Hi. You asked to solve one such system for the values you gave and I tried to think of the most compact way of doing so in Mathematica:
which returns six sets of solutions.Code:coeff = {2, 3, 4, 6, 12, 32}; mycoeff = Table[Subscript[a, n] -> coeff[[n]], {n, 1, 6}]; myvars = Join[Table[Subscript[x, n], {n, 1, 3}], Table[Subscript[y, n], {n, 1, 3}]]; myequations = Table[ Sum[Subscript[x, j]*Subscript[y, j]^ (n - 1), {j, 1, 3}] == Subscript[a, n], {n, 1, 6}]; Solve[myequations /. mycoeff, myvars]
Thanks for your reply. I didn't think at PC program for solving; such sistems are actuel in code theory and Ramanujan discavered method (in 1913) of solving such sistems. This is what I'm interesting.
Update:O my God, I have a book in which this stuff is considered. So, here I will share this with poeple. Languge is russian, but it doesn't metter to much
I hope somebody will find this Ramanujan's paper in english.
And I findet what is neccessary
http://www.ams.org/bookstore-getitem/item=CHEL/159.H
Good bless Google!!!
and here is another one
http://bmf.hu/conferences/cinti2007/18_DombiJozsef.pdf
Well, maybe it was better that I post this in Web-room.
and here you can see this paper at
http://books.google.com/books?id=Efn...ations&f=false
and list of all papers here
http://www.imsc.res.in/~rao/ramanuja...ctedright1.htm