIiIkkieEc2IkYrRis= LCgjIiNMIiM8IiIiKiQpSSJ4RzYiIiIjRiZGJiomIyIjJioiI01GJkYpRiYhIiI= LCYjIiIkIiIjISIiSSJ4RzYiIiIi IiIh LCYjIiIkIiIjISIiSSJ4RzYiIiIi IiIh IiIi LCYjIiIkIiIjISIiSSJ4RzYiIiIi <-- exit PrimitiveEuclidean (now at top level) = -3/2+x} LCYjIiIkIiIjISIiSSJ4RzYiIiIi LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.25. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> -2/4; 2/(-4); 100/(-200); -600/1200; IyEiIiIiIw== IyEiIiIiIw== IyEiIiIiIw== IyEiIiIiIw==
<Text-field style="Heading 2" layout="Heading 2">E 2.26. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> a:=17/100*x^2-3/112*x+1/2; b:=5/9*x^2+4/5; LCgqJiMiIzwiJCsiIiIiKUkieEc2IiIiI0YnRicqJiMiIiQiJDciRidGKUYnISIiI0YnRitGJw== LCYqJiMiIiYiIioiIiIpSSJ4RzYiIiIjRidGJyMiIiVGJUYn a/b; KiYsKComIyIjPCIkKyIiIiIpSSJ4RzYiIiIjRihGKComIyIiJCIkNyJGKEYqRighIiIjRihGLEYoRigsJiomIyIiJiIiKkYoRilGKEYoIyIiJUY2RihGMQ== expand(a*25200)/expand(b*25200); KiYsKComIiUlRyUiIiIpSSJ4RzYiIiIjRiZGJiomIiR2J0YmRihGJiEiIiImK0UiRiZGJiwmKiYiJitTIkYmRidGJkYmIiZnLCNGJkYt expand(a*25200/14000)/expand(b*25200/14000); KiYsKComIyIkYCIiJCsmIiIiKUkieEc2IiIiI0YoRigqJiMiI0YiJGcmRihGKkYoISIiIyIiKiIjNUYoRigsJiokRilGKEYoIyIjTyIjREYoRjE= normal(expand(a/b)); LCQqKCMiIioiJGcmIiIiLCgqJiIkdyVGJylJInhHNiIiIiNGJ0YnKiYiI3ZGJ0YsRichIiIiJSs5RidGJywmKiYiI0RGJ0YrRidGJyIjT0YnRjFGJw== simplify(a/b); LCQqKCMiIioiJGcmIiIiLCgqJiIkdyVGJylJInhHNiIiIiNGJ0YnKiYiI3ZGJ0YsRichIiIiJSs5RidGJywmKiYiI0RGJ0YrRidGJyIjT0YnRjFGJw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.27. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> d:=series(1/(1-x),x); KzFJInhHNiIiIiIiIiFGJUYlRiUiIiNGJSIiJEYlIiIlRiUiIiYtSSJPRyUqcHJvdGVjdGVkRzYjRiUiIic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.28. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> series(1/d,x); KylJInhHNiIiIiIiIiEhIiJGJS1JIk9HJSpwcm90ZWN0ZWRHNiNGJSIiJw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.29. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> with(powseries); NzdJKGNvbXBvc2VHNiJJKGV2YWxwb3dHRiRJKGludmVyc2VHRiRJKm11bHRjb25zdEdGJEkpbXVsdGlwbHlHRiRJKW5lZ2F0aXZlRyUqcHJvdGVjdGVkR0kncG93YWRkR0YkSSdwb3djb3NHRiRJKnBvd2NyZWF0ZUdGJEkocG93ZGlmZkdGJEkncG93ZXhwR0YkSSdwb3dpbnRHRiRJJ3Bvd2xvZ0dGJEkocG93cG9seUdGJEkncG93c2luR0YkSSlwb3dzb2x2ZUdGJEkocG93c3FydEdGJEkpcXVvdGllbnRHRiRJKnJldmVyc2lvbkdGJEkpc3VidHJhY3RHRiRJKHRwc2Zvcm1HRiQ= c:='c'; powcreate(c(n)=1,c(0)=2,c(1)=0,c(2)=0); tpsform(c,x,8); SSJjRzYi KzFJInhHNiIiIiMiIiEiIiIiIiRGJyIiJUYnIiImRiciIidGJyIiKC1JIk9HJSpwcm90ZWN0ZWRHNiNGJyIiKQ== d:=powpoly(1-x,x); tpsform(d,x,8); 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 KydJInhHNiIiIiIiIiEhIiJGJQ== e:=inverse(d); tpsform(e,x,8); 