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In mathematics, a cubic form is a homogeneous polynomial of degree 3, and a cubic hypersurface is the zero set of a cubic form. In the case of a cubic form in three variables, the zero set is a cubic plane curve. In (), Boris Delone and Dmitry Faddeev showed that binary cubic forms with integer coefficients can be used to parametrize orders in cubic fields. Their work was generalized in (, §4) to include all cubic rings, giving a discriminant-preserving bijection between orbits of a GL(2, Z)-action on the space of integral binary cubic forms and cubic rings up to isomorphism.

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  • شكل تكعيبي
  • Cubic form
  • 삼차 형식
  • Kubisk form
rdfs:comment
  • في الرياضيات، شكل تكعيبي هو متعددة حدود متجانسة من الدرجة الثالثة، وتحوي عدة متحولات.
  • 대수기하학과 대수적 수론에서, 삼차 형식(三次型式, 영어: cubic form)은 어떤 벡터 공간 또는 가군 위에 정의된 3차 동차 다항식이다. 즉, 선형 형식과 이차 형식의 다음 차수의 동차 다항식이다.
  • In mathematics, a cubic form is a homogeneous polynomial of degree 3, and a cubic hypersurface is the zero set of a cubic form. In the case of a cubic form in three variables, the zero set is a cubic plane curve. In (), Boris Delone and Dmitry Faddeev showed that binary cubic forms with integer coefficients can be used to parametrize orders in cubic fields. Their work was generalized in (, §4) to include all cubic rings, giving a discriminant-preserving bijection between orbits of a GL(2, Z)-action on the space of integral binary cubic forms and cubic rings up to isomorphism.
  • Kubisk form är inom matematiken ett homogent polynom av grad 3, och en kubisk hyperyta är nollmängd av en kvadratisk form. I () visade och att binära kubiska former med heltalskoefficienter kan användas för att parametrisera i . Deras arbete blev i (, §4) generaliserat till att inkludera alla kubiska ringar, vilket ger en -bevarande bijektion mellan av en GL(2, Z)-verkan på rummet av binära kubiska former med heltalskoefficienter, och kubiska ringar upp till isomorfi.
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first
  • V.A.
  • V.L.
id
  • c/c027260
  • c/c027270
last
  • Popov
  • Iskovskikh
title
  • Cubic form
  • Cubic hypersurface
author2-link
  • Vladimir L. Popov
has abstract
  • في الرياضيات، شكل تكعيبي هو متعددة حدود متجانسة من الدرجة الثالثة، وتحوي عدة متحولات.
  • In mathematics, a cubic form is a homogeneous polynomial of degree 3, and a cubic hypersurface is the zero set of a cubic form. In the case of a cubic form in three variables, the zero set is a cubic plane curve. In (), Boris Delone and Dmitry Faddeev showed that binary cubic forms with integer coefficients can be used to parametrize orders in cubic fields. Their work was generalized in (, §4) to include all cubic rings, giving a discriminant-preserving bijection between orbits of a GL(2, Z)-action on the space of integral binary cubic forms and cubic rings up to isomorphism. The classification of real cubic forms is linked to the classification of umbilical points of surfaces. The equivalence classes of such cubics form a three-dimensional real projective space and the subset of define a surface – the umbilic torus.
  • 대수기하학과 대수적 수론에서, 삼차 형식(三次型式, 영어: cubic form)은 어떤 벡터 공간 또는 가군 위에 정의된 3차 동차 다항식이다. 즉, 선형 형식과 이차 형식의 다음 차수의 동차 다항식이다.
  • Kubisk form är inom matematiken ett homogent polynom av grad 3, och en kubisk hyperyta är nollmängd av en kvadratisk form. I () visade och att binära kubiska former med heltalskoefficienter kan användas för att parametrisera i . Deras arbete blev i (, §4) generaliserat till att inkludera alla kubiska ringar, vilket ger en -bevarande bijektion mellan av en GL(2, Z)-verkan på rummet av binära kubiska former med heltalskoefficienter, och kubiska ringar upp till isomorfi. Klassificeringen av reella kubiska former är kopplad till klassificeringen av av ytor. Ekvivalensklasser av sådana kubiska former bildar ett tredimensionellt och delmängden av definierar en yta – .
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