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238:: the set of positive numbers and the set of negative numbers. Thus, the real numbers have two square classes, the positive numbers and the negative numbers.
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and thus it is sometimes more convenient to talk about the square classes which the quadratic form represents.
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Bilinear
Algebra: An Introduction to the Algebraic Theory of Quadratic Forms
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The
Classical Fields: Structural Features of the Real and Rational Numbers
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of the multiplicative group) consisting of the elements of the form
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Square classes are frequently studied in relation to the theory of
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In a commutative ring, an equivalence class modulo squares
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154:{\displaystyle F=\mathbb {R} }
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483:{\displaystyle q(uv)=au^{2}}
215:{\displaystyle F^{\times 2}}
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114:of the nonzero elements (a
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314:{\displaystyle q:V\to F}
245:. The reason is that if
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232:square root
639:Categories
505:References
495:involution
361:such that
428:×
420:∈
395:×
387:∈
306:→
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102:of the
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236:cosets
122:where
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108:square
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116:coset
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27:of a
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