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> restart;
<Text-field style="Heading 2" layout="Heading 2">E 7.1. P<Font encoding="UTF-8">\303\251lda.</Font> </Text-field> A:=x^8+x^6-3*x^4-3*x^3+8*x^2+2*x-5; B:=3*x^6+5*x^4-4*x^2-9*x+21; LDAqJClJInhHNiIiIikiIiJGKCokKUYlIiInRihGKComIiIkRigpRiUiIiVGKCEiIiomRi1GKClGJUYtRihGMComRidGKClGJSIiI0YoRigqJkY1RihGJUYoRigiIiZGMA== LCwqJiIiJCIiIilJInhHNiIiIidGJUYlKiYiIiZGJSlGJyIiJUYlRiUqJkYtRiUpRiciIiNGJSEiIiomIiIqRiVGJ0YlRjEiI0BGJQ== p:=23; `mod`:=mods; A mod p; B mod p; Rem(%%,%,x) mod p; Rem(%%,%,x) mod p; Rem(%%,%,x) mod p; Rem(%%,%,x) mod p; IiNC SSVtb2RzRyUqcHJvdGVjdGVkRw== LDAqJClJInhHNiIiIikiIiJGKCokKUYlIiInRihGKComIiIkRigpRiUiIiVGKCEiIiomRi1GKClGJUYtRihGMComRidGKClGJSIiI0YoRigqJkY1RihGJUYoRigiIiZGMA== LCwqJiIiJCIiIilJInhHNiIiIidGJUYlKiYiIiZGJSlGJyIiJUYlRiUqJkYtRiUpRiciIiNGJSEiIiomIiIqRiVGJ0YlRjFGMEYx LCgqJiIiIyIiIilJInhHNiIiIiVGJUYlKiYiIiZGJSlGJ0YkRiUhIiIiIilGLQ== LCgqJClJInhHNiIiIiMiIiIhIiIqJiIiKkYoRiVGKEYpRidGKA== LCYqJiIjNSIiIkkieEc2IkYlRiUiIikhIiI= ISIl
<Text-field style="Heading 2" layout="Heading 2">E 7.2. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn A; B; rem(%%,%,x); rem(%%,%,x); rem(%%,%,x); rem(%%,%,x); LDAqJClJInhHNiIiIikiIiJGKCokKUYlIiInRihGKComIiIkRigpRiUiIiVGKCEiIiomRi1GKClGJUYtRihGMComRidGKClGJSIiI0YoRigqJkY1RihGJUYoRigiIiZGMA== LCwqJiIiJCIiIilJInhHNiIiIidGJUYlKiYiIiZGJSlGJyIiJUYlRiUqJkYtRiUpRiciIiNGJSEiIiomIiIqRiVGJ0YlRjEiI0BGJQ== LCgjIiIiIiIkISIiKiYjIiImIiIqRiQpSSJ4RzYiIiIlRiRGJiomI0YkRipGJClGLCIiI0YkRiQ= LCgjIiRUJSIjRCIiIiomIyIkPCJGJUYmKUkieEc2IiIiI0YmISIiKiYiIipGJkYrRiZGLg== LCYjIicrRDUiJSJmJyEiIiomIyInXUpCIiZ0KD4iIiJJInhHNiJGK0Yr IyErQFt1KUciIipEIyplViY=
<Text-field style="Heading 2" layout="Heading 2">E 7.3. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn A; B; rem(3^3*%%,%,x); rem((-15)^3*%%,%,x); rem(15795^3*%%,%,x); rem(1254542875143750^2*%%,%,x); LDAqJClJInhHNiIiIikiIiJGKCokKUYlIiInRihGKComIiIkRigpRiUiIiVGKCEiIiomRi1GKClGJUYtRihGMComRidGKClGJSIiI0YoRigqJkY1RihGJUYoRigiIiZGMA== LCwqJiIiJCIiIilJInhHNiIiIidGJUYlKiYiIiZGJSlGJyIiJUYlRiUqJkYtRiUpRiciIiNGJSEiIiomIiIqRiVGJ0YlRjEiI0BGJQ== LCgiIiohIiIqJiIjOiIiIilJInhHNiIiIiVGJ0YkKiYiIiRGJylGKSIiI0YnRic= LCgiJk4mZiEiIiomIiYmejoiIiIpSSJ4RzYiIiIjRidGJyomIiZ2LiRGJ0YpRidGJw== LCYiMSt2VlEkM1lsIiEiIiomIjFdUDl2R2FhNyIiIkkieEc2IkYnRic= IkQrdj0jKj45SjQ1VjJdJnpRTGY3
