julia> include("parameter_estimation_systems/case_by_case/crn/sys_crn_AAA_abstract_algebra.txt")
44-element Vector{AbstractAlgebra.Generic.MPoly{Rational{BigInt}}}:
 -x2_0 + 1429944776381801//1125899906842624
 k1_0*x1_0*x2_0 - k2_0*x4_0 - k3_0*x4_0 + x2_1
 -x3_0 + 2515238909694429//2251799813685248
 k6_0*x3_0*x5_0 - k3_0*x4_0 - k5_0*x6_0 + x3_1
 -x2_1 + 602852900884729//72057594037927936
 k1_0*x1_1*x2_0 + k1_0*x1_0*x2_1 - k2_0*x4_1 - k3_0*x4_1 + x2_2
 -k1_0*x1_0*x2_0 + k2_0*x4_0 + k3_0*x4_0 + x4_1
 k1_0*x1_0*x2_0 - k2_0*x4_0 - k4_0*x6_0 + x1_1
 -x3_1 + 7014452597828849//2305843009213693952
 k6_0*x3_1*x5_0 + k6_0*x3_0*x5_1 - k3_0*x4_1 - k5_0*x6_1 + x3_2
 -k6_0*x3_0*x5_0 + k4_0*x6_0 + k5_0*x6_0 + x6_1
 k6_0*x3_0*x5_0 - k4_0*x6_0 - k5_0*x6_0 + x5_1
 -x2_2 - 8987165776388313//9223372036854775808
 k1_0*x1_2*x2_0 + 2*k1_0*x1_1*x2_1 + k1_0*x1_0*x2_2 - k2_0*x4_2 - k3_0*x4_2 + x2_3
 -k1_0*x1_1*x2_0 - k1_0*x1_0*x2_1 + k2_0*x4_1 + k3_0*x4_1 + x4_2
 k1_0*x1_1*x2_0 + k1_0*x1_0*x2_1 - k2_0*x4_1 - k4_0*x6_1 + x1_2
 -x3_2 - 432714566648943//1152921504606846976
 k6_0*x3_2*x5_0 + 2*k6_0*x3_1*x5_1 + k6_0*x3_0*x5_2 - k3_0*x4_2 - k5_0*x6_2 + x3_3
 k6_0*x3_1*x5_0 + k6_0*x3_0*x5_1 - k4_0*x6_1 - k5_0*x6_1 + x5_2
 -k6_0*x3_1*x5_0 - k6_0*x3_0*x5_1 + k4_0*x6_1 + k5_0*x6_1 + x6_2
 -x2_3 + 543704441701305//4611686018427387904
 k1_0*x1_3*x2_0 + 3*k1_0*x1_2*x2_1 + 3*k1_0*x1_1*x2_2 + k1_0*x1_0*x2_3 - k2_0*x4_3 - k3_0*x4_3 + x2_4
 k1_0*x1_2*x2_0 + 2*k1_0*x1_1*x2_1 + k1_0*x1_0*x2_2 - k2_0*x4_2 - k4_0*x6_2 + x1_3
 -k1_0*x1_2*x2_0 - 2*k1_0*x1_1*x2_1 - k1_0*x1_0*x2_2 + k2_0*x4_2 + k3_0*x4_2 + x4_3
 -x3_3 + 8660675362133387//147573952589676412928
 k6_0*x3_3*x5_0 + 3*k6_0*x3_2*x5_1 + 3*k6_0*x3_1*x5_2 + k6_0*x3_0*x5_3 - k3_0*x4_3 - k5_0*x6_3 + x3_4
