Items tagged with fsolve

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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 :). 

Hi, 

I need to solve system of 6 non linear equations. 

Down here you can see the code I wrote and at the end used to fsolve function, and it is not running. I get an error about the const 'V': Error, (in fsolve) V is in the equation, and is not solved for.

What is the right way to solve this system?

Thank you very much!

 

 

omega1 := 1.562;
omega2 := 2.449;
omega3 := 3.325;
y1 := c1*sin(omega1*t+phi1)+c2*sin(omega2*t+phi2)+c3*sin(omega3*t+phi3);

 

 

y2 := .1019*c1*sin(omega1*t+phi1)+.75*c2*sin(omega2*t+phi2)+.4608*c3*sin(omega3*t+phi3);

 

 

y3 := .407*c1*sin(omega1*t+phi1)+(0*c2)*sin(omega2*t+phi2)+1.844*c3*sin(omega3*t+phi3);
 
eq1 := subs(t = 0, y1) = 0;
 
eq2 := subs(t = 0, y2) = 0;
 
eq3 := subs(t = 0, y3) = 0;
 
eq4 := subs(t = 0, diff(y1, t)) = V;
eq5 := subs(t = 0, diff(y2, t)) = 0;
eq6 := subs(t = 0, diff(y3, t)) = 0;

 

 

eqs := [eq1, eq2, eq3, eq4, eq5, eq6];
 
vars := [c1, c2, c3, phi1, phi2, phi3];
 
fsolve({eq1, eq2, eq3, eq4, eq5, eq6}, {c1, c2, c3, phi1, phi2, phi3});
 

 

i have set of equations and variable that i want to solve them using fsolve, but after about 20mintues of computations, fsolve retrun these set unevaluated, could anyone help?


 

 restart:with(linalg):with(LinearAlgebra):with(orthopoly):Digits:=40:
M:=3:
N:=2:
l:=2:
for m from 0 to M-1 do
L[m]:=unapply(P(m,t),t);
end do:
for n from 1 to N do;
for m from 0 to M-1 do;
BB[n,m]:=unapply(piecewise((n-1)/N<=t and t<n/N, sqrt(N*(2*m+1))*L[m](2*N*t-2*n+1)),t);
end do:
end do:
##############################################
B:=Vector(N*M,1,[seq(seq(BB[n,m](t),m=0..M-1),n=1..N)]):
BS:=Vector(N*M,1,[seq(seq(BB[n,m](s),m=0..M-1),n=1..N)]):
f[1]:=unapply((23/35)*t,t):
f[2]:=unapply((11/12)*t,t):
P[1]:=evalf(Vector(N*M,1,[seq(seq(int((23/35)*t*BB[n,m](t),t=0..1,t=0..1),m=0..M-1),n=1..N)])):
P[2]:=evalf(Vector(N*M,1,[seq(seq(int((11/12)*t*BB[n,m](t),t=0..1,t=0..1),m=0..M-1),n=1..N)])):
p[1]:=Transpose(P[1]):P[1]^+:
p[2]:=Transpose(P[2]):P[2]^+:

 

#############################################
k:=Matrix(2,2,[[t*s^2,t*s^2],[s*t^2,s*t^2]]):

 

 

 

 

 

 

 

 

 

######################################

for i from 1 to 2 do;
for j from 1 to 2 do;
T[i,j]:=Matrix(N*M,N*M):

for n from 1 to M*N do;
for m from 1 to M*N do;
T[i,j](n,m):=evalf(int(int(B[n]*k(i,j)*BS[m],t=0..1),s=0..1)):
end do:
end do:
od:
od:
evalm(T[1,1]):
evalm(T[1,2]):
evalm(T[2,1]):
evalm(T[2,2]):

 

 

##########################################

X[1]:=Matrix(M*N,1):
for n from 1 to M*N do;
X[1](n,1):=Y[n,1]:
od:
evalm(X[1]):
#### yadet bashe k dar in mesal majhulat y1,y2
####ba bordarhaye X1, X2 neshun dadi...darvaghe
####dar mesale avale maghale 2ta y dashti k bayad moadele ash ro hal mikardi...
 

