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Cremona Transformation


An entire Cremona transformation is a birational transformation of the plane. Cremona transformations are maps of the form

x_(i+1)=f(x_i,y_i)
(1)
y_(i+1)=g(x_i,y_i),
(2)

in which f and g are polynomials. A quadratic Cremona transformation is always factorable.


See also

Noether's Transformation Theorem

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References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, pp. 203-204, 1959.Coolidge, J. L. A History of Geometrical Methods. New York: Dover, p. 287, 1963.Eddy, R. H. and Fritsch, R. "The Conics of Ludwig Kiepert: A Comprehensive Lesson in the Geometry of the Triangle." Math. Mag. 67, 188-205, 1994.

Referenced on Wolfram|Alpha

Cremona Transformation

Cite this as:

Weisstein, Eric W. "Cremona Transformation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CremonaTransformation.html

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