{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "Wir zeichnen ein Dreieck mit seinen Schwerlinien.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "A=[1,1]\n", "B=[5,3]\n", "C=[-1,5]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Die Befehle line, point,\n", "circle etc. erzeugen die entsprechenden\n", "graphischen Objekte und man kann das Bild der Reihe nach aufbauen.\n", "Koordinaten können als Listen, Tupel oder Vektoren übergeben werden.\n", "
" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = line([A,B,C])\n", "g" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g = g+line([A,C])\n", "g.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Die Schwerlinien verbinden die Mittelpunkte der Seiten mit den gegenüberliegenden Scheiteln.
" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "ename": "TypeError", "evalue": "unsupported operand parent(s) for /: 'Listenaddition ist nicht das richtige. Wir müssen die Punkte in Vektoren umwandeln.
" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((1, 1), (5, 3), (-1, 5))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A=vector(A)\n", "B=vector(B)\n", "C=vector(C)\n", "A,B,C" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Ambient free module of rank 2 over the principal ideal domain Integer Ring" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parent(A)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(3, 2)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(A+B)/2" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Vector space of dimension 2 over Rational Field" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parent(_)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = g + line([(A+B)/2,C],color='green')\n", "g" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = g+line([(B+C)/2,A],color='green')\n", "g" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 6 graphics primitives" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = g+line([(C+A)/2,B],color='green')\n", "g" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Um den Schwerpunkt zu bestimmen, müssen die Schwerlinien geschnitten werden.
" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(s, t)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('s,t')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Die Schwerlinien in Parameterdarstellung.
" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(s + 1, 3*s + 1)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sA = A + s * ((B+C)/2-A)\n", "sA" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-5*t + 5, 3)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sB = B + t * ((A+C)/2-B)\n", "sB" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Gleichungen mit Vektoren kann man nicht direkt lösen:
" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "ename": "TypeError", "evalue": "The first argument must be a symbolic expression or a list of symbolic expressions.", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32mwir müssen sie zuerst in Listen zurückverwandeln.
" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[s + 5*t - 4, 3*s - 2]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list(sA-sB)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[[s == (2/3), t == (2/3)]]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "st = solve(list(sA-sB),[s,t])\n", "st" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wie immer wird eine Liste von Lösungen zurückgegeben, auch wenn die Lösung eindeutig ist.
" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5/3, 3)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S = sA.subs(st[0])\n", "S" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Probe" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5/3, 3)" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sB.subs(st[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "oder mit dictionary
" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[{t: 2/3, s: 2/3}]" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "st = solve(list(sA-sB), [s,t], solution_dict=True)\n", "st" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5/3, 3)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S = sA.subs(st[0])\n", "S" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 7 graphics primitives" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g += point(S, color = 'red')\n", "g" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Um ihn besser sichtbar zu machen, ein Kreis.
" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 9 graphics primitives" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g=g+ point(S, size=40, color='red')\n", "g" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Matrizen werden intern als Listen von Zeilen behandelt und sind entsprechend zu erzeugen:
" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1 2 3]\n", "[4 5 6]" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A=matrix ( [[1,2,3], [4,5,6]])\n", "A" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Full MatrixSpace of 2 by 3 dense matrices over Integer Ring" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parent(A)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A[1,1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sage beginnt bei 0 zu zählen!
" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A[0,0]" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1 2]\n", "[3 4]\n", "[5 6]" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "B=matrix(3,2 ,[ 1,2,3,4,5,6])\n", "B" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Matrixprodukt mit *
" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[22 28]\n", "[49 64]" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A*B" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Große Matrizen können aus Funktionen erzeugt werden. Auch hier NB: sage beginnt bei 0 zu zählen!
" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10]\n", "[ 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11]\n", "[ 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12]\n", "[ 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12 1/13]\n", "[ 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12 1/13 1/14]\n", "[ 1/6 1/7 1/8 1/9 1/10 1/11 1/12 1/13 1/14 1/15]\n", "[ 1/7 1/8 1/9 1/10 1/11 1/12 1/13 1/14 1/15 1/16]\n", "[ 1/8 1/9 1/10 1/11 1/12 1/13 1/14 1/15 1/16 1/17]\n", "[ 1/9 1/10 1/11 1/12 1/13 1/14 1/15 1/16 1/17 1/18]\n", "[1/10 1/11 1/12 1/13 1/14 1/15 1/16 1/17 1/18 1/19]" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = 10\n", "H = matrix (n,n, lambda i,j: 1/(i+j+1))\n", "H" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alternative mit einer List Comprehension
" ] }, { "cell_type": "code", "execution_count": 298, "metadata": {}, "outputs": [ { "data": { "text/plain": [] }, "execution_count": 298, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H = matrix ([[1/(i+j+1) for j in range(n)] for i in range(n)])\n", "H" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Matrizen können auch symbolische Einträge (oder Elemente anderer Ringe) haben, allerdings müssen alle Einträge aus dem gleichen Ring kommen.
" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1 x]\n", "[0 1]" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = matrix (2,2,[1,x,0,1])\n", "A" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Full MatrixSpace of 2 by 2 dense matrices over Symbolic Ring" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parent(A)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 1 2*x]\n", "[ 0 1]" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A*A" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 1 2*x]\n", "[ 0 1]" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A^2" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 1 3*x]\n", "[ 0 1]" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A^3" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 1 k*x]\n", "[ 0 1]" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('k')\n", "A^k" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1 0 0 0 0]\n", "[0 1 0 0 0]\n", "[0 0 1 0 0]\n", "[0 0 0 1 0]\n", "[0 0 0 0 1]" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "identity_matrix(5)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0 0 0 0 0]\n", "[0 0 0 0 0]" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zero_matrix(2,5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Die in der Numerik wichtigen dünnbesetzten (engl. sparse) Matrizen kann man platzsparend mit dictionaries definieren.
" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "30 x 30 sparse matrix over Integer Ring (use the '.str()' method to see the entries)" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "B = matrix (30, 30, {(0,0):1, (3,4):1})\n", "B" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "30 x 30 sparse matrix over Integer Ring (use the '.str()' method to see the entries)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(B)" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Full MatrixSpace of 30 by 30 sparse matrices over Integer Ring" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parent(B)" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "B[0,0]" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "B[0,1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Intern werden Matrizen als Listen von Zeilen gespeichert.
" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1, x)" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A[0]" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1, x)" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.row(0)" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1, 0)" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.column(0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Zuweisung einzelner Elemente ändert die ganze Matrix.
" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [], "source": [ "var('y')\n", "A[1,1] = y" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1 x]\n", "[0 y]" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.500000000000000 x]\n", "[ 0 y]" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A[0,0]=0.5\n", "A" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Full MatrixSpace of 2 by 2 dense matrices over Symbolic Ring" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.parent()" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.500000000000000 x]\n", "[ 0 a]" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A[1,1]=\"a\"\n", "A" ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "a" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A[1,1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Beim Zuordnen neuer Einträge darf der Bereich nicht verlassen werden.
" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Full MatrixSpace of 2 by 2 dense matrices over Integer Ring" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "B = matrix ([[1,2],[3,4]])\n", "B.parent()" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "ename": "TypeError", "evalue": "no conversion of this rational to integer", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32mMatlab-Notation
" ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[x]\n", "[a]" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A[:,1]" ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0 a]" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A[1,:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Zurück zur Hilbertmatrix. Wir lösen eine lineare Gleichung $Hx=b$. Zunächst die rechte Seite als einspaltige Matrix.
" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 1]\n", "[ 1/4]\n", "[ 1/9]\n", "[ 1/16]\n", "[ 1/25]\n", "[ 1/36]\n", "[ 1/49]\n", "[ 1/64]\n", "[ 1/81]\n", "[1/100]" ] }, "execution_count": 99, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = matrix(n,1, lambda i,j:1/(i+1)^2)\n", "b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mehrere Möglichkeiten.
" ] }, { "cell_type": "code", "execution_count": 100, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 1451/252]\n", "[ -99]\n", "[ 1188]\n", "[ -8008]\n", "[ 63063/2]\n", "[-378378/5]\n", "[ 112112]\n", "[-700128/7]\n", "[ 196911/4]\n", "[ -92378/9]" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H^-1*b" ] }, { "cell_type": "code", "execution_count": 101, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 1451/252]\n", "[ -99]\n", "[ 1188]\n", "[ -8008]\n", "[ 63063/2]\n", "[-378378/5]\n", "[ 112112]\n", "[-700128/7]\n", "[ 196911/4]\n", "[ -92378/9]" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H\\b" ] }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 1451/252]\n", "[ -99]\n", "[ 1188]\n", "[ -8008]\n", "[ 63063/2]\n", "[-378378/5]\n", "[ 112112]\n", "[-700128/7]\n", "[ 196911/4]\n", "[ -92378/9]" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H.inverse()*b" ] }, { "cell_type": "code", "execution_count": 103, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[ 1451/252]\n", "[ -99]\n", "[ 1188]\n", "[ -8008]\n", "[ 63063/2]\n", "[-378378/5]\n", "[ 112112]\n", "[-700128/7]\n", "[ 196911/4]\n", "[ -92378/9]" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H.solve_right(b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Oder als Vektor.
" ] }, { "cell_type": "code", "execution_count": 104, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1, 1/4, 1/9, 1/16, 1/25, 1/36, 1/49, 1/64, 1/81, 1/100)" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = vector ( [ 1/i^2 for i in [1..n] ])\n", "b" ] }, { "cell_type": "code", "execution_count": 105, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1451/252, -99, 1188, -8008, 63063/2, -378378/5, 112112, -700128/7, 196911/4, -92378/9)" ] }, "execution_count": 105, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H^-1*b" ] }, { "cell_type": "code", "execution_count": 106, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1451/252, -99, 1188, -8008, 63063/2, -378378/5, 112112, -700128/7, 196911/4, -92378/9)" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H.solve_right(b)" ] }, { "cell_type": "code", "execution_count": 107, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1451/252, -99, 1188, -8008, 63063/2, -378378/5, 112112, -700128/7, 196911/4, -92378/9)" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H\\b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vorsicht bei singulären Matrizen.
" ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1 2 3]\n", "[2 4 5]\n", "[0 0 1]" ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = matrix( [[1,2,3], [2,4,5], [0,0,1]] )\n", "A" ] }, { "cell_type": "code", "execution_count": 109, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2" ] }, "execution_count": 109, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.rank()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Es werden nicht alle Lösungen geliefert!
" ] }, { "cell_type": "code", "execution_count": 110, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0, 0, 0)" ] }, "execution_count": 110, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A \\ vector([0,0,0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Um alle Lösungen zu erhalten, muß man den Kern der Matrix kennen.
" ] }, { "cell_type": "code", "execution_count": 111, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Free module of degree 3 and rank 1 over Integer Ring\n", "Echelon basis matrix:\n", "[ 2 -1 0]" ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.right_kernel()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Das ist ein Vektorraum. (In diesem Fall nur ein Modul, weil die ganzen Zahlen keinen Körper bilden)
\n", "\n", "Erzeugen von Elementen.
" ] }, { "cell_type": "code", "execution_count": 128, "metadata": {}, "outputs": [], "source": [ "v1 = V([1,1,1,0,0])\n", "v2 = V([1,-1,1,0,0])\n", "v3 = V([1,0,1,0,0])" ] }, { "cell_type": "code", "execution_count": 129, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1, 1, 1, 0, 0)" ] }, "execution_count": 129, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v1" ] }, { "cell_type": "code", "execution_count": 130, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Vector space of dimension 5 over Rational Field" ] }, "execution_count": 130, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parent(v1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Der von den Vektoren erzeugte Unterraum. Es wird sofort eine Basis gebildet.
" ] }, { "cell_type": "code", "execution_count": 131, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Vector space of degree 5 and dimension 2 over Rational Field\n", "Basis matrix:\n", "[1 0 1 0 0]\n", "[0 1 0 0 0]" ] }, "execution_count": 131, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U = V.subspace([v1,v2,v3])\n", "U" ] }, { "cell_type": "code", "execution_count": 132, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[\n", "(1, 0, 1, 0, 0),\n", "(0, 1, 0, 0, 0)\n", "]" ] }, "execution_count": 132, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U.basis()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Feststellen, ob ein Vektor im Unterraum liegt.
" ] }, { "cell_type": "code", "execution_count": 133, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 133, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v4 = V([0,0,0,1,0])\n", "v4 in U" ] }, { "cell_type": "code", "execution_count": 134, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 134, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v1 in U" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Bestimmung der Koordinaten bezüglich der Basis von $U$.
" ] }, { "cell_type": "code", "execution_count": 135, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1, 1]" ] }, "execution_count": 135, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U.coordinates(v1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Manipulation von Unterräumen (Summe, Durchschnitt, Vergleich).
" ] }, { "cell_type": "code", "execution_count": 136, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Vector space of degree 5 and dimension 1 over Rational Field\n", "Basis matrix:\n", "[0 0 0 1 0]" ] }, "execution_count": 136, "metadata": {}, "output_type": "execute_result" } ], "source": [ "W = V.subspace([V(v4)])\n", "W" ] }, { "cell_type": "code", "execution_count": 137, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 137, "metadata": {}, "output_type": "execute_result" } ], "source": [ "W.is_subspace(U)" ] }, { "cell_type": "code", "execution_count": 138, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 138, "metadata": {}, "output_type": "execute_result" } ], "source": [ "W.is_subspace(V)" ] }, { "cell_type": "code", "execution_count": 139, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Vector space of degree 5 and dimension 3 over Rational Field\n", "Basis matrix:\n", "[1 0 1 0 0]\n", "[0 1 0 0 0]\n", "[0 0 0 1 0]" ] }, "execution_count": 139, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U+W" ] }, { "cell_type": "code", "execution_count": 140, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 140, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U.is_subspace(U+W)" ] }, { "cell_type": "code", "execution_count": 141, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Vector space of degree 5 and dimension 0 over Rational Field\n", "Basis matrix:\n", "[]" ] }, "execution_count": 141, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U.intersection(W)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wir haben oben den Kern einer Matrix betrachtet.
" ] }, { "cell_type": "code", "execution_count": 142, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1 2 3]\n", "[2 4 5]\n", "[0 0 1]" ] }, "execution_count": 142, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A=matrix([[1,2,3],[2,4,5],[0,0,1]])\n", "A" ] }, { "cell_type": "code", "execution_count": 143, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Free module of degree 3 and rank 1 over Integer Ring\n", "Echelon basis matrix:\n", "[ 2 -1 0]" ] }, "execution_count": 143, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.right_kernel()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wir verpflanzen die Matrix in einen Körper.
" ] }, { "cell_type": "code", "execution_count": 147, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Full MatrixSpace of 3 by 3 dense matrices over Rational Field" ] }, "execution_count": 147, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A1 = matrix(QQ, A)\n", "parent(A1)" ] }, { "cell_type": "code", "execution_count": 148, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Vector space of degree 3 and dimension 1 over Rational Field\n", "Basis matrix:\n", "[ 1 -1/2 0]" ] }, "execution_count": 148, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A1.right_kernel()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Der Bildraum.
" ] }, { "cell_type": "code", "execution_count": 149, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Vector space of degree 3 and dimension 2 over Rational Field\n", "Basis matrix:\n", "[1 2 0]\n", "[0 0 1]" ] }, "execution_count": 149, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A1.image()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vorsicht, das ist der Bildraum der Abbildung $x\\mapsto xA$, die Zeilenvektoren auf Zeilenvektoren abbildet!
" ] }, { "cell_type": "code", "execution_count": 150, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Vector space of degree 3 and dimension 2 over Rational Field\n", "Basis matrix:\n", "[1 2 0]\n", "[0 0 1]" ] }, "execution_count": 150, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A1.row_space()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Um den Bildraum der Abbildung $x\\mapsto Ax$ zu bekommen, muß man den Spaltenraum erzeugen:
" ] }, { "cell_type": "code", "execution_count": 151, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Vector space of degree 3 and dimension 2 over Rational Field\n", "Basis matrix:\n", "[ 1 0 2]\n", "[ 0 1 -1]" ] }, "execution_count": 151, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A1.column_space()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In diesem Fall sind Kern und Bildraum komplementär.
" ] }, { "cell_type": "code", "execution_count": 152, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Vector space of degree 3 and dimension 3 over Rational Field\n", "Basis matrix:\n", "[1 0 0]\n", "[0 1 0]\n", "[0 0 1]" ] }, "execution_count": 152, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A1.right_kernel() + A1.column_space()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Das ganze geht auch über endlichen Körpern.
" ] }, { "cell_type": "code", "execution_count": 153, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Finite Field of size 3" ] }, "execution_count": 153, "metadata": {}, "output_type": "execute_result" } ], "source": [ "K = GF(3)\n", "K" ] }, { "cell_type": "code", "execution_count": 154, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Vector space of dimension 3 over Finite Field of size 3" ] }, "execution_count": 154, "metadata": {}, "output_type": "execute_result" } ], "source": [ "V = K^3\n", "V" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Auch der Vektorraum hat nur endlich viele Elemente.
" ] }, { "cell_type": "code", "execution_count": 155, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(0, 0, 0),\n", " (1, 0, 0),\n", " (2, 0, 0),\n", " (0, 1, 0),\n", " (1, 1, 0),\n", " (2, 1, 0),\n", " (0, 2, 0),\n", " (1, 2, 0),\n", " (2, 2, 0),\n", " (0, 0, 1),\n", " (1, 0, 1),\n", " (2, 0, 1),\n", " (0, 1, 1),\n", " (1, 1, 1),\n", " (2, 1, 1),\n", " (0, 2, 1),\n", " (1, 2, 1),\n", " (2, 2, 1),\n", " (0, 0, 2),\n", " (1, 0, 2),\n", " (2, 0, 2),\n", " (0, 1, 2),\n", " (1, 1, 2),\n", " (2, 1, 2),\n", " (0, 2, 2),\n", " (1, 2, 2),\n", " (2, 2, 2)]" ] }, "execution_count": 155, "metadata": {}, "output_type": "execute_result" } ], "source": [ "V.list()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Entsprechendes geht auch für die rationalen Zahlen, allerdings bricht die Schleife nicht ab, wenn man keine Vorsorge trifft.
" ] }, { "cell_type": "code", "execution_count": 157, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0, 0, 0)\n", "(1, 0, 0)\n", "(-1, 0, 0)\n", "(1/2, 0, 0)\n", "(-1/2, 0, 0)\n", "(2, 0, 0)\n", "(-2, 0, 0)\n", "(1/3, 0, 0)\n", "(-1/3, 0, 0)\n", "(3, 0, 0)\n", "(-3, 0, 0)\n", "(2/3, 0, 0)\n", "(-2/3, 0, 0)\n", "(3/2, 0, 0)\n", "(-3/2, 0, 0)\n", "(1/4, 0, 0)\n", "(-1/4, 0, 0)\n", "(4, 0, 0)\n", "(-4, 0, 0)\n", "(3/4, 0, 0)\n", "(-3/4, 0, 0)\n" ] } ], "source": [ "k=0\n", "for v in QQ^3:\n", " if k > 20:\n", " break\n", " k += 1\n", " print v" ] }, { "cell_type": "code", "execution_count": 158, "metadata": {}, "outputs": [ { "ename": "AttributeError", "evalue": "'FreeModule_ambient_field_with_category' object has no attribute 'list'", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32mZurück zum endlichen Vektorraum. Auch die Anzahl der Unterräume ist endlich.
" ] }, { "cell_type": "code", "execution_count": 159, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Vector space of dimension 3 over Finite Field of size 3" ] }, "execution_count": 159, "metadata": {}, "output_type": "execute_result" } ], "source": [ "V" ] }, { "cell_type": "code", "execution_count": 160, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Ein Generator ist ein Spezialfall eines Iterators. Wichtige Anwendungen sind: 'lazy evaluation', Schleifen, elegantes Aufsammeln von Zwischenergebnissen und insbesondere rekursive Erzeugungmathematischer Objekte.
\n", "Praktisch gesehen ist ein Generator eine Art Liste, deren Elemente spontan bei Bedarf erzeugt werden und dann verfallen. Einfache Generatoren kann man ähnlich wie Listen erzeugen, mit runden anstatt eckigen Klammern.
" ] }, { "cell_type": "code", "execution_count": 163, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "Der Generator wird duch die Methode .next()\n", "in Bewegung versetzt. Er gibt daraufhin einen Wert aus und bleibt\n", "bis zum nächsten Aufruf von .next()\n", "stehen (mehr dazu unten).\n", "Von außen betrachtet verhält er sich wie ein Kaugummiautomat,\n", "wobei .next() dem Einwurf einer Münze entspricht.\n", "
" ] }, { "cell_type": "code", "execution_count": 164, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 164, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.next()" ] }, { "cell_type": "code", "execution_count": 165, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2" ] }, "execution_count": 165, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.next()" ] }, { "cell_type": "code", "execution_count": 166, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3" ] }, "execution_count": 166, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.next()" ] }, { "cell_type": "code", "execution_count": 167, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4" ] }, "execution_count": 167, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.next()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Wenn alle Werte ausgegeben sind, bricht der Generator ab.\n", "
" ] }, { "cell_type": "code", "execution_count": 168, "metadata": {}, "outputs": [ { "ename": "StopIteration", "evalue": "", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mStopIteration\u001b[0m Traceback (most recent call last)", "\u001b[0;32mSo wie ein Kaugummi nicht von alleine in den Automaten zurückkehrt, sondern letzterer neu befüllt werden muß, kann ein Generator kann nur einmal von vorne nach hinten durchlaufen werden und nicht in einen vorhergehenden Zustand zurückversetzt werden. Dafür muß ein neuer Generator initialisiert werden.
" ] }, { "cell_type": "code", "execution_count": 169, "metadata": {}, "outputs": [], "source": [ "g = (1..4)" ] }, { "cell_type": "code", "execution_count": 170, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 170, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.next()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Man kann auch alle Kaugummis auf einen Schlag herausholen durch direke Umwandlung in eine Liste:\n", "
" ] }, { "cell_type": "code", "execution_count": 171, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[2, 3, 4]" ] }, "execution_count": 171, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list(g)" ] }, { "cell_type": "code", "execution_count": 172, "metadata": {}, "outputs": [ { "ename": "StopIteration", "evalue": "", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mStopIteration\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\n", "Generatoren spielen eine wichtige Rolle in\n", "Schleifen, insbesondere, wenn dabei sonst eine lange Liste erzeugt werden müßte.\n", "
" ] }, { "cell_type": "code", "execution_count": 173, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1\n", "2\n", "3\n", "4\n" ] } ], "source": [ "for i in (1..4):\n", " print i" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Ein Generator kann auch unendlich groß sein.\n", "In diesem Fall ist es nicht ratsam, ihn in eine Liste umzuwandeln,\n", "weil sage nicht von vornherein erkennen kann, ob ein Generator nach endlich\n", "vielen Schritten abbricht oder nicht.\n", "(Dieses Frage ist nach A.Turing algorithmisch nicht entscheidbar).\n", "
" ] }, { "cell_type": "code", "execution_count": 174, "metadata": {}, "outputs": [], "source": [ "nn = (1..)" ] }, { "cell_type": "code", "execution_count": 175, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 175, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nn.next()" ] }, { "cell_type": "code", "execution_count": 176, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2" ] }, "execution_count": 176, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nn.next()" ] }, { "cell_type": "code", "execution_count": 177, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3\n", "4\n", "5\n", "6\n", "7\n", "8\n", "9\n", "10\n", "11\n" ] } ], "source": [ "for i in nn:\n", " print i\n", " if i > 10:\n", " break" ] }, { "cell_type": "code", "execution_count": 178, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12" ] }, "execution_count": 178, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nn.next()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Aus bereits vorhandenen können mit List Comprehension neue Iteratoren erzeugt werden.
