..............................................................................
 simple reaction :dnAdt = -k*(nA)**1 , no transition state,part 1,version 1.0 
 peter.vlasschaert@gmail.com,15/01/2023                                       
..............................................................................
...........................................................
 simple reaction :dnAdt = -k*(nA)**1 , no transition state 
...........................................................
[[1.        ]
 [0.98994983]
 [0.98000066]
 [0.97015153]
 [0.96040134]
 [0.95074915]
 [0.94119397]
 [0.93173481]
 [0.92237072]
 [0.91310075]
 [0.90392393]
 [0.89483934]
 [0.88584606]
 [0.87694315]
 [0.86812973]
 [0.85940488]
 [0.85076772]
 [0.84221736]
 [0.83375294]
 [0.82537358]
 [0.81707844]
 [0.80886666]
 [0.80073742]
 [0.79268987]
 [0.78472321]
 [0.77683661]
 [0.76902927]
 [0.76130039]
 [0.75364919]
 [0.74607488]
 [0.7385767 ]
 [0.73115387]
 [0.72380565]
 [0.71653128]
 [0.70933002]
 [0.70220114]
 [0.69514391]
 [0.6881576 ]
 [0.68124151]
 [0.67439493]
 [0.66761716]
 [0.66090751]
 [0.65426528]
 [0.64768981]
 [0.64118042]
 [0.63473645]
 [0.62835724]
 [0.62204214]
 [0.61579051]
 [0.60960171]
 [0.60347511]
 [0.59741008]
 [0.59140601]
 [0.58546229]
 [0.57957829]
 [0.57375344]
 [0.56798712]
 [0.56227876]
 [0.55662776]
 [0.55103356]
 [0.54549558]
 [0.54001326]
 [0.53458604]
 [0.52921336]
 [0.52389468]
 [0.51862945]
 [0.51341714]
 [0.50825721]
 [0.50314914]
 [0.49809241]
 [0.4930865 ]
 [0.4881309 ]
 [0.4832251 ]
 [0.47836861]
 [0.47356092]
 [0.46880156]
 [0.46409002]
 [0.45942584]
 [0.45480854]
 [0.45023763]
 [0.44571267]
 [0.44123319]
 [0.43679872]
 [0.43240882]
 [0.42806304]
 [0.42376093]
 [0.41950207]
 [0.415286  ]
 [0.41111231]
 [0.40698056]
 [0.40289034]
 [0.39884123]
 [0.39483281]
 [0.39086468]
 [0.38693642]
 [0.38304765]
 [0.37919796]
 [0.37538696]
 [0.37161425]
 [0.36787947]]
[1.         0.98994983 0.98000066 0.97015153 0.96040134 0.95074915
 0.94119397 0.93173481 0.92237072 0.91310075 0.90392393 0.89483934
 0.88584606 0.87694315 0.86812973 0.85940488 0.85076772 0.84221736
 0.83375294 0.82537358 0.81707844 0.80886666 0.80073742 0.79268987
 0.78472321 0.77683661 0.76902927 0.76130039 0.75364919 0.74607488
 0.7385767  0.73115387 0.72380565 0.71653128 0.70933002 0.70220114
 0.69514391 0.6881576  0.68124151 0.67439493 0.66761716 0.66090751
 0.65426528 0.64768981 0.64118042 0.63473645 0.62835724 0.62204214
 0.61579051 0.60960171 0.60347511 0.59741008 0.59140601 0.58546229
 0.57957829 0.57375344 0.56798712 0.56227876 0.55662776 0.55103356
 0.54549558 0.54001326 0.53458604 0.52921336 0.52389468 0.51862945
 0.51341714 0.50825721 0.50314914 0.49809241 0.4930865  0.4881309
 0.4832251  0.47836861 0.47356092 0.46880156 0.46409002 0.45942584
 0.45480854 0.45023763 0.44571267 0.44123319 0.43679872 0.43240882
 0.42806304 0.42376093 0.41950207 0.415286   0.41111231 0.40698056
 0.40289034 0.39884123 0.39483281 0.39086468 0.38693642 0.38304765
 0.37919796 0.37538696 0.37161425 0.36787947]
initial value =  nA(0) 
.......................