 

X[2]:=Matrix(M*N,1):
for n from 1 to M*N do;
X[2](n,1):=yY[n,1]:
od:
evalm(X[2]):

U[1,1]:=Matrix(M*N,1):
for n from 1 to M*N do;
U[1,1](n,1):=u[n,1]:
od:
evalm(U[1,1]):

U[1,2]:=Matrix(M*N,1):
for n from 1 to M*N do;
U[1,2](n,1):=uU[n,1]:
od:

evalm(U[1,2]):
Transpose(U[1,2]):

U[2,1]:=Matrix(N*M,1):
for n from 1 to M*N do;
U[2,1](n,1):=w[n,1]:
od:
evalm(U[2,1]):

U[2,2]:=Matrix(M*N,1):
for n from 1 to M*N do;
U[2,2](n,1):=wW[n,1]:
od:
evalm(U[2,2]):





 


A:=add(X[j], j=1..2):

z[1]:=Matrix(1,M*N):
z[2]:=Matrix(1,M*N):
for i from 1 to 2 do;
Z[i]:=Transpose(A)-add(Transpose(U[i,j]).T[i,j], j=1..2);
evalm(Z[i]):
z[i]:=Z[i]-convert(p[i],Matrix):
od:
evalm(z[1]):
##############
z[1](1,2):


##########################################
for s from 1 to M*N do;
t:=((2*s)-1)/(2*M*N);
ff[1,1]:=eval(VectorMatrixMultiply(Transpose(X[1]),eval(B,t=((2*s)-1)/(2*M*N))));
F[1,s]:=multiply(ff[1,1],ff[1,1]);
expand(%):
H[1,s]:=VectorMatrixMultiply(Transpose(U[1,1]),eval(B,t=((2*s)-1)/(2*M*N)));
hh[1,s]:=F[1,s]-H[1,s][1];
od:

 

ff[1,1]:


 

F[1,1]:

H[1,1]:

hh[1,2]:

 

for s from 1 to M*N do;
t:=((2*s)-1)/(2*M*N);
ff[2,1]:=eval(VectorMatrixMultiply(Transpose(X[1]),eval(B,t=((2*s)-1)/(2*M*N))));
G[1,s]:=multiply(ff[2,1],ff[2,1]);
expand(%):
J[1,s]:=VectorMatrixMultiply(Transpose(U[2,1]),eval(B,t=((2*s)-1)/(2*M*N)));
JJ[1,s]:=G[1,s]-J[1,s][1];
od:
JJ[1,1]:
JJ[1,2]:

for s from 1 to M*N do;
t:=((2*s)-1)/(2*M*N);
ff[1,2]:=eval(VectorMatrixMultiply(Transpose(X[2]),eval(B,t=((2*s)-1)/(2*M*N))));
GG[1,s]:=multiply(ff[1,2],ff[1,2]);
expand(%):
g[1,s]:=VectorMatrixMultiply(Transpose(U[1,2]),eval(B,t=((2*s)-1)/(2*M*N)));
gg[1,s]:=GG[1,s]-g[1,s][1];
od:
gg[1,1]:
gg[1,2]:

for s from 1 to M*N do;
t:=((2*s)-1)/(2*M*N);
ff[2,2]:=eval(VectorMatrixMultiply(Transpose(X[2]),eval(B,t=((2*s)-1)/(2*M*N))));
DD[1,s]:=multiply(ff[2,2],ff[2,2]);
expand(%):
d[1,s]:=VectorMatrixMultiply(Transpose(U[2,2]),eval(B,t=((2*s)-1)/(2*M*N)));
dd[1,s]:=DD[1,s]-d[1,s][1];
od:
dd[1,1]:
dd[1,2]:


eqq[1]:=seq(hh[1,s],s=1..M*N):

eqq[2]:=seq(gg[1,s],s=1..M*N):

 

eqq[3]:=seq(JJ[1,s],s=1..M*N):

eqq[4]:=seq(dd[1,s],s=1..M*N):
eqq[5]:=seq(z[1](1,s),s=1..M*N):
eqq[6]:=seq(z[2](1,s),s=1..M*N):

eq:=seq(eqq[s],s=1..M*N):

var[1]:=seq(X[1](s,1),s=1..M*N):
var[2]:=seq(X[2](s,1),s=1..M*N):
var[3]:=seq(U[1,1](s,1),s=1..M*N):
var[4]:=seq(U[1,2](s,1),s=1..M*N):
var[5]:=seq(U[2,1](s,1),s=1..M*N):
var[6]:=seq(U[2,2](s,1),s=1..M*N):

