{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# EXERCICES PRÉLIMINAIRES" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 1 - Calculatrice, scalaires, vecteurs" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "5" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "5" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "7" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "2+5" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ 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true }, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cos(2*pi)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "e" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "exp(1)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "I" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sqrt(-1)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "3*I + 2" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "2+3*I" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 2 - Fonctions usuelles" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x=-1; y=2; z=3.4;\n", "abs(x)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "2" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max(x,y) " ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "-1" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "min(x,y)" ] }, { "cell_type": "code", "execution_count": 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"source": [ "sum(i^3,i,1,n)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "1/4*(n + 1)^2*n^2" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum(i^3,i,1,n).factor()" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "1/90*pi^4" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum(1/i^4,i,1,oo)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "2- Limites" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "e" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('x')\n", "((1+1/x)^x).limit(x=oo)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(sin(x)/x).limit(x=0)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "+Infinity" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(1/x).limit(x=0, dir='right')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "3- Dérivées, primitives, intégrales" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "1/2/sqrt(x)" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x=var('x')\n", "sqrt(x).diff(x)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "-cos(x)" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sin(x).integral(x)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "-cos(1) + 1" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sin(x).integral(x,0,1)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "-1/2*I*sqrt(pi)*erf(2*I) - 1/2*I*sqrt(pi)*erf(I)" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "exp(x^2).integral(x,-1,2)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 4 - Graphiques" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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uvBC22y52GkmZrE8fmD4dnn8+dpL0ZIGQJGWFBx6AhQvDJkhJKo9jjoH99w9T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\nW7fYSX6rTZs2FBQUUOQmMknS/5dIJnN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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('x y t')\n", "plot(sin(x),x,-pi,pi) " ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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zo96Rt8Xb7EioIpQGAADg8T766KwGDcpQYKC3vv02Wl261DU7kkt64cgkpRXt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"text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot([x,x^2],x,0,1)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot3d(lambda x,y: x^2 + y^2, (-2,2), (-2,2))" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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+257zJgySatRgnzQ327WLO2ejojhDXquW01ck/lCAFMSWLAEefxwoW5a7SooW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hjh4VyEOXUqsHEj36U3bsxkqWxZa70DXrEiroF74EAuJNXSTv8QE8MEuHdv4Omn2aD/4oumo7rX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\nMyB7AAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p1=parametric_plot((cos(x),sin(x)),(x,0,2*pi))\n", "p2=parametric_plot((cos(x),sin(x)^2),(x,0,2*pi))\n", "p3=parametric_plot((cos(x),sin(x)^3),(x,0,2*pi))\n", "show(p1+p2+p3, axes=false)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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mTDjjDBujiu+0aG28WZtBLFhgyqFLF/jud22NKiIuWSuId981v156\nqa6cFIkLqwWRSMDll9saUURcs1oQJ58M3bvbGlFEXLNSEF99ZRaJ0alNkXixUhAffGBuzPre92yM\nJiK+sFIQb78NF14IbdrYGE1EfGGtIH74QxsjiYhPrBTE4sVw2mk2RhIRn2RcEJ9+au7abNbMQhoR\n8UrGBTF7NpSX24giIr7JuCBWroTjj7cRRUR8k3FBlJTYiCEiPsqoIFavhj59bEUREd9kVBCrVsFR\nR9mKIiK+yagg2ra1FUNEfJRRQey/v60YIuKjJhfEjh1QXGwzioj4pskFoQujZE9akzKerK1JKblJ\na1LGmxaHE5GkVBAikpQKQkSSUkGISFIqCBFJSgUhIkmpIEQkKRWEiCSlghCRpFQQIpKULrWWjARB\nwIYNGygsLCSRSLiOI5apIEQkKe1iiEhSKggRSUoFISJJqSBEJCkVhIgkpYIQkaRUECKS1P8Hfth9\nlZLE13sAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "L=[[-1+cos(pi*i/100)*(1+cos(pi*i/100)),2*sin(pi*i/100)*(1-cos(pi*i/100))] for i in range(200)]\n", "polygon(L).show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 5 - Expressions" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "1- Développement, factorisation, rangement" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "x^3 + 3*x^2 - x - 3" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('x y')\n", "m=(x^2-1)*(x+3)\n", "m.expand()\n" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(x + 3)*(x + 1)*(x - 1)" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.factor()" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "[(x + 3, 1), (x + 1, 1), (x - 