Methods of Algebraic Geometry, Volume 1,Livre 1

a₁ algebraic extension algebraically dependent allowable coordinate system assume b₁ canonical form coefficients coincide collinear collineation columns commutative consider construct contains correlation corresponding d₁ deduce defined degree denote Desargues determined dimensions distinct elementary divisors equivalent exists finite number follows fundamental space given Grassmann coordinates ground field harmonic conjugate Hence highest common factor hypothesis indeterminates induction integers integral domain intersection invariant factors irreducible polynomial isomorphic k-space L(u₁ l₁ latent root left-hand linear space linearly independent linearly independent points matrix meet necessary and sufficient non-singular non-zero element obtain P₁ pairs permissible transformation perspective Ph(K plane PN(K polynomial prime primitive polynomial projective space projective transformation properties prove THEOREM r₁ rank respectively result resultant-forms ring rows simplex of reference solution specialisation submatrix sufficient condition suffixes suppose symmetric triads triangles u₁ unique united points v₁ vectors vertex write x₁ zero Σ Σ