Quadratic Transformation (other)
In mathematics, a quadratic transformation may be *A quadratic transformation in the Cremona group In algebraic geometry, the Cremona group, introduced by , is the group of birational automorphisms of the n-dimensional projective space over a field It is denoted by Cr(\mathbb^n(k)) or Bir(\mathbb^n(k)) or Cr_n(k). The Cremona group is naturall ... * Kummer's quadratic transformation of the hypergeometric function {{mathdab ...
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Cremona Group
In algebraic geometry, the Cremona group, introduced by , is the group of birational automorphisms of the n-dimensional projective space over a field It is denoted by Cr(\mathbb^n(k)) or Bir(\mathbb^n(k)) or Cr_n(k). The Cremona group is naturally identified with the automorphism group \mathrm_k(k(x_1, ..., x_n)) of the field of the rational function In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rat ...s in n indeterminates over k, or in other words a pure transcendental extension of k, with transcendence degree n. The projective general linear group of order n+1, of projective transformations, is contained in the Cremona group of order n. The two are equal only when n=0 or n=1, in which case both the numerator and the denominator of a transformation must be linear. The Cremona g ...
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