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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 import decimal 00027 00028 from core import * 00029 from core.base_calculus import * 00030 00031 from maintenance.autotest import common 00032 00033 check = common.check 00034 00035 00036 def action(): 00037 if common.verbose: 00038 os.write(common.output, bytes("--- PRODUCTS\n", 'utf-8')) 00039 00040 item_1 = Item(1) 00041 item_minus_1 = Item(-1) 00042 item_a = Item('a') 00043 item_b = Item('b') 00044 00045 product_minus_a = Product([Item("-a")]) 00046 product_minus_a_bis = Product([Item(('+', "-a", 1))]) 00047 product_1_times_1 = Product([item_1, item_1]) 00048 product_1_times_1_times_a = Product([item_1, item_1, item_a]) 00049 product_2_times_minus_2 = Product([Item(2), Item(-2)]) 00050 product_minus_2_times_2 = Product([Item(-2), Item(2)]) 00051 00052 product_8_times_minus_6 = Product([Monomial((8, 0)), Monomial((-6, 0))]) 00053 00054 product_2_times_a_times_b = Product([Item(2), item_a, item_b]) 00055 product_1_times_minus_1 = Product([item_1, item_minus_1]) 00056 product_1_times_minus_b_times_1_times_4 = Product([item_1, 00057 Item('-b'), 00058 item_1, 00059 Item(4)]) 00060 product_minus_1_times_minus_4 = Product([Item(-1), Item(-4)]) 00061 00062 product_minus_1_times_4 = Product([Item(-1), Item(4)]) 00063 00064 product_minus_1_times_1_times_1_times_1 = Product([Item(-1), 00065 Item(1), 00066 Item(1), 00067 Item(1)]) 00068 00069 product_a_times_minus_b = Product([Item('a'), (Item('-b'))]) 00070 product_a_times_minus_b.set_compact_display(False) 00071 00072 product_a_times_ebd_minus_b = Product([Item('a'), 00073 Item(('+', "-b", 1)) 00074 ]) 00075 00076 product_a_times_ebd_minus_b.set_compact_display(False) 00077 00078 product_2_times_1 = Product([Item(2), (Item(1))]) 00079 product_2_times_1.set_compact_display(False) 00080 00081 product_1_times_7x = Product([Item(1), (Monomial((7, 1)))]) 00082 product_1_times_7x.set_compact_display(False) 00083 00084 product_minus_1_squared = Product(Item(-1)) 00085 product_minus_1_squared.set_exponent(2) 00086 00087 product_minus_3_times_minus_5_exponent_squared_minus_1 = \ 00088 Product([Item(-3), 00089 Item(-5)]) 00090 00091 product_minus_3_times_minus_5_exponent_squared_minus_1.set_exponent( 00092 Item(('+', 00093 -1, 00094 2 00095 )) 00096 ) 00097 00098 product_4_times_product_minus_2_times_7 = Product([Item(4), 00099 Product([Item(-2), 00100 Item(7)]) 00101 ]) 00102 00103 product_4_times_product_minus_2_times_7_BIS = Product([Item(4), 00104 Product([Item(-2), 00105 Item(7) 00106 ]) 00107 ]) 00108 00109 squared_product_minus_2_times_7 = Product([Item(-2), Item(7)]) 00110 squared_product_minus_2_times_7.set_exponent(2) 00111 00112 product_4_times_squared_product_minus_2_times_7 = Product([Item(4), 00113 squared_product_minus_2_times_7]) 00114 00115 sum_4_plus_2 = Sum([Item(4), Item(2)]) 00116 product_7_times_sum_4_plus_2 = Product([Item(7), sum_4_plus_2]) 00117 product_minus_1_times_sum_4_plus_2 = Product([Item(-1), sum_4_plus_2]) 00118 00119 product_sum_1_plus_2 = Product([Sum([1, 2])]) 00120 00121 product_1_by_sum_3_plus_4 = Product([1, Sum([3, 4])]) 00122 00123 product_sum_3_plus_4_by_1 = Product([Sum([3, 4]), 1]) 00124 00125 product_rubbish = Product([Item(('+', 1, 1)), 00126 Item(('+', "x", 1))]) 00127 00128 product_monom0_times_monom0 = Product([Monomial((7,0)), 00129 (Monomial((8,0))) ]) 00130 product_monom0_times_monom0.set_compact_display(False) 00131 00132 product_sum_3_plus_4_times_monom_minus8x = Product([Sum([Item(3), 00133 Item(4)]), 00134 Monomial((-8, 1))]) 00135 00136 product_4x_times_minus3x = Product([Monomial((4, 1)), 00137 Monomial((-3, 1))]) 00138 00139 product_nc_monomials_4_times_minus3 = Product([Monomial((4, 0)), 00140 Monomial((-3, 0))]) 00141 00142 product_nc_monomials_4_times_minus3.set_compact_display(False) 00143 00144 square_product_monom_6 = Product(Monomial(('+', 6, 0))) 00145 square_product_monom_6.set_exponent(2) 00146 00147 square_product_square_item_6 = Product(Item(('+', 6, 2))) 00148 square_product_square_item_6.set_exponent(2) 00149 00150 square_product_monom_x = Product(Monomial(('+', 1, 1))) 00151 square_product_monom_x.set_exponent(2) 00152 00153 square_product_square_item_x = Product(Item(('+', 'x', 2))) 00154 square_product_square_item_x.set_exponent(2) 00155 00156 product_minus1_fraction_2over3_fraction_3over4 = Product([Item(-1), 00157 Fraction(('+', 00158 2, 00159 3)), 00160 Fraction(('+', 00161 3, 00162 4)) 00163 ]) 00164 00165 product_fraction_6over2_times_fraction_8overminus5 = \ 00166 Product([Fraction(('+', 6, 2)), 00167 Fraction(('+', 8, -5))]) 00168 00169 product_fraction_minus3overminus2_times_fraction_minus1over5 = \ 00170 Product([Fraction(('+', -3, -2)), 00171 Fraction(('+', -1, 5))]) 00172 00173 product_3timesminusx = Product([Item(3), Item(('-', "x"))]) 00174 00175 product_0timesx = Product([Item(0), Item("x")]) 00176 00177 product_1square = Product(Item(1)) 00178 product_1square.set_exponent(2) 00179 00180 product_monom_minus1_times_minus7x = Product([Item(-1), 00181 Product([ 00182 Monomial(('-', 7, 1)) 00183 ]) 00184 ]) 00185 product_monom_minus1_times_minus7x.set_compact_display(False) 00186 00187 temp = Product([Item(('-', "a")), 00188 Item(('+', "b")) 00189 ]) 00190 product_7_times_product_minusa_minusb = Product([Item(7), 00191 temp 00192 ]) 00193 00194 temp.set_compact_display(False) 00195 product_7_times_product_minusa_minusb_BIS \ 00196 = Product([Item(7), 00197 temp 00198 ]) 00199 00200 temp = Product([Item(-2), 00201 Item(7), 00202 Item('a'), 00203 Item('b') 00204 ]) 00205 product_9_times_minus2_times_7ab = Product([ Item(9), 00206 Product([Item(-2), 00207 Item(7), 00208 Item('a'), 00209 Item('b') 00210 ]) 00211 ]) 00212 00213 temp.set_compact_display(False) 00214 product_9_times_minus2_times_7ab_BIS = Product([ Item(9), 00215 temp 00216 ]) 00217 00218 00219 temp = Product([Item(-2), 00220 Item('a'), 00221 Item(4), 00222 Item('b') 00223 ]) 00224 product_9_times_minus2a_times_4b = Product([ Item(9), 00225 temp 00226 ]) 00227 00228 temp.set_compact_display(False) 00229 product_9_times_minus2a_times_4b_BIS = Product([ Item(9), 00230 temp 00231 ]) 00232 00233 product_sum_minus1_plus_4_times_x = Product([ 00234 Sum([Item(-1), 00235 Item(3) 00236 ]), 00237 Item('x') 00238 ]) 00239 00240 product_9_times_Monomial_minusx = Product([Item(9), 00241 Monomial(('-', 1, 1)) 00242 ]) 00243 00244 product_10_times_minusminus4 = Product([Item(10), 00245 Product([Item(-1), Item(-4)]) 00246 ]) 00247 00248 product_15_times_Monomial_3x = Product([Item(15), 00249 Sum([Item(0), 00250 Monomial(('+', 3, 1)) 00251 ]) 00252 ]) 00253 00254 product_15_times_Monomial_3x_BIS = Product([Item(15), Sum([Item(0), 00255 Monomial(('+', 3, 1)) 00256 ]) 00257 ]) 00258 00259 product_15_times_Monomial_3x_TER = Product([Product([Item(15)]), 00260 Sum([Item(0), 00261 Monomial(('+', 3, 1)) 00262 ]) 00263 ]) 00264 00265 00266 product_sum_2_3x_times_sum_minus4_6x = Product([Sum([Item(2), 00267 Monomial(('+', 3, 1)) 00268 ]), 00269 Sum([Item(-4), 00270 Monomial(('+', 6, 1)) 00271 ]) 00272 ]) 00273 00274 product_item_minus0_times_item_x = Product([Item(('-', 0, 1)), 00275 Item(('+', 'x', 1)) 00276 ]) 00277 00278 00279 00280 00281 #1 00282 check(product_minus_a, 00283 ["-a"]) 00284 00285 check(product_minus_a.is_reducible(), 00286 ["False"]) 00287 00288 check(product_minus_a_bis.is_reducible(), 00289 ["False"]) 00290 00291 check(product_1_times_1, 00292 ["1"]) 00293 00294 #5 00295 check(product_1_times_1.is_reducible(), 00296 ["False"]) 00297 00298 product_1_times_1.set_compact_display(False) 00299 check(product_1_times_1, 00300 ["1\\times 1"]) 00301 00302 check(product_1_times_1_times_a, 00303 ["a"]) 00304 00305 00306 check(product_1_times_1_times_a.is_reducible(), 00307 ["False"]) 00308 00309 check(product_2_times_minus_2, 00310 ["2\\times (-2)"]) 00311 00312 #10 00313 check(product_minus_2_times_2, 00314 ["-2\\times 2"]) 00315 00316 check(product_8_times_minus_6, 00317 ["8\\times (-6)"]) 00318 00319 check(product_2_times_a_times_b, 00320 ["2ab"]) 00321 00322 check(product_2_times_a_times_b.is_reducible(), 00323 ["False"]) 00324 00325 check(product_1_times_minus_1, 00326 ["-1"]) 00327 00328 product_1_times_minus_1.set_compact_display(False) 00329 00330 #15 00331 check(product_1_times_minus_1, 00332 ["1\\times (-1)"]) 00333 00334 check(product_1_times_minus_b_times_1_times_4, 00335 ["-b\\times 4"]) 00336 00337 check(product_1_times_minus_b_times_1_times_4.is_reducible(), 00338 ["True"]) 00339 00340 product_1_times_minus_b_times_1_times_4.set_compact_display(False) 00341 check(product_1_times_minus_b_times_1_times_4, 00342 ["1\\times (-b)\\times 1\\times 4"]) 00343 00344 check(product_minus_1_times_minus_4, 00345 ["-(-4)"]) 00346 00347 #20 00348 check(product_minus_1_times_4, 00349 ["-4"]) 00350 00351 check(product_minus_1_times_minus_4.is_reducible(), 00352 ["True"]) 00353 00354 check(product_minus_1_times_minus_4.evaluate(), 00355 ["4"]) 00356 00357 check(product_minus_1_times_1_times_1_times_1, 00358 ["-1"]) 00359 00360 check(product_minus_1_times_1_times_1_times_1.is_reducible(), 00361 ["False"]) 00362 00363 #25 00364 check(product_a_times_minus_b, 00365 ["a\\times (-b)"]) 00366 00367 check(product_a_times_minus_b.is_reducible(), 00368 ["True"]) 00369 00370 check(product_a_times_ebd_minus_b, 00371 ["a\\times (-b)"]) 00372 00373 check(product_a_times_ebd_minus_b.is_reducible(), 00374 ["True"]) 00375 00376 check(product_2_times_1.is_reducible(), 00377 ["True"]) 00378 00379 #30 00380 check(product_1_times_7x.is_reducible(), 00381 ["True"]) 00382 00383 00384 check(product_minus_1_squared, 00385 ["(-1)^{2}"]) 00386 00387 