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 KzVJInhHNiIiIiIiIiFGJUYlRiUiIiNGJSIiJEYlIiIlRiUiIiZGJSIiJ0YlIiIoLUkiT0clKnByb3RlY3RlZEc2I0YlIiIp a:=multiply(e,c); tpsform(a,x,8); 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 KzVJInhHNiIiIiMiIiFGJSIiIkYlRiUiIiRGKCIiJUYpIiImRioiIidGKyIiKEYsLUkiT0clKnByb3RlY3RlZEc2I0YnIiIp b:=multiply(a,e); tpsform(b,x,8); 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 KzVJInhHNiIiIiMiIiEiIiUiIiIiIidGJSIiKiIiJCIjOEYnIiM9IiImIiNDRikiI0oiIigtSSJPRyUqcHJvdGVjdGVkRzYjRigiIik= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.30. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> b:=powlog(d); tpsform(b,x,8); a:=negative(b); tpsform(a,x,8); Zio2I0kocG93cGFybUc2IjYkSSNubkdGJUkjdDFHRiU2I0lhb0NvcHlyaWdodH4oYyl+MTk5MH5ieX50aGV+VW5pdmVyc2l0eX5vZn5XYXRlcmxvby5+QWxsfnJpZ2h0c35yZXNlcnZlZC5HRiVFXHMjIiIhRixJI19rR0YlKiYsJiomRi0iIiItSSJkR0YlNiNGLUYxRjEtSSRzdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2JCooLCZGLUYxSSJpR0YlISIiRjEtSSRhbnNHRiU2I0Y8RjEtRjM2I0Y9RjEvRj07RjEsJkYtRjFGMUY+Rj5GMUYtRj5DJEAlLUkldHlwZUdGODYkRiRJKGludGVnZXJHRjhDJD5GJy0lKXByb2NuYW1lR0Y0QCUzMC1JI29wR0Y4NiQiIiUtRlU2I0ZQSSVOVUxMR0Y4LUkkaGFzR0Y4NiQ3Iy1JKGluZGljZXNHRjg2I0ZURi1DJT5GKC1JJXN1YnNHRjg2JC9GLUYkRic+LUZQNiMlJWFyZ3NHLUklZXZhbEdGODYjRihPRmZvTy5GY29DJD5GY29GW3BGam83JEkncG93bG9nRzYkRjgvSSttb2R1bGVuYW1lR0YlSSpwb3dzZXJpZXNHRjdGM0YlRiVGJQ== KzNJInhHNiIhIiIiIiIjRiUiIiNGKCNGJSIiJEYqI0YlIiIlRiwjRiUiIiZGLiNGJSIiJ0YwI0YlIiIoRjItSSJPRyUqcHJvdGVjdGVkRzYjRiYiIik= 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 KzNJInhHNiIiIiJGJSNGJSIiI0YnI0YlIiIkRikjRiUiIiVGKyNGJSIiJkYtI0YlIiInRi8jRiUiIihGMS1JIk9HJSpwcm90ZWN0ZWRHNiNGJSIiKQ== c:=multiply(a,e); tpsform(c,x,8); 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 KzNJInhHNiIiIiJGJSMiIiQiIiNGKCMiIzYiIidGJyMiI0QiIzciIiUjIiRQIiIjZyIiJiMiI1wiIz9GKyMiJGokIiRTIiIiKC1JIk9HJSpwcm90ZWN0ZWRHNiNGJSIiKQ== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 2.31. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> c:='c'; powcreate(c(n)=1/2^(n-2),c(0)=0,c(1)=0); tpsform(c,x,8); SSJjRzYi KzFJInhHNiIiIiIiIiMjRiVGJiIiJCNGJSIiJUYqI0YlIiIpIiImI0YlIiM7IiInI0YlIiNLIiIoLUkiT0clKnByb3RlY3RlZEc2I0YlRiw= a:=inverse(c); Error, (in powseries:-inverse) inverse will have pole at zero series(1/(x^2*(1-x/2)),x); KzVJInhHNiIiIiIhIiMjRiUiIiMhIiIjRiUiIiUiIiEjRiUiIilGJSNGJSIjO0YoI0YlIiNLIiIkI0YlIiNrRisjRiUiJEciIiImLUkiT0clKnByb3RlY3RlZEc2I0YlIiIn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<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>
<Text-field style="Heading 1" layout="Heading 1">12. A Risch-algoritmus.</Text-field>
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn