0
$\begingroup$

Let's have a look at a following system of equations:

equations={(0.00006637521875078321+0.0000663752187507832*I)+0.0024989587671803417*a[1,0]==0,-0.003331945022907122*a[1,0]-0.006663890045814244*\[Nu]*a[1,0]+0.0008329862557267805*a[1,2]==0,(0.+0.0000594463506148879*I)+(0.00026550087500313283+0.0002655008750031328*I)*a[1,0]+0.015410245730945439*a[1,0]^2+0.003331945022907122*a[2,0]==0,-0.01665972511453561*a[1,0]^2-0.03331945022907122*\[Nu]*a[1,0]^2+0.007496876301541024*a[1,0]*a[1,2]-0.0049979175343606835*a[2,0]-0.009995835068721367*\[Nu]*a[2,0]+0.001665972511453561*a[2,2]==0,0.0049979175343606835*a[1,0]^2+0.00041649312786339027*a[1,2]^2-0.0049979175343606835*a[2,0]-0.001665972511453561*a[2,2]-0.003331945022907122*\[Nu]*a[2,2]+0.001665972511453561*a[2,4]==0,(0.000023117183505744944-0.000023117183505744944*I)+(0.+0.0002377854024595516*I)*a[1,0]+(0.00026550087500313283+0.0002655008750031328*I)*a[1,0]^2+0.036651395251978344*a[1,0]^3+(0.0003982513125046993+0.00039825131250469917*I)*a[2,0]+0.0424822990420658*a[1,0]*a[2,0]+0.004164931278633903*a[3,0]==0,-0.026655560183256977*a[1,0]^3-0.053311120366513955*\[Nu]*a[1,0]^3+0.026655560183256977*a[1,0]^2*a[1,2]-0.04997917534360683*a[1,0]*a[2,0]-0.09995835068721366*\[Nu]*a[1,0]*a[2,0]+0.010828821324448146*a[1,2]*a[2,0]+(0.00013275043750156642+0.0001327504375015664*I)*a[2,2]+0.019158683881715953*a[1,0]*a[2,2]-0.006663890045814244*a[3,0]-0.013327780091628489*\[Nu]*a[3,0]+0.0024989587671803417*a[3,2]==0,0.003331945022907122*a[1,0]*a[1,2]^2+0.019991670137442734*a[1,0]*a[2,0]-0.01665972511453561*a[1,0]*a[2,2]-0.03331945022907122*\[Nu]*a[1,0]*a[2,2]+0.004164931278633903*a[1,2]*a[2,2]+0.006663890045814244*a[1,0]*a[2,4]-0.019991670137442734*a[3,0]-0.003331945022907122*a[3,2]-0.006663890045814244*\[Nu]*a[3,2]+0.0008329862557267805*a[3,4]==0,2.6498246448043595*^-6+(0.00009246873402297978-0.00009246873402297978*I)*a[1,0]+(0.+0.0002377854024595516*I)*a[1,0]^2+0.043315285297792584*a[1,0]^4+(0.+0.0003566781036893274*I)*a[2,0]+(0.0007965026250093986+0.0007965026250093983*I)*a[1,0]*a[2,0]+0.15160349854227406*a[1,0]^2*a[2,0]+0.029154518950437316*a[2,0]^2+(0.0005310017500062657+0.0005310017500062656*I)*a[3,0]+0.054144106622240736*a[1,0]*a[3,0]+0.0049979175343606835*a[4,0]==0,-0.013327780091628489*a[1,0]^4-0.026655560183256977*\[Nu]*a[1,0]^4+0.04664723032069971*a[1,0]^3*a[1,2]-0.11995002082465639*a[1,0]^2*a[2,0]-0.23990004164931278*\[Nu]*a[1,0]^2*a[2,0]+0.07663473552686381*a[1,0]*a[1,2]*a[2,0]-0.037484381507705125*a[2,0]^2-0.07496876301541025*\[Nu]*a[2,0]^2+(0.+0.0001188927012297758*I)*a[2,2]+(0.00026550087500313283+0.0002655008750031328*I)*a[1,0]*a[2,2]+0.068304872969596*a[1,0]^2*a[2,2]+0.026655560183256977*a[2,0]*a[2,2]-0.06663890045814244*a[1,0]*a[3,0]-0.13327780091628488*\[Nu]*a[1,0]*a[3,0]+0.014160766347355268*a[1,2]*a[3,0]+(0.00026550087500313283+0.0002655008750031328*I)*a[3,2]+0.030820491461890878*a[1,0]*a[3,2]-0.008329862557267805*a[4,0]-0.01665972511453561*\[Nu]*a[4,0]+0.003331945022907122*a[4,2]==0,0.009995835068721367*a[1,0]^2*a[1,2]^2+0.0049979175343606835*a[1,2]^2*a[2,0]+0.029987505206164097*a[2,0]^2-0.03998334027488547*a[1,0]^2*a[2,2]-0.07996668054977094*\[Nu]*a[1,0]^2*a[2,2]+0.029987505206164097*a[1,0]*a[1,2]*a[2,2]-0.024989587671803416*a[2,0]*a[2,2]-0.04997917534360683*\[Nu]*a[2,0]*a[2,2]+0.0058309037900874635*a[2,2]^2+0.006663890045814244*a[1,0]^2*a[2,4]+0.009995835068721367*a[2,0]*a[2,4]+0.019991670137442734*a[1,0]*a[3,0]-0.03331945022907122*a[1,0]*a[3,2]-0.06663890045814244*\[Nu]*a[1,0]*a[3,2]+0.007496876301541024*a[1,2]*a[3,2]+0.007496876301541024*a[1,0]*a[3,4]-0.04997917534360683*a[4,0]-0.0049979175343606835*a[4,2]-0.009995835068721367*\[Nu]*a[4,2]+0.001665972511453561*a[4,4]==0,0.001665972511453561*a[1,2]^2*a[2,2]-0.0049979175343606835*a[2,0]*a[2,2]-0.004164931278633903*a[2,2]^2-0.008329862557267805*\[Nu]*a[2,2]^2+0.003331945022907122*a[2,2]*a[2,4]+0.009995835068721367*a[1,0]*a[3,2]+0.0008329862557267805*a[1,2]*a[3,4]-0.0049979175343606835*a[4,2]-0.001665972511453561*a[4,4]-0.003331945022907122*\[Nu]*a[4,4]+0.001665972511453561*a[4,6]==0,(-4.675812194404871*^-6-4.675812194404872*^-6*I)+0.000010599298579217438*a[1,0]+(0.00009246873402297978-0.00009246873402297978*I)*a[1,0]^2+0.026655560183256977*a[1,0]^5+(0.00013870310103446967-0.00013870310103446967*I)*a[2,0]+(0.+0.0007133562073786548*I)*a[1,0]*a[2,0]+0.23656809662640566*a[1,0]^3*a[2,0]+(0.0005973769687570489+0.0005973769687570488*I)*a[2,0]^2+0.20824656393169513*a[1,0]*a[2,0]^2+(0.+0.0004755708049191032*I)*a[3,0]+(0.0010620035000125313+0.0010620035000125311*I)*a[1,0]*a[3,0]+0.19325281132861308*a[1,0]^2*a[3,0]+0.07413577675968347*a[2,0]*a[3,0]+(0.0006637521875078322+0.000663752187507832*I)*a[4,0]+0.06580591420241566*a[1,0]*a[4,0]+0.0058309037900874635*a[5,0]==0,0.03998334027488547*a[1,0]^4*a[1,2]-0.07996668054977094*a[1,0]^3*a[2,0]-0.15993336109954187*\[Nu]*a[1,0]^3*a[2,0]+0.19991670137442732*a[1,0]^2*a[1,2]*a[2,0]-0.17992503123698458*a[1,0]*a[2,0]^2-0.35985006247396917*\[Nu]*a[1,0]*a[2,0]^2+0.054977092877967516*a[1,2]*a[2,0]^2+(0.00004623436701148989-0.00004623436701148989*I)*a[2,2]+(0.