check(product_minus_1_squared.is_displ_as_a_single_1(), 00388 ["False"]) 00389 00390 check(product_minus_1_squared.is_displ_as_a_single_minus_1(), 00391 ["False"]) 00392 00393 check(product_minus_1_squared.is_reducible(), 00394 ["True"]) 00395 00396 #35 00397 check(product_minus_3_times_minus_5_exponent_squared_minus_1, 00398 ["(-3\\times (-5))^{(-1)^{2}}"]) 00399 00400 check(product_minus_3_times_minus_5_exponent_squared_minus_1.evaluate(), 00401 ["15"]) 00402 00403 check(product_4_times_product_minus_2_times_7, 00404 ["4\\times (-2)\\times 7"]) 00405 00406 check(product_4_times_product_minus_2_times_7_BIS, 00407 ["4\\times (-2)\\times 7"]) 00408 00409 check(product_4_times_product_minus_2_times_7.evaluate(), 00410 ["-56"]) 00411 00412 #40 00413 check(product_4_times_squared_product_minus_2_times_7, 00414 ["4\\times (-2\\times 7)^{2}"]) 00415 00416 check(product_4_times_squared_product_minus_2_times_7.is_reducible(), 00417 ["True"]) 00418 00419 check(product_4_times_squared_product_minus_2_times_7.evaluate(), 00420 ["784"]) 00421 00422 check(product_7_times_sum_4_plus_2, 00423 ["7(4+2)"]) 00424 00425 product_7_times_sum_4_plus_2.set_compact_display(False) 00426 check(product_7_times_sum_4_plus_2, 00427 ["7\\times (4+2)"]) 00428 00429 #45 00430 check(product_7_times_sum_4_plus_2.evaluate(), 00431 ["42"]) 00432 00433 check(product_minus_1_times_sum_4_plus_2, 00434 ["-(4+2)"]) 00435 00436 check(product_minus_1_times_sum_4_plus_2.evaluate(), 00437 ["-6"]) 00438 00439 check(product_sum_1_plus_2, 00440 ["1+2"]) 00441 00442 check(product_1_by_sum_3_plus_4, 00443 ["3+4"]) 00444 00445 #50 00446 check(product_sum_3_plus_4_by_1, 00447 ["3+4"]) 00448 00449 check(product_sum_3_plus_4_by_1.is_reducible(), 00450 ["False"]) 00451 00452 check(product_rubbish, 00453 ["x"]) 00454 00455 check(product_rubbish.is_reducible(), 00456 ["False"]) 00457 00458 check(product_monom0_times_monom0, 00459 ["7\\times 8"]) 00460 00461 #55 00462 check(product_sum_3_plus_4_times_monom_minus8x, 00463 ["(3+4)\\times (-8x)"]) 00464 00465 check(product_4x_times_minus3x, 00466 ["4x\\times (-3x)"]) 00467 00468 check(product_nc_monomials_4_times_minus3, 00469 ["4\\times (-3)"]) 00470 00471 check(square_product_monom_6, 00472 ["6^{2}"]) 00473 00474 check(square_product_square_item_6, 00475 ["(6^{2})^{2}"]) 00476 00477 #60 00478 check(square_product_monom_x, 00479 ["x^{2}"]) 00480 00481 check(square_product_square_item_x, 00482 ["(x^{2})^{2}"]) 00483 00484 check(product_minus1_fraction_2over3_fraction_3over4, 00485 ["-\\frac{2}{3}\\times \\frac{3}{4}"]) 00486 00487 check(product_fraction_6over2_times_fraction_8overminus5, 00488 ["\\frac{6}{2}\\times \\frac{8}{-5}"]) 00489 00490 check( \ 00491 product_fraction_minus3overminus2_times_fraction_minus1over5 00492 .calculate_next_step(), 00493 ["-\\frac{3\\times 1}{2\\times 5}"]) 00494 00495 #65 00496 check(product_3timesminusx, 00497 ["3\\times (-x)"]) 00498 00499 check(product_3timesminusx.is_reducible(), 00500 ["True"]) 00501 00502 check(product_0timesx, 00503 ["0x"]) 00504 00505 check(product_0timesx.is_reducible(), 00506 ["True"]) 00507 00508 check(product_1square.is_displ_as_a_single_1(), 00509 ["False"]) 00510 00511 #70 00512 check(product_1square.is_reducible(), 00513 ["True"]) 00514 00515 