Solution without the polynomial ring

Kitonum — Fri, 09 Nov 2012 21:55:11 Z

We look for real solutions. Since the number of unknowns is greater than the number of equations, we set z =t , where t is any real number. Solving the resulting system, we get an infinite number of complex solutions, depending on t , some of which may be real. Equating to 0 the imaginary parts, we find the desired t .

restart;

z:=t:

Sol:=allvalues(solve({x^2+y^2+z^2=3, x+y+z=3}, {x, y}));

assign(Sol[1]);

solve(Im(x)=0, t), solve(Im(y)=0, t) assuming t::real;

subs(t=1, [x, y, z]); # Finding real solutions for the first set of the roots

x:='x': y:='y':

assign(Sol[2]);

solve(Im(x)=0, t), solve(Im(y)=0, t) assuming t::real;

subs(t=1, [x, y, z]); # Finding real solutions for the second set of the roots

Comparison with Mathematica 8.04

Markiyan Hirnyk — Fri, 09 Nov 2012 22:39:20 Z

In[1]:= Reduce[x^3 + y^3 + z^3 == 3 && x + y + z == 3, {x, y, z}, Integers]
Out[1] = (x == -5 && y == 4 && z == 4) || (x == 1 && y == 1 &&
z == 1) || (x == 4 && y == -5 && z == 4) || (x == 4 && y == 4 &&
z == -5)

ArcanaNoir — Mon, 12 Nov 2012 08:55:20 Z

MaplePrimes - answers and comments on Question, diophantine equations

Solution without the polynomial ring

Comparison with Mathematica 8.04