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I have encountered bug in factors/fsolve while working with 19-th degree polynomial: 

 

restart;

Digits:=150:
T:=-6.22380759047872668130713536877030256364968636070065651396334810246948704517800844289400608484048587112392332204805530128070851889819985512874202683743*10^11*x^15+1.30320674544020861155773378297484119553167774488351680864188235543008368581731239587845304516984389100205019741111280194189829856859808540642557769603*10^10*x^6-4.66269056752439302342961934783764679009596024511170531603537327397832302302620600217387943312388922053304167698527169182278585860427802821480352854136*10^11*x^9-2.23704996926446119043671514798254764988240075983626880645807120500701523185370168392321824617257975062292105400290171941856646211919772527234308968846*10^9*x^5+1.70227750800986164284793608409450414651109713000703213281475661248797845709368255736580952492853671050778821135335145407044800619189451776936359075686*10^12*x^12+2.75132914316444017343930750158891109941047127103886960894939389127711887329536485172215512793127850186551483171384960841607262449527761786758828223621*10^8*x^4-34932.1305741980482332724462824276603543110574918698909627427160477228536038554704823433224807581628905769847550345090785500099182662763447500819501675*x+1.14859089243616386902401277001127426741536679789632050800564282457083136981495352758127041512610195469873039580049988570650313838832989727748112868586*10^12*x^14-6.60479740997269404871863401649844958253760499264982628400515571200965556608668632440745621931354881132921476624343305820884923453724427367494415551238*10^10*x^17-5.62833694496139881587566825658979473046292640751330993837612787833792702707901920475562429114656627532669843830531312111426766840057855202536781521123*10^10*x^7-1.41317084251894030640575308228417182186337397538022537825365672333611503622567981167488384741420461775617951229535582868905095341476313150469092017698*10^12*x^11-8.21268191019727949807038061270674769712976810595535494085869238004490345847174711476348954310804852930678468602300916137608391140935636924900016951244*10^8*x^19+397.252699937115297695173788383107213691513398731729934944369484808586994493337920006396692649274392699364304534062337678482629861430643165733668575822+2.45061767631130714142188028061597642324588736935628490184983950396964320020866945354270367821778753632385377702112725604392839751008695021580743844404*10^11*x^16+1.08699947236093139248842860047684411564605736115175003178583710408973712475471303403438454553797809672473740940054172927497665894877177132800140413775*10^10*x^18+1.84485142971549353599220669614768264648023215439682851036030548807708252959822522849421648368214446092969270608024147362000126035954415744321702508798*10^11*x^8-2.30461084758765666852675422975553976835398815305842562217293737088819307979848024374022174488508670823626363788957243202121075401744096241597591787541*10^7*x^3+9.17691101238967627829517731270700894639677345422963842539705370480050031196020089039807157125184117990094461042715726886282973724309183151499484709563*10^11*x^10-1.59505142070054081045558935086478494555622632474984266672719416019069437321867830698450310020630535513817946854845186492455277659549284062382504657541*10^12*x^13+1.21399269842294123787022397507857250840398420627023248941081275489711499859955449395398103964932227544163416388726749227644470585060488880538430515276*10^6*x^2:

infolevel[fsolve]:=3:
fsolve(T,fulldigits); # <-- completes without issues

factors(T);           # <-- freezes with log:
fsolve: ill-conditioned polynom of degree 19, with 0(0) given roots
fsolve: 1th root found in 9 iters at 165 Digits
fsolve: 2th root found in 11 iters at 164 Digits
fsolve: 3th root found in 11 iters at 165 Digits
fsolve: 4th root found in 10 iters at 174 Digits
fsolve: 5th root found in 10 iters at 167 Digits
fsolve: 6th root found in 11 iters at 168 Digits
fsolve: 7th root found in 11 iters at 174 Digits
fsolve: 8th root found in 11 iters at 170 Digits
fsolve: 9th root found in 11 iters at 181 Digits
fsolve: 10th root found in 11 iters at 172 Digits
fsolve: 11th root found in 12 iters at 175 Digits
fsolve: 12th root found in 11 iters at 182 Digits
fsolve: 14th root found in 14 iters at 177 Digits
fsolve: 15th root found in 10 iters at 176 Digits
fsolve: 16th root found in 11 iters at 173 Digits
Warning,  computation interrupted

 

The most interesting thing is that standalone 'fsolve' finishes fine, but 'factors' freezes in 'fsolve:-polyill' on the same polynomial.

My system is: Windows 7 x64, Maple 2017.0.

Would appreciate any help on how to avoid the issue with 'factors'.

i have 4 equation and 4 variables with DirectSearch package it will give me a solution but not in a good time
when i try fsolve it just give me a blank
these are my equations :
POL[0] := .42810/(.65429+c[-2])

 POL[1] := -8.4078*c[-1]-162.64*c[0]+84.228*c[1]-6/(.80888+c[-2])^2+9.7066/(.80888+c[-2])^3-3.9257/(.80888+c[-2])^4+(1/2*(.42786*c[-1]+.42786*c[0]+.42786*c[1]+.65429/(.80888+c[-2])))*(-49.180*c[-1]+31.921*c[0]-8.6921*c[1]+2/(.80888+c[-2])-3.2355/(.80888+c[-2])^2+1.3086/(.80888+c[-2])^3)

POL[2] := 53.965*c[-1]+43.012*c[0]-103.98*c[1]-6/(1.+c[-2])^2+12./(1.+c[-2])^3-6./(1.+c[-2])^4+(1/2*(.50000*c[-1]+.50000*c[0]+.50000*c[1]+1./(1.+c[-2])))*(22.229*c[-1]-37.815*c[0]+22.229*c[1]+2/(1.+c[-2])-4./(1.+c[-2])^2+2./(1.+c[-2])^3)

POL[3] := -30.115*c[-1]+43.264*c[0]+52.171*c[1]-6/(1.2363+c[-2])^2+14.836/(1.2363+c[-2])^3-9.1704/(1.2363+c[-2])^4+(1/2*(.52893*c[-1]+.52893*c[0]+.52893*c[1]+1.5284/(1.2363+c[-2])))*(-4.5997*c[-1]+16.892*c[0]-26.026*c[1]+2/(1.2363+c[-2])-4.9452/(1.2363+c[-2])^2+3.0568/(1.2363+c[-2])^3)

i even change digits to 100 but still no awenser

my fsolve syntax

K := fsolve({seq(POL[v], v = 0 .. 2*N+2)})

the awenser fsolve gave me

K:=

thats all it gave me

Hi, i wonder if there is a way to solve this 20×20 equations system for maple. Im trying fsolve but it doesn't work. aceitoso
 

nu := 6.1795*10^(-5)

0.6179500000e-4

(1)

varepsilon := 0.46e-1

0.46e-1

(2)

L__1 := 10.

10.

(3)

L__2 := 15.

15.

(4)

L__3 := 10.

10.

(5)

L__4 := 5*sqrt(2.)

7.071067810

(6)

L__5 := 6.

6.

(7)

L__6 := 6.

6.

(8)

L__7 := 20*sqrt(3.)*(1/3)

11.54700539

(9)

L__8 := 15.

