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 Solving Equations with Python
#1
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.
Quote
#2
(Sep-09-2019, 04:22 PM)japrap Wrote: 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 Blush ), is going to give you a better answer before I do.

All the best,
newbieAuggie2019

"That's been one of my mantras - focus and simplicity. Simple can be harder than complex: You have to work hard to get your thinking clean to make it simple. But it's worth it in the end because once you get there, you can move mountains."
Steve Jobs
Quote
#3
Thanks newbieAuggie :)
Quote
#4
Hi again!

I have modified once again the program to show that interacting the way you want with such big matrices produce an even more humongous matrix of almost 1 million and a half elements, because matrix 'x' has 800 elements, and matrix 'y' has 1800 elements, so your equation interacting with both of them gives a number of elements equal to the product of 800*1800, that is to say, 1440000 elements!!!
import numpy as np

x = np.arange(4,12,.01)
bigx = len(x)
print("\nThe matrix 'x' has", bigx, "elements.")
y = np.arange(0,18,.01)
bigy = len(y)
print("The matrix 'y' has", bigy, "elements.")
mother_of_matrices = bigx*bigy
print("Therefore, the interaction of matrices 'x' and 'y' produces a huge matrix of:", mother_of_matrices, "elements.")
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)
and that produces the following huge output:
Output:
The matrix 'x' has 800 elements. The matrix 'y' has 1800 elements. Therefore, the interaction of matrices 'x' and 'y' produces a huge matrix of: 1440000 elements. 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 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0.55586437]
All the best,
newbieAuggie2019

"That's been one of my mantras - focus and simplicity. Simple can be harder than complex: You have to work hard to get your thinking clean to make it simple. But it's worth it in the end because once you get there, you can move mountains."
Steve Jobs
Quote
#5
So now the problem is how can I solve the equation. I mean we definitely need pairs such as (x,y) that solve the equation. It would be great if I can have a plot that shows those pairs.
Quote
#6
Hi again!

For what I have read, it seems that numpy doesn't work very well with huge amounts of data, so I thought of a way to go around it: I have modified the program to calculate the different solutions to your equation, by making a loop, calculating the solution for each value of 'y', for each value of 'x' and I got many solutions (too many to be printed here, but you can run the program on your own). Nevertheless, there are some warnings I noticed that I comment further down:

import numpy as np

x = np.arange(4,12,.01)
bigx = len(x)
print("\nThe matrix 'x' has", bigx, "elements.")
y = np.arange(0,18,.01)
bigy = len(y)
print("The matrix 'y' has", bigy, "elements.")
mother_of_matrices = bigx*bigy
print("Therefore, the interaction of matrices 'x' and 'y' produces a huge matrix of:", mother_of_matrices, "elements.")
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)



print('\n\nThese are the values for "x" in the equation:\n\n', x)
for x in x:
    for y in y:
        x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))
        print(x)


As I indicated above, due to some values (for instance, the '0' value), I got also two RuntimeWarning messages:

Error:
Warning (from warnings module): File "C:/Users/User1/AppData/Local/Programs/Python/Python37/equations_04.py", line 22 x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k)) RuntimeWarning: invalid value encountered in power Warning (from warnings module): File "C:/Users/User1/AppData/Local/Programs/Python/Python37/equations_04.py", line 22 x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k)) RuntimeWarning: divide by zero encountered in true_divide
and also this one at the end of the running time:
Error:
Traceback (most recent call last): File "C:/Users/User1/AppData/Local/Programs/Python/Python37/equations_04.py", line 21, in <module> for y in y: TypeError: 'numpy.float64' object is not iterable
I hope it helps,

Hi once again!

As you mention using a plot to display the pairs (x,y), I tried to do it with matplot, but it gives error warnings, but even so, it might give you some ideas:

import numpy as np
import matplotlib.pyplot as plt

x = np.arange(4,12,.01)
bigx = len(x)
print("\nThe matrix 'x' has", bigx, "elements.")
y = np.arange(0,18,.01)
bigy = len(y)
print("The matrix 'y' has", bigy, "elements.")
mother_of_matrices = bigx*bigy
print("Therefore, the interaction of matrices 'x' and 'y' produces a huge matrix of:", mother_of_matrices, "elements.")
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)



print('\n\nThese are the values for "x" in the equation:\n\n', x)
for x in x:
    for y in y:
        x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))
        plt.scatter(x,y)
        plt.show()
and here are the errors related to scatter in matplot:

Error:
Traceback (most recent call last): File "C:/Users/User1/AppData/Local/Programs/Python/Python37/equations_06.py", line 24, in <module> plt.scatter(x,y) File "C:\Users\User1\AppData\Local\Programs\Python\Python37\lib\site-packages\matplotlib\pyplot.py", line 2847, in scatter None else {}), **kwargs) File "C:\Users\User1\AppData\Local\Programs\Python\Python37\lib\site-packages\matplotlib\__init__.py", line 1601, in inner return func(ax, *map(sanitize_sequence, args), **kwargs) File "C:\Users\User1\AppData\Local\Programs\Python\Python37\lib\site-packages\matplotlib\axes\_axes.py", line 4444, in scatter raise ValueError("x and y must be the same size") ValueError: x and y must be the same size
About previous warning messages, maybe you could make some exception commands to avoid dividing by '0', or to prevent encountering invalid values in power...

All the best,
newbieAuggie2019

"That's been one of my mantras - focus and simplicity. Simple can be harder than complex: You have to work hard to get your thinking clean to make it simple. But it's worth it in the end because once you get there, you can move mountains."
Steve Jobs
Quote
#7
Photo 
Hi!

I've been quite busy thinking about this problem with my very limited knowledge of Python, and I keep on modifying the program to try and reach a solution.

As I said previously in another post, numpy doesn't seem to work very well with huge amounts of data, so I have been investigating about that and maybe mpmath would be a solution for that.

mpmath is a free (BSD licensed) Python library for real and complex floating-point arithmetic with arbitrary precision (you can decide with which precision you want your numbers). It has been developed by Fredrik Johansson since 2007, with help from many contributors.
For example, you can compute 50 digits of pi by numerically evaluating the Gaussian integral with mpmath.

To install mpmath (it's free), you can click on the start sign (I'm showing it for Windows 10, but it might be somewhat different with other operating systems and/or versions), which is at the bottom left corner of the computer (it is the image of a window)
   

and then type 'cmd' (without the simple quotes), inside the text box (the one with the circle on the left), and press the 'enter' (or 'return') key.
   

By doing that, the command prompt, cmd or windows prompt window will pop up (a black window with some writings on it).

You need to go on inside that pop-up window, to the root directory, by typing 'cd\' (without the simple quotes) on that pop-up window, and press the 'enter' (or 'return') key.
   

The command prompt window will show now something like 'C:\>' (without the simple quotes).
   

So now you just have to type 'pip install mpmath' (without the simple quotes), and press the 'enter' (or 'return') key.
[Image: to-install-mpmath.png]


It is probably going to take some time to load (maybe a couple of minutes). Once it is installed, you can close the command prompt window.
If I use the program with numpy, it gives the values for 'y' as following:
Output:
These are the values for "y": [0.000e+00 1.000e-02 2.000e-02 ... 1.797e+01 1.798e+01 1.799e+01]
while if I use mpmath, the values are shown with more decimal numbers and bigger precision (it produces 1171 lines in my Python 3.7.4 Shell for just the different values of 'y'):
Output:
[mpf('0.0'), mpf('0.01'), mpf('0.02'), mpf('0.029999999999999999'), mpf('0.040000000000000001'),...]
I've been working with many different twists and tweakings to the original code, and
one of the last versions I'm working on is the following one:
from mpmath import mp
import numpy as np


x = np.arange(4,12,.01)
xnumbers = [x]
bigx = len(x)
print("\nThe matrix 'x' has", bigx, "elements.")
y = mp.arange(0,18,.01)
ynumbers = [y]
bigy = len(y)
print("The matrix 'y' has", bigy, "elements.")
mother_of_matrices = bigx*bigy
print("Therefore, the interaction of matrices 'x' and 'y' produces a huge matrix of:", mother_of_matrices, "elements.")
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)

print('\n\nThese are the new values for "x" (from the equation):\n')
for x in x:
    for y in ynumbers:
        if ((1-k) != 0).all():
            x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))
    print(x, sep=',')

for y in ynumbers:
    if ((1-k) != 0).all():
        x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))
        mp.plot(x, y)
As you can check, most of the values for 'x', 'y', 'k' and the new values of 'x' obtained from the equation are given with about a precision of 15 decimal positions.

With this version, I don't get any warning or error messages, but still it doesn't plot the pairs (x, y).
I'm going to explain some points on the program. You can notice that for 'y', I've used mpmath (line 9):
y = mp.arange(0,18,.01)
but I had to keep using numpy for 'x' (line 5):
x = np.arange(4,12,.01)
otherwise, with mpmath for 'x', it gave an error on the line 15:
k = 10/(6+x)
:
Error:
Traceback (most recent call last): File "C:\Users\User1\AppData\Local\Programs\Python\Python37\equations_15.py", line 15, in <module> k = 10/(6+x) TypeError: unsupported operand type(s) for +: 'int' and 'list'
That error disappears when using numpy for 'x'.
I've also eliminated the problem when the value of (1-k) was '0', that produced warnings of dividing by '0'. I've avoided that problem with the lines 24 and 29:
if ((1-k) != 0).all(): 
that checks every element of the matrix and avoids the values that makes (1-k) = 0.
The line that still doesn't work is the line 31
mp.plot(x, y)
inside the loop (lines 28-31):
for y in ynumbers:
    if ((1-k) != 0).all():
        x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))
        mp.plot(x, y)
The idea for this last loop, was your wish to plot the pairs (x, y). These values for 'x' and 'y' cannot be taken from (line 5):
x = np.arange(4,12,.01)
and (line 9):
y = mp.arange(0,18,.01)
because, as you remember, the list of 'x' values has 800 elements and the list of 'y' values has 1800 elements, so we cannot pair them as the lists have different sizes (that's why if we try, we get the error saying that 'x' and 'y' should have the same size).
Therefore, I thought that for the pairs, we should take just the values of 'y' and then, through the equation, a corresponding value of 'x'. So, if we take the 1800 values of 'y', we should have the 1800 corresponding values of 'x'.
If we move the indentation on line 31
mp.plot(x, y)
and align it to if:
for y in ynumbers:
    if ((1-k) != 0).all():
        x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))
    mp.plot(x, y)
or even align it to for:
for y in ynumbers:
    if ((1-k) != 0).all():
        x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))
mp.plot(x, y)
both produce an error:
Error:
Traceback (most recent call last): File "C:\Users\User1\AppData\Local\Programs\Python\Python37\equations_15.py", line 31, in <module> mp.plot(x, y) File "C:\Users\User1\AppData\Local\Programs\Python\Python37\lib\site-packages\mpmath\visualization.py", line 49, in plot a, b = xlim ValueError: too many values to unpack (expected 2)
probably due to too many values to plot at the same time, so I thought that if we print (plot) every single pair as it is calculated, it would be easier to handle by the program:
for y in ynumbers:
    if ((1-k) != 0).all():
        x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))
        mp.plot(x, y)
It doesn't produce any error, but it doesn't plot the pairs either.
By the way, we don't need to import matplotlib as before:
import matplotlib.pyplot as plt
and then use something like:
plt.scatter(x,y)
plt.show()
because mpmath already incorporates a built-in plot, so we just need to import mpmath (line 1):
from mpmath import mp
and then call the plot inside mpmath, when we need it, like in line 31:
mp.plot(x,y)
Surely, there must be a neater way to code it, but right now, I would be happy enough by just making it work. I think I only need now to make the plot function work, although I'm not sure how to do it yet...

All the best,
newbieAuggie2019

"That's been one of my mantras - focus and simplicity. Simple can be harder than complex: You have to work hard to get your thinking clean to make it simple. But it's worth it in the end because once you get there, you can move mountains."
Steve Jobs
Quote
#8
More on the problem...

