2021/07/08 by Laface, Antonio, Massarenti, Alex, Rischter, Rick
#14N15 #14Q15 #51N35 #Algebraic Geometry (math.AG) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Primary 14N07 #Secondary 14N05 #Symbolic Computation (cs.SC)
paper · doi:10.48550/arxiv.2107.04097
We give algorithms to compute decompositions of a given polynomial, or more generally mixed tensor, as sum of rank one tensors, and to establish whether such a decomposition is unique. In particular, we present methods to compute the decomposition of a general plane quintic in seven powers, and of a general space cubic in five powers; the two decompositions of a general plane sextic of rank nine, and the five decompositions of a general plane septic. Furthermore, we give Magma implementations of all our algorithms.