[0.0, 1.0]
print all values over time (use:range       ),nA(t)
[(0.0, 1.0), (0.10101010101010101, 0.9899498335561975), (0.20202020202020202, 0.9800006550664018), (0.30303030303030304, 0.9701515263995026), (0.40404040404040403, 0.9604013439823427), (0.5050505050505051, 0.9507491520850663), (0.6060606060606061, 0.9411939671052584), (0.7070707070707071, 0.9317348126636106), (0.8080808080808081, 0.9223707241382765), (0.9090909090909091, 0.9131007455449067), (1.0101010101010102, 0.9039239307272446), (1.1111111111111112, 0.8948393442149245), (1.2121212121212122, 0.8858460583525323), (1.3131313131313131, 0.8769431547991724), (1.4141414141414141, 0.8681297281402487), (1.5151515151515151, 0.8594048799587962), (1.6161616161616161, 0.8507677177607406), (1.7171717171717171, 0.8422173605184617), (1.8181818181818181, 0.8337529359530181), (1.9191919191919191, 0.8253735800549873), (2.0202020202020203, 0.8170784380721475), (2.121212121212121, 0.80886666392015), (2.2222222222222223, 0.8007374191657889), (2.323232323232323, 0.7926898746803321), (2.4242424242424243, 0.7847232092820361), (2.525252525252525, 0.7768366084435443), (2.6262626262626263, 0.7690292673326996), (2.727272727272727, 0.761300389607339), (2.8282828282828283, 0.7536491871173401), (2.929292929292929, 0.746074879803953), (3.0303030303030303, 0.7385766955991335), (3.131313131313131, 0.7311538703248746), (3.2323232323232323, 0.7238056475925391), (3.3333333333333335, 0.7165312787021926), (3.4343434343434343, 0.7093300213053604), (3.5353535353535355, 0.7022011398207402), (3.6363636363636362, 0.6951439069179931), (3.7373737373737375, 0.6881576023861732), (3.8383838383838382, 0.6812415130225936), (3.9393939393939394, 0.6743949325219809), (4.040404040404041, 0.6676171613656313), (4.141414141414141, 0.6609075067105659), (4.242424242424242, 0.6542652822786859), (4.343434343434343, 0.64768980862952), (4.444444444444445, 0.641180417288192), (4.545454545454545, 0.6347364451798251), (4.646464646464646, 0.6283572351215355), (4.747474747474747, 0.6220421366933079), (4.848484848484849, 0.6157905061847012), (4.94949494949495, 0.6096017065415555), (5.05050505050505, 0.6034751072438704), (5.151515151515151, 0.5974100824141381), (5.252525252525253, 0.5914060126571153), (5.353535353535354, 0.585462285303087), (5.454545454545454, 0.5795782937417685), (5.555555555555555, 0.5737534373434761), (5.656565656565657, 0.5679871213802966), (5.757575757575758, 0.5622787569562719), (5.858585858585858, 0.5566277620362905), (5.959595959595959, 0.5510335605829746), (6.0606060606060606, 0.5454955818144048), (6.161616161616162, 0.5400132606775466), (6.262626262626262, 0.5345860377867002), (6.363636363636363, 0.5292133593619497), (6.4646464646464645, 0.5238946771676123), (6.565656565656566, 0.5186294485759504), (6.666666666666667, 0.5134171364821845), (6.767676767676767, 0.5082572090716272), (6.8686868686868685, 0.5031491398589257), (6.96969696969697, 0.49809240762906504), (7.070707070707071, 0.4930864963782927), (7.171717171717171, 0.4881308952550456), (7.2727272727272725, 0.48322509864190094), (7.373737373737374, 0.4783686061837503), (7.474747474747475, 0.47356092237213515), (7.575757575757575, 0.46880155665810913), (7.6767676767676765, 0.4640900234012358), (7.777777777777778, 0.4594258418143324), (7.878787878787879, 0.4548085359082132), (7.979797979797979, 0.450237634594803), (8.080808080808081, 0.4457126715649359), (8.181818181818182, 0.441233185261205), (8.282828282828282, 0.43679871861549496), (8.383838383838384, 0.43240881914100676), (8.484848484848484, 0.4280630388788124), (8.585858585858587, 0.42376093434497364), (8.686868686868687, 0.4195020665716688), (8.787878787878787, 0.41528600137131916), (8.88888888888889, 0.41111230863894466), (8.98989898989899, 0.4069805625308079), (9.09090909090909, 0.402890341462827), (9.191919191919192, 0.3988412280645556), (9.292929292929292, 0.39483280913385616), (9.393939393939394, 0.3908646755922653), (9.494949494949495, 0.3869364224410534), (9.595959595959595, 0.38304764871797664), (9.696969696969697, 0.3791979574547221), (9.797979797979798, 0.3753869556350471), (9.8989898989899, 0.37161425429974687), (10.0, 0.36787946891406775)]
print all values over time (use:enumerate   ) ,nA(t)
....................................................
