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>
<Text-field style="Heading 1" layout="Heading 1">12. A Risch-algoritmus.</Text-field> restart; (x*(x+1)*((x^2*exp(2*x^2)-(log(x+1))^2)^2+2*x*exp(3*x^2)*(x-(2*x^3+2*x^2+x+1)*log(x+1))))/((x+1)*(log(x+1))^2-(x^3+x^2)*exp(2*x^2))^2; KipJInhHNiIiIiIsJkYjRiVGJUYlRiUsJiokKSwmKiYpRiMiIiNGJS1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqJkYtRiVGLEYlRiVGJUYlKiQpLUkjbG5HRjA2I0YmRi1GJSEiIkYtRiVGJSoqRi1GJUYjRiUtRi82IywkKiYiIiRGJUYsRiVGJUYlLCZGI0YlKiYsKiomRi1GJSlGI0ZBRiVGJUY1RiVGI0YlRiVGJUYlRjhGJUY7RiVGJUYlKSwmKiZGJkYlRjdGJUYlKiYsJiokRkZGJUYlKiRGLEYlRiVGJUYuRiVGO0YtRjs= int(%,x); LCxJInhHNiIiIiItSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCZGI0YlRiVGJSEiIioqLUkkZXhwR0YoNiMqJClGIyIiI0YlRiVGI0YlRiZGJSwmKiZGM0YlLUYwNiMsJComRjRGJUYzRiVGJUYlRiUqJClGJkY0RiVGLUYtRiUqJiNGJUY0RiUtRic2IywmKiZGL0YlRiNGJUYlRiZGJUYlRiUqJkY+RiUtRic2IywmRkJGLUYmRiVGJUYt int(1/(1+exp(x)),x); simplify(%,symbolic); LCYtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCYiIiJGKy1JJGV4cEdGJTYjSSJ4R0YoRishIiItRiQ2I0YsRis= LCYtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCYiIiJGKy1JJGV4cEdGJTYjSSJ4R0YoRishIiJGL0Yr int(x/(1+exp(x)),x); LCgqJiMiIiIiIiNGJSlJInhHNiJGJkYlRiUqJkYoRiUtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGKTYjLCZGJUYlLUkkZXhwR0YtNiNGKEYlRiUhIiItSShwb2x5bG9nR0YtNiRGJiwkRjJGNUY1 int(1/(1+x^2),x); convert(%,ln); LUknYXJjdGFuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInhHRic= KiYqJiMiIiIiIiNGJV4jRiVGJUYlLCYtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCZGJUYlKiYsJEYnRiVGJUkieEdGLkYlISIiRiUtRio2IywmRiVGJSomRidGJUYzRiVGJUY0RiU= int(cos(x),x); convert(%,exp); LUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInhHRic= LCQqJiwkKiYjIiIiIiIjRideI0YnRidGJ0YnLCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyomRilGJ0kieEdGMEYnRicqJEYrISIiRjVGJ0Y1 int(1/sqrt(1-x^2),x); convert(%,ln); LUknYXJjc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInhHRic= LCQqJiwkXiMiIiJGJkYmLUkjbG5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmKiQpLCZGJkYmKiQpSSJ4R0YsIiIjRiYhIiIjRiZGNUYmRiYqJkYlRiZGNEYmRiZGJkY2 int(arccosh(x),x); convert(arccosh(x),ln); int(%,x); LCYqJkkieEc2IiIiIi1JKGFyY2Nvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0YkRiZGJiomKSwmRiRGJkYmISIiI0YmIiIjRiYpLCZGJEYmRiZGJkYxRiZGMA== LUkjbG5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmSSJ4R0YnIiIiKiYpLCZGKkYrRishIiIjRisiIiNGKyksJkYqRitGK0YrRjBGK0Yr LCYqJi1JI2xuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJkkieEdGKSIiIiomKSwmRixGLUYtISIiI0YtIiIjRi0pLCZGLEYtRi1GLUYyRi1GLUYtRixGLUYtRi5GMQ==
<Text-field style="Heading 2" layout="Heading 2">E 12.1. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn f:=exp(x)+exp(2*x)+exp(x/2); int(f,x); LCgtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieEdGKCIiIi1GJDYjLCQqJiIiI0YrRipGK0YrRistRiQ2IywkKiYjRitGMEYrRipGK0YrRis= LCgtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieEdGKCIiIiomI0YrIiIjRistRiQ2IywkKiZGLkYrRipGK0YrRitGKyomRi5GKy1GJDYjLCQqJkYtRitGKkYrRitGK0Yr
<Text-field style="Heading 2" layout="Heading 2">E 12.2. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> g:=sqrt(log(x^2+3*x+2)*(log(x+1)+log(x+2))); KiQpKiYtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCgqJClJInhHRioiIiMiIiJGMSomIiIkRjFGL0YxRjFGMEYxRjEsJi1GJjYjLCZGL0YxRjFGMUYxLUYmNiMsJkYvRjFGMEYxRjFGMSNGMUYwRjE=
<Text-field style="Heading 2" layout="Heading 2">E 12.3. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn h:=exp(ln(x)/2); KiQpSSJ4RzYiIyIiIiIiI0Yn
<Text-field style="Heading 2" layout="Heading 2">E 12.4. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn g:=log(sqrt(x^2+1)+x)+log(sqrt(x^2+1)-x); theta1:=sqrt(x^2+1); h:=(theta1-x)^k*(theta1+x)^k1; diff(h,x)/h; simplify(%); LCYtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCYqJCksJiokKUkieEdGKCIiIyIiIkYyRjJGMiNGMkYxRjJGMkYwRjJGMi1GJDYjLCZGK0YyRjAhIiJGMg== KiQpLCYqJClJInhHNiIiIiMiIiJGKkYqRiojRipGKUYq KiYpLCYqJCksJiokKUkieEc2IiIiIyIiIkYtRi1GLSNGLUYsRi1GLUYqISIiSSJrR0YrRi0pLCZGJUYtRipGLUkjazFHRitGLQ== KigsJiosKSwmKiQpLCYqJClJInhHNiIiIiMiIiJGL0YvRi8jRi9GLkYvRi9GLCEiIkkia0dGLUYvRjJGLywmKiZGKEYxRixGL0YvRi9GMUYvRiZGMSksJkYnRi9GLEYvSSNrMUdGLUYvRi8qLEYlRi9GNUYvRjdGLywmRjRGL0YvRi9GL0Y2RjFGL0YvRiVGMUY1RjE= LCQqJiwmSSJrRzYiIiIiSSNrMUdGJiEiIkYnKSwmKiQpSSJ4R0YmIiIjRidGJ0YnRicjRidGL0YpRik=
<Text-field style="Heading 2" layout="Heading 2">E 12.5. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn exp(x^2+log(x)/2)/(2*(sqrt(x)-1))+exp(x^2+log(x)/2)/(2*(sqrt(x)+1)); diff(%,x); simplify(%); LCYqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCYqJClJInhHRikiIiMiIiJGMComI0YwRi9GMC1JI2xuR0YmNiNGLkYwRjBGMCwmKiZGL0YwKUYuRjJGMEYwRi8hIiJGOUYwKiZGJEYwLCZGN0YwRi9GMEY5RjA= LCoqKCwmKiYiIiMiIiJJInhHNiJGJ0YnKiYjRidGJkYnRighIiJGJ0YnLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YpNiMsJiokKUYoRiZGJ0YnKiZGK0YnLUkjbG5HRi82I0YoRidGJ0YnLCYqJkYmRicpRihGK0YnRidGJkYsRixGJyooRi1GJylGOkYmRixGPEYsRiwqKEYkRidGLUYnLCZGO0YnRiZGJ0YsRicqKEYtRicpRkBGJkYsRjxGLEYs KiotSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyokKUkieEdGKCIiIyIiIkYuLCgqJkYtRi4pRiwiIiRGLkYuKiZGLUYuRitGLiEiIkYuRjRGLiksJiokKUYsI0YuRi1GLkYuRi5GNEYtRjQpLCZGN0YuRi5GLkYtRjQ= int((2*x^3-2*x^2-1)/(x-1)^2*exp(x^2),x); KigsJkkieEc2IiIiIkYmISIiRidGJEYmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMqJClGJCIiI0YmRiY=
<Text-field style="Heading 2" layout="Heading 2">E 12.6. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn int(1/ln(x),x); LCQtSSNFaUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkIiIiLCQtSSNsbkdGJTYjSSJ4R0YoISIiRjA= resultant(1-z/x,theta,theta); KiYsJkkieEc2IiIiIkkiekdGJSEiIkYmRiRGKA==
<Text-field style="Heading 2" layout="Heading 2">E 12.7. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn int(1/x/ln(x),x); LUkjbG5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy1GIzYjSSJ4R0Yn resultant(1/x-z/x,theta,theta); LCQqJiwmIiIiISIiSSJ6RzYiRiVGJUkieEdGKEYmRiY= oR:=1-z; LCYiIiJGI0kiekc2IiEiIg== v1:=gcd(1/x-1/x,theta); SSZ0aGV0YUc2Ig==
<Text-field style="Heading 2" layout="Heading 2">E 12.8. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn (x*(x+1)*((x^2*exp(2*x^2)-(log(x+1))^2)^2+2*x*exp(3*x^2)*(x-(2*x^3+2*x^2+x+1)*log(x+1))))/((x+1)*(log(x+1))^2-(x^3+x^2)*exp(2*x^2))^2; KipJInhHNiIiIiIsJkYjRiVGJUYlRiUsJiokKSwmKiYpRiMiIiNGJS1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqJkYtRiVGLEYlRiVGJUYlKiQpLUkjbG5HRjA2I0YmRi1GJSEiIkYtRiVGJSoqRi1GJUYjRiUtRi82IywkKiYiIiRGJUYsRiVGJUYlLCZGI0YlKiYsKiomRi1GJSlGI0ZBRiVGJUY1RiVGI0YlRiVGJUYlRjhGJUY7RiVGJUYlKSwmKiZGJkYlRjdGJUYlKiYsJiokRkZGJUYlKiRGLEYlRiVGJUYuRiVGO0YtRjs= int(%,x); LCxJInhHNiIiIiItSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCZGI0YlRiVGJSEiIioqLUkkZXhwR0YoNiMqJClGIyIiI0YlRiVGI0YlRiZGJSwmKiZGM0YlLUYwNiMsJComRjRGJUYzRiVGJUYlRiUqJClGJkY0RiVGLUYtRiUqJiNGJUY0RiUtRic2IywmRiZGJSomRiNGJUYvRiVGLUYlRi0qJkY+RiUtRic2IywmRkJGJUYmRiVGJUYl