" ] }, { "cell_type": "code", "execution_count": 179, "metadata": {}, "outputs": [], "source": [ "a = (1..5)" ] }, { "cell_type": "code", "execution_count": 180, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "dabei läuft im Hintergrund der ursprüngliche Generator mit:
" ] }, { "cell_type": "code", "execution_count": 181, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 181, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a.next()" ] }, { "cell_type": "code", "execution_count": 182, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4" ] }, "execution_count": 182, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b.next()" ] }, { "cell_type": "code", "execution_count": 183, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3" ] }, "execution_count": 183, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a.next()" ] }, { "cell_type": "code", "execution_count": 184, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16" ] }, "execution_count": 184, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b.next()" ] }, { "cell_type": "code", "execution_count": 185, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5" ] }, "execution_count": 185, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a.next()" ] }, { "cell_type": "code", "execution_count": 186, "metadata": {}, "outputs": [ { "ename": "StopIteration", "evalue": "", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mStopIteration\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\n", "ansonsten läßt sich ein Generator wie eine Liste behandeln.\n", "
" ] }, { "cell_type": "code", "execution_count": 188, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "15" ] }, "execution_count": 188, "metadata": {}, "output_type": "execute_result" } ], "source": [ "reduce(operator.add, (1..5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Ein Generator kann wie eine Funktion programmiert werden,\n", "indem anstelle von return der Befehl yield\n", "gesetzt wird. Letzterer hat zwei Funktionen:\n", "
\n", "Dabei ist zu beachten, daß \n", "abc() nicht der Generator an sich ist,\n", "sondern eine Funktion, die bei\n", "jedem Aufruf neuen Generator erzeugt und initialisiert.\n", "
" ] }, { "cell_type": "code", "execution_count": 190, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "Der Aufruf von .next() bewirkt, daß der Generator gestartet wird\n", "und bis zum ersten yield läuft.\n", "Der entsprechende Wert wird zurückgegeben und der Generator hält an.\n", "
" ] }, { "cell_type": "code", "execution_count": 191, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'a'" ] }, "execution_count": 191, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.next()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Beim zweiten Aufruf macht er an der gleichen Stelle weiter,\n", "bis er auf das nächste yield trifft.\n", "
" ] }, { "cell_type": "code", "execution_count": 192, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'b'" ] }, "execution_count": 192, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.next()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "usw.\n", "
" ] }, { "cell_type": "code", "execution_count": 193, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'c'" ] }, "execution_count": 193, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.next()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Bis das Ende des Codes erreicht wird.\n", "
" ] }, { "cell_type": "code", "execution_count": 194, "metadata": {}, "outputs": [ { "ename": "StopIteration", "evalue": "", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mStopIteration\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\n", "Will man einen Generator unter gewissen Bedingungen vorzeitig abbrechen,\n", "wird an der entsprechenden Stelle ein return eingefügt.\n", "
" ] }, { "cell_type": "code", "execution_count": 195, "metadata": {}, "outputs": [], "source": [ "def abc(cnicht):\n", " yield 'a'\n", " yield 'b'\n", " if cnicht:\n", " return\n", " yield 'c'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Ist die Bedingung erfüllt, bricht der Generator an der entsprechenden Stelle ab.\n", "
" ] }, { "cell_type": "code", "execution_count": 196, "metadata": {}, "outputs": [], "source": [ "g = abc(True)" ] }, { "cell_type": "code", "execution_count": 197, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'a'" ] }, "execution_count": 197, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.next()" ] }, { "cell_type": "code", "execution_count": 198, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'b'" ] }, "execution_count": 198, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.next()" ] }, { "cell_type": "code", "execution_count": 199, "metadata": {}, "outputs": [ { "ename": "StopIteration", "evalue": "", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mStopIteration\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\n", "Wenn nicht, wird return übersprungen.\n", "
" ] }, { "cell_type": "code", "execution_count": 200, "metadata": {}, "outputs": [], "source": [ "g = abc(False)" ] }, { "cell_type": "code", "execution_count": 201, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'a'" ] }, "execution_count": 201, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.next()" ] }, { "cell_type": "code", "execution_count": 202, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'b'" ] }, "execution_count": 202, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.next()" ] }, { "cell_type": "code", "execution_count": 203, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'c'" ] }, "execution_count": 203, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.next()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Noch einmal kurz\n", "
" ] }, { "cell_type": "code", "execution_count": 204, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['a', 'b']" ] }, "execution_count": 204, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[t for t in abc(True)]" ] }, { "cell_type": "code", "execution_count": 205, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['a', 'b', 'c']" ] }, "execution_count": 205, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[t for t in abc(False)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generatoren sind auch nützlich, um im Verlauf von Rechnungen Zwischenergebnisse auszuwerfen, ohne dabei explizit eine Liste mitzuführen. Wir betrachten noch einmal das Primzahlzwillingsproblem aus der Übung. p durchläuft alle Primzahlen kleiner als die obere Schranke n und jedes Mal, wenn ein Zwilling auftaucht, wird das Paar ausgeworfen.