+0.0002377854024595516*I)*a[1,0]*a[2,2]+0.10995418575593503*a[1,0]^3*a[2,2]+(0.0003982513125046993+0.00039825131250469917*I)*a[2,0]*a[2,2]+0.18992086630570595*a[1,0]*a[2,0]*a[2,2]-0.15993336109954187*a[1,0]^2*a[3,0]-0.31986672219908374*\[Nu]*a[1,0]^2*a[3,0]+0.09995835068721366*a[1,0]*a[1,2]*a[3,0]-0.09995835068721366*a[2,0]*a[3,0]-0.19991670137442732*\[Nu]*a[2,0]*a[3,0]+0.034152436484798*a[2,2]*a[3,0]+(0.+0.0002377854024595516*I)*a[3,2]+(0.0005310017500062657+0.0005310017500062656*I)*a[1,0]*a[3,2]+0.10995418575593503*a[1,0]^2*a[3,2]+0.0424822990420658*a[2,0]*a[3,2]-0.08329862557267805*a[1,0]*a[4,0]-0.1665972511453561*\[Nu]*a[1,0]*a[4,0]+0.01749271137026239*a[1,2]*a[4,0]+(0.0003982513125046993+0.00039825131250469917*I)*a[4,2]+0.0424822990420658*a[1,0]*a[4,2]-0.009995835068721367*a[5,0]-0.019991670137442734*\[Nu]*a[5,0]+0.004164931278633903*a[5,2]==0,0.013327780091628489*a[1,0]^3*a[1,2]^2+0.029987505206164097*a[1,0]*a[1,2]^2*a[2,0]-0.026655560183256977*a[1,0]^3*a[2,2]-0.053311120366513955*\[Nu]*a[1,0]^3*a[2,2]+0.07996668054977094*a[1,0]^2*a[1,2]*a[2,2]-0.11995002082465639*a[1,0]*a[2,0]*a[2,2]-0.23990004164931278*\[Nu]*a[1,0]*a[2,0]*a[2,2]+0.043315285297792584*a[1,2]*a[2,0]*a[2,2]+(0.00006637521875078321+0.0000663752187507832*I)*a[2,2]^2+0.04164931278633902*a[1,0]*a[2,2]^2+0.019991670137442734*a[1,0]*a[2,0]*a[2,4]+0.006663890045814244*a[1,2]^2*a[3,0]+0.09995835068721366*a[2,0]*a[3,0]-0.03331945022907122*a[2,2]*a[3,0]-0.06663890045814244*\[Nu]*a[2,2]*a[3,0]+0.013327780091628489*a[2,4]*a[3,0]-0.07996668054977094*a[1,0]^2*a[3,2]-0.15993336109954187*\[Nu]*a[1,0]^2*a[3,2]+0.053311120366513955*a[1,0]*a[1,2]*a[3,2]-0.04997917534360683*a[2,0]*a[3,2]-0.09995835068721366*\[Nu]*a[2,0]*a[3,2]+0.019158683881715953*a[2,2]*a[3,2]+0.026655560183256977*a[1,0]^2*a[3,4]+0.010828821324448146*a[2,0]*a[3,4]-0.04997917534360683*a[1,0]*a[4,2]-0.09995835068721366*\[Nu]*a[1,0]*a[4,2]+0.010828821324448146*a[1,2]*a[4,2]+(0.00013275043750156642+0.0001327504375015664*I)*a[4,4]+0.019158683881715953*a[1,0]*a[4,4]-0.09995835068721366*a[5,0]-0.006663890045814244*a[5,2]-0.013327780091628489*\[Nu]*a[5,2]+0.0024989587671803417*a[5,4]==0,0.009995835068721367*a[1,0]*a[1,2]^2*a[2,2]-0.019991670137442734*a[1,0]*a[2,2]^2-0.03998334027488547*\[Nu]*a[1,0]*a[2,2]^2+0.008329862557267805*a[1,2]*a[2,2]^2+0.006663890045814244*a[1,0]*a[2,2]*a[2,4]-0.019991670137442734*a[2,2]*a[3,0]+0.003331945022907122*a[1,2]^2*a[3,2]+0.019991670137442734*a[2,0]*a[3,2]-0.01665972511453561*a[2,2]*a[3,2]-0.03331945022907122*\[Nu]*a[2,2]*a[3,2]+0.006663890045814244*a[2,4]*a[3,2]+0.006663890045814244*a[1,0]*a[1,2]*a[3,4]+0.004164931278633903*a[2,2]*a[3,4]+0.019991670137442734*a[1,0]*a[4,2]-0.01665972511453561*a[1,0]*a[4,4]-0.03331945022907122*\[Nu]*a[1,0]*a[4,4]+0.004164931278633903*a[1,2]*a[4,4]+0.006663890045814244*a[1,0]*a[4,6]-0.019991670137442734*a[5,2]-0.003331945022907122*a[5,4]-0.006663890045814244*\[Nu]*a[5,4]+0.0008329862557267805*a[5,6]==0,(0.