{"id":6844,"date":"2023-10-17T11:55:19","date_gmt":"2023-10-17T02:55:19","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=6844"},"modified":"2024-10-29T14:57:21","modified_gmt":"2024-10-29T05:57:21","slug":"sympy-%e3%81%a7%e3%82%b9%e3%82%ab%e3%82%a4%e3%83%84%e3%83%aa%e3%83%bc%e5%b1%95%e6%9c%9b%e5%8f%b0%e3%81%a7%e3%81%ae%e6%99%82%e9%96%93%e3%81%ae%e9%80%b2%e3%81%bf","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%87%8d%e5%8a%9b%e5%a0%b4%e4%b8%ad%e3%81%ae%e6%99%82%e9%96%93%e3%81%ae%e9%80%b2%e3%81%bf%e6%96%b9\/%e9%87%8d%e5%8a%9b%e5%a0%b4%e4%b8%ad%e3%81%ae%e7%95%b0%e3%81%aa%e3%82%8b%e5%9c%b0%e7%82%b9%e3%81%a7%e3%81%ae%e6%99%82%e9%96%93%e3%81%ae%e9%80%b2%e3%81%bf%e6%96%b9\/sympy-%e3%81%a7%e3%82%b9%e3%82%ab%e3%82%a4%e3%83%84%e3%83%aa%e3%83%bc%e5%b1%95%e6%9c%9b%e5%8f%b0%e3%81%a7%e3%81%ae%e6%99%82%e9%96%93%e3%81%ae%e9%80%b2%e3%81%bf\/","title":{"rendered":"SymPy \u3067\u30b9\u30ab\u30a4\u30c4\u30ea\u30fc\u5c55\u671b\u53f0\u3067\u306e\u6642\u9593\u306e\u9032\u307f"},"content":{"rendered":"

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SymPy \u306e import<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[1]:<\/div>\n
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from<\/span> sympy.abc<\/span> import<\/span> *<\/span>\r\nfrom<\/span> sympy<\/span> import<\/span> *<\/span><\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$\\displaystyle \\frac{\\varDelta \\tau_2}{\\varDelta \\tau_1} = $ Dtratio<\/code> \u3068\u3044\u3046\u5909\u6570\u306b\u5165\u308c\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[2]:<\/div>\n
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# 1\u6587\u5b57\u5909\u6570\u4ee5\u5916\u306f\u5b9a\u7fa9\u3057\u3066\u304a\u304f<\/span>\r\nvar<\/span>(<\/span>'rg'<\/span>)<\/span>\r\n\r\nDtratio<\/span> =<\/span> sqrt<\/span>(<\/span>1<\/span>-<\/span>rg<\/span>\/<\/span>(<\/span>R<\/span> +<\/span> h<\/span>))<\/span>\/<\/span>sqrt<\/span>(<\/span>1<\/span>-<\/span>rg<\/span>\/<\/span>R<\/span>)<\/span>\r\nDtratio<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[2]:<\/div>\n
$\\displaystyle \\frac{\\sqrt{- \\frac{rg}{R + h} + 1}}{\\sqrt{1 – \\frac{rg}{R}}}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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series()<\/code> \u306b\u3088\u308b\u30c6\u30a4\u30e9\u30fc\u5c55\u958b<\/h3>\n
series()<\/code> \u95a2\u6570\u3067\uff0c\u30c6\u30a4\u30e9\u30fc\u5c55\u958b\uff0c\u3084\u3063\u3066\u3093\u304b\u3044\uff01<\/p>\n
\u307e\u305a\uff0c$r_g$ \u306b\u3064\u3044\u30661\u6b21\uff082\u6b21\u672a\u6e80\u3060\u304b\u3089 Python \u6d41\u306b 2<\/code> \u3092\u5165\u308c\u308b\uff09\u307e\u3067\u306e\u30c6\u30a4\u30e9\u30fc\u5c55\u958b\uff0cseries(Dtratio, rg, 0, 2)<\/code>\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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tay<\/span> =<\/span> series<\/span>(<\/span>Dtratio<\/span>,<\/span> rg<\/span>,<\/span> 0<\/span>,<\/span> 2<\/span>)<\/span>\r\ntay<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[3]:<\/div>\n
$\\displaystyle 1 + rg \\left(- \\frac{1}{2 \\left(R + h\\right)} + \\frac{1}{2 R}\\right) + O\\left(rg^{2}\\right)$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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removeO()<\/code> \u3057\u3066\u3055\u3089\u306b\u30c6\u30a4\u30e9\u30fc\u5c55\u958b<\/h3>\n
\u305d\u3057\u3066\u305d\u308c\u3092\u3055\u3089\u306b $h$ \u306b\u3064\u3044\u30661\u6b21\u307e\u3067\u306e\u30c6\u30a4\u30e9\u30fc\u5c55\u958b\u3059\u308b\u305f\u3081\u306b\uff0c\u3044\u3063\u305f\u3093 $O(r_g^2)$ \u306e\u9805\u3092\u53d6\u308a\u9664\u3044\u3066\u666e\u901a\u306e\u95a2\u6570\u306b\u3057\u3066\u304b\u3089\uff0c\u3082\u3046\u4e00\u5ea6 series()<\/code> \u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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tay1<\/span> =<\/span> tay<\/span>.<\/span>removeO<\/span>()<\/span>\r\ntay1<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[4]:<\/div>\n
