︠d2fdcf5e-a06a-49f9-bd70-1b5d6b096c23︠ First experments of Sage Veikko Keränen -2009 Rovaniemi University of Applied Sciences veikko.keranen@ramk.fi Edited by Shijing Zhang iamshijingzhang@gmail.com ︡2614809f-606c-42c5-9474-4bd8940d7326︡︡ ︠889bc4f6-8b7a-4387-ada7-4b1e3285b636︠ First Experments ︡c6746b32-0c0d-472c-9139-7e5eec031806︡︡ ︠a34a7b6d-7c0e-4494-8b4b-085a097fe934︠ 3+3 # To execute, please press Shift+Enter button ︡d11d395b-ee07-4c5a-8f5f-8b488cc9b7dd︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}6"}︡ ︠5dafa529-24e0-4b08-a4e9-3f61ab38de90︠ 2^10 ︡b8dfacea-9a9c-4cb9-9975-36e0d1b11f69︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}1024"}︡ ︠59e19867-14ae-4bff-8093-92de440d3b49︠ Hints for typing In order to get pretty output please choose the "Typeset" button on the top of the this page ︡f15436ee-dc3c-4853-801c-f13851653760︡︡ ︠ff68fe30-06ff-4fb1-a661-3486f8becc31︠ pi ︡2ece47fa-418d-4118-8f8c-fea341060e15︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\pi"}︡ ︠19a11448-f805-4237-8e09-c3ef27c6b22b︠ 1/2 ︡7734e802-bb04-4de2-b5aa-a85caa97489a︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2}"}︡ ︠0ad2ecd5-54c2-43e9-ac90-a7886a18e2ab︠ 1/2*pi ︡8674d44a-2d53-40b6-ae29-93ec46d2d05f︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, \\pi"}︡ ︠1e3838bf-06c0-463d-a5c1-5be980d3f2af︠ sqrt(2) ︡d8e6d14d-e8c9-4940-9e38-8e115375afe6︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sqrt{2}"}︡ ︠faf60cc6-ccc6-46a7-93df-871e2c0ebc85︠ sqrt(1/x^2) ︡48884a92-5928-4d4a-881e-47f8f269d77c︡{"stdout": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sqrt{\\frac{1}{x^{2"}︡ ︠c3e82bab-92b9-4c69-8f3d-e294b41a52a8i︠ %html /span> }}} ︡d93b43b9-48e4-4aca-8d99-576b6362e961︡{"html": "/span>\n}}}"}︡ ︠579603be-0d4e-4d4d-a283-9ed554355f4f︠ precision ︡8eb5b0ec-8c03-4fee-8eac-2670eb2b4fc3︡︡ ︠cad44dd0-87bf-473a-ad81-2ae903d001af︠ 1/3. ︡d0c2394c-7080-49a2-a5af-bd5f3756cb8f︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.333333333333333"}︡ ︠b95fdc75-e8d6-4525-94a6-02d242aafd86︠ n(1/3.,digits=4) ︡8a577f12-7b14-4c93-b7e7-68dc59e720ed︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}0.3333"}︡ ︠7c89d7c2-4ff9-4711-aefb-1932b6b14e8d︠ n(2^(1/2.), digits=4) ︡2f732ad8-aed0-4328-8e47-de5259f0b4bb︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.414"}︡ ︠446c3a6a-97c7-4ce1-ba52-13bde79f5d5c︠ n(sqrt(2), digits=4) ︡5b80703a-d2d8-47bc-91ef-35d15aae6b81︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.414"}︡ ︠f0eb1bf7-1b88-465b-8117-19f79aa6bdb5︠ Some numerical computing ︡20a96508-acea-4bdc-9034-c61666318d99︡︡ ︠0dcb8d68-e0bc-4e33-b039-5666d3788dce︠ 2.^1000 ︡589d976c-3d1b-494b-87c4-30e2ceed0426︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}1.07150860718627 \\times 10^{301}"}︡ ︠5f525778-3352-4327-a723-7ca8fc93a6fc︠ sin(pi/12) ︡4912e29e-1b1e-43bf-a61f-6e63d89db26b︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{1}{12} \\, {(\\sqrt{3} - 3)} \\sqrt{6}"}︡ ︠1ad69cca-58f0-457b-aff4-1f8a33ffb308︠ pi.n(digits=5) ︡9e0acc98-0e4b-42ec-9d2b-34f462d12bf8︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}3.1416"}︡ ︠b1dbf867-4041-44ac-a59b-5abcb276256a︠ pi.n(digits=50) ︡1af246dc-4b9e-49ab-a650-dcb2c94e3443︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}3.1415926535897932384626433832795028841971693993751"}︡ ︠acd438ce-3ffa-42a4-92e8-cc19431dc861︠ Algebraic manipulation ︡d52414e6-c050-402f-b91f-66b80bc0d27e︡︡ ︠0746b741-d1b4-4e78-884d-db271438ef59︠ expand((x+1)*(x-1)) ︡c8fdf801-1a34-4090-9f4e-005c50d3b04a︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}x^{2} - 1"}︡ ︠38c06888-4d7a-4784-bbc6-37d99d023a82︠ expand((x+1)^3) ︡21b8c020-8a63-4b94-b108-d030bcbcaf9c︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}x^{3} + 3 \\, x^{2} + 3 \\, x + 1"}︡ ︠5b8d55e5-7a2f-4db3-b6e8-dadfa914cdb5︠ factor(x^2-1) ︡98d5d423-1307-4b8b-9bb4-0b47b22d1822︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{(x - 1)} {(x + 1)}"}︡ ︠950389ad-f9f5-444c-bef2-d3e7c17c3eda︠ factor(x^2+x-12) ︡cd5934f3-c226-4072-b789-cc2550db7d02︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{(x - 3)} {(x + 4)}"}︡ ︠d8d89683-05b3-46c8-8ab1-cdf00d59d371︠ Greatest common divisor and Least common multiple ︡90530554-46a0-483c-b17a-79ba1fe7f0aa︡︡ ︠939a4050-261f-4318-92ac-6ad9fa31277b︠ gcd(15,150) ︡b0240626-73ed-4c51-8570-e774f09be633︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}15"}︡ ︠a01e0396-fbb7-49e5-8c70-8a1c16166067︠ gcd(1456,456789) ︡c20a8278-c1a8-4891-b324-c82a9c03a7f3︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}1"}︡ ︠1b0eaab8-2797-4231-9ac6-bfe686e0a099︠ lcm(15,150) ︡67d0774c-9eb4-4c27-9368-a53f30a87176︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}150"}︡ ︠bcb2ca46-d3f1-480f-a306-cb98d22788d0︠ lcm(123456,654322) ︡c4bb1a9a-e1cc-48a1-9c94-e5b56911f22d︡{"html": "\\newcommand{\\Bold}[1]{\\mathbf{#1}}40389988416"}︡