+1.248235844435553*^-6*I)-(0.000018703248777619484+0.000018703248777619487*I)*a[1,0]+0.000010599298579217438*a[1,0]^2+0.006663890045814244*a[1,0]^6+0.000015898947868826156*a[2,0]+(0.00027740620206893933-0.00027740620206893933*I)*a[1,0]*a[2,0]+0.17992503123698458*a[1,0]^4*a[2,0]+(0.+0.0005350171555339911*I)*a[2,0]^2+0.4822990420658059*a[1,0]^2*a[2,0]^2+0.09496043315285298*a[2,0]^3+(0.00018493746804595956-0.00018493746804595956*I)*a[3,0]+(0.+0.0009511416098382064*I)*a[1,0]*a[3,0]+0.299875052061641*a[1,0]^3*a[3,0]+(0.001593005250018797+0.0015930052500187967*I)*a[2,0]*a[3,0]+0.5297792586422324*a[1,0]*a[2,0]*a[3,0]+0.0470637234485631*a[3,0]^2+(0.+0.000594463506148879*I)*a[4,0]+(0.0013275043750156643+0.001327504375015664*I)*a[1,0]*a[4,0]+0.2349021241149521*a[1,0]^2*a[4,0]+0.08996251561849229*a[2,0]*a[4,0]+(0.0007965026250093986+0.0007965026250093983*I)*a[5,0]+0.07746772178259059*a[1,0]*a[5,0]+0.006663890045814244*a[6,0]==0,0.013327780091628489*a[1,0]^5*a[1,2]+0.22657226155768428*a[1,0]^3*a[1,2]*a[2,0]-0.17992503123698458*a[1,0]^2*a[2,0]^2-0.35985006247396917*\[Nu]*a[1,0]^2*a[2,0]^2+0.28488129945855895*a[1,0]*a[1,2]*a[2,0]^2-0.08996251561849229*a[2,0]^3-0.17992503123698458*\[Nu]*a[2,0]^3+5.299649289608719*^-6*a[2,2]+(0.00009246873402297978-0.00009246873402297978*I)*a[1,0]*a[2,2]+0.08663057059558517*a[1,0]^4*a[2,2]+(0.+0.0003566781036893274*I)*a[2,0]*a[2,2]+0.45481049562682213*a[1,0]^2*a[2,0]*a[2,2]+0.13161182840483132*a[2,0]^2*a[2,2]-0.10662224073302791*a[1,0]^3*a[3,0]-0.21324448146605582*\[Nu]*a[1,0]^3*a[3,0]+0.2598917117867555*a[1,0]^2*a[1,2]*a[3,0]-0.47980008329862556*a[1,0]*a[2,0]*a[3,0]-0.9596001665972511*\[Nu]*a[1,0]*a[2,0]*a[3,0]+0.14327363598500625*a[1,2]*a[2,0]*a[3,0]+(0.0005310017500062657+0.0005310017500062656*I)*a[2,2]*a[3,0]+0.2432319866722199*a[1,0]*a[2,2]*a[3,0]-0.06663890045814244*a[3,0]^2-0.13327780091628488*\[Nu]*a[3,0]^2+(0.00009246873402297978-0.00009246873402297978*I)*a[3,2]+(0.+0.0004755708049191032*I)*a[1,0]*a[3,2]+0.17326114119117034*a[1,0]^3*a[3,2]+(0.0007965026250093986+0.0007965026250093983*I)*a[2,0]*a[3,2]+0.3032069970845481*a[1,0]*a[2,0]*a[3,2]+0.054144106622240736*a[3,0]*a[3,2]-0.19991670137442732*a[1,0]^2*a[4,0]-0.39983340274885465*\[Nu]*a[1,0]^2*a[4,0]+0.12328196584756351*a[1,0]*a[1,2]*a[4,0]-0.12494793835901707*a[2,0]*a[4,0]-0.24989587671803415*\[Nu]*a[2,0]*a[4,0]+0.04164931278633902*a[2,2]*a[4,0]+(0.