@Christopher2222 

http://en.wikipedia.org/wiki/Genetic_programming

in the diagram of the page, the node can store operator such as +, - , *, /,

can the tree in maple store these operator?

moreover, can tree store diff command such as diff(leaf, x)?

@Christopher2222 

can the tree node have operator such as +, -,* /

@Christopher2222 

can the tree node have operator such as +, -,* /

gen := taylor(ln(genfun), z=0,5);

result := convert(gen, ratpoly);

seriestoratpoly(gen, ['egf']);

result is complicated, is it correct? how to do to make the same result with http://www.solitaryroad.com/c682.html?

I have discovered a method to do the same result in http://www.solitaryroad.com/c680.html

but i do not know whether it is correct, it is like combining lego, and not sure whether it is general method for other example

gen := taylor(ln(genfun), z=0,5);

result := convert(gen, ratpoly);

seriestoratpoly(gen, ['egf']);

result is complicated, is it correct? how to do to make the same result with http://www.solitaryroad.com/c682.html?

I have discovered a method to do the same result in http://www.solitaryroad.com/c680.html

but i do not know whether it is correct, it is like combining lego, and not sure whether it is general method for other example

gen := taylor(ln(genfun), z=0,5);

seriestoratpoly(gen, ['egf'])

result is FAIL

gen := taylor(ln(genfun), z=0,5);

seriestoratpoly(gen, ['egf'])

result is FAIL

> opoly := (1-x^2)*(diff(f(x), `$`(x, 2)))-x*(diff(f(x), x))+n^2*f(x) = 0;
sol := op(2, dsolve(opoly));
genfun := sum(cos(n*arcsin(x))*z^n/factorial(n), n = 0 .. 7);
with(gfun);
algeqtoseries(expand(genfun), x, z, 7, true);

     /     2\ / d  / d      \\     / d      \    2         
     \1 - x / |--- |--- f(x)|| - x |--- f(x)| + n  f(x) = 0
              \ dx \ dx     //     \ dx     /              
          _C1 sin(n arcsin(x)) + _C2 cos(n arcsin(x))
                 (1/2)                          
         /     2\          1                   2
     1 + \1 - x /      z + - cos(2 arcsin(x)) z
                           2                    

          1                   3   1                    4
        + - cos(3 arcsin(x)) z  + -- cos(4 arcsin(x)) z
          6                       24                    

           1                    5    1                    6
        + --- cos(5 arcsin(x)) z  + --- cos(6 arcsin(x)) z
          120                       720                    

           1                     7
        + ---- cos(7 arcsin(x)) z
          5040                    
Error, invalid input: gfun:-algeqtoseries expects its 1st argument, Pol, to be of type polynom(anything, [x, y]), but received 1+(1-x^2)^(1/2)*z+(1/2)*z^2-z^2*x^2+(1/6)*z^3*(1-x^2)^(1/2)-(2/3)*z^3*(1-x^2)^(1/2)*x^2+(1/24)*z^4-(1/3)*z^4*x^2+(1/3)*z^4*x^4+(1/120)*z^5*(1-x^2)^(1/2)-(1/10)*z^5*(1-x^2)^(1/2)*x^2+(2/15)*z^5*(1-x^2)^(1/2)*x^4+(1/720)*z^6-(1/40)*z^6*x^2+(1/15)*z^6*x^4-(2/45)*z^6*x^6+(1/5040)*z^7*(1-x^2)^(1/2)-(1/210)*z^7*(1-x^2)^(1/2)*x^2+(1/63)*z^7*(1-x^2)^(1/2)*x^4-(4/315)*z^7*(1-x^2)^(1/2)*x^6

tried to replace z with y, also the same error

> opoly := (1-x^2)*(diff(f(x), `$`(x, 2)))-x*(diff(f(x), x))+n^2*f(x) = 0;
sol := op(2, dsolve(opoly));
genfun := sum(cos(n*arcsin(x))*z^n/factorial(n), n = 0 .. 7);
with(gfun);
algeqtoseries(expand(genfun), x, z, 7, true);

     /     2\ / d  / d      \\     / d      \    2         
     \1 - x / |--- |--- f(x)|| - x |--- f(x)| + n  f(x) = 0
              \ dx \ dx     //     \ dx     /              
          _C1 sin(n arcsin(x)) + _C2 cos(n arcsin(x))
                 (1/2)                          
         /     2\          1                   2
     1 + \1 - x /      z + - cos(2 arcsin(x)) z
                           2                    

          1                   3   1                    4
        + - cos(3 arcsin(x)) z  + -- cos(4 arcsin(x)) z
          6                       24                    

           1                    5    1                    6
        + --- cos(5 arcsin(x)) z  + --- cos(6 arcsin(x)) z
          120                       720                    

           1                     7
        + ---- cos(7 arcsin(x)) z
          5040                    
Error, invalid input: gfun:-algeqtoseries expects its 1st argument, Pol, to be of type polynom(anything, [x, y]), but received 1+(1-x^2)^(1/2)*z+(1/2)*z^2-z^2*x^2+(1/6)*z^3*(1-x^2)^(1/2)-(2/3)*z^3*(1-x^2)^(1/2)*x^2+(1/24)*z^4-(1/3)*z^4*x^2+(1/3)*z^4*x^4+(1/120)*z^5*(1-x^2)^(1/2)-(1/10)*z^5*(1-x^2)^(1/2)*x^2+(2/15)*z^5*(1-x^2)^(1/2)*x^4+(1/720)*z^6-(1/40)*z^6*x^2+(1/15)*z^6*x^4-(2/45)*z^6*x^6+(1/5040)*z^7*(1-x^2)^(1/2)-(1/210)*z^7*(1-x^2)^(1/2)*x^2+(1/63)*z^7*(1-x^2)^(1/2)*x^4-(4/315)*z^7*(1-x^2)^(1/2)*x^6

tried to replace z with y, also the same error

After restarting maple, it can run. Thank you very much.

After restarting maple, it can run. Thank you very much.

i get it now

i get it now

can mod do algebraic mod?

can mod do algebraic mod?