{"id":2842,"date":"2022-04-01T15:18:51","date_gmt":"2022-04-01T06:18:51","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=2842"},"modified":"2023-03-14T16:35:27","modified_gmt":"2023-03-14T07:35:27","slug":"maxima-%e3%81%a7%e3%81%a7%e3%81%8d%e3%82%8b%e7%a9%8d%e5%88%86%e3%81%8c-sympy-%e3%81%a7%e3%81%a7%e3%81%8d%e3%81%aa%e3%81%84%e3%81%93%e3%81%a8%e3%82%82%e3%81%82%e3%82%8b","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/2842\/","title":{"rendered":"Maxima \u3067\u3067\u304d\u308b\u7a4d\u5206\u304c SymPy \u3067\u3067\u304d\u306a\u3044\u3053\u3068\u3082\u3042\u308b"},"content":{"rendered":"<p><!--more--><\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e9%9d%99%e9%9b%bb%e5%a0%b4%ef%bc%9a%e9%9b%bb%e8%8d%b7%e5%af%86%e5%ba%a6%e3%81%8b%e3%82%89%e7%9b%b4%e6%8e%a5%e9%9b%bb%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b\/%e5%8f%82%e8%80%83%ef%bc%9a%e9%9d%99%e9%9b%bb%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e9%9a%9b%e3%81%ab%e4%bd%bf%e3%81%a3%e3%81%9f%e7%a9%8d%e5%88%86%e3%82%92-maxima-jupyter-%e3%81%a7%e7%a2%ba\/\">\u53c2\u8003\uff1a\u9759\u96fb\u5834\u3092\u6c42\u3081\u308b\u969b\u306b\u4f7f\u3063\u305f\u7a4d\u5206\u3092 Maxima-Jupyter \u3067\u78ba\u8a8d\u3059\u308b<\/a><\/li>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e9%9d%99%e7%a3%81%e5%a0%b4%ef%bc%9a%e9%9b%bb%e6%b5%81%e5%af%86%e5%ba%a6%e3%81%8b%e3%82%89%e7%9b%b4%e6%8e%a5%e9%9d%99%e7%a3%81%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b\/%e5%8f%82%e8%80%83%ef%bc%9a%e9%9d%99%e7%a3%81%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e9%9a%9b%e3%81%ab%e4%bd%bf%e3%81%a3%e3%81%9f%e7%a9%8d%e5%88%86%e3%82%92-maxima-jupyter-%e3%81%a7%e7%a2%ba\/\">\u53c2\u8003\uff1a\u9759\u78c1\u5834\u3092\u6c42\u3081\u308b\u969b\u306b\u4f7f\u3063\u305f\u7a4d\u5206\u3092 Maxima-Jupyter \u3067\u78ba\u8a8d\u3059\u308b<\/a><\/li>\n<\/ul>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u9759\u96fb\u5834\u3092\u6c42\u3081\u308b\u969b\u306b\u4f7f\u3063\u305f\u7a4d\u5206\u3092-SymPy-\u3067\u78ba\u8a8d\u3059\u308b\u3068...\">\u9759\u96fb\u5834\u3092\u6c42\u3081\u308b\u969b\u306b\u4f7f\u3063\u305f\u7a4d\u5206\u3092 SymPy \u3067\u78ba\u8a8d\u3059\u308b\u3068&#8230;<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"kn\">from<\/span> <span class=\"nn\">sympy<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">sympy.abc<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">sympy<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">I<\/span><span class=\"p\">,<\/span> <span class=\"n\">pi<\/span><span class=\"p\">,<\/span> <span class=\"n\">E<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">pip<\/span> <span class=\"n\">show<\/span> <span class=\"n\">sympy<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>Name: sympy\r\nVersion: 1.10.1\r\nSummary: Computer algebra system (CAS) in Python\r\nHome-page: https:\/\/sympy.org\r\nAuthor: SymPy development team\r\nAuthor-email: sympy@googlegroups.com\r\nLicense: BSD\r\nLocation: \/usr\/local\/lib\/python3.8\/dist-packages\r\nRequires: mpmath\r\nRequired-by: einsteinpy\r\nNote: you may need to restart the kernel to use updated packages.\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"1\">1<\/h4>\n<p>$$\\int_{-\\infty}^{\\infty}<br \/>\n\\frac{1}{\\left(x^2 + y^2 + (z-z&#8217;)^2\\right)^{3\/2}} dz&#8217; =\u00a0 \\frac{2}{x^2 + y^2}$$<\/p>\n<p>\u306e\u78ba\u8a8d\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># from sympy.abc import * \u6e08\u307f\u306a\u306e\u3067\uff0c\u6b8b\u308a\u306e\u5909\u6570\u306e\u307f\u3092\u5ba3\u8a00<\/span>\r\n\r\n<span class=\"n\">z1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">Symbol<\/span><span class=\"p\">(<\/span><span class=\"s1\">'z1'<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">integrate<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"o\">-<\/span><span class=\"n\">z1<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">z1<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">oo<\/span><span class=\"p\">,<\/span> <span class=\"n\">oo<\/span><span class=\"p\">))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[4]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle \\int\\limits_{-\\infty}^{\\infty} \\frac{1}{\\left(x^{2} + y^{2} + \\left(z &#8211; z_{1}\\right)^{2}\\right)^{\\frac{3}{2}}}\\, dz_{1}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>SymPy \u306f\u8a08\u7b97\u3067\u304d\u306a\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"2\">2<\/h4>\n<p>$$\\int_{-\\infty}^{\\infty}<br \/>\n\\frac{z &#8211; z&#8217;}{\\left(x^2 + y^2 + (z-z&#8217;)^2\\right)^{3\/2}} dz&#8217; = \\int_{-\\infty}^{\\infty}<br \/>\n\\frac{Z}{\\left(x^2 + y^2 + Z^2\\right)^{3\/2}} dZ =0$$<\/p>\n<p>\u306e\u78ba\u8a8d\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">integrate<\/span><span class=\"p\">((<\/span><span