+0.0003566781036893274*I)*a[4,2]+(0.0007965026250093986+0.0007965026250093983*I)*a[1,0]*a[4,2]+0.15160349854227406*a[1,0]^2*a[4,2]+0.05830903790087463*a[2,0]*a[4,2]-0.09995835068721366*a[1,0]*a[5,0]-0.19991670137442732*\[Nu]*a[1,0]*a[5,0]+0.02082465639316951*a[1,2]*a[5,0]+(0.0005310017500062657+0.0005310017500062656*I)*a[5,2]+0.054144106622240736*a[1,0]*a[5,2]-0.011661807580174927*a[6,0]-0.023323615160349854*\[Nu]*a[6,0]+0.0049979175343606835*a[6,2]==0,0.006663890045814244*a[1,0]^4*a[1,2]^2+0.059975010412328195*a[1,0]^2*a[1,2]^2*a[2,0]+0.022490628904623073*a[1,2]^2*a[2,0]^2+0.09329446064139942*a[1,0]^3*a[1,2]*a[2,2]-0.11995002082465639*a[1,0]^2*a[2,0]*a[2,2]-0.23990004164931278*\[Nu]*a[1,0]^2*a[2,0]*a[2,2]+0.2299042065805914*a[1,0]*a[1,2]*a[2,0]*a[2,2]-0.08996251561849229*a[2,0]^2*a[2,2]-0.17992503123698458*\[Nu]*a[2,0]^2*a[2,2]+(0.+0.0000594463506148879*I)*a[2,2]^2+0.102457309454394*a[1,0]^2*a[2,2]^2+0.05830903790087463*a[2,0]*a[2,2]^2+0.014993752603082049*a[2,0]^2*a[2,4]+0.03998334027488547*a[1,0]*a[1,2]^2*a[3,0]-0.15993336109954187*a[1,0]*a[2,2]*a[3,0]-0.31986672219908374*\[Nu]*a[1,0]*a[2,2]*a[3,0]+0.05664306538942107*a[1,2]*a[2,2]*a[3,0]+0.026655560183256977*a[1,0]*a[2,4]*a[3,0]+0.09995835068721366*a[3,0]^2-0.053311120366513955*a[1,0]^3*a[3,2]-0.10662224073302791*\[Nu]*a[1,0]^3*a[3,2]+0.13994169096209913*a[1,0]^2*a[1,2]*a[3,2]-0.23990004164931278*a[1,0]*a[2,0]*a[3,2]-0.47980008329862556*\[Nu]*a[1,0]*a[2,0]*a[3,2]+0.07663473552686381*a[1,2]*a[2,0]*a[3,2]+(0.00026550087500313283+0.0002655008750031328*I)*a[2,2]*a[3,2]+0.136609745939192*a[1,0]*a[2,2]*a[3,2]-0.06663890045814244*a[3,0]*a[3,2]-0.13327780091628488*\[Nu]*a[3,0]*a[3,2]+0.015410245730945439*a[3,2]^2+0.04664723032069971*a[1,0]^3*a[3,4]+0.07663473552686381*a[1,0]*a[2,0]*a[3,4]+0.014160766347355268*a[3,0]*a[3,4]+0.008329862557267805*a[1,2]^2*a[4,0]+0.12494793835901707*a[2,0]*a[4,0]-0.04164931278633902*a[2,2]*a[4,0]-0.08329862557267805*\[Nu]*a[2,2]*a[4,0]+0.01665972511453561*a[2,4]*a[4,0]-0.11995002082465639*a[1,0]^2*a[4,2]-0.23990004164931278*\[Nu]*a[1,0]^2*a[4,2]+0.07663473552686381*a[1,0]*a[1,2]*a[4,2]-0.07496876301541025*a[2,0]*a[4,2]-0.1499375260308205*\[Nu]*a[2,0]*a[4,2]+0.026655560183256977*a[2,2]*a[4,2]+(0.