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→History: unlink: sum of squares - the use here is not to a specific method but just a general notion; only certain integers can be represented as a sum of two squares and the latter half of the paragraph covers these early developments. |
m Capitalising the coefficients of binary quadratic form in Arndt's method |
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A variety of definitions of composition of forms has been given, often in an attempt to simplify the extremely technical and general definition of Gauss. We present here Arndt's method, because it remains rather general while being simple enough to be amenable to computations by hand. An alternative definition is described at [[Bhargava cube]]s.
Suppose we wish to compose forms <math>f_1 =
# Compute <math>B = \tfrac{B_1 + B_2}{2}</math> and <math> e = \gcd(A_1, A_2, B)</math>, and <math>A = \tfrac{A_1 A_2}{e^2}</math>
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