{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introdução ao Uso do Sage para Modelagem Matemática\n", "\n", "**Flávio Codeço Coelho -- Escola de Matemática Aplicada -- Fundação Getulio Vargas**\n", "\n", "Nesta planilha iremos apresentar algumas características básicas do Sage, com especial atenção ao uso para modelagem matemática. Vários dos exemplos mostrados aqui foram retirados do tutorial do Sage. Para um maior aprofundamento, recomendo a sua leitura.\n", "\n", "## Linguagem de programação(s)\n", "\n", "A linguagem básica para programação no Sage é o Python. \n", "\n", "Este tutorial também assume que o leitor tenha conhecimentos básicos de Python. Apenas introduziremos aspectos da linguagem do Sage onde houver construções sintáticas não compatíveis com o Python, como por exemplo:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "3^2 == 3**2 # Isto não é verdadeiro em Python!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "O Sage també é capaz de renderizar expressões matemáticas usando $\\LaTeX$. Para ativar esta renderização:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%display typeset" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A divisão também é um pouco diferente no Sage:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{5}{6}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{5}{6}$$" ], "text/plain": [ "5/6" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "5/2 *1/3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "O Sage procura retornar expressões exatas sempre que possível." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, \\sqrt{3}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, \\sqrt{3}$$" ], "text/plain": [ "1/2*sqrt(3)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sin(pi/3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Para aproximações numéricas use a função n()." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.866025403784439$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.866025403784439$$" ], "text/plain": [ "0.866025403784439" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n(sin(pi/3))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|<class|\\phantom{\\verb!x!}\\verb|'sage.symbolic.expression.Expression'>|$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb||$$" ], "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(sin(10))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sin\\left(10\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sin\\left(10\\right)$$" ], "text/plain": [ "sin(10)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = sin(10)\n", "x." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.54402$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-0.54402$$" ], "text/plain": [ "-0.54402" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sin(10).n(digits=5)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "9.86960440108936\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}9.8696044010893586188344909998761511353$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}9.8696044010893586188344909998761511353$$" ], "text/plain": [ "9.8696044010893586188344909998761511353" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(n(pi^2))\n", "(pi^2).n(prec=128) # Precisão em bits." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "O Sage também introduz tipos extendidos, por exemplo:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}3$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}3$$" ], "text/plain": [ "3" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = 5/3 # Agora a é um número racional\n", "print(type(a))\n", "a.denominator()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Álgebra e Cálculo\n", "\n", "O ponto forte to Sage é a computação simbólica. Vamos ver alguns exemplos.\n", "### Manipulando Expressões Simbólicas\n", "\n", "Vamos construir uma expressão simples:\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(x + y\\right)}^{3}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(x + y\\right)}^{3}$$" ], "text/plain": [ "(x + y)^3" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('x y')\n", "z = (x+y)^3\n", "z" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|<class|\\phantom{\\verb!x!}\\verb|'sage.symbolic.expression.Expression'>|$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb||$$" ], "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos expandir este binômio" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}x^{3} + 3 \\, x^{2} y + 3 \\, x y^{2} + y^{3}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}x^{3} + 3 \\, x^{2} y + 3 \\, x y^{2} + y^{3}$$" ], "text/plain": [ "x^3 + 3*x^2*y + 3*x*y^2 + y^3" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expand(z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Agora façamos o caminho de volta:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(x + y\\right)}^{3}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(x + y\\right)}^{3}$$" ], "text/plain": [ "(x + y)^3" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "factor(expand(z))\n", "#show(expand(z))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "O sage também nos permite fazer matemática de forma mais interativa:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "3e4eae24595b4e58a60fd8bc24e0883f", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Interactive function with 1 widget\n", " n: IntSlider(value=5, description='…" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 48.6 ms, sys: 431 µs, total: 49.1 ms\n", "Wall time: 47.2 ms\n" ] } ], "source": [ "%%time\n", "y = var('y') # Definindo y como uma variável simbólica também\n", "@interact\n", "def binomios(n=(2,9,1)): # n varia de 2 a 9 em intervalos de 1\n", " z = (x+y)^n\n", " show(expand(z))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos brincar com algo um pouquinho mais