1, 1)]" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.factor_list()" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(x + 1)^2*x + (x + 1)^2*y" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n=(x+y)*(x+1)^2\n", "n.collect(x)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "x^3 + x^2*(y + 2) + x*(2*y + 1) + y" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n.expand().collect(x)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "x^3 + 2*x^2 + (x^2 + 2*x + 1)*y + x" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n.expand().collect(y)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "x^3 + x^2*(y + 2) + x*(2*y + 1) + y" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n.expand().collect(y).collect(x)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "x^2 + 2*x*y + y^2 + 2*(x + y)*sin(x) + sin(x)^2" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "((x+y+sin(x))^2).expand().collect(sin(x))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "2- Fractions rationnelles" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(x^2 + (x + 1)*y + x)/(x^2 + y)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('x y')\n", "r=(x^3+x^2*y+3*x^2+3*x*y+2*x+2*y)/(x^3+2*x^2+x*y+2*y)\n", "show(r.simplify_rational())" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(x + y)*(x + 1)/(x^2 + y)" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r.factor()" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "x^2/(x^2 + y) + x*y/(x^2 + y) + x/(x^2 + y) + y/(x^2 + y)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(r.factor().expand())" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "((x - 1)*x + y^2)/(x^2 - 7) + (b + c)/a + 1/(x + 1)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('x y a b c')\n", "r=(x-1)*x/(x^2-7)+y^2/(x^2-7)+b/a+c/a+1/(x+1)\n", "show(r.combine())" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/(x + 2) - 1/(x + 1) + 1/(x + 1)^2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r=1/((x+1)^2*(x+2))\n", "show(r.partial_fraction())" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/(x + 2) - 1/(x + 1) + 1/(x + 1)^2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r=1/((x+1)^2*(x+2))\n", "show(r.partial_fraction(x))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "3- Opérations trigonométriques" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "cos(x)^2 + sin(x)^2" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('x')\n", "(cos(x)^2+sin(x)^2).simplify()" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(cos(x)^2+sin(x)^2).simplify_trig()" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "2*cos(x)*sin(x)" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sin(2*x).expand_trig()" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "-1/2*cos(2*x) + 1/2" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(sin(x)^2).reduce_trig()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "4- Autres opérations" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "n + 1" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('n x')\n", "f=factorial(n+1)/factorial(n)\n", "f.simplify_factorial()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*(a^2 - 2*a*b + b^2)/(a + 2*sqrt(a)*sqrt(b) + b)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "1/2*a - sqrt(a)*sqrt(b) + 1/2*b" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('a b')\n", "f=(a-b)^2/(2*(sqrt(a)+sqrt(b))^2)\n", "show(f.canonicalize_radical())" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 6 - Polynômes" ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "6" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "(2) * (x - 1) * (x + 1/2) * (x + 1) * (x + 2) * (x^2 + 1)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x=polygen(QQ,'x'); # polynôme dans Q\n", "p=(2*x+1)*(x+2)*(x^4-1);\n", "show(p.degree())\n", "show(p.factor())" ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "6" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "(x^2 + 1)*(2*x + 1)*(x + 2)*(x + 1)*(x - 1)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Autre possibilité\n", "var('x')\n", "p=(2*x+1)*(x+2)*(x^4-1);\n", "show(p.degree(x)) # attention, on doit ajouter degree(x)\n", "show(p.factor())" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(2.00000000000000) * (x - 1.00000000000000) * (x + 0.500000000000000) * (x + 1.00000000000000) * (x + 2.00000000000000) * (x^2 + 1.00000000000000)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x=polygen(RR,'x')\n", "p=(2*x+1)*(x+2)*(x^4-1)\n", "show(p.factor())" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(2.00000000000000) * (x - 1.00000000000000) * (x - I) * (x + I) * (x + 0.500000000000000) * (x + 1.00000000000000) * (x + 2.00000000000000)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x=polygen(CC,'x')\n", "p=(2*x+1)*(x+2)*(x^4-1)\n", "show(p.factor())" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 7 - Résolution" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "[[x == (4/3), y == (-1/3)]]" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('x y z')\n", "solve([x+y==1, 2*x-y==3], x, y)" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "[[x == (7/8), y == (1/2), z == (-3/8)]]" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve([x+y+z==1, 3*x-2*y-z==2, -x+y-z==0], x,y,z)" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "[[x == -1/2*I*sqrt(3) - 1/2, y == -sqrt(-1/2*I*sqrt(3) + 3/2)], [x == -1/2*I*sqrt(3) - 1/2, y == sqrt(-1/2*I*sqrt(3) + 3/2)], [x == 1/2*I*sqrt(3) - 1/2, y == -sqrt(1/2*I*sqrt(3) + 3/2)], [x == 1/2*I*sqrt(3) - 1/2, y == sqrt(1/2*I*sqrt(3) + 3/2)], [x == 0, y == -1], [x == 0, y == 1]]" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve([x^2+y^2==1, y^2==x^3+x+1], x, y)" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "1/2*I*sqrt(3) - 1/2" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E=solve([x^2+y^2==1, y^2==x^3+x+1], x, y)\n", "E[2][0].rhs()" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "[[x == -r1 + 3, y == r1]]" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve([x+y==3, 2*x+2*y==6], x, y)" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "[[x == 1/4*pi + pi*z62, y == -1/4*pi - pi*z62]]" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve([cos(x)*sin(x)==1/2, x+y==0], x, y)" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "[x == -I, x == I]" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(x^2+1==0,x)" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "[x == -I, x == I]" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(x^2+1,x)" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "[(-I, 1), (I, 1)]" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(x^2+1).roots()" ] }, { "cell_type": "code", "execution_count": 85, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "[(-1/2*(1/18*sqrt(59)*sqrt(3) - 1/2)^(1/3)*(I*sqrt(3) + 1) - 1/3*(I*sqrt(3) - 1)/(1/18*sqrt(59)*sqrt(3) - 1/2)^(1/3),\n", " 1),\n", " (-1/2*(1/18*sqrt(59)*sqrt(3) - 1/2)^(1/3)*(-I*sqrt(3) + 1) - 1/3*(-I*sqrt(3) - 1)/(1/18*sqrt(59)*sqrt(3) - 1/2)^(1/3),\n", " 1),\n", " ((1/18*sqrt(59)*sqrt(3) - 1/2)^(1/3) - 2/3/(1/18*sqrt(59)*sqrt(3) - 1/2)^(1/3),\n", " 1)]" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(x^3+2*x+1).roots(x)" ] }, { "cell_type": "code", "execution_count": 86, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "[(-0.453397651516404, 1)]" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(x^3+2*x+1).roots(x, ring=RR)" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "[(-0.453397651516404, 1),\n", " (0.226698825758202 - 1.46771150871022*I, 1),\n", " (0.226698825758202 + 1.46771150871022*I, 1)]" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(x^3+2*x+1).roots(x, ring=CC)" ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "[sin(3*x) == -sin(2*x) - sin(x)]" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "q=sin(x)+sin(2*x)+sin(3*x)\n", "solve(q,x) " ] }, { "cell_type": "code", "execution_count": 89, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "[x == 0, x == 2/3*pi, x == 1/2*pi]" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f=q.simplify_trig()\n", "solve(f,x)" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "2.0943951023931957" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "find_root(q,0.1,pi)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# EXERCICES D'APPLICATION" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 1" ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[[x == 1/2*(2*R1^2 - R2^2)/R1, y == -1/2*sqrt(4*R1^2 - R2^2)*R2/R1], [x == 1/2*(2*R1^2 - R2^2)/R1, y == 1/2*sqrt(4*R1^2 - R2^2)*R2/R1]]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('x y R1 R2');\n", "show(solve([x^2+y^2==R1^2,(x-R1)^2+y^2==R2^2],x,y))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 2" ] }, { "cell_type": "code", "execution_count": 92, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "False" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "641 * 6700417" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# La propriété est fausse pour n=5\n", "\n", "n=5;\n", "show((2^2^n+1).is_prime())\n", "show((2^2^n+1).factor())" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 3" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(7*x^2 - 4)^2*(x + 6)" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('x y');\n", "(49*x^5+294*x^4-56*x^3-336*x^2+16*x+96).factor()" ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(x^4 + x^2*sin(y) + sin(y)^2)*(x^2 - sin(y))" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(x^6-sin(y)^3).factor()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 4" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t^5 + 10*(t^2 - 1)*t^3 + 5*(t^2 - 1)^2*t" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "5" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "cos(5*arccos(2))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "362" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('n t');\n", "P5=(cos(5*arccos(t)));\n", "show(P5.expand_trig())\n", "show(P5.expand_trig().degree(t))\n", "r=P5(t=2)\n", "show(r)\n", "r=P5(t=2).simplify_trig()\n", "show(r)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 5" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "j=exp(I*2*pi/3);\n", "show((j^3).expand())\n", "show((1+j+j^2).expand())" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 6" ] }, { "cell_type": "code", "execution_count": 97, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(x + y)^n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var('n k x y');\n", "show(sum(binomial(n,k)*x^k*y^(n-k), k, 0, n))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 7" ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-4.364154457393982337096304744139452851379282742232409848251593494611746930419107778727995637066508844e-96" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "s=2*sqrt(2)/9801*(sum((factorial(4*k))*(1103+26390*k)/((factorial(k))^4*396^(4*k)) for k in (0..11)))\n", "show((pi-1/s).n(digits=100))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 8" ] }, { "cell_type": "code", "execution_count": 99, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-2*x^2/(x^2 + y^2)^2 - 2*y^2/(x^2 + y^2)^2 + 2/(x^2 + y^2)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "0" ] }, "execution_count": 99, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('x