[(0.0, 1.0), (0.10101010101010101, 0.9899498335561975), (0.20202020202020202, 0.9800006550664018), (0.30303030303030304, 0.9701515263995026), (0.40404040404040403, 0.9604013439823427), (0.5050505050505051, 0.9507491520850663), (0.6060606060606061, 0.9411939671052584), (0.7070707070707071, 0.9317348126636106), (0.8080808080808081, 0.9223707241382765), (0.9090909090909091, 0.9131007455449067), (1.0101010101010102, 0.9039239307272446), (1.1111111111111112, 0.8948393442149245), (1.2121212121212122, 0.8858460583525323), (1.3131313131313131, 0.8769431547991724), (1.4141414141414141, 0.8681297281402487), (1.5151515151515151, 0.8594048799587962), (1.6161616161616161, 0.8507677177607406), (1.7171717171717171, 0.8422173605184617), (1.8181818181818181, 0.8337529359530181), (1.9191919191919191, 0.8253735800549873), (2.0202020202020203, 0.8170784380721475), (2.121212121212121, 0.80886666392015), (2.2222222222222223, 0.8007374191657889), (2.323232323232323, 0.7926898746803321), (2.4242424242424243, 0.7847232092820361), (2.525252525252525, 0.7768366084435443), (2.6262626262626263, 0.7690292673326996), (2.727272727272727, 0.761300389607339), (2.8282828282828283, 0.7536491871173401), (2.929292929292929, 0.746074879803953), (3.0303030303030303, 0.7385766955991335), (3.131313131313131, 0.7311538703248746), (3.2323232323232323, 0.7238056475925391), (3.3333333333333335, 0.7165312787021926), (3.4343434343434343, 0.7093300213053604), (3.5353535353535355, 0.7022011398207402), (3.6363636363636362, 0.6951439069179931), (3.7373737373737375, 0.6881576023861732), (3.8383838383838382, 0.6812415130225936), (3.9393939393939394, 0.6743949325219809), (4.040404040404041, 0.6676171613656313), (4.141414141414141, 0.6609075067105659), (4.242424242424242, 0.6542652822786859), (4.343434343434343, 0.64768980862952), (4.444444444444445, 0.641180417288192), (4.545454545454545, 0.6347364451798251), (4.646464646464646, 0.6283572351215355), (4.747474747474747, 0.6220421366933079), (4.848484848484849, 0.6157905061847012), (4.94949494949495, 0.6096017065415555), (5.05050505050505, 0.6034751072438704), (5.151515151515151, 0.5974100824141381), (5.252525252525253, 0.5914060126571153), (5.353535353535354, 0.585462285303087), (5.454545454545454, 0.5795782937417685), (5.555555555555555, 0.5737534373434761), (5.656565656565657, 0.5679871213802966), (5.757575757575758, 0.5622787569562719), (5.858585858585858, 0.5566277620362905), (5.959595959595959, 0.5510335605829746), (6.0606060606060606, 0.5454955818144048), (6.161616161616162, 0.5400132606775466), (6.262626262626262, 0.5345860377867002), (6.363636363636363, 0.5292133593619497), (6.4646464646464645, 0.5238946771676123), (6.565656565656566, 0.5186294485759504), (6.666666666666667, 0.5134171364821845), (6.767676767676767, 0.5082572090716272), (6.8686868686868685, 0.5031491398589257), (6.96969696969697, 0.49809240762906504), (7.070707070707071, 0.4930864963782927), (7.171717171717171, 0.4881308952550456), (7.2727272727272725, 0.48322509864190094), (7.373737373737374, 0.4783686061837503), (7.474747474747475, 0.47356092237213515), (7.575757575757575, 0.46880155665810913), (7.6767676767676765, 0.4640900234012358), (7.777777777777778, 0.4594258418143324), (7.878787878787879, 0.4548085359082132), (7.979797979797979, 0.450237634594803), (8.080808080808081, 0.4457126715649359), (8.181818181818182, 0.441233185261205), (8.282828282828282, 0.43679871861549496), (8.383838383838384, 0.43240881914100676), (8.484848484848484, 0.4280630388788124), (8.585858585858587, 0.42376093434497364), (8.686868686868687, 0.4195020665716688), (8.787878787878787, 0.41528600137131916), (8.88888888888889, 0.41111230863894466), (8.98989898989899, 0.4069805625308079), (9.09090909090909, 0.402890341462827), (9.191919191919192, 0.3988412280645556), (9.292929292929292, 0.39483280913385616), (9.393939393939394, 0.3908646755922653), (9.494949494949495, 0.3869364224410534), (9.595959595959595, 0.38304764871797664), (9.696969696969697, 0.3791979574547221), (9.797979797979798, 0.3753869556350471), (9.8989898989899, 0.37161425429974687), (10.0, 0.36787946891406775)]
select values over time    (use,integer list) ,nA(t)
....................................................