EQ:=Matrix(36,1):

for i to 6 do
EQ(6*i-5,1):=hh[1,i];
EQ(6*i-4,1):=gg[1,i];
EQ(6*i-3,1):=JJ[1,i];
EQ(6*i-2,1):=dd[1,i];
EQ(6*i-1,1):=z[1](1,i);
EQ(6*i,1):=z[2](1,i);
od:

 

indets(EQ);

{Y[1, 1], Y[2, 1], Y[3, 1], Y[4, 1], Y[5, 1], Y[6, 1], u[1, 1], u[2, 1], u[3, 1], u[4, 1], u[5, 1], u[6, 1], uU[1, 1], uU[2, 1], uU[3, 1], uU[4, 1], uU[5, 1], uU[6, 1], w[1, 1], w[2, 1], w[3, 1], w[4, 1], w[5, 1], w[6, 1], wW[1, 1], wW[2, 1], wW[3, 1], wW[4, 1], wW[5, 1], wW[6, 1], yY[1, 1], yY[2, 1], yY[3, 1], yY[4, 1], yY[5, 1], yY[6, 1]}

(1)

``

``

Var:=[seq](var[s],s=1..M*N);

[Y[1, 1], Y[2, 1], Y[3, 1], Y[4, 1], Y[5, 1], Y[6, 1], yY[1, 1], yY[2, 1], yY[3, 1], yY[4, 1], yY[5, 1], yY[6, 1], u[1, 1], u[2, 1], u[3, 1], u[4, 1], u[5, 1], u[6, 1], uU[1, 1], uU[2, 1], uU[3, 1], uU[4, 1], uU[5, 1], uU[6, 1], w[1, 1], w[2, 1], w[3, 1], w[4, 1], w[5, 1], w[6, 1], wW[1, 1], wW[2, 1], wW[3, 1], wW[4, 1], wW[5, 1], wW[6, 1]]

(2)

seq(indets(EQ[i][1]), i = 1 .. 36):

``

``

 

for i to 36 do
EQQ[i]:=simplify(expand(subs([seq](indets(EQ)[i]=AA[i],i=1..36),EQ[i][1])=0));
od;

(1/18)*(12*AA[8]*3^(1/2)-3*AA[9]*5^(1/2)-18*AA[7])*2^(1/2)-(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0

 

(1/18)*(12*AA[14]*3^(1/2)-3*AA[15]*5^(1/2)-18*AA[13])*2^(1/2)-(8/3)*((1/6)*AA[33]*5^(1/2)+AA[31])*AA[32]*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0

 

(1/18)*(12*AA[20]*3^(1/2)-3*AA[21]*5^(1/2)-18*AA[19])*2^(1/2)-(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0

 

(1/18)*(12*AA[26]*3^(1/2)-3*AA[27]*5^(1/2)-18*AA[25])*2^(1/2)-(8/3)*((1/6)*AA[33]*5^(1/2)+AA[31])*AA[32]*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0

 

AA[1]+AA[31]-0.1041666666666666666666666666666666666667e-1*AA[7]-0.6014065304058601713636966463562056829663e-2*AA[8]-0.3125000000000000000000000000000000000000e-1*AA[10]-0.6014065304058601713636966463562056829663e-2*AA[11]-0.1041666666666666666666666666666666666667e-1*AA[13]-0.6014065304058601713636966463562056829663e-2*AA[14]-0.3125000000000000000000000000000000000000e-1*AA[16]-0.6014065304058601713636966463562056829663e-2*AA[17]-.1161675426235042361515672880600823421682 = 0

 

AA[1]+AA[31]-0.1041666666666666666666666666666666666667e-1*AA[19]-0.9021097956087902570455449695343085244494e-2*AA[20]-0.2329237476562280933759555904928412745252e-2*AA[21]-0.7291666666666666666666666666666666666667e-1*AA[22]-0.2706329386826370771136634908602925573348e-1*AA[23]-0.2329237476562280933759555904928412745252e-2*AA[24]-0.1041666666666666666666666666666666666667e-1*AA[25]-0.9021097956087902570455449695343085244494e-2*AA[26]-0.2329237476562280933759555904928412745252e-2*AA[27]-0.7291666666666666666666666666666666666667e-1*AA[28]-0.2706329386826370771136634908602925573348e-1*AA[29]-0.2329237476562280933759555904928412745252e-2*AA[30]-.1620453040219171410085268329823612381694 = 0