complexo:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{{\\left(x + 1\\right)} \\sqrt{x - 1} - {\\left(x - 1\\right)}^{\\frac{3}{2}}}{\\sqrt{{\\left(x + 1\\right)} {\\left(x - 1\\right)}}}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{{\\left(x + 1\\right)} \\sqrt{x - 1} - {\\left(x - 1\\right)}^{\\frac{3}{2}}}{\\sqrt{{\\left(x + 1\\right)} {\\left(x - 1\\right)}}}$$" ], "text/plain": [ "-((x + 1)*sqrt(x - 1) - (x - 1)^(3/2))/sqrt((x + 1)*(x - 1))" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "z = ((x - 1)^(3/2) - (x + 1)*sqrt(x - 1))/sqrt((x - 1)*(x + 1))\n", "z" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podemos simplificar a expressão:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{2 \\, \\sqrt{x - 1}}{\\sqrt{x^{2} - 1}}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{2 \\, \\sqrt{x - 1}}{\\sqrt{x^{2} - 1}}$$" ], "text/plain": [ "-2*sqrt(x - 1)/sqrt(x^2 - 1)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "z.simplify_full()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Resolvendo Equações\n", "\n", "Para fazer operações com símbolos, é sempre necessário informar ao sage que variáveis devem ser tratadas como símbolos ao invés de variáveis comuns. O símbolo $x$ é tratado como variável simbólica, por padrão, a menos que lhe seja atribuído um valor.\n" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[x = \\left(-i\\right), x = i\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[x = \\left(-i\\right), x = i\\right]$$" ], "text/plain": [ "[x == -I, x == I]" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(x^2==-1,x)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[x = \\left(-2\\right), x = \\left(-1\\right)\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[x = \\left(-2\\right), x = \\left(-1\\right)\\right]$$" ], "text/plain": [ "[x == -2, x == -1]" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(x^2 + 3*x + 2, x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vários símbolos podem ser declarados simultâneamente. Isto é útil quando desejamos resolver uma equação sem especificar os coeficientes." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[x = -\\frac{b + \\sqrt{b^{2} - 4 \\, a c}}{2 \\, a}, x = -\\frac{b - \\sqrt{b^{2} - 4 \\, a c}}{2 \\, a}\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[x = -\\frac{b + \\sqrt{b^{2} - 4 \\, a c}}{2 \\, a}, x = -\\frac{b - \\sqrt{b^{2} - 4 \\, a c}}{2 \\, a}\\right]$$" ], "text/plain": [ "[x == -1/2*(b + sqrt(b^2 - 4*a*c))/a, x == -1/2*(b - sqrt(b^2 - 4*a*c))/a]" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a, b, c = var('a b c')\n", "solve([a*x^2 + b*x + c],x)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 12.6 ms, sys: 23 µs, total: 12.6 ms\n", "Wall time: 12.3 ms\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{\\sqrt{-12 \\, b - 12 \\, c + 1} + 1}{2 \\, {\\left(b + c\\right)}}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{\\sqrt{-12 \\, b - 12 \\, c + 1} + 1}{2 \\, {\\left(b + c\\right)}}$$" ], "text/plain": [ "-1/2*(sqrt(-12*b - 12*c + 1) + 1)/(b + c)" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%time\n", "sols = solve([a*x^2 + b*x + c],x)\n", "sols[0].rhs().subs(a=c+b,c=3,b=1)#.subs(b=1).subs(c=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Também podemos resolver sistemas de equações." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left[x = 5, y = 1\\right]\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left[x = 5, y = 1\\right]\\right]$$" ], "text/plain": [ "[[x == 5, y == 1]]" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x, y = var('x y')\n", "solve([x+y==6, x-y==4], x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "Note o uso do sinal de == para espressar uma igualdade algébrica.\n", "\n", "## Resolvendo Equações Numericamente\n", "\n", "Às vezes solve não encontra uma solução para uma dada equação ou sistema de equações, nestes casos podemo buscar aproximações numéricas por meio da função `find_root`.\n" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\sin\\left(\\theta\\right) = \\cos\\left(\\theta\\right)\\right]$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\sin\\left(\\theta\\right) = \\cos\\left(\\theta\\right)\\right]$$" ], "text/plain": [ "[sin(theta) == cos(theta)]" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta = var('theta')\n", "solve(cos(theta)==sin(theta), theta)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.7853981633974483$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.7853981633974483$$" ], "text/plain": [ "0.7853981633974483" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "find_root(cos(theta)==sin(theta),0.5,1.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podemos verificar a existência da solução gráficamente:" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p = plot([cos(theta),sin(theta)], (theta, 0, pi))\n", "q = point2d((0.785398163397,cos(0.785398163397)),color='red', size=30)\n", "p+q" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parametric_plot([sin(theta),cos(theta)],(theta, 0, 2*pi))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Cálculo\n", "### Diferenciação e Integração\n", "\n", "Vamos começar com uma derivada simples.