+0.0001188927012297758*I)*a[4,4]+(0.00026550087500313283+0.0002655008750031328*I)*a[1,0]*a[4,4]+0.068304872969596*a[1,0]^2*a[4,4]+0.026655560183256977*a[2,0]*a[4,4]-0.04997917534360683*a[1,0]*a[5,0]-0.06663890045814244*a[1,0]*a[5,2]-0.13327780091628488*\[Nu]*a[1,0]*a[5,2]+0.014160766347355268*a[1,2]*a[5,2]+(0.00026550087500313283+0.0002655008750031328*I)*a[5,4]+0.030820491461890878*a[1,0]*a[5,4]-0.1749271137026239*a[6,0]-0.008329862557267805*a[6,2]-0.01665972511453561*\[Nu]*a[6,2]+0.003331945022907122*a[6,4]==0,0.019991670137442734*a[1,0]^2*a[1,2]^2*a[2,2]+0.014993752603082049*a[1,2]^2*a[2,0]*a[2,2]-0.019991670137442734*a[1,0]^2*a[2,2]^2-0.03998334027488547*\[Nu]*a[1,0]^2*a[2,2]^2+0.044981257809246146*a[1,0]*a[1,2]*a[2,2]^2-0.029987505206164097*a[2,0]*a[2,2]^2-0.059975010412328195*\[Nu]*a[2,0]*a[2,2]^2+0.008329862557267805*a[2,2]^3+0.009995835068721367*a[2,0]*a[2,2]*a[2,4]+0.019991670137442734*a[1,0]*a[1,2]^2*a[3,2]-0.07996668054977094*a[1,0]*a[2,2]*a[3,2]-0.15993336109954187*\[Nu]*a[1,0]*a[2,2]*a[3,2]+0.029987505206164097*a[1,2]*a[2,2]*a[3,2]+0.013327780091628489*a[1,0]*a[2,4]*a[3,2]+0.019991670137442734*a[3,0]*a[3,2]-0.01665972511453561*a[3,2]^2-0.03331945022907122*\[Nu]*a[3,2]^2+0.019991670137442734*a[1,0]^2*a[1,2]*a[3,4]+0.009995835068721367*a[1,2]*a[2,0]*a[3,4]+0.029987505206164097*a[1,0]*a[2,2]*a[3,4]+0.007496876301541024*a[3,2]*a[3,4]-0.04997917534360683*a[2,2]*a[4,0]+0.0049979175343606835*a[1,2]^2*a[4,2]+0.059975010412328195*a[2,0]*a[4,2]-0.024989587671803416*a[2,2]*a[4,2]-0.04997917534360683*\[Nu]*a[2,2]*a[4,2]+0.009995835068721367*a[2,4]*a[4,2]-0.03998334027488547*a[1,0]^2*a[4,4]-0.07996668054977094*\[Nu]*a[1,0]^2*a[4,4]+0.029987505206164097*a[1,0]*a[1,2]*a[4,4]-0.024989587671803416*a[2,0]*a[4,4]-0.04997917534360683*\[Nu]*a[2,0]*a[4,4]+0.011661807580174927*a[2,2]*a[4,4]+0.006663890045814244*a[1,0]^2*a[4,6]+0.009995835068721367*a[2,0]*a[4,6]+0.019991670137442734*a[1,0]*a[5,2]-0.03331945022907122*a[1,0]*a[5,4]-0.06663890045814244*\[Nu]*a[1,0]*a[5,4]+0.007496876301541024*a[1,2]*a[5,4]+0.007496876301541024*a[1,0]*a[5,6]-0.04997917534360683*a[6,2]-0.0049979175343606835*a[6,4]-0.009995835068721367*\[Nu]*a[6,4]+0.001665972511453561*a[6,6]==0,0.0024989587671803417*a[1,2]^2*a[2,2]^2-0.003331945022907122*a[2,2]^3-0.006663890045814244*\[Nu]*a[2,2]^3+0.001665972511453561*a[2,2]^2*a[2,4]+0.0049979175343606835*a[3,2]^2+0.003331945022907122*a[1,2]*a[2,2]*a[3,4]+0.00041649312786339027*a[3,4]^2-0.0049979175343606835*a[2,2]*a[4,2]+0.001665972511453561*a[1,2]^2*a[4,4]-0.0049979175343606835*a[2,0]*a[4,4]-0.008329862557267805*a[2,2]*a[4,4]-0.01665972511453561*\[Nu]*a[2,2]*a[4,4]+0.003331945022907122*a[2,4]*a[4,4]+0.003331945022907122*a[2,2]*a[4,6]+0.009995835068721367*a[1,0]*a[5,4]+0.0008329862557267805*a[1,2]*a[5,6]-0.0049979175343606835*a[6,4]-0.001665972511453561*a[6,6]-0.003331945022907122*\[Nu]*a[6,6]+0.001665972511453561*a[6,8]==0}

