Geodesic
Quadratic modules over polynomial rings
Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 114-124

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One gives the complete solution of the problem of the reduction of quadratic spaces for the polynomial ring over a field. 
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     author = {V. I. Kopeiko and A. A. Suslin},
     title = {Quadratic modules over polynomial rings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {114--124},
     publisher = {mathdoc},
     volume = {86},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a10/}
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V. I. Kopeiko; A. A. Suslin. Quadratic modules over polynomial rings. Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 114-124. http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a10/