 k6_0*x3_2*x5_0 + 2*k6_0*x3_1*x5_1 + k6_0*x3_0*x5_2 - k4_0*x6_2 - k5_0*x6_2 + x5_3
 -k6_0*x3_2*x5_0 - 2*k6_0*x3_1*x5_1 - k6_0*x3_0*x5_2 + k4_0*x6_2 + k5_0*x6_2 + x6_3
 -x2_4 - 8329732142157469//590295810358705651712
 k1_0*x1_4*x2_0 + 4*k1_0*x1_3*x2_1 + 6*k1_0*x1_2*x2_2 + 4*k1_0*x1_1*x2_3 + k1_0*x1_0*x2_4 - k2_0*x4_4 - k3_0*x4_4 + x2_5
 k1_0*x1_3*x2_0 + 3*k1_0*x1_2*x2_1 + 3*k1_0*x1_1*x2_2 + k1_0*x1_0*x2_3 - k2_0*x4_3 - k4_0*x6_3 + x1_4
 -k1_0*x1_3*x2_0 - 3*k1_0*x1_2*x2_1 - 3*k1_0*x1_1*x2_2 - k1_0*x1_0*x2_3 + k2_0*x4_3 + k3_0*x4_3 + x4_4
 -x3_4 - 5559897746056903//590295810358705651712
 k6_0*x3_4*x5_0 + 4*k6_0*x3_3*x5_1 + 6*k6_0*x3_2*x5_2 + 4*k6_0*x3_1*x5_3 + k6_0*x3_0*x5_4 - k3_0*x4_4 - k5_0*x6_4 + x3_5
 k6_0*x3_3*x5_0 + 3*k6_0*x3_2*x5_1 + 3*k6_0*x3_1*x5_2 + k6_0*x3_0*x5_3 - k4_0*x6_3 - k5_0*x6_3 + x5_4
 -k6_0*x3_3*x5_0 - 3*k6_0*x3_2*x5_1 - 3*k6_0*x3_1*x5_2 - k6_0*x3_0*x5_3 + k4_0*x6_3 + k5_0*x6_3 + x6_4
 -x2_5 + 7521685809799907//4722366482869645213696
 k1_0*x1_5*x2_0 + 5*k1_0*x1_4*x2_1 + 10*k1_0*x1_3*x2_2 + 10*k1_0*x1_2*x2_3 + 5*k1_0*x1_1*x2_4 + k1_0*x1_0*x2_5 - k2_0*x4_5 - k3_0*x4_5 + x2_6
 k1_0*x1_4*x2_0 + 4*k1_0*x1_3*x2_1 + 6*k1_0*x1_2*x2_2 + 4*k1_0*x1_1*x2_3 + k1_0*x1_0*x2_4 - k2_0*x4_4 - k4_0*x6_4 + x1_5
 -k1_0*x1_4*x2_0 - 4*k1_0*x1_3*x2_1 - 6*k1_0*x1_2*x2_2 - 4*k1_0*x1_1*x2_3 - k1_0*x1_0*x2_4 + k2_0*x4_4 + k3_0*x4_4 + x4_5
 -x3_5 + 1749874162744839//1180591620717411303424
 k6_0*x3_5*x5_0 + 5*k6_0*x3_4*x5_1 + 10*k6_0*x3_3*x5_2 + 10*k6_0*x3_2*x5_3 + 5*k6_0*x3_1*x5_4 + k6_0*x3_0*x5_5 - k3_0*x4_5 - k5_0*x6_5 + x3_6
 k6_0*x3_4*x5_0 + 4*k6_0*x3_3*x5_1 + 6*k6_0*x3_2*x5_2 + 4*k6_0*x3_1*x5_3 + k6_0*x3_0*x5_4 - k4_0*x6_4 - k5_0*x6_4 + x5_5
 -k6_0*x3_4*x5_0 - 4*k6_0*x3_3*x5_1 - 6*k6_0*x3_2*x5_2 - 4*k6_0*x3_1*x5_3 - k6_0*x3_0*x5_4 + k4_0*x6_4 + k5_0*x6_4 + x6_5