where each a[m_,n_] means an unknown to solve and $\nu$ is just a parameter. If you look at the system of equations you notice a specific arrangement of that equations. From first equation we can obtain first unknown a[1,0]. Next equation depends on a[1,0] and a[1,2], but we already know the value of a[1,0]! All we have to do in the second equation is to evaluate the only unknown a[1,2]. Third equation depends on a[1,0], a[1,2] and a[2,0] and we evaluate a[2,0] and so on in further equations.

To solve the system of equations I decided to use memoization defined as:

memoization:=memoization=Solve[#,wspolczynnikia]&

with attribute

Attributes[memoization] = {Listable}

where

wspolczynnikia={a[1, 0], a[1, 2], a[2, 0], a[2, 2], a[2, 4], a[3, 0], a[3, 2], a[3, 4], a[4, 0], a[4, 2], a[4, 4], a[4, 6], a[5, 0], a[5, 2], a[5, 4], a[5, 6], a[6, 0], a[6, 2], a[6, 4], a[6, 6], a[6, 8]}

is a list of all unknowns from the system of equations.

Solving the the system of equation

valuesa=(memoization[equations]//Simplify)[[1]]

I obtain such an answer enter image description here

I have two questions:

  1. How to avoid General::munfl error for such small values?
  2. Does pure function $memoization$ is well defined? I mean if the $memoization$ actually remember every unknown after its evaluation?
$\endgroup$

1 Answer 1

2
$\begingroup$

Using your definitions, convert your equations to exact values

equations2 = equations // Rationalize[#, 0] &;

valuesa = (memoization[equations2] // Simplify)[[1]];

Verifying the solutions

And @@ (equations2 /. valuesa // Simplify)

(* True *)

The approximate numeric values are

valuesaN = valuesa /. 
  r_Rational | r_Complex :> N[Chop[N[r, 200], 10^-15], 15]

(* {a[1, 0] -> -0.0265611500367717 - 0.0265611500367717 I, 
 a[1, 2] -> (-0.106244600147087 - 0.106244600147087 I) (1 + 2 ν), 
 a[2, 0] -> -0.0201341937249399 I, 
 a[2, 2] -> -0.0716904962352341 I (1 + 2 ν), a[2, 4] -> 0, 
 a[3, 0] -> -0.00377713180320597 + 0.00377713180320597 I, 
 a[3, 2] -> (-0.00190736625364759 + 0.00190736625364759 I) (1 + 2 ν), 
 a[3, 4] -> 0, a[4, 0] -> -0.000597491326682612, 
 a[4, 2] -> -0.000353896458668377 (1 + 2 ν), a[4, 4] -> 0, a[4, 6] -> 0, 
 a[5, 0] -> 0.000429676896338970 + 0.000429676896338970 I, 
 a[5, 2] -> (0.0000972372066957019 + 0.0000972372066957019 I) (1 + 2 ν), 
 a[5, 4] -> 0, a[5, 6] -> 0, a[6, 0] -> -0.0000663591807939109 I, 
 a[6, 2] -> -5.38936321670388*10^-6 I (1 + 2 ν), a[6, 4] -> 0, 
 a[6, 6] -> 0, a[6, 8] -> 0} *)
$\endgroup$
1
  • $\begingroup$ Actually, I need such extremely small values of a[m_,n_] so I change last command to 'valuesaN = valuesa /. r_Rational | r_Complex :> N[r, 5] '. It allows me to obtain non-zero value of a[6,8]. $\endgroup$
    – kozapdh
    Oct 7, 2022 at 8:44

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