Perpetuants sentence example

perpetuants
  • In this case the ground forms, called also perpetuants, have been enumerated and actual representative seminvariant forms established.
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  • For these two cases the perpetuants are enumerated by z 2 23 -z2' and l -z2.1-z3 respectively.
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  • When 0=4 it is clear that no form, whose partition contains a part 3, can be reduced; but every form, whose partition is composed of the parts 4 and 2, is by elementary algebra reducible by means of perpetuants of degree 2.
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  • The generating function is I - z2' 52 For 0 =3, (alai +a2a2+a3a3) 10; the condition is clearly a1a2a3 = A3 = 0, and since every seminvariant, of proper degree 3, is associated, as coefficient, with a product containing A3, all such are perpetuants.
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  • The Complete Theory Of The Perpetuants Appertaining To Two Or More Forms Of Infinite Order Has Not Yet Been Established.
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  • For w = i the form is A i ai+Bib i, which we may write aob l -albo = ao(I) b -(I)abo; the remaining perpetuants, enumerated by z I - 2' have been set forth above.
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