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| author | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
| commit | ab8cc85adde879fb963c94d15675783f2cf4b183 (patch) | |
| tree | c202482327f474583b750b2c45dedfc4e4312b1d /src/input/linalg.input.pamphlet | |
| download | open-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz | |
Initial population.
Diffstat (limited to 'src/input/linalg.input.pamphlet')
| -rw-r--r-- | src/input/linalg.input.pamphlet | 116 |
1 files changed, 116 insertions, 0 deletions
diff --git a/src/input/linalg.input.pamphlet b/src/input/linalg.input.pamphlet new file mode 100644 index 00000000..c39e5c77 --- /dev/null +++ b/src/input/linalg.input.pamphlet @@ -0,0 +1,116 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input linalg.input} +\author{The Axiom Team} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +<<*>>= + +-- Input for page MatrixMoreFunctionsPage +)clear all + +m1 := matrix([[1,-2,1],[4,2,-4]]) +m2 := matrix([[0,1,2],[2,3,4],[3,4,5]]) +m3 := matrix([[1,2,3],[2,4,6]]) +m1 + m3 +100 * m1 +m1 * m2 +-m1 + m3 * m2 +m2 * m1 +v := vector([1,0,1]) +m3 * v +m5 : MATRIX POLY INT := new(4,4,1) +vars : LIST POLY INT := [x,y,z,u] +for i in 1..4 repeat for j in 1..3 repeat m5(i,j + 1) := (vars.i)**j +m5 +trace(m5) +det := determinant(m5) +factor(det) +m6 := matrix([[1,2,1],[-2,3,4],[-1,5,6]]) +m6inv := inverse(m6) +m6 * m6inv +m7 := matrix([[1,2,1],[-2,3,4],[-1,5,5]]) +inverse(m7) +determinant(m7) +m8 : SQMATRIX(2,INT) := matrix([[1,2],[2,3]]) +m9 : SQMATRIX(2,INT) := matrix([[1,1],[0,1]]) +m8 ** 2 +m9 ** 3 +mm : SQMATRIX(2,SQMATRIX(2,INT)) := matrix([[1,m8],[m9,0]]) +100 * mm +m8 * mm +mm * mm +p : POLY SQMATRIX(2,INT) := m8 * x**2 + m9 * x + m8 * m9 +100 * p +m8 * p +p * p + +-- Input for page MatrixCanonicalFormsPage +)clear all + +m1 := matrix([[0,4,1],[5,3,-7],[-5,5,9]]) +rank(m1) +rowEchelon(m1) +nullSpace(m1) +t := eigenMatrix(m1) +inverse(t) * m1 * t + +-- Input for page MatrixBasicFunctionsPage +)clear all + +m1 := matrix([[1,2,3,4],[2,3,4,5],[3,4,5,6],[4,5,6,7]]) +m2 := matrix([[1,0,2],[20,30,10],[0,200,100]]) +(m3,m4) : MATRIX PF 7 +m3 := matrix([[1,0,1],[5,0,1]]) +m4 := matrix([[1],[2],[5],[6]]) +m2(1,1) +m2(1,1) := 99 +m2 +row(m2,2) +setRow!(m2,2,vector [66,77,88]) +r := column(m2,1) +setColumn!(m2,2,r) +nrows(m1) +m5 : MATRIX INT := new(12,12,0) +for i in 2..nrows(m5) repeat m5(i-1,i):= 1 +m5 +d : MATRIX INT := diagonalMatrix([1,2,3,2,1]) +m6 := matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]]) +m7 := subMatrix(m6,1,3,2,4) +horizConcat(m6,m7) +vertConcat(m6,subMatrix(m6,1,1,1,5)) +transpose(m6) +setsubMatrix(m6,1,3,1,3,transpose(subMatrix(m6,1,3,1,3))) +m6 +m8 := matrix([[1,2],[3,4]]) +m9 := m8 +m10 := copy(m8) +m8(1,1) := 1000000 +m8 +m9 +m10 + +-- Input for page EigenPage +)clear all + +m1 : MATRIX FRAC INT := [[1,2,1],[2,1,-2],[1,-2,4]] +leig := eigenvalues(m1) +eigenvector(first(leig),m1) +eigenvectors(m1) +radicalEigenvectors(m1) +eigenMatrix(m1) +m2 : MATRIX FRAC INT := [[-5,-2],[18,7]] +eigenMatrix(m2) +m3 : MATRIX FRAC INT := [[1,2],[2,1]] +orthonormalBasis(m3) +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |