Solving Equations with Python

[newbieAuggie2019]

Hello Everyone,

I am new to python and I was wondering if we can solve the following equation with python using numpy/scipy libraries:

x = np.arange(4,12,.01)
y = np.arange(0,18,.01)
k = 10/(6+x)

x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))

I tried numpy.roots but unfortunately it seems that for this type of equation using numpy.roots is inappropriate. So I was wondering if you guys have any idea to help me to find roots of this equation.

Hi!

I'm also a newbie, so I got interested by your question. The first part of your program seems to be fine. I made some slight modifications to show clearly the output:

import numpy as np

x = np.arange(4,12,.01)
y = np.arange(0,18,.01)
k = 10/(6+x)

print('\n\nThese are the values for "x":\n\n', x)
print('\n\nThese are the values for "y":\n\n', y)
print('\n\nThese are the values for "k":\n\n', k)

that produces a huge output (200 lines in my Python 3.7.4 Shell for the values of "x", and 267 lines in my Python 3.7.4 Shell for the values of "k"):

Output:
These are the values for "x":

 [ 4.    4.01  4.02  4.03  4.04  4.05  4.06  4.07  4.08  4.09  4.1   4.11
  4.12  4.13  4.14  4.15  4.16  4.17  4.18  4.19  4.2   4.21  4.22  4.23
  4.24  4.25  4.26  4.27  4.28  4.29  4.3   4.31  4.32  4.33  4.34  4.35
  4.36  4.37  4.38  4.39  4.4   4.41  4.42  4.43  4.44  4.45  4.46  4.47
  4.48  4.49  4.5   4.51  4.52  4.53  4.54  4.55  4.56  4.57  4.58  4.59
  4.6   4.61  4.62  4.63  4.64  4.65  4.66  4.67  4.68  4.69  4.7   4.71
  4.72  4.73  4.74  4.75  4.76  4.77  4.78  4.79  4.8   4.81  4.82  4.83
  4.84  4.85  4.86  4.87  4.88  4.89  4.9   4.91  4.92  4.93  4.94  4.95
  4.96  4.97  4.98  4.99  5.    5.01  5.02  5.03  5.04  5.05  5.06  5.07
  5.08  5.09  5.1   5.11  5.12  5.13  5.14  5.15  5.16  5.17  5.18  5.19
  5.2   5.21  5.22  5.23  5.24  5.25  5.26  5.27  5.28  5.29  5.3   5.31
  5.32  5.33  5.34  5.35  5.36  5.37  5.38  5.39  5.4   5.41  5.42  5.43
  5.44  5.45  5.46  5.47  5.48  5.49  5.5   5.51  5.52  5.53  5.54  5.55
  5.56  5.57  5.58  5.59  5.6   5.61  5.62  5.63  5.64  5.65  5.66  5.67
  5.68  5.69  5.7   5.71  5.72  5.73  5.74  5.75  5.76  5.77  5.78  5.79
  5.8   5.81  5.82  5.83  5.84  5.85  5.86  5.87  5.88  5.89  5.9   5.91
  5.92  5.93  5.94  5.95  5.96  5.97  5.98  5.99  6.    6.01  6.02  6.03
  6.04  6.05  6.06  6.07  6.08  6.09  6.1   6.11  6.12  6.13  6.14  6.15
  6.16  6.17  6.18  6.19  6.2   6.21  6.22  6.23  6.24  6.25  6.26  6.27
  6.28  6.29  6.3   6.31  6.32  6.33  6.34  6.35  6.36  6.37  6.38  6.39
  6.4   6.41  6.42  6.43  6.44  6.45  6.46  6.47  6.48  6.49  6.5   6.51
  6.52  6.53  6.54  6.55  6.56  6.57  6.58  6.59  6.6   6.61  6.62  6.63
  6.64  6.65  6.66  6.67  6.68  6.69  6.7   6.71  6.72  6.73  6.74  6.75
  6.76  6.77  6.78  6.79  6.8   6.81  6.82  6.83  6.84  6.85  6.86  6.87
  6.88  6.89  6.9   6.91  6.92  6.93  6.94  6.95  6.96  6.97  6.98  6.99
  7.    7.01  7.02  7.03  7.04  7.05  7.06  7.07  7.08  7.09  7.1   7.11
  7.12  7.13  7.14  7.15  7.16  7.17  7.18  7.19  7.2   7.21  7.22  7.23
  7.24  7.25  7.26  7.27  7.28  7.29  7.3   7.31  7.32  7.33  7.34  7.35
  7.36  7.37  7.38  7.39  7.4   7.41  7.42  7.43  7.44  7.45  7.46  7.47
  7.48  7.49  7.5   7.51  7.52  7.53  7.54  7.55  7.56  7.57  7.58  7.59
  7.6   7.61  7.62  7.63  7.64  7.65  7.66  7.67  7.68  7.69  7.7   7.71
  7.72  7.73  7.74  7.75  7.76  7.77  7.78  7.79  7.8   7.81  7.82  7.83
  7.84  7.85  7.86  7.87  7.88  7.89  7.9   7.91  7.92  7.93  7.94  7.95
  7.96  7.97  7.98  7.99  8.    8.01  8.02  8.03  8.04  8.05  8.06  8.07
  8.08  8.09  8.1   8.11  8.12  8.13  8.14  8.15  8.16  8.17  8.18  8.19
  8.2   8.21  8.22  8.23  8.24  8.25  8.26  8.27  8.28  8.29  8.3   8.31
  8.32  8.33  8.34  8.35  8.36  8.37  8.38  8.39  8.4   8.41  8.42  8.43
  8.44  8.45  8.46  8.47  8.48  8.49  8.5   8.51  8.52  8.53  8.54  8.55
  8.56  8.57  8.58  8.59  8.6   8.61  8.62  8.63  8.64  8.65  8.66  8.67
  8.68  8.69  8.7   8.71  8.72  8.73  8.74  8.75  8.76  8.77  8.78  8.79
  8.8   8.81  8.82  8.83  8.84  8.85  8.86  8.87  8.88  8.89  8.9   8.91
  8.92  8.93  8.94  8.95  8.96  8.97  8.98  8.99  9.    9.01  9.02  9.03
  9.04  9.05  9.06  9.07  9.08  9.09  9.1   9.11  9.12  9.13  9.14  9.15
  9.16  9.17  9.18  9.19  9.2   9.21  9.22  9.23  9.24  9.25  9.26  9.27
  9.28  9.29  9.3   9.31  9.32  9.33  9.34  9.35  9.36  9.37  9.38  9.39
  9.4   9.41  9.42  9.43  9.44  9.45  9.46  9.47  9.48  9.49  9.5   9.51
  9.52  9.53  9.54  9.55  9.56  9.57  9.58  9.59  9.6   9.61  9.62  9.63
  9.64  9.65  9.66  9.67  9.68  9.69  9.7   9.71  9.72  9.73  9.74  9.75
  9.76  9.77  9.78  9.79  9.8   9.81  9.82  9.83  9.84  9.85  9.86  9.87
  9.88  9.89  9.9   9.91  9.92  9.93  9.94  9.95  9.96  9.97  9.98  9.99
 10.   10.01 10.02 10.03 10.04 10.05 10.06 10.07 10.08 10.09 10.1  10.11
 10.12 10.13 10.14 10.15 10.16 10.17 10.18 10.19 10.2  10.21 10.22 10.23
 10.24 10.25 10.26 10.27 10.28 10.29 10.3  10.31 10.32 10.33 10.34 10.35
 10.36 10.37 10.38 10.39 10.4  10.41 10.42 10.43 10.44 10.45 10.46 10.47
 10.48 10.49 10.5  10.51 10.52 10.53 10.54 10.55 10.56 10.57 10.58 10.59
 10.6  10.61 10.62 10.63 10.64 10.65 10.66 10.67 10.68 10.69 10.7  10.71
 10.72 10.73 10.74 10.75 10.76 10.77 10.78 10.79 10.8  10.81 10.82 10.83
 10.84 10.85 10.86 10.87 10.88 10.89 10.9  10.91 10.92 10.93 10.94 10.95
 10.96 10.97 10.98 10.99 11.   11.01 11.02 11.03 11.04 11.05 11.06 11.07
 11.08 11.09 11.1  11.11 11.12 11.13 11.14 11.15 11.16 11.17 11.18 11.19
 11.2  11.21 11.22 11.23 11.24 11.25 11.26 11.27 11.28 11.29 11.3  11.31
 11.32 11.33 11.34 11.35 11.36 11.37 11.38 11.39 11.4  11.41 11.42 11.43
 11.44 11.45 11.46 11.47 11.48 11.49 11.5  11.51 11.52 11.53 11.54 11.55
 11.56 11.57 11.58 11.59 11.6  11.61 11.62 11.63 11.64 11.65 11.66 11.67
 11.68 11.69 11.7  11.71 11.72 11.73 11.74 11.75 11.76 11.77 11.78 11.79
 11.8  11.81 11.82 11.83 11.84 11.85 11.86 11.87 11.88 11.89 11.9  11.91
 11.92 11.93 11.94 11.95 11.96 11.97 11.98 11.99]