15.

(10)

L__9 := 15.

15.

(11)

L__10 := 20.

20.

(12)

Re1 := 4*Q__1/(Pi*D__1*nu)

20604.24864*Q__1/D__1

(13)

Re2 := 4*Q__2/(Pi*D__2*nu)

20604.24864*Q__2/D__2

(14)

Re3 := 4*Q__3/(Pi*D__3*nu)

20604.24864*Q__3/D__3

(15)

Re4 := 4*Q__4/(Pi*D__4*nu)

20604.24864*Q__4/D__4

(16)

Re5 := 4*Q__5/(Pi*D__5*nu)

20604.24864*Q__5/D__5

(17)

Re6 := 4*Q__6/(Pi*D__6*nu)

20604.24864*Q__6/D__6

(18)

Re7 := 4*Q__7/(Pi*D__7*nu)

20604.24864*Q__7/D__7

(19)

Re8 := 4*Q__8/(Pi*D__8*nu)

20604.24864*Q__8/D__8

(20)

Re9 := 4*Q__9/(Pi*D__9*nu)

20604.24864*Q__9/D__9

(21)

Re10 := 4*Q__10/(Pi*D__10*nu)

20604.24864*Q__10/D__10

(22)

A__1 := (2.457*ln(1/((7/Re1)^.9+.27*varepsilon/D__1)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__1/Q__1)^.9+0.1242e-1/D__1))^16

(23)

A__2 := (2.457*ln(1/((7/Re2)^.9+.27*varepsilon/D__2)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__2/Q__2)^.9+0.1242e-1/D__2))^16

(24)

A__3 := (2.457*ln(1/((7/Re3)^.9+.27*varepsilon/D__3)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__3/Q__3)^.9+0.1242e-1/D__3))^16

(25)

A__4 := (2.457*ln(1/((7/Re4)^.9+.27*varepsilon/D__4)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__4/Q__4)^.9+0.1242e-1/D__4))^16

(26)

A__5 := (2.457*ln(1/((7/Re5)^.9+.27*varepsilon/D__5)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__5/Q__5)^.9+0.1242e-1/D__5))^16

(27)

A__6 := (2.457*ln(1/((7/Re6)^.9+.27*varepsilon/D__6)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__6/Q__6)^.9+0.1242e-1/D__6))^16

(28)

A__7 := (2.457*ln(1/((7/Re7)^.9+.27*varepsilon/D__7)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__7/Q__7)^.9+0.1242e-1/D__7))^16

(29)

A__8 := (2.457*ln(1/((7/Re8)^.9+.27*varepsilon/D__8)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__8/Q__8)^.9+0.1242e-1/D__8))^16

(30)

A__9 := (2.457*ln(1/((7/Re9)^.9+.27*varepsilon/D__9)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__9/Q__9)^.9+0.1242e-1/D__9))^16

(31)

A__10 := (2.457*ln(1/((7/Re10)^.9+.27*varepsilon/D__10)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__10/Q__10)^.9+0.1242e-1/D__10))^16

(32)

B__1 := (37530/Re1)^16

14680.75929*D__1^16/Q__1^16

(33)

B__2 := (37530/Re2)^16

14680.75929*D__2^16/Q__2^16

(34)

B__3 := (37530/Re3)^16

14680.75929*D__3^16/Q__3^16

(35)

B__4 := (37530/Re4)^16

14680.75929*D__4^16/Q__4^16

(36)

B__5 := (37530/Re5)^16

14680.75929*D__5^16/Q__5^16

(37)

B__6 := (37530/Re6)^16

14680.75929*D__6^16/Q__6^16

(38)

B__7 := (37530/Re7)^16

14680.75929*D__7^16/Q__7^16

(39)

B__8 := (37530/Re8)^16

14680.75929*D__8^16/Q__8^16

(40)

B__9 := (37530/Re9)^16

14680.75929*D__9^16/Q__9^16

(41)

B__10 := (37530/Re10)^16

14680.75929*D__10^16/Q__10^16

(42)

f__1 := 8*((8/Re1)^12+1/(A__1+B__1)^1.5)^(1/12)

8*(0.1173811769e-40*D__1^12/Q__1^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__1/Q__1)^.9+0.1242e-1/D__1))^16+14680.75929*D__1^16/Q__1^16)^1.5)^(1/12)

(43)

f__2 := 8*((8/Re2)^12+1/(A__2+B__2)^1.5)^(1/12)

8*(0.1173811769e-40*D__2^12/Q__2^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__2/Q__2)^.9+0.1242e-1/D__2))^16+14680.75929*D__2^16/Q__2^16)^1.5)^(1/12)

(44)

f__3 := 8*((8/Re3)^12+1/(A__3+B__3)^1.5)^(1/12)

8*(0.1173811769e-40*D__3^12/Q__3^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__3/Q__3)^.9+0.1242e-1/D__3))^16+14680.75929*D__3^16/Q__3^16)^1.5)^(1/12)

(45)

f__4 := 8*((8/Re4)^12+1/(A__4+B__4)^1.5)^(1/12)

8*(0.1173811769e-40*D__4^12/Q__4^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__4/Q__4)^.9+0.1242e-1/D__4))^16+14680.75929*D__4^16/Q__4^16)^1.5)^(1/12)

(46)

f__5 := 8*((8/Re5)^12+1/(A__5+B__5)^1.5)^(1/12)

8*(0.1173811769e-40*D__5^12/Q__5^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__5/Q__5)^.9+0.1242e-1/D__5))^16+14680.75929*D__5^16/Q__5^16)^1.5)^(1/12)

(47)

f__6 := 8*((8/Re6)^12+1/(A__6+B__6)^1.5)^(1/12)

8*(0.1173811769e-40*D__6^12/Q__6^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__6/Q__6)^.9+0.1242e-1/D__6))^16+14680.75929*D__6^16/Q__6^16)^1.5)^(1/12)

(48)

f__7 := 8*((8/Re7)^12+1/(A__7+B__7)^1.5)^(1/12)

8*(0.1173811769e-40*D__7^12/Q__7^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__7/Q__7)^.9+0.1242e-1/D__7))^16+14680.75929*D__7^16/Q__7^16)^1.5)^(1/12)

(49)

f__8 := 8*((8/Re8)^12+1/(A__8+B__8)^1.5)^(1/12)

8*(0.1173811769e-40*D__8^12/Q__8^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__8/Q__8)^.9+0.1242e-1/D__8))^16+14680.75929*D__8^16/Q__8^16)^1.5)^(1/12)

(50)

f__9 := 8*((8/Re9)^12+1/(A__9+B__9)^1.5)^(1/12)

8*(0.1173811769e-40*D__9^12/Q__9^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__9/Q__9)^.9+0.1242e-1/D__9))^16+14680.75929*D__9^16/Q__9^16)^1.5)^(1/12)

(51)

f__10 := 8*((8/Re10)^12+1/(A__10+B__10)^1.5)^(1/12)

8*(0.1173811769e-40*D__10^12/Q__10^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__10/Q__10)^.9+0.1242e-1/D__10))^16+14680.75929*D__10^16/Q__10^16)^1.5)^(1/12)

(52)

