# Question:how to find use all possible reduce result

## Question:how to find use all possible reduce result

with(Groebner):
K := {y1-(x1^3)*(x2^4),y2-(x2^(1+2))*(w^2),y3-(x1^(1+1))*(w^1),y4-(x2^1)*w,x1*x2*w - 1};
G := Basis(K, plex(x1, x2, w, y1, y2, y3, y4));
Reduce((x2^(5+1))*(w^1), G, plex(x1, x2, w, y1, y2, y3, y4));
(1,1,0,2)

subs({rho1=1,rho2=1,rho3=0,rho4=2},3*rho1 - 2*rho2 + rho3 - rho4);
subs({rho1=1,rho2=1,rho3=0,rho4=2},4*rho1 +   rho2 - rho3       );

can also reduce with G8,G7

R1 := Reduce((x2^(5+1))*(w^1), {G[7],G[8]}, plex(x1, x2, w, y1, y2, y3, y4));
(6,0,19,38)

subs({rho1=6,rho2=0,rho3=19,rho4=38},3*rho1 - 2*rho2 + rho3 - rho4);
subs({rho1=6,rho2=0,rho3=19,rho4=38},4*rho1 +   rho2 - rho3       );

R2 := Reduce(R1, {G[6]}, plex(x1, x2, w, y1, y2, y3, y4));

Question 1. R2 skip the result (y1^5)*(y3^15)*(y4^31) !!!!!!!! Is Maple error?

subs({rho1=5,rho2=0,rho3=15,rho4=31},3*rho1 - 2*rho2 + rho3 - rho4);
subs({rho1=5,rho2=0,rho3=15,rho4=31},4*rho1 +   rho2 - rho3       );

Question 2. how to find use all possible reduce result ?
use combination of all G to test whether its remainder equal 0?

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