These are the values for "y":

 [0.000e+00 1.000e-02 2.000e-02 ... 1.797e+01 1.798e+01 1.799e+01]


These are the values for "k":

 [1.         0.999001   0.99800399 0.99700897 0.99601594 0.99502488
 0.99403579 0.99304866 0.99206349 0.99108028 0.99009901 0.98911968
 0.98814229 0.98716683 0.98619329 0.98522167 0.98425197 0.98328417
 0.98231827 0.98135427 0.98039216 0.97943193 0.97847358 0.97751711
 0.9765625  0.97560976 0.97465887 0.97370983 0.97276265 0.9718173
 0.97087379 0.9699321  0.96899225 0.96805421 0.96711799 0.96618357
 0.96525097 0.96432015 0.96339114 0.96246391 0.96153846 0.96061479
 0.9596929  0.95877277 0.95785441 0.9569378  0.95602294 0.95510984
 0.95419847 0.95328885 0.95238095 0.95147479 0.95057034 0.94966762
 0.9487666  0.9478673  0.9469697  0.94607379 0.94517958 0.94428706
 0.94339623 0.94250707 0.94161959 0.94073377 0.93984962 0.93896714
 0.9380863  0.93720712 0.93632959 0.9354537  0.93457944 0.93370682
 0.93283582 0.93196645 0.9310987  0.93023256 0.92936803 0.92850511
 0.92764378 0.92678406 0.92592593 0.92506938 0.92421442 0.92336103
 0.92250923 0.92165899 0.92081031 0.9199632  0.91911765 0.91827365
 0.91743119 0.91659028 0.91575092 0.91491308 0.91407678 0.91324201
 0.91240876 0.91157703 0.91074681 0.90991811 0.90909091 0.90826521
 0.90744102 0.90661831 0.9057971  0.90497738 0.90415913 0.90334237
 0.90252708 0.90171326 0.9009009  0.90009001 0.89928058 0.8984726
 0.89766607 0.89686099 0.89605735 0.89525515 0.89445438 0.89365505
 0.89285714 0.89206066 0.8912656  0.89047195 0.88967972 0.88888889
 0.88809947 0.88731145 0.88652482 0.88573959 0.88495575 0.8841733
 0.88339223 0.88261253 0.88183422 0.88105727 0.88028169 0.87950748
 0.87873462 0.87796313 0.87719298 0.87642419 0.87565674 0.87489064
 0.87412587 0.87336245 0.87260035 0.87183958 0.87108014 0.87032202
 0.86956522 0.86880973 0.86805556 0.86730269 0.86655113 0.86580087
 0.8650519  0.86430424 0.86355786 0.86281277 0.86206897 0.86132644
 0.8605852  0.85984523 0.85910653 0.8583691  0.85763293 0.85689803
 0.85616438 0.85543199 0.85470085 0.85397096 0.85324232 0.85251492
 0.85178876 0.85106383 0.85034014 0.84961767 0.84889643 0.84817642
 0.84745763 0.84674005 0.84602369 0.84530854 0.84459459 0.84388186
 0.84317032 0.84245998 0.84175084 0.84104289 0.84033613 0.83963056
 0.83892617 0.83822297 0.83752094 0.83682008 0.8361204  0.83542189
 0.83472454 0.83402836 0.83333333 0.83263947 0.83194676 0.8312552
 0.83056478 0.82987552 0.8291874  0.82850041 0.82781457 0.82712986
 0.82644628 0.82576383 0.82508251 0.82440231 0.82372323 0.82304527
 0.82236842 0.82169269 0.82101806 0.82034454 0.81967213 0.81900082
 0.81833061 0.81766149 0.81699346 0.81632653 0.81566069 0.81499593
 0.81433225 0.81366965 0.81300813 0.81234768 0.81168831 0.81103001
 0.81037277 0.8097166  0.80906149 0.80840744 0.80775444 0.8071025
 0.80645161 0.80580177 0.80515298 0.80450523 0.80385852 0.80321285
 0.80256822 0.80192462 0.80128205 0.80064051 0.8        0.79936051
 0.79872204 0.7980846  0.79744817 0.79681275 0.79617834 0.79554495
 0.79491256 0.79428118 0.79365079 0.79302141 0.79239303 0.79176564
 0.79113924 0.79051383 0.78988942 0.78926598 0.78864353 0.78802206
 0.78740157 0.78678206 0.78616352 0.78554595 0.78492936 0.78431373
 0.78369906 0.78308536 0.78247261 0.78186083 0.78125    0.78064012
 0.7800312  0.77942323 0.7788162  0.77821012 0.77760498 0.77700078
 0.77639752 0.77579519 0.7751938  0.77459334 0.77399381 0.7733952
 0.77279753 0.77220077 0.77160494 0.77101002 0.77041602 0.76982294
 0.76923077 0.76863951 0.76804916 0.76745971 0.76687117 0.76628352
 0.76569678 0.76511094 0.76452599 0.76394194 0.76335878 0.76277651
 0.76219512 0.76161462 0.76103501 0.76045627 0.75987842 0.75930144
 0.75872534 0.75815011 0.75757576 0.75700227 0.75642965 0.7558579
 0.75528701 0.75471698 0.75414781 0.7535795  0.75301205 0.75244545
 0.7518797  0.7513148  0.75075075 0.75018755 0.74962519 0.74906367
 0.74850299 0.74794316 0.74738416 0.74682599 0.74626866 0.74571216
 0.74515648 0.74460164 0.74404762 0.74349442 0.74294205 0.7423905
 0.74183976 0.74128984 0.74074074 0.74019245 0.73964497 0.7390983
 0.73855244 0.73800738 0.73746313 0.73691968 0.73637703 0.73583517
 0.73529412 0.73475386 0.73421439 0.73367572 0.73313783 0.73260073
 0.73206442 0.7315289  0.73099415 0.73046019 0.72992701 0.7293946
 0.72886297 0.72833212 0.72780204 0.72727273 0.72674419 0.72621641
 0.7256894  0.72516316 0.72463768 0.72411296 0.723589   0.7230658
 0.72254335 0.72202166 0.72150072 0.72098053 0.7204611  0.7199424
 0.71942446 0.71890726 0.7183908  0.71787509 0.71736011 0.71684588
 0.71633238 0.71581961 0.71530758 0.71479628 0.71428571 0.71377587
 0.71326676 0.71275837 0.71225071 0.71174377 0.71123755 0.71073205
 0.71022727 0.70972321 0.70921986 0.70871722 0.7082153  0.70771408
 0.70721358 0.70671378 0.70621469 0.7057163  0.70521862 0.70472163
 0.70422535 0.70372977 0.70323488 0.70274069 0.70224719 0.70175439
 0.70126227 0.70077085 0.70028011 0.69979006 0.6993007  0.69881202
 0.69832402 0.69783671 0.69735007 0.69686411 0.69637883 0.69589422
 0.69541029 0.69492703 0.69444444 0.69396253 0.69348128 0.69300069
 0.69252078 0.69204152 0.69156293 0.691085   0.69060773 0.69013112
 0.68965517 0.68917988 0.68870523 0.68823125 0.68775791 0.68728522
 0.68681319 0.6863418  0.68587106 0.68540096 0.68493151 0.6844627
 0.68399453 0.683527   0.68306011 0.68259386 0.68212824 0.68166326
 0.68119891 0.68073519 0.68027211 0.67980965 0.67934783 0.67888663
 0.67842605 0.6779661  0.67750678 0.67704807 0.67658999 0.67613252
 0.67567568 0.67521945 0.67476383 0.67430883 0.67385445 0.67340067
 0.67294751 0.67249496 0.67204301 0.67159167 0.67114094 0.67069081
 0.67024129 0.66979236 0.66934404 0.66889632 0.6684492  0.66800267
 0.66755674 0.66711141 0.66666667 0.66622252 0.66577896 0.66533599
 0.66489362 0.66445183 0.66401062 0.66357001 0.66312997 0.66269052
 0.66225166 0.66181337 0.66137566 0.66093853 0.66050198 0.66006601
 0.65963061 0.65919578 0.65876153 0.65832785 0.65789474 0.6574622
 0.65703022 0.65659882 0.65616798 0.6557377  0.65530799 0.65487885
 0.65445026 0.65402224 0.65359477 0.65316786 0.65274151 0.65231572
 0.65189048 0.6514658  0.65104167 0.65061809 0.65019506 0.64977258
 0.64935065 0.64892927 0.64850843 0.64808814 0.64766839 0.64724919
 0.64683053 0.64641241 0.64599483 0.64557779 0.64516129 0.64474533
 0.6443299  0.643915   0.64350064 0.64308682 0.64267352 0.64226076
 0.64184852 0.64143682 0.64102564 0.64061499 0.64020487 0.63979527
 0.63938619 0.63897764 0.6385696  0.63816209 0.6377551  0.63734863
 0.63694268 0.63653724 0.63613232 0.63572791 0.63532402 0.63492063
 0.63451777 0.63411541 0.63371356 0.63331222 0.63291139 0.63251107
 0.63211125 0.63171194 0.63131313 0.63091483 0.63051702 0.63011972
 0.62972292 0.62932662 0.62893082 0.62853551 0.6281407  0.62774639
 0.62735257 0.62695925 0.62656642 0.62617408 0.62578223 0.62539087
 0.625      0.62460962 0.62421973 0.62383032 0.6234414  0.62305296
 0.62266501 0.62227754 0.62189055 0.62150404 0.62111801 0.62073246
 0.62034739 0.6199628  0.61957869 0.61919505 0.61881188 0.61842919
 0.61804697 0.61766523 0.61728395 0.61690315 0.61652281 0.61614295
 0.61576355 0.61538462 0.61500615 0.61462815 0.61425061 0.61387354
 0.61349693 0.61312078 0.6127451  0.61236987 0.6119951  0.6116208
 0.61124694 0.61087355 0.61050061 0.61012813 0.6097561  0.60938452
 0.6090134  0.60864273 0.60827251 0.60790274 0.60753341 0.60716454
 0.60679612 0.60642814 0.60606061 0.60569352 0.60532688 0.60496068
 0.60459492 0.60422961 0.60386473 0.6035003  0.60313631 0.60277275
 0.60240964 0.60204696 0.60168472 0.60132291 0.60096154 0.6006006
 0.6002401  0.59988002 0.59952038 0.59916117 0.5988024  0.59844405
 0.59808612 0.59772863 0.59737157 0.59701493 0.59665871 0.59630292
 0.59594756 0.59559261 0.5952381  0.594884   0.59453032 0.59417706
 0.59382423 0.59347181 0.59311981 0.59276823 0.59241706 0.59206631
 0.59171598 0.59136606 0.59101655 0.59066745 0.59031877 0.5899705
 0.58962264 0.58927519 0.58892815 0.58858152 0.58823529 0.58788948
 0.58754407 0.58719906 0.58685446 0.58651026 0.58616647 0.58582308
 0.58548009 0.58513751 0.58479532 0.58445354 0.58411215 0.58377116
 0.58343057 0.58309038 0.58275058 0.58241118 0.58207218 0.58173357
 0.58139535 0.58105752 0.58072009 0.58038305 0.5800464  0.57971014
 0.57937428 0.5790388  0.5787037  0.578369   0.57803468 0.57770075
 0.57736721 0.57703405 0.57670127 0.57636888 0.57603687 0.57570524
 0.57537399 0.57504313 0.57471264 0.57438254 0.57405281 0.57372347
 0.5733945  0.5730659  0.57273769 0.57240985 0.57208238 0.57175529
 0.57142857 0.57110223 0.57077626 0.57045066 0.57012543 0.56980057
 0.56947608 0.56915196 0.56882821 0.56850483 0.56818182 0.56785917
 0.56753689 0.56721497 0.56689342 0.56657224 0.56625142 0.56593096
 0.56561086 0.56529112 0.56497175 0.56465274 0.56433409 0.56401579
 0.56369786 0.56338028 0.56306306 0.5627462  0.5624297  0.56211355
 0.56179775 0.56148231 0.56116723 0.5608525  0.56053812 0.56022409
 0.55991041 0.55959709 0.55928412 0.55897149 0.55865922 0.55834729
 0.55803571 0.55772448 0.5574136  0.55710306 0.55679287 0.55648303
 0.55617353 0.55586437]

But when I tried to add the two following lines to the code:

x = eval((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))

print('\n\nThese are the values for "x" in the equation:\n\n', x)

it produces the following error (in addition to the already shown output):

Error:
Traceback (most recent call last):
  File "C:/Users/User1/AppData/Local/Programs/Python/Python37/equations_02.py", line 18, in <module>
    x = eval((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))
ValueError: operands could not be broadcast together with shapes (1800,) (800,)

that it seems to be produced when the values are taken as matrices and the dimensions are incompatible (according to the various sites I've seen about this problem).

Although I'm going to keep on investigating this problem, I'm sure that somebody more knowledgeable (that's easy ), is going to give you a better answer before I do.

All the best,