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\cos\\left(u\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\cos\\left(u\\right)$$" ], "text/plain": [ "cos(u)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('u')\n", "diff(sin(u), u)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Agora a quarta derivada de $sin(x^2)$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}16 \\, x^{4} \\sin\\left(x^{2}\\right) - 48 \\, x^{2} \\cos\\left(x^{2}\\right) - 12 \\, \\sin\\left(x^{2}\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}16 \\, x^{4} \\sin\\left(x^{2}\\right) - 48 \\, x^{2} \\cos\\left(x^{2}\\right) - 12 \\, \\sin\\left(x^{2}\\right)$$" ], "text/plain": [ "16*x^4*sin(x^2) - 48*x^2*cos(x^2) - 12*sin(x^2)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(sin(x^2), x, 4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Derivadas parciais também não são problema:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $f(x,y)=x^{2} + 17 \\, y^{2}$ " ], "text/plain": [ " $f(x,y)=x^{2} + 17 \\, y^{2}$ " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}2 \\, x$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}2 \\, x$$" ], "text/plain": [ "2*x" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x, y = var('x,y')\n", "f = x^2 + 17*y^2\n", "pretty_print(html(f'$f(x,y)={latex(f)}$'))\n", "f.diff(x)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}34 \\, y$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}34 \\, y$$" ], "text/plain": [ "34*y" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.diff(y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Integrais indefinidas e definidas\n", "\n", "$$\\int x sin(x^2) dx$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, \\log\\left(2\\right)$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, \\log\\left(2\\right)$$" ], "text/plain": [ "1/2*log(2)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integral(x/(x^2+1), x, 0,1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Decomposição por frações parciais de $\\frac{1}{x^2-1}$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{1}{2 \\, {\\left(x + 1\\right)}} + \\frac{1}{2 \\, {\\left(x - 1\\right)}}$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{1}{2 \\, {\\left(x + 1\\right)}} + \\frac{1}{2 \\, {\\left(x - 1\\right)}}$$" ], "text/plain": [ "-1/2/(x + 1) + 1/2/(x - 1)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = 1/(x^2-1)\n", "f.partial_fraction(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotando Funções" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "f(x)=x^3+1\n", "P=plot(f,(x,-1,1))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ x^{3} + 1$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ x^{3} + 1$$" ], "text/plain": [ "x |--> x^3 + 1" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Como o objeto \"plot\" foi atribuído a uma variável, nehuma saída gráfica é gerada. Antes de visualizarmos este gráfico, vamos gerar outro e aprender como visualizar multiplos gráficos combinados." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Q=plot(1,(x,-1,1),color=\"red\", linestyle=\"--\")\n", "P+Q" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podemos modificar atributos do gráfico, para por exemplo, examinar mais de perto uma região:" ] }, { "cell_type": "code", "execution_count": 13, "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": [ "(P+Q).show(xmin=-.1,xmax=.1,ymin=.99,ymax=1.01)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podemos também adicionar nomes aos eixos e adicionar legendas." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(f,(x,-1,1),axes_labels=['$x$','$y$'],legend_label='$f(x)$',show_legend=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Como já percebemos a escala do gráfico é ajustada automáticamente, logo, funções que vão para infinito sao melhor visualizadas com limites explícitos:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(1/x^2,(x,-10,10),ymax=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Outra excelente ferramenta de exploração matemática do Sage, são as funções interativas." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2021-08-31T16:56:19.154906Z", "start_time": "2021-08-31T16:56:18.141509Z" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "6169c500dcb146b3bc0a53736111895a", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Interactive function with 12 widgets\n", " f: EvalText(value='sin(x^2)',…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "@interact\n", "def plot_example(f=sin(x^2),r=range_slider(-5,5,step_size=0.25,default=(-3,3)),\n", " color=color_selector(widget='colorpicker'),\n", " thickness=(3,(1..10)),\n", " adaptive_recursion=(5,(0..10)), adaptive_tolerance=(0.01,(0.001,1)),\n", " plot_points=(20,(1..100)),\n", " linestyle=['-','--','-.',':'],\n", " gridlines=False, fill=False,\n", " frame=False, axes=True\n", " ):\n", " show(plot(f, (x,r[0],r[1]), color=color, thickness=thickness,\n", " adaptive_recursion=adaptive_recursion,\n", " adaptive_tolerance=adaptive_tolerance, plot_points=plot_points,\n", " linestyle=linestyle, fill=fill if fill else None),\n", " gridlines=gridlines, frame=frame, axes=axes)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podemos também fazer gráficos em três dimensões:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(x,y)=sin(x^2+y^2)\n", "plot3d(g,(x,-5,5),(y,-5,5), plot_points=300)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Também podemos sobrepor gráficos tridimensionais:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = 2.2\n", "P=plot3d(sin(x^2-y^2),(x,-b,b),(y,-b,b), opacity=.7)\n", "Q=plot3d(0, (x,-b,b), (y,-b,b), color='red')\n", "P+Q" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Agora um gráfico mais interessante: Um gráfico implícito!" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('x y z')\n", "T = golden_ratio\n", "p = 2 - (cos(x + T*y) + cos(x - T*y) + cos(y + T*z) + cos(y - T*z) + cos(z - T*x) + cos(z + T*x))\n", "r = 4.78\n", "implicit_plot3d(p, (x, -r, r), (y, -r, r), (z, -r, r), plot_points=100, color='yellow')" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.61803398874989$ " ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.61803398874989$$" ], "text/plain": [ "1.61803398874989" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T.n()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.3", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.2" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, 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