Sentence Examples

  • This is of degree 8 in the coefficients, and degree 6 in the variables, and, for the canonical form, has the expression -9m 6 (x 3 +y 3 +z 3) 2 - (2m +5m 4 +20m 7) (x3 +y3+z3)xyz - (15m 2 +78m 5 -12m 8) Passing on to the ternary quartic we find that the number of ground forms is apparently very great.
  • Hermite expresses the quintic in a forme-type in which the constants are invariants and the variables linear covariants.
  • He proves, by means of the six linear partial differential equations satisfied by the concomitants, that, if any concomitant be expanded in powers of xi, x 2, x 3, the point variables-and of u 8, u 2, u3, the contragredient line variables-it is completely determinate if its leading coefficient be known.
  • V., established the important result that in the case of a form in n variables, the concomitants of the form, or of a system of such forms, involve in the aggregate n-1 classes of aa =5135 4 +4B8 3 p) =0, =5(135 4 - 4A 2 p 4) =0, P yield by elimination of S and p the discriminant D =64B-A2.
  • Let a covariant of degree e in the variables, and of degree 8 in the coefficients (the weight of the leading coefficient being w and n8-2w = �), be Coxl -}- ec l l 1 x 2 -{-...

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