H__1 := piecewise(Q__1 > 0, 8000*10^6*f__1*L__1*Q__1^2/((9.8*(Pi^2))*D__1^5), -8000*10^6*f__1*L__1*Q__1^2/((9.8*(Pi^2))*D__1^5))

piecewise(0 < `#msub(mi("Q"),mi("1"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5)

(53)

H__2 := piecewise(Q__2 > 0, 8000*10^6*f__2*L__2*Q__2^2/((9.8*(Pi^2))*D__2^5), -8000*10^6*f__2*L__2*Q__2^2/((9.8*(Pi^2))*D__2^5))

piecewise(0 < `#msub(mi("Q"),mi("2"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^12/`#msub(mi("Q"),mi("2"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("2"))`/`#msub(mi("Q"),mi("2"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("2"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^16/`#msub(mi("Q"),mi("2"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("2"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("2"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^12/`#msub(mi("Q"),mi("2"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("2"))`/`#msub(mi("Q"),mi("2"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("2"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^16/`#msub(mi("Q"),mi("2"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("2"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("2"))`^5)

(54)

H__3 := piecewise(Q__3 > 0, 8000*10^6*f__3*L__3*Q__3^2/((9.8*(Pi^2))*D__3^5), -8000*10^6*f__3*L__3*Q__3^2/((9.8*(Pi^2))*D__3^5))

piecewise(0 < `#msub(mi("Q"),mi("3"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5)

(55)

H__4 := piecewise(Q__4 > 0, 8000*10^6*f__4*L__4*Q__4^2/((9.8*(Pi^2))*D__4^5), -8000*10^6*f__4*L__4*Q__4^2/((9.8*(Pi^2))*D__4^5))

piecewise(0 < `#msub(mi("Q"),mi("4"))`, 4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5, -4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5)

(56)

H__5 := piecewise(Q__5 > 0, 8000*10^6*f__5*L__5*Q__5^2/((9.8*(Pi^2))*D__5^5), -8000*10^6*f__5*L__5*Q__5^2/((9.8*(Pi^2))*D__5^5))

piecewise(0 < `#msub(mi("Q"),mi("5"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5)

(57)

H__6 := piecewise(Q__6 > 0, 8000*10^6*f__6*L__6*Q__6^2/((9.8*(Pi^2))*D__6^5), -8000*10^6*f__6*L__6*Q__6^2/((9.8*(Pi^2))*D__6^5))

piecewise(0 < `#msub(mi("Q"),mi("6"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5)

(58)

H__7 := piecewise(Q__7 > 0, 8000*10^6*f__7*L__7*Q__7^2/((9.8*(Pi^2))*D__7^5), -8000*10^6*f__7*L__7*Q__7^2/((9.8*(Pi^2))*D__7^5))

piecewise(0 < `#msub(mi("Q"),mi("7"))`, 7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5, -7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5)

(59)

H__8 := piecewise(Q__8 > 0, 8000*10^6*f__8*L__8*Q__8^2/((9.8*(Pi^2))*D__8^5), -8000*10^6*f__8*L__8*Q__8^2/((9.8*(Pi^2))*D__8^5))

piecewise(0 < `#msub(mi("Q"),mi("8"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5)

(60)

H__9 := piecewise(Q__9 > 0, 8000*10^6*f__9*L__9*Q__9^2/((9.8*(Pi^2))*D__9^5), -8000*10^6*f__9*L__9*Q__9^2/((9.8*(Pi^2))*D__9^5))

piecewise(0 < `#msub(mi("Q"),mi("9"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^12/`#msub(mi("Q"),mi("9"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("9"))`/`#msub(mi("Q"),mi("9"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("9"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^16/`#msub(mi("Q"),mi("9"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("9"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("9"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^12/`#msub(mi("Q"),mi("9"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("9"))`/`#msub(mi("Q"),mi("9"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("9"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^16/`#msub(mi("Q"),mi("9"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("9"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("9"))`^5)

(61)

H__10 := piecewise(Q__10 > 0, 8000*10^6*f__10*L__10*Q__10^2/((9.8*(Pi^2))*D__10^5), -8000*10^6*f__10*L__10*Q__10^2/((9.8*(Pi^2))*D__10^5))

piecewise(0 < `#msub(mi("Q"),mi("10"))`, 1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5, -1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5)

(62)

NULL

fsolve({Q__1 = Q__4, Q__3 = Q__7, 4*Q__1/(Pi*D__1^2) = 3.5, 4*Q__10/(Pi*D__10^2) = 3.5, 4*Q__2/(Pi*D__2^2) = 3.5, 4*Q__3/(Pi*D__3^2) = 3.5, 4*Q__4/(Pi*D__4^2) = 3.5, 4*Q__5/(Pi*D__5^2) = 3.5, 4*Q__6/(Pi*D__6^2) = 3.5, 4*Q__7/(Pi*D__7^2) = 3.5, 4*Q__8/(Pi*D__8^2) = 3.5, 4*Q__9/(Pi*D__9^2) = 3.5, H__1+H__4 = H__5+H__8, H__3+H__7 = H__6+H__10, Q__1+Q__5 = Q__2, Q__4+Q__8 = 980*(1/60), Q__5+Q__9 = Q__8+17, Q__7+Q__10 = 950*(1/60), Q__2+Q__3+Q__6 = 4000*(1/60), Q__9+Q__10+17.5 = Q__6}, {D__1 = 30, D__10 = 30, D__2 = 30, D__3 = 30, D__4 = 30, D__5 = 30, D__6 = 30, D__7 = 30, D__8 = 30, D__9 = 30, Q__1 = 20, Q__10 = 5, Q__2 = 40, Q__3 = 20, Q__4 = 20, Q__5 = 20, Q__6 = 20, Q__7 = 20, Q__8 = 5, Q__9 = 5})

fsolve({`#msub(mi("Q"),mi("1"))` = `#msub(mi("Q"),mi("4"))`, `#msub(mi("Q"),mi("3"))` = `#msub(mi("Q"),mi("7"))`, 4*`#msub(mi("Q"),mi("1"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("10"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("2"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("3"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("4"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("5"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("6"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("7"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("8"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("9"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^2) = 3.5, `#msub(mi("Q"),mi("1"))`+`#msub(mi("Q"),mi("5"))` = `#msub(mi("Q"),mi("2"))`, `#msub(mi("Q"),mi("4"))`+`#msub(mi("Q"),mi("8"))` = 49/3, `#msub(mi("Q"),mi("5"))`+`#msub(mi("Q"),mi("9"))` = `#msub(mi("Q"),mi("8"))`+17, `#msub(mi("Q"),mi("7"))`+`#msub(mi("Q"),mi("10"))` = 95/6, piecewise(0 < `#msub(mi("Q"),mi("1"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("4"))`, 4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5, -4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5) = piecewise(0 < `#msub(mi("Q"),mi("5"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("8"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5), piecewise(0 < `#msub(mi("Q"),mi("3"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("7"))`, 7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5, -7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5) = piecewise(0 < `#msub(mi("Q"),mi("6"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("10"))`, 1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5, -1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5), `#msub(mi("Q"),mi("2"))`+`#msub(mi("Q"),mi("3"))`+`#msub(mi("Q"),mi("6"))` = 200/3, `#msub(mi("Q"),mi("9"))`+`#msub(mi("Q"),mi("10"))`+17.5 = `#msub(mi("Q"),mi("6"))`}, {`#msub(mi("Q"),mi("1"))` = 20, `#msub(mi("Q"),mi("10"))` = 5, `#msub(mi("Q"),mi("2"))` = 40, `#msub(mi("Q"),mi("3"))` = 20, `#msub(mi("Q"),mi("4"))` = 20, `#msub(mi("Q"),mi("5"))` = 20, `#msub(mi("Q"),mi("6"))` = 20, `#msub(mi("Q"),mi("7"))` = 20, `#msub(mi("Q"),mi("8"))` = 5, `#msub(mi("Q"),mi("9"))` = 5, `#msub(mi("D",fontstyle = "normal"),mi("1"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("10"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("2"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("3"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("4"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("5"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("6"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("7"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("8"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("9"))` = 30})

