An Introduction to the Algebra of Quantics |
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Common terms and phrases
a₁ ac-b² annihilated ax³ b₁ binary cubic binary p-ic binary quantic Boolian invariants canonical form catalecticant Cayley complete system contravariants covariants and invariants da₁ denote differences Diophantine equations discriminant dx dy equal equation evectants expressed in terms fact factor finite number gradient harmonic conjugates Hessian homogeneous homogeneous function identity invariant of degree invariants and covariants irreducible concomitants irreducible invariants isobaric Jacobian leading coefficient linear covariant linear form linear substitution linear transformation linearly independent modulus notation number of linearly numerical multiple obtained orthogonal positive integral powers protomorphs prove rational integral function rationally and integrally roots seminvariant sets of solutions sextic suffix symmetric functions syzygy terms free theorem transformed transvectants values vanish variables variants zero α₁ α₂
Popular passages
Page vii - PREFACE. nnHE object of this book is to provide an English introduction to the symbolical method in the theory of Invariants. It was started as an attempt to meet the need expressed by Elliott in the preface to The Algebra of Quantics — 'a whole book which shall present to the English reader in his own language a worthy exposition of the method of the great German masters remains a desideratum.
Page 193 - T can be expressed rationally and integrally in terms of a finite number of the forms of ((7), I'll ^f •••, t/n then all C"s up to and including those derived from can be expressed in terms of rfff V 2...
Page 201 - ICr'+Ste3— 4x*+2ox — 30=0 into another one in which the coefficient of the first term is unity and the other coefficients are integral.
Page 113 - I shall now make the hypothesis that > the eccentricity of the ellipse, is very small, so that its square and higher powers may be neglected. Let us write for brevity =«. 9. We have now to find the electric force at tt' due to the change of magnetic force H in the element of volume at P.
Page vii - To the difficulty with regard to Cayley and Sylvester may in particular be added that of discriminating between what in Salmon's work should be ascribed to them or others at all and what to Salmon himself.
Page 78 - The method, which is spoken of as that of ' hyperdeterminants,' did not, in its originator's form, succeed in establishing the finiteness of complete systems of irreducible covariants in general. That triumph was reserved for another symbolical method, having much in common with it, which will be referred to in the following article.
Page 270 - The reduction of the quintic to a sum of three fifth powers will be discussed in Ch.
Page 38 - ... applies even when the invariant is irrational, for an irrational invariant may be expressed as a sum, not necessarily finite, of terms to which the reasoning may be applied.