Notes on computing minimal approximant bases

  title={Notes on computing minimal approximant bases},
  author={Arne Storjohann},
  booktitle={Challenges in Symbolic Computation Software},
  • Arne Storjohann
  • Published 2006 in Challenges in Symbolic Computation Software
When s = 1 and N = ‖n‖ − 1 this is the classical Hermite Padé approximation problem. Here we allow N to be arbitrary. We describe algorithms for computing an order N genset of type n: a matrix V ∈ k[x]∗×m such that every row of V is a solution to (1) and every solution P of (1) can be expressed as a k[x]-linear combination of the rows of V . Ideally, V will be a minbasis of solutions: V has full row rank, and if n̄ ≥ maxi ni then V diag(n̄−n1, . . . , n̄−nm) is row reduced (e.g., in weak Popov… CONTINUE READING

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