I have been working also on other versions of the program. One of them, is the following one (going back to numpy, even if the precision and the ability to handle so many numbers or just long numbers, are not very good). The positive point of this version, is that at least prints (plots) the values (x, y), but not all of them are correct, as we can see clearly (check by running the program) that the values for 'y' seem to be correct, going through a range from '0' to '18' as line 7 indicates:
y = np.arange(0,18,.01)
but for the values of 'x', they all seem to be changed to '1'. I still have to find out why, and to correct it:
import numpy as np
import matplotlib.pyplot as plt

x = np.arange(4,12,.01)
bigx = len(x)
print("\nThe matrix 'x' has", bigx, "elements.")
y = np.arange(0,18,.01)
ynumbers = [y]
bigy = len(y)
print("The matrix 'y' has", bigy, "elements.")
mother_of_matrices = bigx*bigy
print("Therefore, the interaction of matrices 'x' and 'y' produces a huge matrix of:", mother_of_matrices, "elements.")
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)

for y in ynumbers:
        validynumbers = list(filter(lambda k: (1-k) != 0 and k != 0, k))
        for k in k:
            x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))
            plt.scatter(x,y)
            plt.show()

I tried to avoid problems related to dividing by '0' (or values of 'k' that seem to produce powers and fractions difficult to be handled by numpy), by adding line 20:
validynumbers = list(filter(lambda k: (1-k) != 0 and k != 0, k))
which filters the values of 'k' equal to '0' or that makes (1-k) = 0.
Nevertheless, it still gives us a warning message (it lets the program run, but warns us about something, in this case, still problems with the value '0'):
Error:
Warning (from warnings module): File "C:/Users/User1/AppData/Local/Programs/Python/Python37/equations_16.py", line 22 x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k)) RuntimeWarning: divide by zero encountered in double_scalars
All the best,

I have just noticed, trying to close the matplot window, before closing the Python 3.7.4 Shell window, that another matplot window pops up, showing values for 'y' from around '6' to around '18' and for values for 'x' from around '5' to around '40', which I think they are still incorrect, as the values for 'x', supposedly go from '4' to '12'.
newbieAuggie2019

"That's been one of my mantras - focus and simplicity. Simple can be harder than complex: You have to work hard to get your thinking clean to make it simple. But it's worth it in the end because once you get there, you can move mountains."
Steve Jobs
Quote
#9
I just modified the program to format a bit the output on matplot:
import numpy as np
import matplotlib.pyplot as plt

x = np.arange(4,12,.01)
bigx = len(x)
print("\nThe matrix 'x' has", bigx, "elements.")
y = np.arange(0,18,.01)
ynumbers = [y]
bigy = len(y)
print("The matrix 'y' has", bigy, "elements.")
mother_of_matrices = bigx*bigy
print("Therefore, the interaction of matrices 'x' and 'y' produces a huge matrix of:", mother_of_matrices, "elements.")
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)



for y in ynumbers:
        validynumbers = list(filter(lambda k: (1-k) != 0 and k != 0, k))
        for k in k:
            x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))
            plt.scatter(x, y, s=10, c='red', marker='^')
# s: size of point, default = 20
# c: color, sequence, or sequence of color, default = ‘b’ (blue)
# marker: point symbol, default = 'o’

            plt.xlim(0,50)
            plt.ylim(0,20)
            plt.title('x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))')
            plt.xlabel("Values for 'x'")
            plt.ylabel("Values for 'y'")
            plt.show()
This version of the program, as I said in a previous post, produces a first ouput in matplot that I attach here:
[Image: first-output-of-the-function-in-matplot.png]
where it seems that the values for 'y' are correct, going from '0' to '18' as indicated by line 7:
y = np.arange(0,18,.01)
but the values for 'x' have been changed all to '1'.
The formatting lines for the matplot output are these lines (25-35):
plt.scatter(x, y, s=10, c='red', marker='^')
# s: size of point, default = 20
# c: color, sequence, or sequence of color, default = ‘b’ (blue)
# marker: point symbol, default = 'o’
 
