Hi

I should calculate the intersection E and W subspases by sage software. The 
field is Zp(y1), where  y1=-0.5000 + 0.8660*i. I do not know  how  enter 
the field  Zp(y1).  *I would appreciate it if you have helped me.*

 
sage: y1=CC(-0.5000,0.8660) 
sage: print(y1)
sage: V = CC^9
sage: v1 = vector(CC, [0,0,0,-y1-1,1,0,0,0,0])
sage: v2 = vector(CC, [y1,-y1,-1,1,0,y1,1,0,0])
sage: v3 = vector(CC, [0,y1,-y1,0,0,0,0,0,1])
sage: v4 = vector(CC, [y1,0,0,0,0,0,0,1,0])
sage: W = V.span([v1, v2, v3, v4])
sage: W
sage: U = CC^9
sage: u1 = vector(CC, [0,0,1,0,0,0,1,0,0])
sage: u2 = vector(CC, [0,0,0,1,0,1,0,0,0])
sage: u3 = vector(CC, [1,0,0,0,0,0,0,0,0])
sage: u4 = vector(CC, [0,0,0,0,0,0,0,0,1])
sage: u5 = vector(CC, [0,0,0,0,1,0,0,0,0])
sage: u6 = vector(CC, [0,1,0,0,0,0,0,1,0])
sage: E = U.span([u1, u2, u3, u4, u5, u6])
sage: E
sage: H = W.intersection(E)
sage: H 

  *The *field  is  Zp(y1).  

 Best Regard






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