00516 check(product_monom_minus1_times_minus7x, 00517 ["-1\\times (-7x)"]) 00518 00519 check(product_7_times_product_minusa_minusb, 00520 ["7\\times (-ab)"]) 00521 00522 check(product_7_times_product_minusa_minusb_BIS, 00523 ["7\\times (-a)\\times b"]) 00524 00525 check(product_9_times_minus2_times_7ab, 00526 ["9\\times (-2)\\times 7ab"]) 00527 00528 #75 00529 check(product_9_times_minus2_times_7ab_BIS, 00530 ["9\\times (-2)\\times 7\\times a\\times b"]) 00531 00532 check(product_9_times_minus2a_times_4b, 00533 ["9\\times (-2a)\\times 4b"]) 00534 00535 check(product_9_times_minus2a_times_4b_BIS, 00536 ["9\\times (-2)\\times a\\times 4\\times b"]) 00537 00538 check(product_sum_minus1_plus_4_times_x, 00539 ["(-1+3)x"]) 00540 00541 check(product_9_times_Monomial_minusx, 00542 ["9\\times (-x)"]) 00543 00544 #80 00545 check(product_10_times_minusminus4, 00546 ["10\\times (-(-4))"]) 00547 00548 check(product_15_times_Monomial_3x, 00549 ["15\\times 3x"]) 00550 00551 check(product_15_times_Monomial_3x_BIS, 00552 ["15\\times 3x"]) 00553 00554 check(product_15_times_Monomial_3x_TER, 00555 ["15\\times 3x"]) 00556 00557 check(product_sum_2_3x_times_sum_minus4_6x.is_reducible(), 00558 ["False"]) 00559 00560 #check(product_item_minus0_times_item_x.is_displ_as_a_single_0(), 00561 # ["True"]) 00562 00563 p = Product([Monomial(('-', 10, 1))]) 00564 p.set_exponent(2) 00565 00566 check(p, 00567 ["(-10x)^{2}"]) 00568 00569 check(p.calculate_next_step(), 00570 ["100x^{2}"]) 00571 00572 fraction_and_item = Product([Fraction((Item(5), Item(7))), 00573 Item(8) 00574 ]) 00575 00576 check(fraction_and_item.calculate_next_step(), 00577 ["\\frac{5\\times 8}{7}"]) 00578 00579 fraction_and_item = Product([Item(8), 00580 Fraction((Item(5), Item(7))) 00581 ]) 00582 00583 check(fraction_and_item.calculate_next_step(), 00584 ["\\frac{8\\times 5}{7}"]) 00585 00586 fractions_and_items = Product([Fraction((Item(3), Item(5))), 00587 Item(8), 00588 Fraction((Item(7), Item(11))), 00589 Item(4), 00590 Fraction((Item(13), Item(17))) 00591 ]) 00592 00593 check(fractions_and_items.calculate_next_step(), 00594 ["\\frac{3\\times 8\\times 7\\times 4\\times 13}"\ 00595 + "{5\\times 11\\times 17}"]) 00596 00597 00598 00599 if common.verbose: 00600 os.write(common.output, bytes("\n--- PRODUCTS - evaluate\n", 'utf-8')) 00601 00602 a = Item(2.5) 00603 b = Item(3.5) 00604 00605 check(isinstance(a.evaluate(), decimal.Decimal), 00606 ["True"]) 00607 00608 c = Product([a, b]).evaluate() 00609 00610 check(isinstance(c, decimal.Decimal), 00611 ["True"]) 00612 00613 check(c, 00614 ["8.75"]) 00615 00616 d = Fraction((Item(3), Item(8))) 00617 00618 check(d.evaluate(), 00619 ["0.375"]) 00620 00621 e = Fraction((Item(3), Item(7))) 00622 00623 check(e.evaluate(), 00624 ["0.4285714285714285714285714286"]) 00625 00626 check(e.evaluate(keep_not_decimal_nb_as_fractions=True), 00627 ["\\frac{3}{7}"]) 00628 00629 f = Product([Fraction((Item(3), Item(7))), 00630 Fraction((Item(7), Item(4)))]) 00631 00632 check(f.evaluate(), 00633 ["0.75"]) 00634 00635 check(f.evaluate(keep_not_decimal_nb_as_fractions=True), 00636 ["0.75"]) 00637 00638 g = Product([Item(6), 00639 Fraction((Item(5), Item(3)))]) 00640 00641 check(g.evaluate(), 00642 ["10"])
1.7.6.1