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mathmaker
0.6(alpha)
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00001 # -*- coding: utf-8 -*- 00002 00003 # Mathmaker creates automatically maths exercises sheets 00004 # with their answers 00005 # Copyright 2006-2014 Nicolas Hainaux <nico_h@users.sourceforge.net> 00006 00007 # This file is part of Mathmaker. 00008 00009 # Mathmaker is free software; you can redistribute it and/or modify 00010 # it under the terms of the GNU General Public License as published by 00011 # the Free Software Foundation; either version 3 of the License, or 00012 # any later version. 00013 00014 # Mathmaker is distributed in the hope that it will be useful, 00015 # but WITHOUT ANY WARRANTY; without even the implied warranty of 00016 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 00017 # GNU General Public License for more details. 00018 00019 # You should have received a copy of the GNU General Public License 00020 # along with Mathmaker; if not, write to the Free Software 00021 # Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA 00022 00023 import os 00024 import sys 00025 00026 from lib.common import latex 00027 00028 from core import * 00029 from core.base_calculus import * 00030 from core.calculus import * 00031 00032 from maintenance.autotest import common 00033 00034 check = common.check 00035 00036 00037 def action(): 00038 if common.verbose: 00039 os.write(common.output, bytes("--- --- EXPANSION & REDUCTION\n", 'utf-8')) 00040 00041 expd_2_times_sum_of_1_and_5x = Expandable((Item(2), 00042 Sum([Item(1), 00043 Monomial((5, 1)) 00044 ]) 00045 )) 00046 00047 expd_1_minus_11x_times_11_plus_7x = Expandable((Sum([Item(1), 00048 Monomial((-11, 1)) 00049 ]), 00050 Sum([Item(11), 00051 Monomial((7, 1)) 00052 ]) 00053 )) 00054 00055 expd_3x_minus_sum_xplus3_times_sum_6minus2x = \ 00056 Sum([Monomial((3, 1)), 00057 Expandable((Item(-1), 00058 Expandable((Sum([Item('x'), Item(3)]), 00059 Sum([Item(6), Monomial((2, 1))]) \ 00060 )) 00061 )) 00062 ]) 00063 00064 expd_minus1_times_sum_3x_minus_2 = Expandable((Item(-1), 00065 Sum([Monomial((3, 1)), 00066 Item(-2) 00067 ]) 00068 )) 00069 red_1 = Sum([Product([Item(-3), Item(10)]), 00070 Product([Monomial(('-', 10, 1)), Monomial(('-', 9, 1))]), 00071 Product([Monomial(('+', 7, 1)), Monomial(('+', 8, 1))]), 00072 Product([Item(8), Item(10)]) 00073 ]) 00074 00075 red_2 = Product([Sum([Item(146)]), Item(('+', "x", 2))]) 00076 00077 # -2×(-6) - 1 + 3 × (-x) - 8x × (-3) 00078 red_3 = Sum([Product([Item(-2), Item(-6)]), 00079 Item(-1), 00080 Product([Item(3), Item(('-', "x", 1))]), 00081 Product([Monomial(('-', 8, 1)), Item(-3)]) 00082 ]) 00083 00084 # 5x + 7x × 8x + 5x × (-1) + 7×8 00085 red_4 = Sum([Monomial(('+', 5, 1)), 00086 Product([Monomial(('+', 7, 1)), Monomial(('+', 8, 1))]), 00087 Product([Monomial(('+', 5, 1)), Item(-1)]), 00088 Product([Item(7), Item(8)]) 00089 ]) 00090 00091 # -30 + 80 + x² 00092 red_5 = Sum([Item(-30), Item(80), Monomial(('+', 1, 2))]) 00093 00094 # 4x + (-15x + 8 - 5x) 00095 red_6 = Sum([Monomial(('+', 4, 1)), 00096 Expandable((Monomial(('+', 1, 0)), 00097 Polynomial([Monomial(('-', 15, 1)), 00098 Monomial(('+', 8, 0)), 00099 Monomial(('-', 5, 1)) 00100 ]) 00101 )) 00102 ]) 00103 00104 # (3+3x)(3-3x) 00105 red_7 = BinomialIdentity((Item(3), 00106 Monomial(('+', 3, 1)) 00107 ), 00108 squares_difference='OK') 00109 00110 # (1 - 10x)(1 + 10x) 00111 red_8 = BinomialIdentity((Item(1), 00112 Monomial(('+', 10, 1)) 00113 ), 00114 squares_difference='OK') 00115 00116 # -2 -x + 8x² + x 00117 red_9 = Sum([Item(-2), 00118 Monomial(('-', 1, 1)), 00119 Monomial(('+', 8, 2)), 00120 Monomial(('+', 1, 1)) 00121 ]) 00122 00123 # -15 + (10 + 14x - 10x²) 00124 red_10 = Sum([Monomial((-15, 0)), 00125 Expandable((Item(1), 00126 Sum([Item(10), 00127 Monomial((14, 1)), 00128 Monomial(('-', 10, 2)) 00129 ]) 00130 )) 00131 ]) 00132 00133 # -(2x+9)(-3x-7)+4(-3x+9)+13 00134 red_11 = Sum([Expandable((Monomial(('-', 1, 0)), 00135 Expandable((Sum([Monomial((2, 1)), 00136 Monomial((9, 0)) 00137 ]), 00138 Sum([Monomial((-3, 1)), 00139 Monomial((-7, 0)) 00140 ]) 00141 )) 00142 )), 00143 Expandable((Monomial((4, 0)), 00144 Sum([Monomial((-3, 1)), 00145 Monomial((9, 0)) 00146 ]) 00147 )), 00148 Monomial((13, 0)) 00149 ]) 00150 00151 00152 dev_1 = Sum([Expandable((Monomial(('+', 7, 0)), 00153 Sum([Monomial(('-', 6, 1)), 00154 Monomial((6, 0)) 00155 ]) 00156 )), 00157 BinomialIdentity((Monomial(('-', 10, 1)), 00158 Monomial(('-', 3, 0)) 00159 ), 00160 difference_square='OK' 00161 ) 00162 ]) 00163 00164 00165 00166 00167 00168 00169 expr_1 = Expression("A", expd_2_times_sum_of_1_and_5x) 00170 check(expr_1.auto_expansion_and_reduction(), 00171 [ "$A=2(1+5x)$\\newline $A=2\\times 1+2\\times 5x$\\newline " \ 00172 + "$A=2+10x$\\newline "]) 00173 00174 expr_2 = Expression("B", expd_1_minus_11x_times_11_plus_7x) 00175 check(expr_2.auto_expansion_and_reduction(), 00176 [ "$B=(1-11x)(11+7x)$\\newline $B=1\\times 11+1\\times 7x-11x\\times"\ 00177 + " 11-11x\\times 7x$\\newline $B=11+7x-121x-77x^{2}$\\newline " \ 00178 + "$B=11+(7-121)x-77x^{2}$\\newline $B=11-114x-77x^{2}$\\newline "]) 00179 00180 expr_3 = Expression("C", expd_3x_minus_sum_xplus3_times_sum_6minus2x) 00181 check(expr_3.auto_expansion_and_reduction(), 00182 [ "$C=3x-(x+3)(6+2x)$\\newline " \ 00183 + "$C=3x-(x\\times 6+x\\times 2x+3\\times 6+3\\times 2x)$\\newline "\ 00184 + "$C=3x-(6x+2x^{2}+18+6x)$\\newline " \ 00185 + "$C=3x-6x-2x^{2}-18-6x$\\newline " \ 00186 + "$C=(3-6-6)x-2x^{2}-18$\\newline " \ 00187 + "$C=-9x-2x^{2}-18$\\newline "]) 00188 00189 expr_4 = Expression("D", expd_minus1_times_sum_3x_minus_2) 00190 check(expr_4.auto_expansion_and_reduction(), 00191 [ "$D=-(3x-2)$\\newline " \ 00192 + "$D=-3x+2$\\newline "]) 00193 00194 expr_5 = Expression("E", red_1) 00195 check(expr_5.auto_expansion_and_reduction(), 00196 [ "$E=-3\\times 10-10x\\times (-9x)+7x\\times 8x+8\\times 10" \ 00197 + "$\\newline $E=-30+90x^{2}+56x^{2}+80$\\newline " \ 00198 + "$E=-30+80+(90+56)x^{2}$\\newline $E=50+146x^{2}$\\newline "]) 