(63)

NULL


 

Download aceitoso.mw

 

hey everyone
i got a little problem here i really dont get it why my fsolve give me this error

Error, (in sqrfree) argument must be a polynomial or a rational function in {cf[-2], cf[-1], cf[0], cf[1]}
these are my variables :


cf[-2], cf[-1], cf[0], cf[1]}


thats part of my code :

res1;
(34.30563197 cf[-1] - 10.13498047 cf[0] + 5.197134649 cf[1]

   - 0.4714805434) (0.3095515346 cf[-2] + 0.3822521253) - (cf[-1](2.466022067

  ) + cf[0](-0.6605923783) + cf[1](1.076415647))^2

   - cf[-1](2.466022067) - cf[0](-0.6605923783)

   - cf[1](1.076415647) - 333.1166471 cf[-1] + 186.8672744 cf[0]

   - 128.6145289 cf[1] + 0.8737683108, (-39.73727883 cf[-1]

   + 26.25682759 cf[0] - 7.289811219 cf[1] - 0.3506934780)

  (0.4161980514 cf[-1] + 0.4402863507) - (cf[-1](0.3227083347)

   + cf[0](2.517826949) + cf[1](-0.7889944208))^2

   - cf[-1](0.3227083347) - cf[0](2.517826949)

   - cf[1](-0.7889944208) - 15.03436409 cf[-1]

   - 129.5665191 cf[0] + 68.25827819 cf[1] + 0.5888637790,

  (17.36111111 cf[-1] - 29.80788311 cf[0] + 17.36111111 cf[1]

   - 0.2500000000) (0.5000000000 cf[0] + 0.5000000000)

                                                            2
   - (cf[-1](-1.833333334) + cf[0](0.) + cf[1](2.333333334))

   - cf[-1](-1.833333334) - cf[0](0.) - cf[1](2.333333334)

   + 38.17276297 cf[-1] + 34.00261850 cf[0] - 77.23526300 cf[1]

   + 0.3750000000, (-3.548332053 cf[-1] + 12.78057007 cf[0]

   - 19.34221012 cf[1] - 0.1707008416) (0.5290914191 cf[1]

   + 0.5597136492) - (cf[-1](1.060931345) + cf[0](-1.540306477)

   + cf[1](-0.2297630675))^2 - cf[-1](1.060931345)

   - cf[0](-1.540306477) - cf[1](-0.2297630675)

   - 20.59209188 cf[-1] + 28.27859544 cf[0] + 40.45630289 cf[1]

         -10                      
   + 1 10    cf[-2] + 0.2254717519


fsolve({seq(res1[v] = 0, v = 1 .. 2*N+2)})     ( N here is 1 )

why i cant get the awenser and if you can plz solve it for me

i would be happy that anyone can give me an explanation with details

tnX a lot

Arian
 

 

I wonder what the built-in algorithm is used in "fsolve". From some references, it seems to be Newton iteration. 
But fsolve succeeds to quickly find a root of multiplicity more than 1, which can't be achieved by Newton iteration. So I wonder whether there are other techniques involved? Thank you!

I am new to Maple and I am trying to add units to the "Flow Through an Expansion Valve" Application Demonstration.  I was trying pressure in [PSI], temperature in [degC] and flow rate in [kg/hour] everything else in SI units.  I included with(Units:-Standard) but had no luck with the fsolve function.

Any chance someone could make a version of this demonstration applicaton that includes units?

 

Thanks

 


 

A geometric construction for the Summer Holiday

 
Does every plane simple closed curve contain all four vertices of some square?

 This is an old classical conjecture. See:
https://en.wikipedia.org/wiki/Inscribed_square_problem

Maybe someone finds a counterexample (for non-analytic curves) using the next procedure and becomes famous!

 

SQ:=proc(X::procedure, Y::procedure, rng::range(realcons), r:=0.49)
local t1:=lhs(rng), t2:=rhs(rng), a,b,c,d,s;
s:=fsolve({ X(a)+X(c) = X(b)+X(d),
            Y(a)+Y(c) = Y(b)+Y(d),
            (X(a)-X(c))^2+(Y(a)-Y(c))^2 = (X(b)-X(d))^2+(Y(b)-Y(d))^2,
            (X(a)-X(c))*(X(b)-X(d)) + (Y(a)-Y(c))*(Y(b)-Y(d)) = 0},
          {a=t1..t1+r*(t2-t1),b=rng,c=rng,d=t2-r*(t2-t1)..t2});  #lprint(s);
if type(s,set) then s:=rhs~(s)[];[s,s[1]] else WARNING("No solution found"); {} fi;
end:

 

Example

 

X := t->(10-sin(7*t)*exp(-t))*cos(t);
Y := t->(10+sin(6*t))*sin(t);
rng := 0..2*Pi;

proc (t) options operator, arrow; (10-sin(7*t)*exp(-t))*cos(t) end proc

 

proc (t) options operator, arrow; (10+sin(6*t))*sin(t) end proc

 

0 .. 2*Pi

(1)

s:=SQ(X, Y, rng):
plots:-display(
   plot([X,Y,rng], scaling=constrained),
   plot([seq( eval([X(t),Y(t)],t=u),u=s)], color=blue, thickness=2));

 

hello.i have a problem for solving this equation.i dont why my past post about this is deleted.!!!

please help me

thanks,,,

9.mw
 

restart:

A1:= 27159:  n:= 0.59:  A2:= 70941:  h0:= 3e-4:   
L:= 0.8:  dpx := -98100:  uc:= 0.007:  k:=2.7:

ODE:= (A3,y)->
   (h0^(n+1)*L/sqrt(n)*(A1*exp(sqrt(n)*y/L)-A2*exp(-sqrt(n)*y/L))/k+dpx*y*h0^(n+1)/k+A3*(h0)^n/k)^(1/n)
;

proc (A3, y) options operator, arrow; (h0^(n+1)*L*(A1*exp(sqrt(n)*y/L)-A2*exp(-sqrt(n)*y/L))/(sqrt(n)*k)+dpx*y*h0^(n+1)/k+A3*h0^n/k)^(1/n) end proc

(1)

