|
| 1 | +{ |
| 2 | + "cell_id": 3391536610896426838, |
| 3 | + "cells": [ |
| 4 | + { |
| 5 | + "cell_id": 9970128145502107243, |
| 6 | + "cell_origin": "client", |
| 7 | + "cell_type": "latex", |
| 8 | + "cells": [ |
| 9 | + { |
| 10 | + "cell_id": 16204355368752002978, |
| 11 | + "cell_origin": "client", |
| 12 | + "cell_type": "latex_view", |
| 13 | + "source": "This notebook illustrates how the automatic multi-term simplification algorithm \\algo{meld} can\nbe used in a \\verb|post_process| function to simplify expressions immediately." |
| 14 | + } |
| 15 | + ], |
| 16 | + "hidden": true, |
| 17 | + "source": "This notebook illustrates how the automatic multi-term simplification algorithm \\algo{meld} can\nbe used in a \\verb|post_process| function to simplify expressions immediately." |
| 18 | + }, |
| 19 | + { |
| 20 | + "cell_id": 16589852709921553693, |
| 21 | + "cell_origin": "client", |
| 22 | + "cell_type": "input", |
| 23 | + "source": "def post_process(ex):\n meld(ex)\n collect_terms(ex)" |
| 24 | + }, |
| 25 | + { |
| 26 | + "cell_id": 1137909878511905740, |
| 27 | + "cell_origin": "client", |
| 28 | + "cell_type": "input", |
| 29 | + "cells": [ |
| 30 | + { |
| 31 | + "cell_id": 3984991681506874828, |
| 32 | + "cell_origin": "server", |
| 33 | + "cell_type": "latex_view", |
| 34 | + "source": "\\begin{dmath*}{}\\text{Property TableauSymmetry attached to~}R_{a b c d}.\\end{dmath*}" |
| 35 | + } |
| 36 | + ], |
| 37 | + "source": "R_{a b c d}::RiemannTensor;" |
| 38 | + }, |
| 39 | + { |
| 40 | + "cell_id": 10442559150589961051, |
| 41 | + "cell_origin": "client", |
| 42 | + "cell_type": "input", |
| 43 | + "cells": [ |
| 44 | + { |
| 45 | + "cell_id": 16272566471204925814, |
| 46 | + "cell_origin": "server", |
| 47 | + "cell_type": "latex_view", |
| 48 | + "cells": [ |
| 49 | + { |
| 50 | + "cell_id": 1708705026185000243, |
| 51 | + "cell_origin": "server", |
| 52 | + "cell_type": "input_form", |
| 53 | + "source": "R_{a b c d} + R_{b c a d} + R_{c a b d}" |
| 54 | + } |
| 55 | + ], |
| 56 | + "source": "\\begin{dmath*}{}R_{a b c d}+R_{b c a d}+R_{c a b d}\\end{dmath*}" |
| 57 | + } |
| 58 | + ], |
| 59 | + "source": "ex:=R_{a b c d} + R_{b c a d} + R_{c a b d};" |
| 60 | + }, |
| 61 | + { |
| 62 | + "cell_id": 17665426107502293019, |
| 63 | + "cell_origin": "client", |
| 64 | + "cell_type": "input", |
| 65 | + "cells": [ |
| 66 | + { |
| 67 | + "cell_id": 4864102099047927703, |
| 68 | + "cell_origin": "server", |
| 69 | + "cell_type": "latex_view", |
| 70 | + "source": "\\begin{dmath*}{}\\text{Property AntiSymmetric attached to~}A^{a b c}.\\end{dmath*}" |
| 71 | + } |
| 72 | + ], |
| 73 | + "source": "A^{a b c}::AntiSymmetric;" |
| 74 | + }, |
| 75 | + { |
| 76 | + "cell_id": 11231869119195730671, |
| 77 | + "cell_origin": "client", |
| 78 | + "cell_type": "input", |
| 79 | + "cells": [ |
| 80 | + { |
| 81 | + "cell_id": 775906003630772013, |
| 82 | + "cell_origin": "server", |
| 83 | + "cell_type": "latex_view", |
| 84 | + "source": "\\begin{dmath*}{}\\text{Property Symmetric attached to~}S_{a b c}.\\end{dmath*}" |
| 85 | + } |
| 86 | + ], |
| 87 | + "source": "S_{a b c}::Symmetric;" |
| 88 | + }, |
| 89 | + { |
| 90 | + "cell_id": 15440997254477550604, |
| 91 | + "cell_origin": "client", |
| 92 | + "cell_type": "input", |
| 93 | + "cells": [ |
| 94 | + { |
| 95 | + "cell_id": 228473189702070848, |
| 96 | + "cell_origin": "server", |
| 97 | + "cell_type": "latex_view", |
| 98 | + "cells": [ |
| 99 | + { |
| 100 | + "cell_id": 9500934661811827513, |
