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In mathematics, the genus is a classificat … In mathematics, the genus is a classification of quadratic forms and lattices over the ring of integers. An integral quadratic form is a quadratic form on Zn, or equivalently a free Z-module of finite rank. Two such forms are in the same genus if they are equivalent over the local rings Zp for each prime p and also equivalent over R. Equivalent forms are in the same genus, but the converse does not hold. For example, x2 + 82y2 and 2x2 + 41y2 are in the same genus but not equivalent over Z. Forms in the same genus have equal discriminant and hence there are only finitely many equivalence classes in a genus. The Smith–Minkowski–Siegel mass formula gives the weight or mass of the quadratic forms in a genus, the count of equivalence classes weighted by the reciprocals of the orders of their automorphism groups.f the orders of their automorphism groups.
, 이차 형식 이론에서, 종수(種數, 영어: genus)는 대역체의 대수적 정수환 계수의 이차 형식 위에 정의되는 동치 관계이다. 이는 이차 형식의 동치보다 더 엉성하다.
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이차 형식 이론에서, 종수(種數, 영어: genus)는 대역체의 대수적 정수환 계수의 이차 형식 위에 정의되는 동치 관계이다. 이는 이차 형식의 동치보다 더 엉성하다.
, In mathematics, the genus is a classificat … In mathematics, the genus is a classification of quadratic forms and lattices over the ring of integers. An integral quadratic form is a quadratic form on Zn, or equivalently a free Z-module of finite rank. Two such forms are in the same genus if they are equivalent over the local rings Zp for each prime p and also equivalent over R. The Smith–Minkowski–Siegel mass formula gives the weight or mass of the quadratic forms in a genus, the count of equivalence classes weighted by the reciprocals of the orders of their automorphism groups.f the orders of their automorphism groups.
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| rdfs:label |
이차 형식 종수
, Genus of a quadratic form
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