julia> @time rur, sep = zdim_parameterization(sys, get_separating_element=true);

       # Find solutions
primes of bitsize 28
G-Q-Pt-FG-LT-LP(C)
Dimension of the quotient :7
Degree of the radical :7
Use last variable as separating element
Run Groebner learn
Test cyclic optimization
Apply cyclic optimization 
Multi-modular computation (1 threads): G-Q-Pt-FG-LT-LP(C)
5-9-13-17-21-25-29-33-37-41-45-49-53-61-69-77-85-93-105-117-129-141-157-173-193-213-237-261-289-317-349-385-425-469-517-569-625-689-
check-G-Q-Pt-FG-LT-LP(C)
Nb Primes used :689
  0.700939 seconds (10.74 M allocations: 582.861 MiB, 17.83% gc time)

julia> sep
44-element Vector{Int64}:
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 0
 1

julia> @time sol = RS.rs_isolate(rur, sep, output_precision=Int32(100));
  0.035352 seconds (7.14 k allocations: 1.824 MiB)

julia> gens(R)
44-element Vector{AbstractAlgebra.Generic.MPoly{Rational{BigInt}}}:
 k1_0
 k2_0
 k3_0
 k4_0
 k5_0
 k6_0
 x1_0
 x1_1
 x1_2
 x1_3
 x1_4
 x1_5
 x2_0
 x2_1
 x2_2
 x2_3
 x2_4
 x2_5
 x2_6
 x3_0
 x3_1
 x3_2
 x3_3
 x3_4
 x3_5
 x3_6
 x4_0
 x4_1
 x4_2
 x4_3
 x4_4
 x4_5
 x5_0
 x5_1
 x5_2
 x5_3
 x5_4
 x5_5
 x6_0
 x6_1
 x6_2
 x6_3
 x6_4
 x6_5

julia> sol_i = filter(x -> abs(x[1][1] - 0.03) < 0.01, sol)
3-element Vector{Vector{Vector{BigFloat}}}:
 [[0.021874020642434014314661826482101, 0.021874020642434014314661826482126], [0.020873750375401236389796217769987, 0.020873750375401236389796217770012], [0.027494330571879682604302342513578, 0.027494330571879682604302342513602], [0.041964405937328906913635182751635, 0.041964405937328906913635182751685], [0.039482378282843965363652082136884, 0.039482378282843965363652082136933], [0.015796525779249767267993627457452, 0.015796525779249767267993627457477], [2.4862981661127366198207611745941, 2.4862981661127366198207611745972], [0.0041297331246682069156483216141544, 0.0041297331246682069156483216141606], [-0.00069423923751452826652655322767461, -0.00069423923751452826652655322767384], [9.5100597222180439096760266518332e-05, 9.5100597222180439096760266518428e-05]  …  [-9.5168830171295938462810851984102e-05, -9.5168830171295938462810851984006e-05], [3.5890508863270185833583634718955e-05, 3.5890508863270185833583634719003e-05], [-7.6834549881075233011573988077447e-06, -7.6834549881075233011573988077327e-06], [1.4166570293274132522234607286335e-06, 1.416657029327413252223460728635e-06], [0.94800284444100905909195379352517, 0.94800284444100905909195379352596], [0.0011944976149904109672495625295872, 0.0011944976149904109672495625295887], [9.5168830171295938462810851984006e-05, 9.5168830171295938462810851984102e-05], [-3.5890508863270185833583634719003e-05, -3.5890508863270185833583634718955e-05], [7.6834549881075233011573988077327e-06, 7.6834549881075233011573988077447e-06], [-1.416657029327413252223460728635e-06, -1.4166570293274132522234607286335e-06]]
 [[0.028809847663823155758242294369828, 0.028809847663823155758242294369853], [0.027180487246532102765323170109017, 0.027180487246532102765323170109041], [0.046884922355315345683793224112516, 0.046884922355315345683793224112565], [0.032076790080047884407603289022545, 0.032076790080047884407603289022594], [0.043790266802791527809739055811902, 0.043790266802791527809739055811952], [0.027560683238198373414194039320324, 0.027560683238198373414194039320349], [1.0193787558269019995213987740897, 1.0193787558269019995213987740913], [0.0029800069732603046689103220516789, 0.002980006973260304668910322051682], [-0.00050694362432189501217505169769958, -0.00050694362432189501217505169769881], [6.925775455814723684525790933373e-05, 6.9257754558147236845257909333826e-05]  …  [9.212678302133731588869067799064e-05, 9.2126783021337315888690677990736e-05], [1.0047666199236983582081277534353e-05, 1.0047666199236983582081277534365e-05], [-4.2135333027533926825676230870545e-06, -4.2135333027533926825676230870485e-06], [9.5575915531114794674426754144493e-07, 9.5575915531114794674426754144643e-07], [0.73326312889379611552222335698074, 0.73326312889379611552222335698153], [0.0023442237663983132139875620920627, 0.0023442237663983132139875620920658], [-9.2126783021337315888690677990736e-05, -9.212678302133731588869067799064e-05], [-1.0047666199236983582081277534365e-05, -1.0047666199236983582081277534353e-05], [4.2135333027533926825676230870485e-06, 4.2135333027533926825676230870545e-06], [-9.5575915531114794674426754144643e-07, -9.5575915531114794674426754144493e-07]]
 [[0.029827606996921119343368668398436, 0.029827606996921119343368668398485], [0.019479010523996285196003964983687, 0.019479010523996285196003964983712], [0.04942864033154101206154242284153, 0.049428640331541012061542422841579], [0.030442422332194363693705248613916, 0.030442422332194363693705248613941], [0.018983585574207091310118332483982, 0.018983585574207091310118332484007], [0.050462831262145297202188406753266, 0.050462831262145297202188406753315], [1.1624854384399464265085517156098, 1.1624854384399464265085517156114], [0.0028455835200326758303505605446934, 0.0028455835200326758303505605446964], [-0.00048540135475189836125995041224315, -0.00048540135475189836125995041224276], [6.6273950188751282167848267773322e-05, 6.6273950188751282167848267773418e-05]  …  [0.00011366905259133396680379196344697, 0.00011366905259133396680379196344707], [7.0638618298410289046716359739755e-06, 7.0638618298410289046716359739815e-06], [-3.80638049702771536843659170322e-06, -3.806380497027715368436591703217e-06], [9.0058327748405271329569101917542e-07, 9.0058327748405271329569101917617e-07], [1.0534522793562293290106632497286, 1.0534522793562293290106632497301], [0.0024786472196259420525473235990483, 0.0024786472196259420525473235990513], [-0.00011366905259133396680379196344707, -0.00011366905259133396680379196344697], [-7.0638618298410289046716359739815e-06, -7.0638618298410289046716359739755e-06], [3.806380497027715368436591703217e-06, 3.80638049702771536843659170322e-06], [-9.0058327748405271329569101917617e-07, -9.0058327748405271329569101917542e-07]]