| 101 | + "cell_origin": "server", |
| 102 | + "cell_type": "input_form", |
| 103 | + "source": "R_{a b c d} A^{a b c}" |
| 104 | + } |
| 105 | + ], |
| 106 | + "source": "\\begin{dmath*}{}R_{a b c d} A^{a b c}\\end{dmath*}" |
| 107 | + } |
| 108 | + ], |
| 109 | + "source": "ex:=R_{a b c d} A^{a b c};" |
| 110 | + }, |
| 111 | + { |
| 112 | + "cell_id": 6001193804290926265, |
| 113 | + "cell_origin": "client", |
| 114 | + "cell_type": "input", |
| 115 | + "cells": [ |
| 116 | + { |
| 117 | + "cell_id": 16452054599630373227, |
| 118 | + "cell_origin": "server", |
| 119 | + "cell_type": "latex_view", |
| 120 | + "cells": [ |
| 121 | + { |
| 122 | + "cell_id": 17144787782815941213, |
| 123 | + "cell_origin": "server", |
| 124 | + "cell_type": "input_form", |
| 125 | + "source": "(A^{a b c} + A^{c a b}) S_{a b c}" |
| 126 | + } |
| 127 | + ], |
| 128 | + "source": "\\begin{dmath*}{}\\left(A^{a b c}+A^{c a b}\\right) S_{a b c}\\end{dmath*}" |
| 129 | + } |
| 130 | + ], |
| 131 | + "source": "ex:= (A^{a b c} + A^{c a b}) S_{a b c};" |
| 132 | + }, |
| 133 | + { |
| 134 | + "cell_id": 14929753163657422384, |
| 135 | + "cell_origin": "client", |
| 136 | + "cell_type": "input", |
| 137 | + "cells": [ |
| 138 | + { |
| 139 | + "cell_id": 1137671033037866650, |
| 140 | + "cell_origin": "server", |
| 141 | + "cell_type": "latex_view", |
| 142 | + "cells": [ |
| 143 | + { |
| 144 | + "cell_id": 1039654011058708309, |
| 145 | + "cell_origin": "server", |
| 146 | + "cell_type": "input_form", |
| 147 | + "source": "2A^{a b c} S_{a b c}" |
| 148 | + } |
| 149 | + ], |
| 150 | + "source": "\\begin{dmath*}{}2A^{a b c} S_{a b c}\\end{dmath*}" |
| 151 | + } |
| 152 | + ], |
| 153 | + "source": "meld(ex, repeat=True);" |
| 154 | + }, |
| 155 | + { |
| 156 | + "cell_id": 10182337157813236277, |
| 157 | + "cell_origin": "client", |
| 158 | + "cell_type": "input", |
| 159 | + "cells": [ |
| 160 | + { |
| 161 | + "cell_id": 16001156654425651111, |
| 162 | + "cell_origin": "server", |
| 163 | + "cell_type": "latex_view", |
| 164 | + "cells": [ |
| 165 | + { |
| 166 | + "cell_id": 15399389374269644662, |
| 167 | + "cell_origin": "server", |
| 168 | + "cell_type": "input_form", |
| 169 | + "source": "(a-b) A^{a b c}" |
| 170 | + } |
| 171 | + ], |
| 172 | + "source": "\\begin{dmath*}{}\\left(a-b\\right) A^{a b c}\\end{dmath*}" |
| 173 | + } |
| 174 | + ], |
| 175 | + "source": "ex:= a A^{a b c} + b A^{b a c};" |
| 176 | + }, |
| 177 | + { |
| 178 | + "cell_id": 2655562479605535632, |
| 179 | + "cell_origin": "client", |
| 180 | + "cell_type": "input", |
| 181 | + "cells": [ |
| 182 | + { |
| 183 | + "cell_id": 3165433391968790005, |
| 184 | + "cell_origin": "server", |
| 185 | + "cell_type": "latex_view", |
| 186 | + "cells": [ |
| 187 | + { |
| 188 | + "cell_id": 14527276633063001349, |
| 189 | + "cell_origin": "server", |
| 190 | + "cell_type": "input_form", |
| 191 | + "source": " 3/2 R_{a b c d} R_{a b c d}" |
| 192 | + } |
| 193 | + ], |
| 194 | + "source": "\\begin{dmath*}{}\\frac{3}{2}R_{a b c d} R_{a b c d}\\end{dmath*}" |
| 195 | + } |
| 196 | + ], |
| 197 | + "source": "ex:=R_{a b c d} R_{a b c d} + R_{a b c d} R_{a c b d};" |
| 198 | + }, |
| 199 | + { |
| 200 | + "cell_id": 12588425984072827898, |
| 201 | + "cell_origin": "client", |
| 202 | + "cell_type": "input", |
| 203 | + "source": "" |
| 204 | + } |
| 205 | + ], |
| 206 | + "description": "Cadabra JSON notebook format", |
| 207 | + "version": 1.0 |
| 208 | +} |
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