On the Piano Movers Problem Ii General Techniques for Computing Topological P
On the Piano Movers Problem Ii General Techniques for Computing Topological P
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In our eReader you can find the full English version of the book. Read On the Piano Movers Problem Ii General Techniques for Computing Topological P Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book On the Piano Movers Problem Ii General Techniques for Computing Topological P
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-51- The technique for resultant calculation given in [Sc] depends only on the identities (l)-(5) and hence can be adapted to the calculation of subresultants. Fleshing out this summary remark, we shall now present an efficient technique for the simultaneous calculation of all subresultants of a given pair of polynomials P and Q. To this end, we make the following definition.
Definition 2l ^^^ a pair of polynomials w = [P, Q] of degree d, d' with coefficients in a field F be given, and let d = ...max(d, d'). Write P mod Q for the remainder of P upon division by Q. Then the RQ-sequence RQ(w) of w is the sequence tj, i = d, d-l, ... , 0, of quadruples ti = [[Pi. Qi], a^, bi, M^], defined as follows: (1) P^, Q^ are polynomials, a^ is a quantity of F, b^^ is always +1 or -1, and >L is a 2x2 matrix of polynomials with coefficients in F.
(2) tj = [ [P, Q], 1, 1, 1], where I is the 2 x 2 identity matrix.
(3) roax(deg(P^), deg(Q^)) > i > min(deg(P^), deg(Q^) ) for i > 0.
(4a) If min(deg(Pi), deg(Qi))
What to read after On the Piano Movers Problem Ii General Techniques for Computing Topological P?
You can find similar books in the "Read Also" column, or choose other free books by Jacob T Schwartz to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
-51- The technique for resultant calculation given in [Sc] depends only on the identities (l)-(5) and hence can be adapted to the calculation of subresultants. Fleshing out this summary remark, we shall now present an efficient technique for the simultaneous calculation of all subresultants of a given pair of polynomials P and Q. To this end, we make the following definition.
Definition 2l ^^^ a pair of polynomials w = [P, Q] of degree d, d' with coefficients in a field F be given, and let d = ...max(d, d'). Write P mod Q for the remainder of P upon division by Q. Then the RQ-sequence RQ(w) of w is the sequence tj, i = d, d-l, ... , 0, of quadruples ti = [[Pi. Qi], a^, bi, M^], defined as follows: (1) P^, Q^ are polynomials, a^ is a quantity of F, b^^ is always +1 or -1, and >L is a 2x2 matrix of polynomials with coefficients in F.
(2) tj = [ [P, Q], 1, 1, 1], where I is the 2 x 2 identity matrix.
(3) roax(deg(P^), deg(Q^)) > i > min(deg(P^), deg(Q^) ) for i > 0.
(4a) If min(deg(Pi), deg(Qi))
What to read after On the Piano Movers Problem Ii General Techniques for Computing Topological P?
You can find similar books in the "Read Also" column, or choose other free books by Jacob T Schwartz to read onlineMoreLess
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