P(Q,Q),P(R,R+),P(Q,Q+).
P(Q,Q)
m i j 0m
δi,j δi,j = 0 i6=j δi,i = 1
q0, q1, . . . , qmm+ 1
j= 0,1, . . . , m LjRm[X]
Lj(qi) = δi,j i= 0,1, . . . , m
(Lj)0≤j≤m
Rm[X]
PRm[X]P
(Lj)0≤j≤m(P(qj))0≤j≤m
P(Q,Q)Q[X]
P(R,R+)
∀(a, b, c, d)∈R4,∃(x, y)∈R2(a2+b2)(c2+d2) = x2+y2.
x y a, b, c, d t z
t2+z2
A
RA
S={z∈A| ∃x∈A, ∃y∈A, z =x2+y2}
S0 1
PP(R,R+)
P
(X−a)α(X2+bX +c)βa, b, c α β
X2+bX +cR[X]
P
α
P
R[X]
P(R,R+)
P(Q,Q+)
P(Q,Q+)P(R,R+)
2X2+4
R[X]
a, b, c, d
2X2+ 4 = (aX +b)2+ (cX +d)2