<Text-field style="Heading 2" layout="Heading 2">E 7.4. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn A; B; rem(3^3*%%,%,x); %/igcd(coeffs(%)); rem(5^3*%%%,%,x); %/igcd(coeffs(%)); rem((-13)^3*%%%,%,x); %/igcd(coeffs(%)); rem((-4663)^2*%%%,%,x); %/igcd(coeffs(%)); LDAqJClJInhHNiIiIikiIiJGKCokKUYlIiInRihGKComIiIkRigpRiUiIiVGKCEiIiomRi1GKClGJUYtRihGMComRidGKClGJSIiI0YoRigqJkY1RihGJUYoRigiIiZGMA== LCwqJiIiJCIiIilJInhHNiIiIidGJUYlKiYiIiZGJSlGJyIiJUYlRiUqJkYtRiUpRiciIiNGJSEiIiomIiIqRiVGJ0YlRjEiI0BGJQ== LCgiIiohIiIqJiIjOiIiIilJInhHNiIiIiVGJ0YkKiYiIiRGJylGKSIiI0YnRic= LCgiIiQhIiIqJiIiJiIiIilJInhHNiIiIiVGJ0YkKiQpRikiIiNGJ0Yn LCgiJTBBIiIiKiYiJCZlRiQpSSJ4RzYiIiIjRiQhIiIqJiIlRDZGJEYoRiRGKw== LCgiI1wiIiIqJiIjOEYkKUkieEc2IiIiI0YkISIiKiYiI0RGJEYoRiRGKw== LCYiJyt2SSIiIiomIiddSkJGJEkieEc2IkYkISIi LCYiJV1oIiIiKiYiJWpZRiRJInhHNiJGJCEiIg== ISpwUT5WIg== ISIi
<Text-field style="Heading 2" layout="Heading 2">E 7.5. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn R[0]:=A; R[1]:=B; r[1]:=lcoeff(R[1]); delta[1]:=degree(R[0])-degree(R[1]); alpha[1]:=r[1]^(delta[1]+1); beta[1]:=1; R[2]:=rem(alpha[1]*R[0],R[1],x)/beta[1]; LDAqJClJInhHNiIiIikiIiJGKCokKUYlIiInRihGKComIiIkRigpRiUiIiVGKCEiIiomRi1GKClGJUYtRihGMComRidGKClGJSIiI0YoRigqJkY1RihGJUYoRigiIiZGMA== LCwqJiIiJCIiIilJInhHNiIiIidGJUYlKiYiIiZGJSlGJyIiJUYlRiUqJkYtRiUpRiciIiNGJSEiIiomIiIqRiVGJ0YlRjEiI0BGJQ== IiIk IiIj IiNG IiIi LCgiIiohIiIqJiIjOiIiIilJInhHNiIiIiVGJ0YkKiYiIiRGJylGKSIiI0YnRic= r[2]:=lcoeff(R[2]); delta[2]:=degree(R[1])-degree(R[2]); alpha[2]:=r[2]^(delta[2]+1); beta[2]:=alpha[1]; R[3]:=rem(alpha[2]*R[1],R[2],x)/beta[2]; ISM6 IiIj ISV2TA== IiNG LCgiJTBBISIiKiYiJCZlIiIiKUkieEc2IiIiI0YnRicqJiIlRDZGJ0YpRidGJw== r[3]:=lcoeff(R[3]); delta[3]:=degree(R[2])-degree(R[3]); alpha[3]:=r[3]^(delta[3]+1); beta[3]:=alpha[2]; R[4]:=rem(alpha[3]*R[2],R[3],x)/beta[3]; IiQmZQ== IiIj IipEOz8rIw== ISV2TA== LCYiKSt2IVwjIiIiKiYiKV1eKSk9RiRJInhHNiJGJCEiIg== r[4]:=lcoeff(R[4]); delta[4]:=degree(R[3])-degree(R[4]); alpha[4]:=r[4]^(delta[4]+1); beta[4]:=alpha[3]; R[5]:=rem(alpha[4]*R[3],R[4],x)/beta[4]; ISldXikpPQ== IiIi IjArRF8hKilbbU4= IipEOz8rIw== IiorUCR6Xw==
<Text-field style="Heading 2" layout="Heading 2">E 7.6. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn R[0]:=A; R[1]:=B; r[1]:=lcoeff(R[1]); delta[1]:=degree(R[0])-degree(R[1]); alpha[1]:=r[1]^(delta[1]+1); psi[1]:=-1; beta[1]:=(-1)^(delta[1]+1); R[2]:=rem(alpha[1]*R[0],R[1],x)/beta[1]; LDAqJClJInhHNiIiIikiIiJGKCokKUYlIiInRihGKComIiIkRigpRiUiIiVGKCEiIiomRi1GKClGJUYtRihGMComRidGKClGJSIiI0YoRigqJkY1RihGJUYoRigiIiZGMA== LCwqJiIiJCIiIilJInhHNiIiIidGJUYlKiYiIiZGJSlGJyIiJUYlRiUqJkYtRiUpRiciIiNGJSEiIiomIiIqRiVGJ0YlRjEiI0BGJQ== IiIk IiIj IiNG ISIi ISIi LCgiIioiIiIqJiIjOkYkKUkieEc2IiIiJUYkRiQqJiIiJEYkKUYoIiIjRiQhIiI= r[2]:=lcoeff(R[2]); delta[2]:=degree(R[1])-degree(R[2]); alpha[2]:=r[2]^(delta[2]+1); psi[2]:=(-r[1])^delta[1]*psi[1]^(1-delta[1]); beta[2]:=-r[1]*psi[2]^delta[2]; R[3]:=rem(alpha[2]*R[1],R[2],x)/beta[2]; IiM6 IiIj IiV2TA== ISIq ISRWIw== LCgiJFgjISIiKiYiI2wiIiIpSSJ4RzYiIiIjRidGJyomIiREIkYnRilGJ0Yn r[3]:=lcoeff(R[3]); delta[3]:=degree(R[2])-degree(R[3]); alpha[3]:=r[3]^(delta[3]+1); psi[3]:=(-r[2])^delta[2]*psi[2]^(1-delta[2]); beta[3]:=-r[2]*psi[3]^delta[3]; R[4]:=rem(alpha[3]*R[2],R[3],x)/beta[3]; IiNs IiIj IidEWUY= ISNE ISV2JCo= LCYiJitCIiEiIiomIiVFJCoiIiJJInhHNiJGJ0Yn r[4]:=lcoeff(R[4]); delta[4]:=degree(R[3])-degree(R[4]); alpha[4]:=r[4]^(delta[4]+1); psi[4]:=(-r[3])^delta[3]*psi[3]^(1-delta[3]); beta[4]:=-r[3]*psi[4]^delta[4]; R[5]:=rem(alpha[4]*R[3],R[4],x)/beta[4]; IiVFJCo= IiIi Iil3VShwKQ== ISRwIg== IiYmKTQi IiczMkU=
<Text-field style="Heading 2" layout="Heading 2">E 7.7. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn with(LinearAlgebra); 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 A:=3*x^4+3*x^3+x^2-x-2; B:=x^3-3*x^2+x+5; LCwqJiIiJCIiIilJInhHNiIiIiVGJUYlKiZGJEYlKUYnRiRGJUYlKiQpRiciIiNGJUYlRichIiJGLkYv LCoqJClJInhHNiIiIiQiIiJGKComRidGKClGJSIiI0YoISIiRiVGKCIiJkYo S0:=SylvesterMatrix(A,B,x); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKkcmUiRbIg==
<Text-field style="Heading 2" layout="Heading 2">E 7.8. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn Determinant(S0); IiIh S1:=SubMatrix(S0,[1..2,4..6],[1..5]): S1[1,5]:=x*A: S1[2,5]:=A: S1[3,5]:=x^2*B: S1[4,5]:=x*B: S1[5,5]:=B: S1; Determinant(S1); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKl9bXVsi LCYqJiIlIz4iIiIiSSJ4RzYiRiVGJUYkRiU= S2:=SubMatrix(S0,[1..1,4..5],[1..3]): S2[1,3]:=A: S2[2,3]:=x*B: S2[3,3]:=B: S2; Determinant(S2); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKk8jWyZbIg== LCgqJiIjTSIiIilJInhHNiIiIiNGJUYlKiYiI0dGJUYnRiUhIiIiI2lGLA== S3:=SubMatrix(S0,[4],[1]): S3[1,1]:=B: S3; Determinant(S3); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKlcxZFsi LCoqJClJInhHNiIiIiQiIiJGKComRidGKClGJSIiI0YoISIiRiVGKCIiJkYo
<Text-field style="Heading 2" layout="Heading 2">E 7.9. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> A:=x^8+x^6-3*x^4-3*x^3+8*x^2+2*x-5; B:=3*x^6+5*x^4-4*x^2-9*x+21; LDAqJClJInhHNiIiIikiIiJGKCokKUYlIiInRihGKComIiIkRigpRiUiIiVGKCEiIiomRi1GKClGJUYtRihGMComRidGKClGJSIiI0YoRigqJkY1RihGJUYoRigiIiZGMA== LCwqJiIiJCIiIilJInhHNiIiIidGJUYlKiYiIiZGJSlGJyIiJUYlRiUqJkYtRiUpRiciIiNGJSEiIiomIiIqRiVGJ0YlRjEiI0BGJQ== S0:=SylvesterMatrix(A,B,x); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKl90aFsi Determinant(S0); IiczMkU= S1:=SubMatrix(S0,[1..5,7..13],[1..12]): S1[1,12]:=x^4*A: S1[2,12]:=x^3*A: S1[3,12]:=x^2*A: S1[4,12]:=x*A: S1[5,12]:=A: S1[6,12]:=x^6*B: S1[7,12]:=x^5*B: S1[8,12]:=x^4*B: S1[9,12]:=x^3*B: S1[10,12]:=x^2*B: S1[11,12]:=x*B: S1[12,12]:=B: S1; Determinant(S1); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKi83JilbIg== LCYiJitCIiEiIiomIiVFJCoiIiJJInhHNiJGJ0Yn S2:=SubMatrix(S0,[1..4,7..12],[1..10]): S2[1,10]:=x^3*A: S2[2,10]:=x^2*A: S2[3,10]:=x*A: S2[4,10]:=A: S2[5,10]:=x^5*B: S2[6,10]:=x^4*B: S2[7,10]:=x^3*B: S2[8,10]:=x^2*B: S2[9,10]:=x*B: S2[10,10]:=B: S2; Determinant(S2); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKiUpPWtaIg== LCgiJFAnISIiKiYiJEQkIiIiSSJ4RzYiRidGJyomIiRwIkYnKUYoIiIjRidGJw== S3:=SubMatrix(S0,[1..3,7..11],[1..8]): S3[1,8]:=x^2*A: S3[2,8]:=x*A: S3[3,8]:=A: S3[4,8]:=x^4*B: S3[5,8]:=x^3*B: S3[6,8]:=x^2*B: S3[7,8]:=x*B: S3[8,8]:=B: S3; Determinant(S3); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKiM+Ong5 LCgiJFgjISIiKiYiI2wiIiIpSSJ4RzYiIiIjRidGJyomIiREIkYnRilGJ0Yn S4:=SubMatrix(S0,[1..2,7..10],[1..6]): S4[1,6]:=x*A: S4[2,6]:=A: S4[3,6]:=x^3*B: S4[4,6]:=x^2*B: S4[5,6]:=x*B: S4[6,6]:=B: S4; Determinant(S4); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKndmKilbIg== LCgiIzoiIiIqJiIiJkYkKUkieEc2IiIiI0YkISIiKiYiI0RGJClGKCIiJUYkRiQ= S5:=SubMatrix(S0,[1..1,7..9],[1..4]): S5[1,4]:=A: S5[2,4]:=x^2*B: S5[3,4]:=x*B: S5[4,4]:=B: S5; Determinant(S5); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKi8qKT1cIg== LCgiIioiIiIqJiIjOkYkKUkieEc2IiIiJUYkRiQqJiIiJEYkKUYoIiIjRiQhIiI= S6:=SubMatrix(S0,[7..8],[1..2]): S6[1,2]:=x*B: S6[2,2]:=B: S6; Determinant(S6); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKmM3Zlsi LCwqJiIiKiIiIilJInhHNiIiIidGJUYlKiYiIzpGJSlGJyIiJUYlRiUqJiIjN0YlKUYnIiIjRiUhIiIqJiIjRkYlRidGJUYyIiNqRiU= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 7.10. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn A:=3*x^4+3*x^3+x^2-x-2; B:=x^3-3*x^2+x+5; A=(3*x+12)*B+34*x^2-28*x-62; expand(%); LCwqJiIiJCIiIilJInhHNiIiIiVGJUYlKiZGJEYlKUYnRiRGJUYlKiQpRiciIiNGJUYlRichIiJGLkYv LCoqJClJInhHNiIiIiQiIiJGKComRidGKClGJSIiI0YoISIiRiVGKCIiJkYo LywsKiYiIiQiIiIpSSJ4RzYiIiIlRiZGJiomRiVGJilGKEYlRiZGJiokKUYoIiIjRiZGJkYoISIiRi9GMCwqKiYsJiomRiVGJkYoRiZGJiIjN0YmRiYsKiokRixGJkYmKiZGJUYmRi5GJkYwRihGJiIiJkYmRiZGJiomIiNNRiZGLkYmRiYqJiIjR0YmRihGJkYwIiNpRjA= LywsKiYiIiQiIiIpSSJ4RzYiIiIlRiZGJiomRiVGJilGKEYlRiZGJiokKUYoIiIjRiZGJkYoISIiRi9GMEYj 0; 1192*x-1192; 34*x^2-288*x-62; IiIh LCYqJiIlIz4iIiIiSSJ4RzYiRiVGJUYkISIi LCgqJiIjTSIiIilJInhHNiIiIiNGJUYlKiYiJClHRiVGJ0YlISIiIiNpRiw=
<Text-field style="Heading 2" layout="Heading 2">E 7.11. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field>
<Text-field style="Heading 2" layout="Heading 2">E 7.12. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field>
<Text-field style="Heading 2" layout="Heading 2">E 7.13. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn A:=x^8+x^6-3*x^4-3*x^3+8*x^2+2*x-5; B:=3*x^6+5*x^4-4*x^2-9*x+21; LDAqJClJInhHNiIiIikiIiJGKCokKUYlIiInRihGKComIiIkRigpRiUiIiVGKCEiIiomRi1GKClGJUYtRihGMComRidGKClGJSIiI0YoRigqJkY1RihGJUYoRigiIiZGMA== LCwqJiIiJCIiIilJInhHNiIiIidGJUYlKiYiIiZGJSlGJyIiJUYlRiUqJkYtRiUpRiciIiNGJSEiIiomIiIqRiVGJ0YlRjEiI0BGJQ== Gcd(A,B) mod 23; IiIi
<Text-field style="Heading 2" layout="Heading 2">E 7.14. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn Gcd(A,B) mod 2; LCgqJClJInhHNiIiIiMiIiJGKEYlRihGKEYo
<Text-field style="Heading 2" layout="Heading 2">E 7.15. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn A:=x^4+25*x^3+145*x^2-171*x-360; B:=x^5+14*x^4+15*x^3-x^2-14*x-15; LCwqJClJInhHNiIiIiUiIiJGKComIiNERigpRiUiIiRGKEYoKiYiJFgiRigpRiUiIiNGKEYoKiYiJHIiRihGJUYoISIiIiRnJEYz LC4qJClJInhHNiIiIiYiIiJGKComIiM5RigpRiUiIiVGKEYoKiYiIzpGKClGJSIiJEYoRigqJClGJSIiI0YoISIiKiZGKkYoRiVGKEY0Ri5GNA== A mod 5; B mod 5; Gcd(A,B) mod 5; LCYqJClJInhHNiIiIiUiIiJGKEYlISIi LCoqJClJInhHNiIiIiYiIiJGKCokKUYlIiIlRighIiIqJClGJSIiI0YoRixGJUYo LCYqJClJInhHNiIiIiUiIiJGKEYlISIi A mod 7; B mod 7; Gcd(A,B) mod 7; LCwqJClJInhHNiIiIiUiIiJGKComIiIkRigpRiVGKkYoISIiKiYiIiNGKClGJUYuRihGLComRipGKEYlRihGLEYqRiw= LCoqJClJInhHNiIiIiYiIiJGKCokKUYlIiIkRihGKCokKUYlIiIjRighIiJGKEYv LCYqJClJInhHNiIiIiMiIiJGKEYoRig= A mod 11; B mod 11; Gcd(A,B) mod 11; LCwqJClJInhHNiIiIiUiIiJGKComIiIkRigpRiVGKkYoRigqJiIiI0YoKUYlRi1GKEYoKiYiIiZGKEYlRihGKEYqRig= LC4qJClJInhHNiIiIiYiIiJGKComIiIkRigpRiUiIiVGKEYoKiZGLEYoKUYlRipGKEYoKiQpRiUiIiNGKCEiIiomRipGKEYlRihGMkYsRjI= LCgqJClJInhHNiIiIiMiIiJGKComIiIkRihGJUYoRigiIiVGKA== C:=x^2+14*x+15; C mod 7; C mod 11; LCgqJClJInhHNiIiIiMiIiJGKComIiM5RihGJUYoRigiIzpGKA== LCYqJClJInhHNiIiIiMiIiJGKEYoRig= LCgqJClJInhHNiIiIiMiIiJGKComIiIkRihGJUYoRigiIiVGKA== rem(A,C,x); rem(B,C,x); IiIh IiIh
<Text-field style="Heading 2" layout="Heading 2">E 7.16. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn `mod`:=mods; SSVtb2RzRyUqcHJvdGVjdGVkRw== A:=9*x^5+2*x^4*y*z-189*x^3*y^3*z+117*x^3*y*z^2+3*x^3-42*x^2*y^4*z^2+26*x^2*y^2*z^3+18*x^2-63*x*y^3*z+39*x*y*z^2+4*x*y*z+6; B:=6*x^6-126*x^4*y^3*z+78*x^4*y*z^2+x^4*y+x^4*z+13*x^3-21*x^2*y^4*z-21*x^2*y^3*z^2+13*x^2*y^2*z^2+13*x^2*y*z^3-21*x*y^3*z+13*x*y*z^2+2*x*y+2*x*z+2; LDoqJiIiKiIiIilJInhHNiIiIiZGJUYlKioiIiNGJSlGJyIiJUYlSSJ5R0YoRiVJInpHRihGJUYlKioiJCo9RiUpRiciIiRGJSlGLkYzRiVGL0YlISIiKioiJDwiRiVGMkYlRi5GJSlGL0YrRiVGJSomRjNGJUYyRiVGJSoqIiNVRiUpRidGK0YlKUYuRi1GJUY4RiVGNSoqIiNFRiVGPEYlKUYuRitGJSlGL0YzRiVGJSomIiM9RiVGPEYlRiUqKiIjakYlRidGJUY0RiVGL0YlRjUqKiIjUkYlRidGJUYuRiVGOEYlRiUqKkYtRiVGJ0YlRi5GJUYvRiVGJSIiJ0Yl LEAqJiIiJyIiIilJInhHNiJGJEYlRiUqKiIkRSJGJSlGJyIiJUYlKUkieUdGKCIiJEYlSSJ6R0YoRiUhIiIqKiIjeUYlRitGJUYuRiUpRjAiIiNGJUYlKiZGK0YlRi5GJUYlKiZGK0YlRjBGJUYlKiYiIzhGJSlGJ0YvRiVGJSoqIiNARiUpRidGNUYlKUYuRixGJUYwRiVGMSoqRjxGJUY9RiVGLUYlRjRGJUYxKipGOUYlRj1GJSlGLkY1RiVGNEYlRiUqKkY5RiVGPUYlRi5GJSlGMEYvRiVGJSoqRjxGJUYnRiVGLUYlRjBGJUYxKipGOUYlRidGJUYuRiVGNEYlRiUqKEY1RiVGJ0YlRi5GJUYlKihGNUYlRidGJUYwRiVGJUY1RiU= A11:=A mod 11; B11:=B mod 11; LDoqJiIiIyIiIilJInhHNiIiIiZGJSEiIioqRiRGJSlGJyIiJUYlSSJ5R0YoRiVJInpHRihGJUYlKipGJEYlKUYnIiIkRiUpRi5GMkYlRi9GJUYqKipGLUYlRjFGJUYuRiUpRi9GJEYlRioqJkYyRiVGMUYlRiUqKkYkRiUpRidGJEYlKUYuRi1GJUY1RiVGJSoqRi1GJUY4RiUpRi5GJEYlKUYvRjJGJUYlKiZGLUYlRjhGJUYqKipGMkYlRidGJUYzRiVGL0YlRiUqKkYpRiVGJ0YlRi5GJUY1RiVGKioqRi1GJUYnRiVGLkYlRi9GJUYlRilGKg== LEAqJiIiJiIiIilJInhHNiIiIidGJSEiIioqRiRGJSlGJyIiJUYlKUkieUdGKCIiJEYlSSJ6R0YoRiVGKiooRixGJUYvRiUpRjEiIiNGJUYlKiZGLEYlRi9GJUYlKiZGLEYlRjFGJUYlKiZGNEYlKUYnRjBGJUYlKigpRidGNEYlKUYvRi1GJUYxRiVGJSooRjpGJUYuRiVGM0YlRiUqKkY0RiVGOkYlKUYvRjRGJUYzRiVGJSoqRjRGJUY6RiVGL0YlKUYxRjBGJUYlKihGJ0YlRi5GJUYxRiVGJSoqRjRGJUYnRiVGL0YlRjNGJUYlKihGNEYlRidGJUYvRiVGJSooRjRGJUYnRiVGMUYlRiVGNEYl A11_2:=subs(z=2,A11) mod 11; B11_2:=subs(z=2,B11) mod 11; LDgqJiIiIyIiIilJInhHNiIiIiZGJSEiIiooIiIlRiUpRidGLEYlSSJ5R0YoRiVGJSooRixGJSlGJyIiJEYlKUYuRjFGJUYqKihGKUYlRjBGJUYuRiVGKiomRjFGJUYwRiVGJSooRjFGJSlGJ0YkRiUpRi5GLEYlRioqJkY2RiUpRi5GJEYlRioqJkYsRiVGNkYlRioqKEYpRiVGJ0YlRjJGJUYqKiZGJ0YlRi5GJUYqRilGKg== LDwqJiIiJiIiIilJInhHNiIiIidGJSEiIiomKUYnIiIlRiUpSSJ5R0YoIiIkRiVGJSooRiRGJUYsRiVGL0YlRiUqJiIiI0YlRixGJUYlKiZGM0YlKUYnRjBGJUYlKihGM0YlKUYnRjNGJSlGL0YtRiVGJSooRi1GJUY3RiVGLkYlRiUqKEYwRiVGN0YlKUYvRjNGJUYqKihGJEYlRjdGJUYvRiVGJSooRjNGJUYnRiVGLkYlRiUqJkYnRiVGL0YlRioqJkYtRiVGJ0YlRiVGM0Yl A11_3_2:=subs(y=3,A11_2) mod 11; B11_3_2:=subs(y=3,B11_2) mod 11; LC4qJiIiIyIiIilJInhHNiIiIiZGJSEiIiokKUYnIiIlRiVGJSokKUYnIiIkRiVGJSomRjBGJSlGJ0YkRiVGKiomRilGJUYnRiVGJUYpRio= LCoqJiIiJiIiIilJInhHNiIiIidGJSEiIiomIiIjRiUpRiciIiRGJUYlKiZGJEYlKUYnRixGJUYlRixGJQ== Gcd(A11_3_2,B11_3_2) mod 11; LCgqJClJInhHNiIiIiQiIiJGKEYlRigiIiNGKA== Gcd(subs(y=5,A11_2)mod 11,subs(y=5,B11_2)mod 11) mod 11; LCgqJClJInhHNiIiIiQiIiJGKComIiIlRihGJUYoRigiIiNGKA== Gcd(subs(y=-4,A11_2)mod 11,subs(y=-4,B11_2)mod 11) mod 11; LCgqJClJInhHNiIiIiQiIiJGKComIiImRihGJUYoRigiIiNGKA== Gcd(subs(y=-2,A11_2)mod 11,subs(y=-2,B11_2)mod 11) mod 11; LCgqJClJInhHNiIiIiQiIiJGKEYlRigiIiNGKA== Gcd(subs(y=2,A11_2)mod 11,subs(y=2,B11_2)mod 11) mod 11; LCgqJClJInhHNiIiIiQiIiJGKEYlISIiIiIjRig= with(CurveFitting); NypJKEJTcGxpbmVHNiJJLUJTcGxpbmVDdXJ2ZUdGJEksSW50ZXJhY3RpdmVHRiRJLUxlYXN0U3F1YXJlc0dGJEk4UG9seW5vbWlhbEludGVycG9sYXRpb25HRiRJNlJhdGlvbmFsSW50ZXJwb2xhdGlvbkdGJEknU3BsaW5lR0YkSTRUaGllbGVJbnRlcnBvbGF0aW9uR0Yk PolynomialInterpolation([3,5,-4,-2,2],[x^3+x+2,x^3+4*x+2,x^3+5*x+2,x^3+x+2,x^3-x+2],y,form=Lagrange) mod 11; expand(%) mod 11; LCwqLiIiJCIiIiwoKiQpSSJ4RzYiRiRGJUYlRilGJSIiI0YlRiUsJkkieUdGKkYlIiImISIiRiUsJkYtRiUiIiVGJUYlLCZGLUYlRitGJUYlLCZGLUYlRitGL0YlRi8qLkYkRiUsKEYnRiUqJkYxRiVGKUYlRiVGK0YlRiUsJkYtRiVGJEYvRiVGMEYlRjJGJUYzRiVGJSouRjFGJSwoRidGJSomRi5GJUYpRiVGJUYrRiVGJUY3RiVGLEYlRjJGJUYzRiVGLyouRitGJUYmRiVGN0YlRixGJUYwRiVGM0YlRiUqLkYrRiUsKEYnRiVGKUYvRitGJUYlRjdGJUYsRiVGMEYlRjJGJUYl LCoiIiMiIiIqJClJInhHNiIiIiRGJEYkKihGKUYkRidGJEkieUdGKEYkISIiKihGI0YkRidGJClGK0YpRiRGJA== PolynomialInterpolation([2,-5,-3,5],[x^3+2*x*y^3-3*x*y+2,x^3-5*x*y^3-5*x*y+2,x^3-3*x*y^3-4*x*y+2,x^3+5*x*y^3-5*x*y+2],z,form=Lagrange) mod 11; expand(%) mod 11; LCoqLCIiIyIiIiwqRiRGJSokKUkieEc2IiIiJEYlRiUqKEYrRiVGKUYlSSJ5R0YqRiUhIiIqKEYkRiVGKUYlKUYtRitGJUYlRiUsJkkiekdGKkYlIiImRiVGJSwmRjJGJUYrRiVGJSwmRjJGJUYzRi5GJUYuKiwiIiVGJSwqRidGJSooRjNGJUYpRiVGMEYlRi4qKEYzRiVGKUYlRi1GJUYuRiRGJUYlLCZGMkYlRiRGLkYlRjRGJUY1RiVGJSosRjdGJSwqRidGJSooRitGJUYpRiVGMEYlRi4qKEY3RiVGKUYlRi1GJUYuRiRGJUYlRjtGJUYxRiVGNUYlRiUqLEYzRiUsKkYnRiVGOUYlRjpGLkYkRiVGJUY7RiVGMUYlRjRGJUYl LCoiIiMiIiIqJClJInhHNiIiIiRGJEYkKipGI0YkRidGJEkieUdGKEYkKUkiekdGKEYjRiRGJCooRidGJClGK0YpRiRGLUYkRiQ= chrem([3*x^3+3*x*y^3*z-5*x*y*z^2-5,3*x^3+2*x*y^3*z+6,3*x^3+5*x*y^3*z+5*x*y*z^2+6],[11,13,17]); LCoqJiIiJCIiIilJInhHNiJGJEYlRiUqKiIjakYlRidGJSlJInlHRihGJEYlSSJ6R0YoRiUhIiIqKiIjUkYlRidGJUYsRiUpRi0iIiNGJUYlIiInRiU= C:=%/igcd(coeffs(%)); LCoqJClJInhHNiIiIiQiIiJGKCoqIiNARihGJUYoKUkieUdGJkYnRihJInpHRiZGKCEiIioqIiM4RihGJUYoRixGKClGLSIiI0YoRihGMkYo simplify(A/C); simplify(B/C); LCgqJiIiKiIiIilJInhHNiIiIiNGJUYlKipGKUYlRidGJUkieUdGKEYlSSJ6R0YoRiVGJSIiJEYl LCoqJiIiJyIiIilJInhHNiIiIiRGJUYlKiZGJ0YlSSJ5R0YoRiVGJSomRidGJUkiekdGKEYlRiVGJUYl
<Text-field style="Heading 2" layout="Heading 2">A 7.1. Algoritmus. </Text-field>
<Text-field style="Heading 2" layout="Heading 2">A 7.2. Algoritmus. </Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 7.17. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">A 7.3. Algoritmus. </Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 7.18. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 7.19. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 7.20. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 7.21. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">E 7.22. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 2" layout="Heading 2">A 7.4. Algoritmus. </Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<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