$\\displaystyle rg \\left(- \\frac{1}{2 \\left(R + h\\right)} + \\frac{1}{2 R}\\right) + 1$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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tay11<\/span> =<\/span> series<\/span>(<\/span>tay1<\/span>,<\/span> h<\/span>,<\/span> 0<\/span>,<\/span> 2<\/span>)<\/span>.<\/span>removeO<\/span>()<\/span>\r\ntay11<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[5]:<\/div>\n
$\\displaystyle 1 + \\frac{h rg}{2 R^{2}}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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tay1<\/code> \u306e $r_g$ \u306b\u6bd4\u4f8b\u3059\u308b\u4e00\u822c\u76f8\u5bfe\u8ad6\u7684\u88dc\u6b63\u9805\u3092\u3068\u308a\u3060\u3057\uff0c\u5909\u6570 ans<\/code> \u306b\u4ee3\u5165\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[6]:<\/div>\n
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ans<\/span> =<\/span> tay11<\/span> -<\/span> 1<\/span>\r\nans<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[6]:<\/div>\n
$\\displaystyle \\frac{h rg}{2 R^{2}}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u3042\u3068\u306f\uff0c$r_g, h, R$ \u306b\u305d\u308c\u305e\u308c\u6570\u5024\u3092\u5165\u308c\u3066 ans<\/code> \u306e\u5024\u3092\u6c42\u3081\uff0c\u3053\u308c\u306f1\u79d2\u3042\u305f\u308a\u306e\u9032\u307f\u306e\u9055\u3044\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\uff0c1\u65e5\u3042\u305f\u308a\u306e\u6642\u8a08\u306e\u9032\u307f\u3092\u6c42\u3081\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[7]:<\/div>\n
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G<\/span> =<\/span> 6.674E-11<\/span>\r\n# \u5730\u7403\u8cea\u91cf <\/span>\r\nM<\/span> =<\/span> 5.972E24<\/span>\r\n# \u5149\u901f <\/span>\r\nc<\/span> =<\/span> 299792458<\/span>\r\n# \u91cd\u529b\u534a\u5f84<\/span>\r\nnrg<\/span> =<\/span> 2<\/span>*<\/span>G<\/span>*<\/span>M<\/span>\/<\/span>c<\/span>**<\/span>2<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[8]:<\/div>\n
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# \u5730\u7403\u534a\u5f84 <\/span>\r\n# \u8d64\u9053\u534a\u5f84\u3092\u4f7f\u3046\u3079\u304d\u304b\u306f\uff0c\u60a9\u3080\u3068\u3053\u308d\u3002<\/span>\r\n# \u3061\u3087\u3063\u3068\u5927\u304d\u3081\u306a\u5024\u3092\u5165\u308c\u3066\u3044\u308b\u3053\u3068\u306b\u306a\u308b\u304b\u3082\u3002<\/span>\r\nnR<\/span> =<\/span> 6378E3<\/span>\r\n# \u30b9\u30ab\u30a4\u30c4\u30ea\u30fc\u5c55\u671b\u53f0\u306e\u9ad8\u3055 <\/span>\r\nnh<\/span> =<\/span> 450<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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subs()<\/code> \u3067\u6570\u5024\u3092\u4ee3\u5165<\/h3>\n
\u5909\u6570 ans<\/code> \u3092\u69cb\u6210\u3059\u308b\u5909\u6570\u306b\u4ee5\u4e0b\u306e\u3088\u3046\u306b .subs()<\/code> \u3067\u5024\u3092\u4ee3\u5165\u3057\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[9]:<\/div>\n
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ans<\/span>.<\/span>subs<\/span>([(<\/span>h<\/span>,<\/span> nh<\/span>),<\/span> (<\/span>rg<\/span>,<\/span> nrg<\/span>),<\/span> (<\/span>R<\/span>,<\/span> nR<\/span>)])<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[9]:<\/div>\n
$\\displaystyle 4.90578012575303 \\cdot 10^{-14}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u3053\u308c\u306b\uff0c1\u65e5\u306e\u79d2\u6570\u3092\u304b\u3051\u3066\uff0c1\u65e5\u3042\u305f\u308a\u306e\u6642\u9593\u306e\u9032\u307f\u306b\u3059\u308b\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[10]:<\/div>\n
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_<\/span> *<\/span> 60<\/span> *<\/span> 60<\/span> *<\/span> 24<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[10]:<\/div>\n
$\\displaystyle 4.23859402865062 \\cdot 10^{-9}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u7d50\u8ad6<\/h3>\n
\u30b9\u30ab\u30a4\u30c4\u30ea\u30fc\u5c55\u671b\u53f0\u3067\u306f\uff0c\u6642\u9593\u306f1\u65e5\u3042\u305f\u308a10\u5104\u5206\u306e4.2\u79d2 \u3059\u3059\u3080\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":33,"featured_media":0,"parent":1199,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-6844","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t