Solving quadratic equations over polynomial rings of characteristic two.
Publicacions Matemàtiques, Tome 42 (1998) no. 1, p. 131-142.
We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation antn + ...+ a0 = 0 with coefficients ai in A, our problem is to find its roots in A.We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction, we obtain a finite algorithm for solving a polynomial equation over A when A is F[x1, ..., xN] or F(x1, ..., xN) for any finite field F and any number N of variables.The case of quadratic equations in characteristic two is studied in detail.
Source:
Zbl
Classification : 13P05, 13F20, 13B25, 12E12, 11T06 
@article{PMATES_1998__42_1_41332,
     author = {Jorgen Cherly and Luis Gallardo and Leonid Vaserstein and Ethel Wheland},
     title = {Solving quadratic equations over polynomial rings of characteristic two.},
     journal = {Publicacions Matem\`atiques},
     pages = {131-142},
     volume = {42},
     number = {1},
     year = {1998},
     zbl = {an:0915.13017},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/PMATES_1998__42_1_41332/}
}
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Jorgen Cherly; Luis Gallardo; Leonid Vaserstein; Ethel Wheland. Solving quadratic equations over polynomial rings of characteristic two.. Publicacions Matemàtiques, Tome 42 (1998) no. 1, p. 131-142. https://geodesic-test.mathdoc.fr/item/PMATES_1998__42_1_41332/