[(0.0, 1.0), (0.10101010101010101, 0.9899498335561975), (0.20202020202020202, 0.9800006550664018), (0.30303030303030304, 0.9701515263995026), (0.40404040404040403, 0.9604013439823427), (0.5050505050505051, 0.9507491520850663), (0.6060606060606061, 0.9411939671052584), (0.7070707070707071, 0.9317348126636106), (0.8080808080808081, 0.9223707241382765), (0.9090909090909091, 0.9131007455449067), (1.0101010101010102, 0.9039239307272446), (1.1111111111111112, 0.8948393442149245), (1.2121212121212122, 0.8858460583525323), (1.3131313131313131, 0.8769431547991724), (1.4141414141414141, 0.8681297281402487), (1.5151515151515151, 0.8594048799587962), (1.6161616161616161, 0.8507677177607406), (1.7171717171717171, 0.8422173605184617), (1.8181818181818181, 0.8337529359530181), (1.9191919191919191, 0.8253735800549873), (2.0202020202020203, 0.8170784380721475), (2.121212121212121, 0.80886666392015), (2.2222222222222223, 0.8007374191657889), (2.323232323232323, 0.7926898746803321), (2.4242424242424243, 0.7847232092820361), (2.525252525252525, 0.7768366084435443), (2.6262626262626263, 0.7690292673326996), (2.727272727272727, 0.761300389607339), (2.8282828282828283, 0.7536491871173401), (2.929292929292929, 0.746074879803953), (3.0303030303030303, 0.7385766955991335), (3.131313131313131, 0.7311538703248746), (3.2323232323232323, 0.7238056475925391), (3.3333333333333335, 0.7165312787021926), (3.4343434343434343, 0.7093300213053604), (3.5353535353535355, 0.7022011398207402), (3.6363636363636362, 0.6951439069179931), (3.7373737373737375, 0.6881576023861732), (3.8383838383838382, 0.6812415130225936), (3.9393939393939394, 0.6743949325219809), (4.040404040404041, 0.6676171613656313), (4.141414141414141, 0.6609075067105659), (4.242424242424242, 0.6542652822786859), (4.343434343434343, 0.64768980862952), (4.444444444444445, 0.641180417288192), (4.545454545454545, 0.6347364451798251), (4.646464646464646, 0.6283572351215355), (4.747474747474747, 0.6220421366933079), (4.848484848484849, 0.6157905061847012), (4.94949494949495, 0.6096017065415555), (5.05050505050505, 0.6034751072438704), (5.151515151515151, 0.5974100824141381), (5.252525252525253, 0.5914060126571153), (5.353535353535354, 0.585462285303087), (5.454545454545454, 0.5795782937417685), (5.555555555555555, 0.5737534373434761), (5.656565656565657, 0.5679871213802966), (5.757575757575758, 0.5622787569562719), (5.858585858585858, 0.5566277620362905), (5.959595959595959, 0.5510335605829746), (6.0606060606060606, 0.5454955818144048), (6.161616161616162, 0.5400132606775466), (6.262626262626262, 0.5345860377867002), (6.363636363636363, 0.5292133593619497), (6.4646464646464645, 0.5238946771676123), (6.565656565656566, 0.5186294485759504), (6.666666666666667, 0.5134171364821845), (6.767676767676767, 0.5082572090716272), (6.8686868686868685, 0.5031491398589257), (6.96969696969697, 0.49809240762906504), (7.070707070707071, 0.4930864963782927), (7.171717171717171, 0.4881308952550456), (7.2727272727272725, 0.48322509864190094), (7.373737373737374, 0.4783686061837503), (7.474747474747475, 0.47356092237213515), (7.575757575757575, 0.46880155665810913), (7.6767676767676765, 0.4640900234012358), (7.777777777777778, 0.4594258418143324), (7.878787878787879, 0.4548085359082132), (7.979797979797979, 0.450237634594803), (8.080808080808081, 0.4457126715649359), (8.181818181818182, 0.441233185261205), (8.282828282828282, 0.43679871861549496), (8.383838383838384, 0.43240881914100676), (8.484848484848484, 0.4280630388788124), (8.585858585858587, 0.42376093434497364), (8.686868686868687, 0.4195020665716688), (8.787878787878787, 0.41528600137131916), (8.88888888888889, 0.41111230863894466), (8.98989898989899, 0.4069805625308079), (9.09090909090909, 0.402890341462827), (9.191919191919192, 0.3988412280645556), (9.292929292929292, 0.39483280913385616), (9.393939393939394, 0.3908646755922653), (9.494949494949495, 0.3869364224410534), (9.595959595959595, 0.38304764871797664), (9.696969696969697, 0.3791979574547221), (9.797979797979798, 0.3753869556350471), (9.8989898989899, 0.37161425429974687), (10.0, 0.36787946891406775)]
select values over time    (use,integer list) ,nA(t)
....................................................
[(0, 0.0, 1.0), (1, 0.10101010101010101, 0.9899498335561975), (2, 0.20202020202020202, 0.9800006550664018), (-1, 10.0, 0.36787946891406775)]