class=\"n\">z<\/span><span class=\"o\">-<\/span><span class=\"n\">z1<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"o\">-<\/span><span class=\"n\">z1<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">z1<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">oo<\/span><span class=\"p\">,<\/span> <span class=\"n\">oo<\/span><span class=\"p\">))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[5]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle 0$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u308c\u306f SymPy \u3067\u3082\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"3\">3<\/h4>\n<p>$$\\int_{-\\infty}^{\\infty} \\int_{-\\infty}^{\\infty}\\frac{x }{\\left(x^2 + (y-y&#8217;)^2 + (z-z&#8217;)^2\\right)^{3\/2}}dy&#8217; dz&#8217; = 2 \\pi \\frac{x}{|x|}$$<\/p>\n<p>\u306e\u78ba\u8a8d\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">y1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">Symbol<\/span><span class=\"p\">(<\/span><span class=\"s1\">'y1'<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">integrate<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">integrate<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span><span class=\"n\">y<\/span><span class=\"o\">-<\/span><span class=\"n\">y1<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"o\">-<\/span><span class=\"n\">z1<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">y1<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">oo<\/span><span class=\"p\">,<\/span> <span class=\"n\">oo<\/span><span class=\"p\">)),<\/span> \r\n    <span class=\"p\">(<\/span><span class=\"n\">z1<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">oo<\/span><span class=\"p\">,<\/span> <span class=\"n\">oo<\/span><span class=\"p\">))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[7]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle 2 x \\int\\limits_{-\\infty}^{\\infty} \\frac{1}{\\operatorname{polar\\_lift}{\\left(x^{2} + \\operatorname{polar\\_lift}^{2}{\\left(z &#8211; z_{1} \\right)} \\right)}}\\, dz_{1}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>SymPy \u306f <code>polar_lift<\/code> \u306a\u3069\u3068\u3044\u3046\u602a\u3057\u3052\u306a\u6587\u53e5\u3092\u8a00\u3044\u306a\u304c\u3089\u8a08\u7b97\u3057\u3066\u304f\u308c\u306a\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u9759\u78c1\u5834\u3092\u6c42\u3081\u308b\u969b\u306b\u4f7f\u3063\u305f\u7a4d\u5206\u3092-SymPy-\u3067\u78ba\u8a8d\u3059\u308b\u3068...\">\u9759\u78c1\u5834\u3092\u6c42\u3081\u308b\u969b\u306b\u4f7f\u3063\u305f\u7a4d\u5206\u3092 SymPy \u3067\u78ba\u8a8d\u3059\u308b\u3068&#8230;<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"kn\">from<\/span> <span class=\"nn\">sympy<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">sympy.abc<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">sympy<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">I<\/span><span class=\"p\">,<\/span> <span class=\"n\">pi<\/span><span class=\"p\">,<\/span> <span class=\"n\">E<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">pip<\/span> <span class=\"n\">show<\/span> <span class=\"n\">sympy<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>Name: sympy\r\nVersion: 1.10.1\r\nSummary: Computer algebra system (CAS) in Python\r\nHome-page: https:\/\/sympy.org\r\nAuthor: SymPy development team\r\nAuthor-email: sympy@googlegroups.com\r\nLicense: BSD\r\nLocation: \/usr\/local\/lib\/python3.8\/dist-packages\r\nRequires: mpmath\r\nRequired-by: einsteinpy\r\nNote: you may need to restart the kernel to use updated packages.\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"1\">1<\/h4>\n<p>$$\\int_{-\\infty}^{\\infty}<br \/>\n\\frac{1}{\\left(x^2 + y^2 + (z-z&#8217;)^2\\right)^{3\/2}} dz&#8217; =\u00a0 \\frac{2}{x^2 + y^2}$$<\/p>\n<p>\u306e\u78ba\u8a8d\u3002\uff08\u96fb\u5834\u3092\u6c42\u3081\u308b\u3068\u304d\u306b\u3082\u51fa\u307e\u3057\u305f\u3002\uff09<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># from sympy.abc import * \u6e08\u307f\u306a\u306e\u3067\uff0c\u6b8b\u308a\u306e\u5909\u6570\u306e\u307f\u3092\u5ba3\u8a00<\/span>\r\n\r\n<span class=\"n\">z1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">Symbol<\/span><span class=\"p\">(<\/span><span class=\"s1\">'z1'<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">integrate<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"o\">-<\/span><span class=\"n\">z1<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">z1<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">oo<\/span><span class=\"p\">,<\/span> <span class=\"n\">oo<\/span><span class=\"p\">))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[4]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle \\int\\limits_{-\\infty}^{\\infty} \\frac{1}{\\left(x^{2} + y^{2} + \\left(z &#8211; z_{1}\\right)^{2}\\right)^{\\frac{3}{2}}}\\, dz_{1}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>SymPy \u306f\u8a08\u7b97\u3067\u304d\u306a\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"2\">2<\/h4>\n<p>$$\\int_{-\\infty}^{\\infty}<br \/>\n\\frac{z &#8211; z&#8217;}{\\left((x-x&#8217;)^2 + (y-y&#8217;)^2 + (z-z&#8217;)^2\\right)^{3\/2}} dz&#8217; =0$$<\/p>\n<p>\u306e\u78ba\u8a8d\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">x1<\/span><span class=\"p\">,<\/span> <span class=\"n\">y1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">symbols<\/span><span class=\"p\">(<\/span><span class=\"s1\">'x1 y1'<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">integrate<\/span><span class=\"p\">((<\/span><span class=\"n\">z<\/span><span class=\"o\">-<\/span><span class=\"n\">z1<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">((<\/span><span class=\"n\">x<\/span><span class=\"o\">-<\/span><span class=\"n\">x1<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span><span class=\"n\">y<\/span><span class=\"o\">-<\/span><span class=\"n\">y1<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"o\">-<\/span><span class=\"n\">z1<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">z1<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">oo<\/span><span class=\"p\">,<\/span> <span class=\"n\">oo<\/span><span class=\"p\">))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[6]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle 0$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u308c\u306f SymPy \u3067\u3082\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"3\">3<\/h4>\n<p>\\begin{eqnarray}<br \/>\n\\int_0^{2\\pi}\u00a0 \\,d\\phi&#8217;\u00a0 \\frac{ a^2\u00a0 &#8211; a\u00a0 y\\sin\\phi&#8217; &#8211; a x\\cos\\phi&#8217;\u00a0 }{x^2 + y^2 + a^2 &#8211; 2 a x \\cos\\phi&#8217; &#8211; 2 a y \\sin\\phi&#8217; } &amp;&amp; \\\\<br \/>\n= \\left\\{<br \/>\n\\begin{array}{ll}<br \/>\n2\\pi\u00a0 &amp; (a &gt; \\sqrt{x^2 + y^2})\\\\<br \/>\n0 &amp; (a &lt; \\sqrt{x^2 + y^2})<br \/>\n\\end{array}<br \/>\n\\right.<br \/>\n\\end{eqnarray}<\/p>\n<p>\u306e\u78ba\u8a8d\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4e0a\u8a18\u306e\u307e\u307e\u3060\u3068\u56fa\u307e\u308b\u306e\u3067\uff0c$y=0$ \u306e\u5834\u5408\u306b\u3057\u3066\u89e3\u304f\u3068&#8230;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">phi1<\/span><span class=\"o\">=<\/span><span class=\"n\">Symbol<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"phi1\"<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[8]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">Integral<\/span><span class=\"p\">((<\/span><span class=\"n\">a<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">-<\/span> <span class=\"n\">a<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span><span class=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">phi1<\/span><span class=\"p\">))<\/span>\r\n          <span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">a<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">a<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span><span class=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">phi1<\/span><span class=\"p\">)),<\/span> \r\n         <span class=\"p\">(<\/span><span class=\"n\">phi1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/span><span class=\"p\">))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[8]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle \\int\\limits_{0}^{2 \\pi} \\frac{a^{2} &#8211; a x \\cos{\\left(\\phi_{1} \\right)}}{a^{2} &#8211; 2 a x \\cos{\\left(\\phi_{1} \\right)} + x^{2}}\\, d\\phi_{1}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">_<\/span><span class=\"o\">.<\/span><span class=\"n\">doit<\/span><span class=\"p\">()<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[9]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle \\pi$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>SymPy \u306f\uff0c\u4e0a\u8a18\u306e\u3088\u3046\u306b\u9593\u9055\u3063\u305f\u7d50\u679c\u3092\u51fa\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[12],"tags":[],"class_list":["post-2842","post","type-post","status-publish","format-standard","hentry","category-sympy","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/2842","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=2842"}],"version-history":[{"count":2,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/2842\/revisions"}],"predecessor-version":[{"id":2844,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/2842\/revisions\/2844"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=2842"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=2842"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=2842"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}