subs(exp(x^2)=theta1,%%); KipJInhHNiIiIiIsJkYjRiVGJUYlRiUsJiokKSwmKiYpRiMiIiNGJS1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqJkYtRiVGLEYlRiVGJUYlKiQpLUkjbG5HRjA2I0YmRi1GJSEiIkYtRiVGJSoqRi1GJUYjRiUtRi82IywkKiYiIiRGJUYsRiVGJUYlLCZGI0YlKiYsKiomRi1GJSlGI0ZBRiVGJUY1RiVGI0YlRiVGJUYlRjhGJUY7RiVGJUYlKSwmKiZGJkYlRjdGJUYlKiYsJiokRkZGJUYlKiRGLEYlRiVGJUYuRiVGO0YtRjs= subs(exp(2*x^2)=theta1^2,%); KipJInhHNiIiIiIsJkYjRiVGJUYlRiUsJiokKSwmKiYpRiMiIiNGJSlJJ3RoZXRhMUdGJEYtRiVGJSokKS1JI2xuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJkYtRiUhIiJGLUYlRiUqKkYtRiVGI0YlLUkkZXhwR0Y0NiMsJComIiIkRiVGLEYlRiVGJSwmRiNGJSomLCoqJkYtRiUpRiNGP0YlRiUqJkYtRiVGLEYlRiVGI0YlRiVGJUYlRjJGJUY4RiVGJUYlKSwmKiZGJkYlRjFGJUYlKiYsJiokRkRGJUYlKiRGLEYlRiVGJUYuRiVGOEYtRjg= subs(exp(3*x^2)=theta1^3,%); KipJInhHNiIiIiIsJkYjRiVGJUYlRiUsJiokKSwmKiYpRiMiIiNGJSlJJ3RoZXRhMUdGJEYtRiVGJSokKS1JI2xuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJkYtRiUhIiJGLUYlRiUqKkYtRiVGI0YlKUYvIiIkRiUsJkYjRiUqJiwqKiZGLUYlKUYjRjtGJUYlKiZGLUYlRixGJUYlRiNGJUYlRiVGJUYyRiVGOEYlRiVGJSksJiomRiZGJUYxRiVGJSomLCYqJEZARiVGJSokRixGJUYlRiVGLkYlRjhGLUY4 f:=subs(ln(x+1)=theta2,%); KipJInhHNiIiIiIsJkYjRiVGJUYlRiUsJiokKSwmKiYpRiMiIiNGJSlJJ3RoZXRhMUdGJEYtRiVGJSokKUkndGhldGEyR0YkRi1GJSEiIkYtRiVGJSoqRi1GJUYjRiUpRi8iIiRGJSwmRiNGJSomLCoqJkYtRiUpRiNGNkYlRiUqJkYtRiVGLEYlRiVGI0YlRiVGJUYlRjJGJUYzRiVGJUYlKSwmKiZGJkYlRjFGJUYlKiYsJiokRjtGJUYlKiRGLEYlRiVGJUYuRiVGM0YtRjM= convert(f,parfrac,theta2,sqrfree); LCYqJiwmSSJ4RzYiIiIiRidGJyEiIkYlRidGJyouIiIjRicpRiVGKkYnKUkndGhldGExR0YmIiIkRicsLCooRipGJ0kndGhldGEyR0YmRicpRiVGLkYnRicqKEYqRidGMUYnRitGJ0YnKiZGMUYnRiVGJ0YnRjFGJ0YlRihGJyksJiomRitGJylGLUYqRidGKCokKUYxRipGJ0YnRipGKEYkRihGKA== a:=(2*x^2+1)*theta1*theta2-x/(x+1)*theta1; LCYqKCwmKiYiIiMiIiIpSSJ4RzYiRiZGJ0YnRidGJ0YnSSd0aGV0YTFHRipGJ0kndGhldGEyR0YqRidGJyooRilGJywmRilGJ0YnRichIiJGK0YnRi8= b:=theta2^2-x^2*theta1^2; LCYqJilJInhHNiIiIiMiIiIpSSd0aGV0YTFHRiZGJ0YoISIiKiQpSSd0aGV0YTJHRiZGJ0YoRig= oR:=4*z^2-1; c1:=1/2; c2:=-1/2; LCYqJiIiJSIiIilJInpHNiIiIiNGJUYlRiUhIiI= IyIiIiIiIw== IyEiIiIiIw== v1:=theta2+x*theta1; v2:=theta2-x*theta1; LCZJJ3RoZXRhMkc2IiIiIiomSSJ4R0YkRiVJJ3RoZXRhMUdGJEYlRiU= LCZJJ3RoZXRhMkc2IiIiIiomSSJ4R0YkRiVJJ3RoZXRhMUdGJEYlISIi
<Text-field style="Heading 2" layout="Heading 2">E 12.9. P<Font encoding="UTF-8">\303\251lda.</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
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