From 683fd0ccda929459f5dadedb49373ef820aa2bef Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 4 Feb 2021 22:20:47 +0100 Subject: =?UTF-8?q?Rechnen=20in=20der=20K=C3=B6rpererweiterung?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../30-endlichekoerper/rechnungen/inverse.maxima | 35 ++++++++++++++++++++++ 1 file changed, 35 insertions(+) create mode 100644 buch/chapters/30-endlichekoerper/rechnungen/inverse.maxima (limited to 'buch/chapters/30-endlichekoerper/rechnungen/inverse.maxima') diff --git a/buch/chapters/30-endlichekoerper/rechnungen/inverse.maxima b/buch/chapters/30-endlichekoerper/rechnungen/inverse.maxima new file mode 100644 index 0000000..5f3682f --- /dev/null +++ b/buch/chapters/30-endlichekoerper/rechnungen/inverse.maxima @@ -0,0 +1,35 @@ +/* + * inverse.maxima + * + * (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + */ +n: 5; +m: X^5 + 15*X^3 - 30*X^2 + 45; + +M: matrix( + [ 0, 0, 0, 0, -45 ], + [ 1, 0, 0, 0, 0 ], + [ 0, 1, 0, 0, 30 ], + [ 0, 0, 1, 0, -15 ], + [ 0, 0, 0, 1, 0 ] +); +M2: M.M; +M3: M.M2; +M4: M.M3; + +y: a0 + a1*X + a2*X^2 + a3*X^3 + a4*X^4; +Y: a0*identfor(M) + a1*M + a2*M2 + a3*M3 + a4*M4; + +B: invert(Y); + +b0: B[1,1]; +b1: B[2,1]; +b2: B[3,1]; +b3: B[4,1]; +b4: B[5,1]; + +Z: b0*identfor(M) + b1*M + b2*M2 + b3*M3 + b4*M4; +z: b0 + b1*X + b2*X^2 + b3*X^3 + b4*X^4; + +w: expand(y*z); +remainder(w, m, X); -- cgit v1.2.1