julia> sol_i = filter(x -> abs(x[1][1] - 0.03) < 0.001, sol)
1-element Vector{Vector{Vector{BigFloat}}}:
 [[0.029827606996921119343368668398436, 0.029827606996921119343368668398485], [0.019479010523996285196003964983687, 0.019479010523996285196003964983712], [0.04942864033154101206154242284153, 0.049428640331541012061542422841579], [0.030442422332194363693705248613916, 0.030442422332194363693705248613941], [0.018983585574207091310118332483982, 0.018983585574207091310118332484007], [0.050462831262145297202188406753266, 0.050462831262145297202188406753315], [1.1624854384399464265085517156098, 1.1624854384399464265085517156114], [0.0028455835200326758303505605446934, 0.0028455835200326758303505605446964], [-0.00048540135475189836125995041224315, -0.00048540135475189836125995041224276], [6.6273950188751282167848267773322e-05, 6.6273950188751282167848267773418e-05]  …  [0.00011366905259133396680379196344697, 0.00011366905259133396680379196344707], [7.0638618298410289046716359739755e-06, 7.0638618298410289046716359739815e-06], [-3.80638049702771536843659170322e-06, -3.806380497027715368436591703217e-06], [9.0058327748405271329569101917542e-07, 9.0058327748405271329569101917617e-07], [1.0534522793562293290106632497286, 1.0534522793562293290106632497301], [0.0024786472196259420525473235990483, 0.0024786472196259420525473235990513], [-0.00011366905259133396680379196344707, -0.00011366905259133396680379196344697], [-7.0638618298410289046716359739815e-06, -7.0638618298410289046716359739755e-06], [3.806380497027715368436591703217e-06, 3.80638049702771536843659170322e-06], [-9.0058327748405271329569101917617e-07, -9.0058327748405271329569101917542e-07]]

