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‎sage-start-here.ipynb

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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This document is one of [More SageMath Tutorials](https://more-sagemath-tutorials.readthedocs.io/en/latest/).\n",
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"You may [edit it on github](http://github.com/sagemath/more-sagemath-tutorials/).\n",
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"$ \\def\\NN{\\mathbb{N}} $\n",
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"$ \\def\\ZZ{\\mathbb{Z}} $\n",
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"$ \\def\\QQ{\\mathbb{Q}} $\n",
@@ -18,7 +20,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Tutorial: start here!"
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"# Start here!"
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]
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},
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{
@@ -278,48 +280,97 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Algebra\n",
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"\n",
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"\n",
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" sage: factor(x^100 - 1)\n",
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"\n",
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"sage: p = 54*x^4+36*x^3-102*x^2-72*x-12\n",
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"sage: p.factor()\n",
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"6*(x^2 - 2)*(3*x + 1)^2\n",
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"\n",
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"sage: for K in [ZZ, QQ, ComplexField(16), QQ[sqrt(2)], GF(5)]:\n",
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"….: print K, “:”; print K[‘x’](p).factor()\n",
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"Integer Ring :\n",
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"2 * 3 * (3*x + 1)^2 * (x^2 - 2)\n",
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"Rational Field :\n",
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"(54) * (x + 1/3)^2 * (x^2 - 2)\n",
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"Complex Field with 16 bits of precision :\n",
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"(54.00) * (x - 1.414) * (x + 0.3333)^2 * (x + 1.414)\n",
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"Number Field in sqrt2 with defining polynomial x^2 - 2 :\n",
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"(54) * (x - sqrt2) * (x + sqrt2) * (x + 1/3)^2\n",
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"Finite Field of size 5 :\n",
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"(4) * (x + 2)^2 * (x^2 + 3)\n",
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"\n",
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"sage: ZZ.category()\n",
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"Category of euclidean domains\n",
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"\n",
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"sage: sorted( ZZ.category().axioms() )\n",
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"[‘AdditiveAssociative’, ‘AdditiveCommutative’, ‘AdditiveInverse’, ‘AdditiveUnital’,\n",
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"\n",
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"‘Associative’, ‘Commutative’,\n",
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"‘Distributive’, ‘NoZeroDivisors’, ‘Unital’]\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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" ‘Associative’, ‘Commutative’,\n",
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"‘Distributive’, ‘NoZeroDivisors’, ‘Unital’]"
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"### Algebra"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"factor(x^100 - 1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"6*(x^2 - 2)*(3*x + 1)^2\n"
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]
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}
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],
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"source": [
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"p = 54*x^4+36*x^3-102*x^2-72*x-12\n",
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"p.factor()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Integer Ring :\n",
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"2 * 3 * (3*x + 1)^2 * (x^2 - 2)\n",
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"Rational Field :\n",
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"(54) * (x + 1/3)^2 * (x^2 - 2)\n",
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"Complex Field with 16 bits of precision :\n",
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"(54.00) * (x - 1.414) * (x + 0.3333)^2 * (x + 1.414)\n",
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"Number Field in sqrt2 with defining polynomial x^2 - 2 :\n",
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"(54) * (x - sqrt2) * (x + sqrt2) * (x + 1/3)^2\n",
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"Finite Field of size 5 :\n",
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"(4) * (x + 2)^2 * (x^2 + 3)\n"
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]
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}
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],
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"source": [
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"for K in [ZZ, QQ, ComplexField(16), QQ[sqrt(2)], GF(5)]:\n",
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" print K, \":\"; print K['x'](p).factor()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Category of euclidean domains\n"
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]
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}
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],
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"source": [
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"ZZ.category()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"['AdditiveAssociative', 'AdditiveCommutative', 'AdditiveInverse', 'AdditiveUnital',\n",
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" 'Associative', 'Commutative',\n",
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" 'Distributive', 'NoZeroDivisors', 'Unital']"
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]
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}
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],
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"source": [
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"sorted( ZZ.category().axioms() )"
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]
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},
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{
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}
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],
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"source": [
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"Suit = Set([\"Coeur\", \"Carreau\", \"Pique\", \"Trefle\"])\n",
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"Values = Set([2, 3, 4, 5, 6, 7, 8, 9, 10, \"Valet\", \"Dame\", \"Roi\", \"As\"])\n",
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"Suits = Set([\"Hearts\", \"Diamonds\", \"Spades\", \"Clubs\"])\n",
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"Values = Set([2, 3, 4, 5, 6, 7, 8, 9, 10, \"Jack\", \"Queen\", \"King\", \"Ace\"])\n",
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"Cards = cartesian_product([Values, Suits])\n",
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"Hands = Subsets(Cartes, 5)\n",
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"Hands = Subsets(Cards, 5)\n",
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"Hands.random_element()"
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]
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},
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}
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],
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"source": [
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"Mains.cardinality()"
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"Hands.cardinality()"
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]
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},
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{
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"metadata": {},
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"outputs": [],
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"source": [
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"L = RootSystem([\"G\",2,1]).ambient_space()\n",
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"L = RootSystem([\"G\", 2, 1]).ambient_space()\n",
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"p = L.plot(affine=False, level=1)\n",
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"p.show(aspect_ratio=[1,1,2], frame=False)"
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"p.show(aspect_ratio=[1, 1, 2], frame=False)"
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]
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},
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{
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"outputs": [],
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"source": [
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"E = EllipticCurve('389a')\n",
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"plot(E,thickness=3)"
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"plot(E, thickness=3)"
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]
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},
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{
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"- Ask Sage: [https://ask.sagemath.org](https://ask.sagemath.org) \n",
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"- Bug Tracker: [https://trac.sagemath.org](https://trac.sagemath.org) \n",
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"- The open book [Computational Mathematics with Sage](http://sagebook.gforge.inria.fr/english.html)\n",
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" (originally written in $ French <http://sagebook.gforge.inria.fr/> $; also translated in $ German <http://www.loria.fr/~zimmerma/sagebook/CalculDeutsch.pdf/> $) \n",
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"- [Sage’s main tutorial](http://doc.sagemath.org/html/en/tutorial/index.html#tutorial) \n",
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" (originally written in [French](http://sagebook.gforge.inria.fr/); also translated in $ German <http://www.loria.fr/~zimmerma/sagebook/CalculDeutsch.pdf/> $) \n",
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"- :ref:`Sage's main tutorial <tutorial>`_ \n",
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"- [Sage’s official thematic tutorials](https://doc.sagemath.org/html/en/thematic_tutorials/index.html) \n",
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"- [More Sage tutorials](https://more-sagemath-tutorials.readthedocs.io/) \n",
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"- [Sage’s quick reference cards](https://wiki.sagemath.org/quickref) "

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