Logic and Number Theory<Text-field layout="Section" style="Section">Diophantine equations and sets</Text-field>Positive values of polynomialsf:=(x,y)->2*y-x^4*y-2*x^3*y^2+x^2*y^3+2*x*y^4-y^5for x from 1 to 100 do
for y from 1 to 100 do
if f(x,y)>0 then
print([f(x,y),[x,y]])
end if;
end do;
end do;<Text-field layout="Section" style="Section">Logic background</Text-field>Recursive and recursively enumerable setssolutionsearch:=proc(mypolynomial,bound)
local i, j;
for i from 0 to bound do
for j from 0 to bound do
if mypolynomial(i,j)=0 then
print([i,j])
end if;
end do;
end do;
end proc:f:=(x,y)->y^2-x^3+x-1:solutionseach(f,100);