00199 00200 check(red_2.expand_and_reduce_next_step(), 00201 ["None"]) 00202 00203 expr_6 = Expression("F", red_3) 00204 check(expr_6.auto_expansion_and_reduction(), 00205 [ "$F=-2\\times (-6)-1+3\\times (-x)-8x\\times (-3)$\\newline " \ 00206 + "$F=12-1-3x+24x$\\newline " \ 00207 + "$F=11+(-3+24)x$\\newline " \ 00208 + "$F=11+21x$\\newline "]) 00209 00210 00211 # 5x + 7x × 8x + 5x × (-1) + 7×8 00212 expr_7 = Expression("G", red_4) 00213 check(expr_7.auto_expansion_and_reduction(), 00214 [ "$G=5x+7x\\times 8x+5x\\times (-1)+7\\times 8$\\newline " \ 00215 + "$G=5x+56x^{2}-5x+56$\\newline " \ 00216 + "$G=(5-5)x+56x^{2}+56$\\newline " \ 00217 + "$G=0x+56x^{2}+56$\\newline " \ 00218 + "$G=56x^{2}+56$\\newline "]) 00219 00220 00221 expr_8 = Expression("H", red_5) 00222 check(expr_8.auto_expansion_and_reduction(), 00223 [ "$H=-30+80+x^{2}$\\newline " \ 00224 + "$H=50+x^{2}$\\newline "]) 00225 00226 expr_9 = Expression("I", red_6) 00227 check(expr_9.auto_expansion_and_reduction(), 00228 [ "$I=4x+(-15x+8-5x)$\\newline " \ 00229 + "$I=4x-15x+8-5x$\\newline " \ 00230 + "$I=(4-15-5)x+8$\\newline " \ 00231 + "$I=-16x+8$\\newline "]) 00232 00233 expr_10 = Expression("J", red_7) 00234 check(expr_10.auto_expansion_and_reduction(), 00235 [ "$J=(3+3x)(3-3x)$\\newline " \ 00236 + "$J=3^{2}-(3x)^{2}$\\newline " \ 00237 + "$J=9-9x^{2}$\\newline "]) 00238 00239 expr_11 = Expression("K", red_8) 00240 check(expr_11.auto_expansion_and_reduction(), 00241 [ "$K=(1+10x)(1-10x)$\\newline " \ 00242 + "$K=1^{2}-(10x)^{2}$\\newline " \ 00243 + "$K=1-100x^{2}$\\newline "]) 00244 00245 expr_12 = Expression("L", red_9) 00246 check(expr_12.auto_expansion_and_reduction(), 00247 [ "$L=-2-x+8x^{2}+x$\\newline " \ 00248 + "$L=-2+(-1+1)x+8x^{2}$\\newline " \ 00249 + "$L=-2+0x+8x^{2}$\\newline " \ 00250 + "$L=-2+8x^{2}$\\newline "]) 00251 00252 expr_13 = Expression("M", red_10) 00253 check(expr_13.auto_expansion_and_reduction(), 00254 [ "$M=-15+(10+14x-10x^{2})$\\newline " \ 00255 + "$M=-15+10+14x-10x^{2}$\\newline " \ 00256 + "$M=-5+14x-10x^{2}$\\newline "]) 00257 00258 # -(2x+9)(-3x-7)+4(-3x+9)+13 00259 expr_14 = Expression("N", red_11) 00260 check(expr_14.auto_expansion_and_reduction(), 00261 [ "$N=-(2x+9)(-3x-7)+4(-3x+9)+13$\\newline " \ 00262 + "$N=-(2x\\times (-3x)+2x\\times (-7)+9\\times (-3x)" \ 00263 + "+9\\times (-7))+4\\times (-3x)+4\\times 9+13$\\newline " \ 00264 + "$N=-(-6x^{2}-14x-27x-63)-12x+36+13$\\newline " \ 00265 + "$N=6x^{2}+14x+27x+63-12x+49$\\newline " \ 00266 + "$N=6x^{2}+(14+27-12)x+63+49$\\newline " \ 00267 + "$N=6x^{2}+29x+112$\\newline "]) 00268 00269 # 7(-6x + 6) + (-10x - 3)² 00270 expr_15 = Expression("P", dev_1) 00271 check(expr_15.auto_expansion_and_reduction(), 00272 [ "$P=7(-6x+6)+(-10x-3)^{2}$\\newline " \ 00273 + "$P=7\\times (-6x)+7\\times 6+(-10x)^{2}-2\\times (-10x)\\times 3"\ 00274 + "+3^{2}$\\newline "\ 00275 + "$P=-42x+42+100x^{2}+60x+9$\\newline "\ 00276 + "$P=(-42+60)x+42+9+100x^{2}$\\newline "\ 00277 + "$P=18x+51+100x^{2}$\\newline " 00278 ]) 00279 00280 00281 00282
1.7.6.1