ODEINT:= proc(A3)
option remember;
local y;
   evalf(Int(ODE(A3,y), y= 0..1, epsilon= 1e-7)) - uc
end proc:

ReINT:= proc(A3x, A3y)
   Digits:= 15:
   Re(ODEINT(A3x + I*A3y))
end proc:

ImINT:= subs(Re= Im, eval(ReINT)):

Digits:= 7:
a3:= fsolve([ReINT, ImINT]);

fsolve([ReINT, ImINT])

(2)

A3:= Complex(a3[]);

Complex(fsolve([ReINT, ImINT])[])

(3)

Solve as IVP:

Digits:= 15:
sol:= dsolve({diff(u(y),y) = ODE(A3,y), u(0)=0}, numeric, range=0..1,  output=listprocedure):

Warning,  computation interrupted

 

NULL

``

NULL

NULL

plots:-odeplot(
   sol, [[y, Re(u(y))], [y, Im(u(y))]], y= 0..1,
   legend= [real, imag], labels= [y, u(y)]
);

Verify that boundary condition at u(1) is satisfied:

 

 

 

abs(eval(u(y), sol(1)) - uc);

sol(.5);

"\"

fy3 := eval(u(y), sol); with(CurveFitting); fy33 := PolynomialInterpolation([[0, fy3(0)], [.1, fy3(.1)], [.2, fy3(.2)], [.3, fy3(.3)], [.4, fy3(.4)], [.5, fy3(.5)], [.6, fy3(.6)], [.7, fy3(.7)], [.8, fy3(.8)], [.9, fy3(.9)], [1, fy3(1)]], y)

DEBI := int(fy33, y = 0 .. 1)

NULL

``

plot(DEBI, y = 0 .. 1)

``

``

``

``

``


 

Download 9.mw

 

Greetings Sirs,

I have recently aquired Maple for some mathematics, and being a new user, I basically google for everything at the moment.

While it has gone well so far, I seem to have hit a bump that I cannot figure out.

I have a function: f(x)=3.2+0.4sin(1.25x), 0<x<5

Trying to find the places where "f(x)=3.5" would normally be done with the equation "3.5=3.2+0.4sin(1.25x)", and when I solve for the equation in Maple I get a solution too.

Problem is though, I know there is supposed to be multiple solutions. Having used wolframalpha, and being capable of seeing the plot in Maple, I know there is two points within the period "x=0..5" that is the solution.

But when I try to solve the equation, I get only one solution per solve, and the second solve doesn't make much sense for me. These are what I use:

As you can see, in the first solve the entire function is being taking into consideration, yet I only get one solution... In the second solve I have tried specifying a period, but I still only get one solution.

Basically any help here is appreciated, because from what I understand, having read google, the solve command or fsolve command is supposed to give multiple results if they are there.

With appreciation,
Ciesi

(Edit: Image size changed)

when i want to get awenser i have to solve it for 36 equation and 36 variabales
but maple will not give me a solution (just toss me back my variabales ) i dont know whats wrong
it will give me an awenser for lower like 20equ and 20var ?
parameters :

there is m for power an equation (equation^m) its between 2 , 2.5 , 3 , 4
and N give 2N+2var and 2N+2equ
its a hard calculation i copy it here hope u get it

h= "a number "

p := proc (x) c[-N-1]*x^2+1 end proc

dp := diff(p(x), x)

ddp := diff(p(x), x, x)

DELTA2 := piecewise(k <> j, -2*(-1)^(j-k)/(j-k)^2, k = j, -(1/3)*Pi^2)/h^2

DELTA1 := piecewise(k <> j, (-1)^(j-k)/(j-k), k = j, 0)/h

DELTA0 := piecewise(k <> j, 0, k = j, 1)

PHI := proc (x) ln(sinh(x)) end proc

dPHI := diff(PHI(x), x)

ddPHI := diff(PHI(x), x, x)
 

for i from -N-1 to N do x[i] := ln(exp(i*h)+(exp(2*i*h)+1)^(1/2)) end do

variabales : c[-N-1],c[-N],c[-N+1]...c[N-1],c[N] total 2N+2 var



My equations

POL := seq(simplify(eval(sum(c[k]*((eval(2*dPHI*DELTA1), x = x[j])+eval(x[j]*ddPHI*DELTA1, x = x[j])+x[j]*(eval(dPHI^2, x = x[j]))*DELTA2), k = -N .. N)+eval(ddp, x = x[j])+2*(sum(c[k]*(eval(x[j]*dPHI*DELTA1, x = x[j])+DELTA0), k = -N .. N)+eval(dp, x = x[j]))/x[j]+(c[j]*x[j]+p(x[j]))^m, x = x[j])), j = -N-1 .. N)

solving

K := fsolve({seq(POL[v] = 0, v = 1 .. 2*N+2)})

it can calculate for m=2.5 , N=15 , h=0.29669

if you can calculate it for m=3 , N=17 , h=0.41600

Regarding my recent question http://www.mapleprimes.com/questions/221909-How-To-Extract-Data-From-Implicit-Function I would like to share an interesting observation. Here the code of the program:

restart;
R0 := ln(y)+Re(Psi(1/2+(2*(p^2+(1/2)*sqrt(2*I+4*ksi_fs^2*p^2)*tanh(sqrt(2*I+4*ksi_fs^2*p^2)*x)/(tau+0.5e-2*a)))/y))+gamma+2*ln(2)
tau:= 10.000:ksi_fs:=10:p:=0.037:
R0p:= unapply(R0, [a,x]):
R0f:= proc(a,x)
local r:= fsolve(R0p(a,x), y= 0..1);
   `if`(r::float, r, Float(undefined))
end proc:
M:= Matrix(
   (100,100),
   (i,j)-> R0f(i, 1 + (j-1)*(0.5-0)/(100-1)),
   datatype= float[8]
);

After approximately 2 hours of calculations I get a message window

But I repeat this calculations on another computer with the same Windows 7 64 bit and Maple 17 I don't get such error and I obtain desired data.

So can Maple be sensitive to the hardware? 

I am trying to solve system consisting of two equations and two unknowns. I tried solve but it gives back unevaluated then I tried fsolve which gives an error.
 

restart; x := 2.891022275*`&epsilon;`^4*sin(phi)^5*cos(phi)+1.080128320*`&epsilon;`^8*sin(phi)^11*cos(phi)+.1742483217*`&epsilon;`^10*sin(phi)^9*cos(phi)+3.293959886*`&epsilon;`^4*sin(phi)^15*cos(phi)+0.1414814731e-3*`&epsilon;`^12*sin(phi)*cos(phi)+0.1186386550e-1*`&epsilon;`^10*sin(phi)^3*cos(phi)+4.689119196*`&epsilon;`^2*sin(phi)^11*cos(phi)+.2775645236*`&epsilon;`^8*sin(phi)^5*cos(phi)+2.242139502*`&epsilon;`^6*sin(phi)^7*cos(phi)+6.170463035*`&epsilon;`^4*sin(phi)^9*cos(phi)+.2212715683*`&epsilon;`^2*sin(phi)*cos(phi)+.2565381358*`&epsilon;`^4*sin(phi)*cos(phi)+6.282275004*`&epsilon;`^4*sin(phi)^11*cos(phi)+0.9582543506e-5*`&epsilon;`^14*sin(phi)*cos(phi)+1.375810863*`&epsilon;`^2*sin(phi)^3*cos(phi)+0.4588193106e-1*`&epsilon;`^10*sin(phi)^5*cos(phi)+.6194422970*`&epsilon;`^8*sin(phi)^7*cos(phi)+0.1249753779e-2*`&epsilon;`^12*sin(phi)^3*cos(phi)+3.258184644*`&epsilon;`^6*sin(phi)^9*cos(phi)+3.520102051*`&epsilon;`^2*sin(phi)^13*cos(phi)+0.9608710101e-4*`&epsilon;`^14*sin(phi)^3*cos(phi)+5.222697446*`&epsilon;`^4*sin(phi)^13*cos(phi)+0.4740690151e-6*`&epsilon;`^16*sin(phi)*cos(phi)+.1124269022*`&epsilon;`^10*sin(phi)^7*cos(phi)+0.5349926002e-2*`&epsilon;`^12*sin(phi)^5*cos(phi)+.9885168554*`&epsilon;`^8*sin(phi)^9*cos(phi)+3.656113028*`&epsilon;`^6*sin(phi)^11*cos(phi)+2.252753163*`&epsilon;`^2*sin(phi)^15*cos(phi)+0.1562649478e-2*`&epsilon;`^10*sin(phi)*cos(phi)+0.8234222560e-1*`&epsilon;`^8*sin(phi)^3*cos(phi)+0.1277730241e-1*`&epsilon;`^12*sin(phi)^7*cos(phi)+1.148250169*`&epsilon;`^6*sin(phi)^5*cos(phi)+0.4933078791e-5*`&epsilon;`^16*sin(phi)^3*cos(phi)+4.857729947*`&epsilon;`^4*sin(phi)^7*cos(phi)+5.282506255*`&epsilon;`^2*sin(phi)^9*cos(phi)+0.1560418629e-7*`&epsilon;`^18*sin(phi)*cos(phi)-.6257226193*sin(phi)*cos(phi)+.6645139802*sin(phi)^11*cos(phi)+0.4077214292e-3*`&epsilon;`^14*sin(phi)^5*cos(phi)+.1265580305*sin(phi)^17*cos(phi)+.2494189998*sin(phi)^15*cos(phi)+.4337136311*sin(phi)^13*cos(phi)-.1331733921*sin(phi)^3*cos(phi)+.5467360220*sin(phi)^5*cos(phi)+.8861408610*sin(phi)^7*cos(phi)+4.820745909*`&epsilon;`^2*sin(phi)^7*cos(phi)+1.134364300*`&epsilon;`^2*sin(phi)^17*cos(phi)+0.7437311918e-1*`&epsilon;`^6*sin(phi)*cos(phi)+0.1283200926e-1*`&epsilon;`^8*sin(phi)*cos(phi)+1.168884099*`&epsilon;`^4*sin(phi)^3*cos(phi)+.3981616844*`&epsilon;`^6*sin(phi)^3*cos(phi)+3.270035435*`&epsilon;`^2*sin(phi)^5*cos(phi)+.8667852062*sin(phi)^9*cos(phi)+0.5208654259e-1*sin(phi)^19*cos(phi)+2.975771526*`&epsilon;`^6*sin(phi)^13*cos(phi); y := 2.891022275*`&epsilon;`^4*sin(phi)^5*cos(phi)+1.080128320*`&epsilon;`^8*sin(phi)^11*cos(phi)+.1742483217*`&epsilon;`^10*sin(phi)^9*cos(phi)+3.293959886*`&epsilon;`^4*sin(phi)^15*cos(phi)+0.1414814731e-3*`&epsilon;`^12*sin(phi)*cos(phi)+0.1186386550e-1*`&epsilon;`^10*sin(phi)^3*cos(phi)+4.689119196*`&epsilon;`^2*sin(phi)^11*cos(phi)+.2775645236*`&epsilon;`^8*sin(phi)^5*cos(phi)+2.242139502*`&epsilon;`^6*sin(phi)^7*cos(phi)+6.170463035*`&epsilon;`^4*sin(phi)^9*cos(phi)+.2212715683*`&epsilon;`^2*sin(phi)*cos(phi)+.2565381358*`&epsilon;`^4*sin(phi)*cos(phi)+6.282275004*`&epsilon;`^4*sin(phi)^11*cos(phi)+0.9582543506e-5*`&epsilon;`^14*sin(phi)*cos(phi)+1.375810863*`&epsilon;`^2*sin(phi)^3*cos(phi)+0.4588193106e-1*`&epsilon;`^10*sin(phi)^5*cos(phi)+.6194422970*`&epsilon;`^8*sin(phi)^7*cos(phi)+0.1249753779e-2*`&epsilon;`^12*sin(phi)^3*cos(phi)+3.258184644*`&epsilon;`^6*sin(phi)^9*cos(phi)+3.520102051*`&epsilon;`^2*sin(phi)^13*cos(phi)+0.9608710101e-4*`&epsilon;`^14*sin(phi)^3*cos(phi)+5.222697446*`&epsilon;`^4*sin(phi)^13*cos(phi)+0.4740690151e-6*`&epsilon;`^16*sin(phi)*cos(phi)+.1124269022*`&epsilon;`^10*sin(phi)^7*cos(phi)+0.5349926002e-2*`&epsilon;`^12*sin(phi)^5*cos(phi)+.9885168554*`&epsilon;`^8*sin(phi)^9*cos(phi)+3.656113028*`&epsilon;`^6*sin(phi)^11*cos(phi)+2.252753163*`&epsilon;`^2*sin(phi)^15*cos(phi)+0.1562649478e-2*`&epsilon;`^10*sin(phi)*cos(phi)+0.8234222560e-1*`&epsilon;`^8*sin(phi)^3*cos(phi)+0.1277730241e-1*`&epsilon;`^12*sin(phi)^7*cos(phi)+1.148250169*`&epsilon;`^6*sin(phi)^5*cos(phi)+0.4933078791e-5*`&epsilon;`^16*sin(phi)^3*cos(phi)+4.857729947*`&epsilon;`^4*sin(phi)^7*cos(phi)+5.282506255*`&epsilon;`^2*sin(phi)^9*cos(phi)+0.1560418629e-7*`&epsilon;`^18*sin(phi)*cos(phi)-.6257226193*sin(phi)*cos(phi)+.6645139802*sin(phi)^11*cos(phi)+0.4077214292e-3*`&epsilon;`^14*sin(phi)^5*cos(phi)+.1265580305*sin(phi)^17*cos(phi)+.2494189998*sin(phi)^15*cos(phi)+.4337136311*sin(phi)^13*cos(phi)-.1331733921*sin(phi)^3*cos(phi)+.5467360220*sin(phi)^5*cos(phi)+.8861408610*sin(phi)^7*cos(phi)+4.820745909*`&epsilon;`^2*sin(phi)^7*cos(phi)+1.134364300*`&epsilon;`^2*sin(phi)^17*cos(phi)+0.7437311918e-1*`&epsilon;`^6*sin(phi)*cos(phi)+0.1283200926e-1*`&epsilon;`^8*sin(phi)*cos(phi)+1.168884099*`&epsilon;`^4*sin(phi)^3*cos(phi)+.3981616844*`&epsilon;`^6*sin(phi)^3*cos(phi)+3.270035435*`&epsilon;`^2*sin(phi)^5*cos(phi)+.8667852062*sin(phi)^9*cos(phi)+0.5208654259e-1*sin(phi)^19*cos(phi)+2.975771526*`&epsilon;`^6*sin(phi)^13*cos(phi); evalf(solve({x = 0, y = 0}, {phi, `&epsilon;`})); fsolve({x = 0, y = 0}, {phi, `&epsilon;`})

.9885168554*`&epsilon;`^8*sin(phi)^9*cos(phi)+0.1249753779e-2*`&epsilon;`^12*sin(phi)^3*cos(phi)+3.258184644*`&epsilon;`^6*sin(phi)^9*cos(phi)+.1124269022*`&epsilon;`^10*sin(phi)^7*cos(phi)+0.4588193106e-1*`&epsilon;`^10*sin(phi)^5*cos(phi)+.2565381358*`&epsilon;`^4*sin(phi)*cos(phi)+6.282275004*`&epsilon;`^4*sin(phi)^11*cos(phi)+0.4933078791e-5*`&epsilon;`^16*sin(phi)^3*cos(phi)+5.282506255*`&epsilon;`^2*sin(phi)^9*cos(phi)+2.242139502*`&epsilon;`^6*sin(phi)^7*cos(phi)+6.170463035*`&epsilon;`^4*sin(phi)^9*cos(phi)+0.8234222560e-1*`&epsilon;`^8*sin(phi)^3*cos(phi)+0.9608710101e-4*`&epsilon;`^14*sin(phi)^3*cos(phi)+3.656113028*`&epsilon;`^6*sin(phi)^11*cos(phi)+5.222697446*`&epsilon;`^4*sin(phi)^13*cos(phi)+0.1562649478e-2*`&epsilon;`^10*sin(phi)*cos(phi)+.6194422970*`&epsilon;`^8*sin(phi)^7*cos(phi)+3.520102051*`&epsilon;`^2*sin(phi)^13*cos(phi)+0.1186386550e-1*`&epsilon;`^10*sin(phi)^3*cos(phi)+4.689119196*`&epsilon;`^2*sin(phi)^11*cos(phi)+1.375810863*`&epsilon;`^2*sin(phi)^3*cos(phi)+0.4740690151e-6*`&epsilon;`^16*sin(phi)*cos(phi)+0.4077214292e-3*`&epsilon;`^14*sin(phi)^5*cos(phi)+0.9582543506e-5*`&epsilon;`^14*sin(phi)*cos(phi)+0.5349926002e-2*`&epsilon;`^12*sin(phi)^5*cos(phi)+.1742483217*`&epsilon;`^10*sin(phi)^9*cos(phi)+1.148250169*`&epsilon;`^6*sin(phi)^5*cos(phi)+0.1277730241e-1*`&epsilon;`^12*sin(phi)^7*cos(phi)+0.7437311918e-1*`&epsilon;`^6*sin(phi)*cos(phi)+1.080128320*`&epsilon;`^8*sin(phi)^11*cos(phi)+2.975771526*`&epsilon;`^6*sin(phi)^13*cos(phi)+1.134364300*`&epsilon;`^2*sin(phi)^17*cos(phi)+3.293959886*`&epsilon;`^4*sin(phi)^15*cos(phi)+1.168884099*`&epsilon;`^4*sin(phi)^3*cos(phi)+3.270035435*`&epsilon;`^2*sin(phi)^5*cos(phi)+0.1283200926e-1*`&epsilon;`^8*sin(phi)*cos(phi)+4.820745909*`&epsilon;`^2*sin(phi)^7*cos(phi)+.3981616844*`&epsilon;`^6*sin(phi)^3*cos(phi)+2.891022275*`&epsilon;`^4*sin(phi)^5*cos(phi)+0.1414814731e-3*`&epsilon;`^12*sin(phi)*cos(phi)+.2212715683*`&epsilon;`^2*sin(phi)*cos(phi)+2.252753163*`&epsilon;`^2*sin(phi)^15*cos(phi)+4.857729947*`&epsilon;`^4*sin(phi)^7*cos(phi)+.2775645236*`&epsilon;`^8*sin(phi)^5*cos(phi)+0.1560418629e-7*`&epsilon;`^18*sin(phi)*cos(phi)-.6257226193*sin(phi)*cos(phi)+.8667852062*sin(phi)^9*cos(phi)+0.5208654259e-1*sin(phi)^19*cos(phi)+.1265580305*sin(phi)^17*cos(phi)+.2494189998*sin(phi)^15*cos(phi)+.4337136311*sin(phi)^13*cos(phi)-.1331733921*sin(phi)^3*cos(phi)+.5467360220*sin(phi)^5*cos(phi)+.8861408610*sin(phi)^7*cos(phi)+.6645139802*sin(phi)^11*cos(phi)

 

.9885168554*`&epsilon;`^8*sin(phi)^9*cos(phi)+0.1249753779e-2*`&epsilon;`^12*sin(phi)^3*cos(phi)+3.258184644*`&epsilon;`^6*sin(phi)^9*cos(phi)+.1124269022*`&epsilon;`^10*sin(phi)^7*cos(phi)+0.4588193106e-1*`&epsilon;`^10*sin(phi)^5*cos(phi)+.2565381358*`&epsilon;`^4*sin(phi)*cos(phi)+6.282275004*`&epsilon;`^4*sin(phi)^11*cos(phi)+0.4933078791e-5*`&epsilon;`^16*sin(phi)^3*cos(phi)+5.282506255*`&epsilon;`^2*sin(phi)^9*cos(phi)+2.242139502*`&epsilon;`^6*sin(phi)^7*cos(phi)+6.170463035*`&epsilon;`^4*sin(phi)^9*cos(phi)+0.8234222560e-1*`&epsilon;`^8*sin(phi)^3*cos(phi)+0.9608710101e-4*`&epsilon;`^14*sin(phi)^3*cos(phi)+3.656113028*`&epsilon;`^6*sin(phi)^11*cos(phi)+5.222697446*`&epsilon;`^4*sin(phi)^13*cos(phi)+0.1562649478e-2*`&epsilon;`^10*sin(phi)*cos(phi)+.6194422970*`&epsilon;`^8*sin(phi)^7*cos(phi)+3.520102051*`&epsilon;`^2*sin(phi)^13*cos(phi)+0.1186386550e-1*`&epsilon;`^10*sin(phi)^3*cos(phi)+4.689119196*`&epsilon;`^2*sin(phi)^11*cos(phi)+1.375810863*`&epsilon;`^2*sin(phi)^3*cos(phi)+0.4740690151e-6*`&epsilon;`^16*sin(phi)*cos(phi)+0.4077214292e-3*`&epsilon;`^14*sin(phi)^5*cos(phi)+0.9582543506e-5*`&epsilon;`^14*sin(phi)*cos(phi)+0.5349926002e-2*`&epsilon;`^12*sin(phi)^5*cos(phi)+.1742483217*`&epsilon;`^10*sin(phi)^9*cos(phi)+1.148250169*`&epsilon;`^6*sin(phi)^5*cos(phi)+0.1277730241e-1*`&epsilon;`^12*sin(phi)^7*cos(phi)+0.7437311918e-1*`&epsilon;`^6*sin(phi)*cos(phi)+1.080128320*`&epsilon;`^8*sin(phi)^11*cos(phi)+2.975771526*`&epsilon;`^6*sin(phi)^13*cos(phi)+1.134364300*`&epsilon;`^2*sin(phi)^17*cos(phi)+3.293959886*`&epsilon;`^4*sin(phi)^15*cos(phi)+1.168884099*`&epsilon;`^4*sin(phi)^3*cos(phi)+3.270035435*`&epsilon;`^2*sin(phi)^5*cos(phi)+0.1283200926e-1*`&epsilon;`^8*sin(phi)*cos(phi)+4.820745909*`&epsilon;`^2*sin(phi)^7*cos(phi)+.3981616844*`&epsilon;`^6*sin(phi)^3*cos(phi)+2.891022275*`&epsilon;`^4*sin(phi)^5*cos(phi)+0.1414814731e-3*`&epsilon;`^12*sin(phi)*cos(phi)+.2212715683*`&epsilon;`^2*sin(phi)*cos(phi)+2.252753163*`&epsilon;`^2*sin(phi)^15*cos(phi)+4.857729947*`&epsilon;`^4*sin(phi)^7*cos(phi)+.2775645236*`&epsilon;`^8*sin(phi)^5*cos(phi)+0.1560418629e-7*`&epsilon;`^18*sin(phi)*cos(phi)-.6257226193*sin(phi)*cos(phi)+.8667852062*sin(phi)^9*cos(phi)+0.5208654259e-1*sin(phi)^19*cos(phi)+.1265580305*sin(phi)^17*cos(phi)+.2494189998*sin(phi)^15*cos(phi)+.4337136311*sin(phi)^13*cos(phi)-.1331733921*sin(phi)^3*cos(phi)+.5467360220*sin(phi)^5*cos(phi)+.8861408610*sin(phi)^7*cos(phi)+.6645139802*sin(phi)^11*cos(phi)

 

{phi = 0., `&epsilon;` = `&epsilon;`}, {phi = 1.570796327, `&epsilon;` = `&epsilon;`}, {phi = phi, `&epsilon;` = RootOf(1560418629*_Z^18+(47406901510+493307879100*sin(phi)^2)*_Z^16+(40772142920000*sin(phi)^4+9608710101000*sin(phi)^2+958254350600)*_Z^14+(14148147310000+124975377900000*sin(phi)^2+534992600200000*sin(phi)^4+1277730241000000*sin(phi)^6)*_Z^12+(11242690220000000*sin(phi)^6+1186386550000000*sin(phi)^2+17424832170000000*sin(phi)^8+156264947800000+4588193106000000*sin(phi)^4)*_Z^10+(8234222560000000*sin(phi)^2+61944229700000000*sin(phi)^6+98851685540000000*sin(phi)^8+108012832000000000*sin(phi)^10+27756452360000000*sin(phi)^4+1283200926000000)*_Z^8+(7437311918000000+114825016900000000*sin(phi)^4+297577152600000000*sin(phi)^12+325818464400000000*sin(phi)^8+365611302800000000*sin(phi)^10+224213950200000000*sin(phi)^6+39816168440000000*sin(phi)^2)*_Z^6+(485772994700000000*sin(phi)^6+628227500400000000*sin(phi)^10+522269744600000000*sin(phi)^12+329395988600000000*sin(phi)^14+25653813580000000+617046303500000000*sin(phi)^8+116888409900000000*sin(phi)^2+289102227500000000*sin(phi)^4)*_Z^4+(22127156830000000+137581086300000000*sin(phi)^2+468911919600000000*sin(phi)^10+352010205100000000*sin(phi)^12+225275316300000000*sin(phi)^14+528250625500000000*sin(phi)^8+327003543500000000*sin(phi)^4+113436430000000000*sin(phi)^16+482074590900000000*sin(phi)^6)*_Z^2-62572261930000000-13317339210000000*sin(phi)^2+12655803050000000*sin(phi)^16+54673602200000000*sin(phi)^4+86678520620000000*sin(phi)^8+43371363110000000*sin(phi)^12+66451398020000000*sin(phi)^10+88614086100000000*sin(phi)^6+24941899980000000*sin(phi)^14+5208654259000000*sin(phi)^18)}

 

Error, (in fsolve) number of equations, 1, does not match number of variables, 2

 

``


 

Download equations_solve.mw

I am trying to evaluate the following equation analytically but it gives back unevaluated then I tried fsolve which giving me the answer but I need phi greater than  zero. How can I avoid negative values. Also Is there any ways to solve it analytically. 

Please see the attachment

 

Download ANALYTIC.mw

 

Hi,

I have three simultaneous equations  with three unknown variables (E, W, T). When I solve these  simultaneous equations with fsolve command without specifying any range for variables, I don't get desirable root ( equation sol4 in maple worksheet- {E = 0.1007672475e-2, T = .7969434549, W = 0.1937272759e-2}). For this problem, I know the correct root {E = 2843.916504, T = .2782913990, W = 5344.844134} beforehand which maximize the objective function TP (equation sol8 in maple worksheet) and when I specify the narrow range of variables around the already known correct root in the fsolve command, then I get correct root ( equation sol5 in maple worksheet). If I don't know the actual answer (correct roots of the simultaneous equation) beforehand, How  could I get the correct root with fsolve command because it is very tedious work to specify different range in fsolve command repetitively to solve it by trial and error.

I also tried Direct Search method as suggested in this forum  but DirectSearch is also not able to provide the correct root (equation sol6 in maple worksheet). If I specify the narrow range around known root in direct search method ( equation sol6a in maple worksheet), then it would provide close to optimal root but if I don't know the correct root beforehand, then I couldn't specify the narrow range of variables, then how can I get correct root through direct search command.

Equation sol10 in maple worksheet  (objective function value at correct root) confirms that {E = 2843.916504, T = .2782913990, W = 5344.844134} is the correct root because it provide the value of objective function (TP) equal to 78285.85621 as opposed to negative value (TP value -12.53348074 in equation sol9)  produced by incorrect root  {E = 0.1007672475e-2, T = .7969434549, W = 0.1937272759e-2}).

Is there any method which would provide all the roots of these simultaneous equations which also include correct root. Maple worksheet is attached.

I am trying fsolve and direct search method with known root so that I could get the proper procedure to get the correct root which I can apply to another problem (set of similar simultaneous equations) for which I don't know correct root beforehand.

Thanks for your anticipated help.fsolve_question.mw

Ok, so i have this functions

where f(x) represent urban population and g(x) represent the rural population.

And i have to implement an algortihm in Maple to find out after what period of time x the rural population will be with 20% bigger than urban population.

I'm new in Maple and is a little bit hard for me to implement algorithms in this program.If you can help me with any idea, i will really apreciate.Thank you :). 

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