Evaluating polynomial functions to get integer as answer

I am trying to evaluate:

syms x y
eq = (x^2 + y^3 == 31)
solve(eq)

eqs = [x^2 + y^3 == 31, x^2 == 31 - y^3]
S = solve(eq,[x y])
S.x and S.y still not 2 and 3

i am expecting to get as answer two integer: x=2 and y=3. How can i do it?

Thanks

Answer 1

[Walter Roberson]

syms x y integer
eq = (x^2 + y^3 == 31)

eq = 

solx = solve(eq,x,'returnconditions',true)

solx = struct with fields:
             x: [2×1 sym]
    parameters: [1×0 sym]
    conditions: [2×1 sym]

soly = solve(solx.conditions)

soly = 

3

X = subs(solx.x,y,soly)

X = 

Y = soly

Y = 

3

Caution: this kind of process will not generally attempt to find more than one solution for solx.conditions. But you could

soly = solve(eq,y,'returnconditions',true)

soly = struct with fields:
             y: [3×1 sym]
    parameters: [1×0 sym]
    conditions: [3×1 sym]

solx = arrayfun(@solve, soly.conditions, 'uniform', 0)

Warning: Unable to find explicit solution. For options, see help.

solx = 3×1 cell array
    {0×1 sym}
    {2×1 sym}
    {0×1 sym}

X = solx{2}

X = 

Y = subs(soly.y(2), x, X)

Y = 

Answer 2

[darova]

solve can be used for simple problems. Use fsolve or vpasolve to get numerical results

[Walter Roberson]

Not the point. The point is that solve() is having difficulty processing integer constraints in this case. fsolve and vpasolve have no chance of processing integer constraints.