            plt.xlim(0,50)
            plt.ylim(0,20)
            plt.title('x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))')
            plt.xlabel("Values for 'x'")
            plt.ylabel("Values for 'y'")
            plt.show()
where in line 25:
plt.scatter(x, y, s=10, c='red', marker='^')
the 's' value indicates the size of the point on the matplot output,
the c='red' indicates the colour of the point on the matplot output,
the marker='^' indicates the shape of the point on the matplot output,
Lines 30-31:
            plt.xlim(0,50)
            plt.ylim(0,20)
indicate the range values for the axis for 'x' (0-50) and for 'y' (0-20).
Lines 32-34:
            plt.title('x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))')
            plt.xlabel("Values for 'x'")
            plt.ylabel("Values for 'y'")
indicates the title we want for the function (or for the window), for the 'x' axis, and for the 'y' axis, respectively.
The line 35:
            plt.show()
is necessary for the points of the function to be shown (seen) on the matplot window.
Then when I tried to close the matplot window (without having closed the Python 3.7.4 Shell yet), the matplot window pops up again, producing this second output of the function:
[Image: second-output-of-the-function-in-matplot.png]
where the values of 'y' seem to be almost correct (still the upper limit is 18) but the lower limit has changed from '0' to '6', and the values for 'x' are supposedly wrong, because the values for 'x' should be between '4' and '12' according to line 4:
x = np.arange(4,12,.01)
, but as I said in another post, we shouln't use these values of 'x' (800 values) to pair them with the values of 'y' (1800 values) given by line 7 (the sizes are different and would produce an error):
y = np.arange(0,18,.01)
to form the pairs (x, y). Instead, we should use these values of 'y' and then apply them in the equation (line 24):
            x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))
to produce 1800 values for 'x' that can be paired to the 1800 values of 'y'.

Nevertheless, these two warning messages appear on the Python shell:

Error:
Warning (from warnings module): File "C:\Users\User1\AppData\Local\Programs\Python\Python37\equations_18.py", line 49 x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k)) RuntimeWarning: divide by zero encountered in double_scalars Warning (from warnings module): File "C:\Users\User1\AppData\Local\Programs\Python\Python37\equations_18.py", line 49 x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k)) RuntimeWarning: invalid value encountered in power
I don't know why, but it seems that when I fixed an issue, then another one comes out... Wall

Doh All the best,

FINAL (? Big Grin Think ) UPDATE!!!
Keeping in mind that both a number divided by '0' tends to infinite, and also if infinite becomes the power of an expression, make the representation of those values difficult to represent with numpy, I found a way to, at least not producing those warning messages:
import numpy as np
import matplotlib.pyplot as plt

x = np.arange(4,12,.01)
bigx = len(x)
print("\nThe matrix 'x' has", bigx, "elements.")
y = np.arange(0,18,.01)
ynumbers = [y]
bigy = len(y)
print("The matrix 'y' has", bigy, "elements.")
mother_of_matrices = bigx*bigy
print("Therefore, the interaction of matrices 'x' and 'y' produces a huge matrix of:", mother_of_matrices, "elements.")
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)

print('\n\nThese are the new values for "x" (from the equation):\n')
for x in x:
    for y in ynumbers:
        if ((1-k) != 0).all():
            old_settings = np.seterr(all='ignore') # It ignores the warnings. 
            x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))
    print(x, sep=',')

    

for y in ynumbers:
        validynumbers = list(filter(lambda k: (1-k) != 0 and k != 0, k))
        for k in k:
            old_settings = np.seterr(all='ignore') # It ignores the warnings. 
            x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))
            plt.scatter(x, y, s=10, c='red', marker='^')
# s: size of point, default = 20
# c: color, sequence, or sequence of color, default = ‘b’
# marker: point symbol, default = 'o’

            plt.xlim(0,50)
            plt.ylim(0,20)
            plt.title('x = ((y**(1/k)-(y-6)**(1/k))/6)**(k/(1-k))')
            plt.xlabel("Values for 'x'")
            plt.ylabel("Values for 'y'")
            plt.show()

np.seterr(**old_settings) # It resets to default warnings.
Lines 23 and 32:
            old_settings = np.seterr(all='ignore') # It ignores the warnings.
make the program ignore the warning messages, so they are not shown.
With line 46:
np.seterr(**old_settings) # It resets to default warnings.
the program goes back to set the errors (seterr) warning messages to the default values.

I think I'm going to leave it as that. I'm not completely happy with it, and I don't understand throughly why the program behaves like that (producing two outputs on matplot), but people here are probably going to give you a better answer. (Maybe some day I will be back to it, just to satisfy my curiosity, but I don't think it's going to be in the near future... There are still lots of things I have to learn first!!!)

I thank you, Japrap, for your question, because while trying to give you an answer, I've been learning a lot, as I had never used before, numpy, matplot, arange(), seterr(), .all(), filter(), lambda, or mpmath!!!

All the best,
newbieAuggie2019

"That's been one of my mantras - focus and simplicity. Simple can be harder than complex: You have to work hard to get your thinking clean to make it simple. But it's worth it in the end because once you get there, you can move mountains."
Steve Jobs
Quote

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