" ] }, { "cell_type": "code", "execution_count": 206, "metadata": {}, "outputs": [], "source": [ "def primzw(n=oo):\n", " p=3\n", " while p\n", "Dabei kann im Prinzip die Anzahl der Zwillinge offen gelassen werden:\n", "
" ] }, { "cell_type": "code", "execution_count": 208, "metadata": {}, "outputs": [], "source": [ "pp = primzw(oo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Um zum Beispiel die ersten 10 Paare zu erzeugen,\n", "schreiben wir einen zweiten Generator um den ersten herum, der die Paare mitzählt:\n", "
" ] }, { "cell_type": "code", "execution_count": 209, "metadata": {}, "outputs": [], "source": [ "def firstn(n,g):\n", " for i in range(n):\n", " yield g.next()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Und wir bekommen das gewünschte Resultat ohne darüber nachdenken\n", "zu müssen, wie groß wir die obere Grenze wählen müssen.\n", "
" ] }, { "cell_type": "code", "execution_count": 210, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[[3, 5],\n", " [5, 7],\n", " [11, 13],\n", " [17, 19],\n", " [29, 31],\n", " [41, 43],\n", " [59, 61],\n", " [71, 73],\n", " [101, 103],\n", " [107, 109]]" ] }, "execution_count": 210, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list(firstn(10,pp))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Besonders elegant werden Generatoren, wenn sie rekursiv angewandt werden.\n", "Als Beispiel erzeugen wir rekursiv alle Elemente der kartesischen Potenz einer Menge.\n", "Die kartesische Potenz kann induktiv definiert werden, \n", "was sich unmittelbar in einen Generator übersetzen läßt:\n", "
" ] }, { "cell_type": "code", "execution_count": 211, "metadata": {}, "outputs": [], "source": [ "def cart(S,n):\n", " if n == 1:\n", " for s in S:\n", " yield [s]\n", " else:\n", " for s in S:\n", " for p in cart(S,n-1):\n", " yield [s]+p" ] }, { "cell_type": "code", "execution_count": 212, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[[1, 1, 1, 1],\n", " [1, 1, 1, 2],\n", " [1, 1, 2, 1],\n", " [1, 1, 2, 2],\n", " [1, 2, 1, 1],\n", " [1, 2, 1, 2],\n", " [1, 2, 2, 1],\n", " [1, 2, 2, 2],\n", " [2, 1, 1, 1],\n", " [2, 1, 1, 2],\n", " [2, 1, 2, 1],\n", " [2, 1, 2, 2],\n", " [2, 2, 1, 1],\n", " [2, 2, 1, 2],\n", " [2, 2, 2, 1],\n", " [2, 2, 2, 2]]" ] }, "execution_count": 212, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list(cart([1,2],4))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Ganz analog kann man alle Permutationen der Elemente einer Liste erzeugen,\n", "indem jeweils ein Element an die Spitze gestellt und der Rest permutiert wird.\n", "
" ] }, { "cell_type": "code", "execution_count": 213, "metadata": {}, "outputs": [], "source": [ "def perm(S):\n", " n = len(S)\n", " if n==0: yield []\n", " else:\n", " for i in range(n):\n", " for p in perm(S[:i]+S[i+1:]):\n", " yield [S[i]] + p" ] }, { "cell_type": "code", "execution_count": 214, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]" ] }, "execution_count": 214, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list(perm([1,2,3]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Einfacher zu lesen und zu Programmieren wird es mit Set:\n", "
" ] }, { "cell_type": "code", "execution_count": 215, "metadata": {}, "outputs": [], "source": [ "def permset(S):\n", " S1=Set(S)\n", " n = len(S1)\n", " if n == 0:\n", " yield []\n", " else:\n", " for s in S1:\n", " for p in perm(S1.difference([s])):\n", " yield [s]+p" ] }, { "cell_type": "code", "execution_count": 216, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]" ] }, "execution_count": 216, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list(permset([1,2,3]))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.3", "language": "", "name": "sagemath" }, "language": "python", "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 2 }