julia> sol_i[1]
44-element Vector{Vector{BigFloat}}:
 [0.029827606996921119343368668398436, 0.029827606996921119343368668398485]
 [0.019479010523996285196003964983687, 0.019479010523996285196003964983712]
 [0.04942864033154101206154242284153, 0.049428640331541012061542422841579]
 [0.030442422332194363693705248613916, 0.030442422332194363693705248613941]
 [0.018983585574207091310118332483982, 0.018983585574207091310118332484007]
 [0.050462831262145297202188406753266, 0.050462831262145297202188406753315]
 [1.1624854384399464265085517156098, 1.1624854384399464265085517156114]
 [0.0028455835200326758303505605446934, 0.0028455835200326758303505605446964]
 [-0.00048540135475189836125995041224315, -0.00048540135475189836125995041224276]
 [6.6273950188751282167848267773322e-05, 6.6273950188751282167848267773418e-05]
 [-8.4986624808985104753155481518299e-06, -8.4986624808985104753155481518179e-06]
 [1.011161133039056522755607326331e-06, 1.0111611330390565227556073263325e-06]
 [1.2700460917452369713487314584184, 1.2700460917452369713487314584215]
 [0.0083662646378036692462742962561483, 0.0083662646378036692462742962561729]
 [-0.00097439046592475841036123940242041, -0.00097439046592475841036123940241887]
 [0.0001178971073765146346939980404044, 0.00011789710737651463469399804040459]
 [-1.4111115132421035226460183376064e-05, -1.411111513242103522646018337604e-05]
 [1.5927789249489159895833588140286e-06, 1.5927789249489159895833588140316e-06]
 [-1.5036435227925641041428705788213e-07, -1.5036435227925641041428705788194e-07]
 [1.116990459990331974182709018349, 1.1169904599903319741827090183522]
 [0.0030420338981450513633764121124128, 0.003042033898145051363376412112419]
 [-0.00037532005858152608229749702673, -0.00037532005858152608229749702672923]
 [5.8687019017604381430821408605022e-05, 5.8687019017604381430821408605118e-05]
 [-9.4188331485502401195812269274597e-06, -9.4188331485502401195812269274356e-06]
 [1.4822010693939121801234425068723e-06, 1.4822010693939121801234425068753e-06]
 [-2.2396642162155358676790117782865e-07, -2.2396642162155358676790117782846e-07]
 [0.76049674967003467110874267982399, 0.76049674967003467110874267982478]
 [-0.0083662646378036692462742962561729, -0.0083662646378036692462742962561483]
 [0.00097439046592475841036123940241887, 0.00097439046592475841036123940242041]
 [-0.00011789710737651463469399804040459, -0.0001178971073765146346939980404044]
 [1.411111513242103522646018337604e-05, 1.4111115132421035226460183376064e-05]
 [-1.5927789249489159895833588140316e-06, -1.5927789249489159895833588140286e-06]
 [0.96771285852106746840650115560235, 0.96771285852106746840650115560314]
 [-0.0024786472196259420525473235990513, -0.0024786472196259420525473235990483]
 [0.00011366905259133396680379196344697, 0.00011366905259133396680379196344707]
 [7.0638618298410289046716359739755e-06, 7.0638618298410289046716359739815e-06]
 [-3.80638049702771536843659170322e-06, -3.806380497027715368436591703217e-06]
 [9.0058327748405271329569101917542e-07, 9.0058327748405271329569101917617e-07]
 [1.0534522793562293290106632497286, 1.0534522793562293290106632497301]
 [0.0024786472196259420525473235990483, 0.0024786472196259420525473235990513]
 [-0.00011366905259133396680379196344707, -0.00011366905259133396680379196344697]
 [-7.0638618298410289046716359739815e-06, -7.0638618298410289046716359739755e-06]
 [3.806380497027715368436591703217e-06, 3.80638049702771536843659170322e-06]
 [-9.0058327748405271329569101917617e-07, -9.0058327748405271329569101917542e-07]

julia> (0.02 - 0.018983585574207091310118332483982)
0.001016414425792908

julia> (0.02 - 0.018983585574207091310118332483982) / 0.02 * 100
5.0820721289645405
