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Encyclopedia Britannica



A2(z)

This article appears in Volume V01, Page 637 of the Encyclopedia Britannica.

Encyclopedia Britannica - Main :: A10-ADA
A2(z) z2Ai 4z/ ,
where
= 1 A2(z)
az2.1a2'
and this is the red'iced generating
function
  which tells us, by its denominator factors, that the
complete
 
system
  of the quadratic is composed of the form itself of degree
order
  I, 2 shown by az2, and of the
Hessian
  of degree
order
  2, o shown by a2.
Again, for the cubic, we can find
Aa(z) 1 aez6
1az2 .1a2z2.1a2z2 .1a*,
where the ground forms are indicated by the denominator factors, viz.: these are the cubic itself of degree order I, 3; the
Hessian
  of degree order 2, 2; the cubi-covariant G of degree order 3, 3, and the quartic invariant of degree order 4, o. Further, the numerator factor establishes that these are not all algebraically
independent
 , but are connected by a
syzygy
  of degree order 6, 6.
Similarly for the quartic


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