y'); \n", "f=ln(x**2+y**2)/2\n", "delta=diff(f,x,2)+diff(f,y,2)\n", "show(delta)\n", "delta.simplify_full()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 9" ] }, { "cell_type": "code", "execution_count": 100, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "1/2*pi*e^(-x)" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u=var('u');\n", "f=x*cos(u)/(u^2+x^2)\n", "\n", "assume(x>0); f.integrate(u,0,infinity)" ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "-1/2*pi*e^x" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "forget()\n", "assume(x<0); f.integrate(u,0,infinity)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 10" ] }, { "cell_type": "code", "execution_count": 102, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "1/6*pi^2" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('k')\n", "sum(1/k^2,k,1,oo)" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('k')\n", "integral(1/k^2,k,1,oo)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Exercice 11" ] }, { "cell_type": "code", "execution_count": 104, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "(a*q^(n + 1) - a)/(q - 1)" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('a q k n')\n", "sum(a*q^k, k, 0, n)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "terme convergent lorsque abs(q) <1, divergent sinon" ] }, { "cell_type": "code", "execution_count": 105, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "-a/(q - 1)" ] }, "execution_count": 105, "metadata": {}, "output_type": "execute_result" } ], "source": [ "assume(abs(q)<1);\n", "sum(a*q^k, k, 0, oo)" ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "ename": "ValueError", "evalue": "Sum is divergent.", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mforget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0massume\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m>\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mq\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moo\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m/opt/sage/8.0/local/lib/python2.7/site-packages/sage/misc/functional.pyc\u001b[0m in \u001b[0;36msymbolic_sum\u001b[0;34m(expression, *args, **kwds)\u001b[0m\n\u001b[1;32m 561\u001b[0m \"\"\"\n\u001b[1;32m 562\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpression\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'sum'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 563\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mexpression\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 564\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 565\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpression\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m/opt/sage/8.0/src/sage/symbolic/expression.pyx\u001b[0m in \u001b[0;36msage.symbolic.expression.Expression.sum (/opt/sage/8.0/src/build/cythonized/sage/symbolic/expression.cpp:69147)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 12165\u001b[0m \"\"\"\n\u001b[1;32m 12166\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0msage\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcalculus\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcalculus\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0msymbolic_sum\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m> 12167\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0msymbolic_sum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 12168\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 12169\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mprod\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m/opt/sage/8.0/local/lib/python2.7/site-packages/sage/calculus/calculus.pyc\u001b[0m in \u001b[0;36msymbolic_sum\u001b[0;34m(expression, v, a, b, algorithm, hold)\u001b[0m\n\u001b[1;32m 616\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 617\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0malgorithm\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'maxima'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 618\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mmaxima\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msr_sum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpression\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 619\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 620\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0malgorithm\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'mathematica'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m/opt/sage/8.0/local/lib/python2.7/site-packages/sage/interfaces/maxima_lib.pyc\u001b[0m in \u001b[0;36msr_sum\u001b[0;34m(self, *args)\u001b[0m\n\u001b[1;32m 896\u001b[0m \u001b[0;31m# could not find an example where 'Pole encountered' occurred, though\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 897\u001b[0m \u001b[0;31m# if \"divergent\" in s or 'Pole encountered' in s:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 898\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Sum is divergent.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 899\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0;34m\"Is\"\u001b[0m \u001b[0;32min\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# Maxima asked for a condition\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 900\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_missing_assumption\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mValueError\u001b[0m: Sum is divergent." ] } ], "source": [ "forget(); \n", "assume(q>1); \n", "sum(a*q^k, k, 0, oo)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "4" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.0", "language": "", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }