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Question: Why do match and solve not work in this case?

Question:Why do match and solve not work in this case?

ComputerUser 535 Maple
solve groebner
March 01 2013
1 
restart;
with(Groebner):
g1 := x^2-w*y;
g2 := x*y-w*z;
g3 := y^2-x*z;
S13 := -y^3*w+x^3*z;
eq1:= S13 = h131*g1 + h132*g2 + h133*g3;

hsol := solve(identity(eq1, x), [h131, h132, h133]);
match(eq1,{x,y,z,w},'s');
s;
 
h131 should be x*z
h312 should be 0
h133 should be -y*w
 
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