 

(1/2)*(AA[9]*5^(1/2)-2*AA[7])*2^(1/2)-2*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(5/2)*AA[3]^2 = 0

 

(1/2)*(AA[15]*5^(1/2)-2*AA[13])*2^(1/2)-2*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(5/2)*AA[33]^2 = 0

 

(1/2)*(AA[21]*5^(1/2)-2*AA[19])*2^(1/2)-2*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(5/2)*AA[3]^2 = 0

 

(1/2)*(AA[27]*5^(1/2)-2*AA[25])*2^(1/2)-2*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(5/2)*AA[33]^2 = 0

 

AA[2]+AA[32]-0.9021097956087902570455449695343085244494e-2*AA[7]-0.5208333333333333333333333333333333333333e-2*AA[8]-0.2706329386826370771136634908602925573348e-1*AA[10]-0.5208333333333333333333333333333333333333e-2*AA[11]-0.9021097956087902570455449695343085244494e-2*AA[13]-0.5208333333333333333333333333333333333333e-2*AA[14]-0.2706329386826370771136634908602925573348e-1*AA[16]-0.5208333333333333333333333333333333333333e-2*AA[17]-0.6706936200477749554587801633123274049430e-1 = 0

 

AA[2]+AA[32]-0.6014065304058601713636966463562056829663e-2*AA[19]-0.5208333333333333333333333333333333333333e-2*AA[20]-0.1344785884099797529576133819368888753762e-2*AA[21]-0.4209845712841021199545876524493439780765e-1*AA[22]-0.1562500000000000000000000000000000000000e-1*AA[23]-0.1344785884099797529576133819368888753762e-2*AA[24]-0.6014065304058601713636966463562056829663e-2*AA[25]-0.5208333333333333333333333333333333333333e-2*AA[26]-0.1344785884099797529576133819368888753762e-2*AA[27]-0.4209845712841021199545876524493439780765e-1*AA[28]-0.1562500000000000000000000000000000000000e-1*AA[29]-0.1344785884099797529576133819368888753762e-2*AA[30]-0.9355689989796860791725737785335001844313e-1 = 0

 

(1/18)*(-12*AA[8]*3^(1/2)-3*AA[9]*5^(1/2)-18*AA[7])*2^(1/2)+(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0

 

(1/18)*(-12*AA[14]*3^(1/2)-3*AA[15]*5^(1/2)-18*AA[13])*2^(1/2)+(8/3)*((1/6)*AA[33]*5^(1/2)+AA[31])*AA[32]*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0

 

(1/18)*(-12*AA[20]*3^(1/2)-3*AA[21]*5^(1/2)-18*AA[19])*2^(1/2)+(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0

 

(1/18)*(-12*AA[26]*3^(1/2)-3*AA[27]*5^(1/2)-18*AA[25])*2^(1/2)+(8/3)*((1/6)*AA[33]*5^(1/2)+AA[31])*AA[32]*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0

 

AA[3]+AA[33]-0.2329237476562280933759555904928412745252e-2*AA[7]-0.1344785884099797529576133819368888753762e-2*AA[8]-0.6987712429686842801278667714785238235753e-2*AA[10]-0.1344785884099797529576133819368888753762e-2*AA[11]-0.2329237476562280933759555904928412745252e-2*AA[13]-0.1344785884099797529576133819368888753762e-2*AA[14]-0.6987712429686842801278667714785238235753e-2*AA[16]-0.1344785884099797529576133819368888753762e-2*AA[17] = 0

 

AA[3]+AA[33] = 0

 

(1/18)*(12*AA[11]*3^(1/2)-3*AA[12]*5^(1/2)-18*AA[10])*2^(1/2)-(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0

 

(1/18)*(12*AA[17]*3^(1/2)-3*AA[18]*5^(1/2)-18*AA[16])*2^(1/2)-(8/3)*((1/6)*AA[36]*5^(1/2)+AA[34])*AA[35]*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0

 

(1/18)*(12*AA[23]*3^(1/2)-3*AA[24]*5^(1/2)-18*AA[22])*2^(1/2)-(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0

 

(1/18)*(12*AA[29]*3^(1/2)-3*AA[30]*5^(1/2)-18*AA[28])*2^(1/2)-(8/3)*((1/6)*AA[36]*5^(1/2)+AA[34])*AA[35]*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0

 

AA[4]+AA[34]-0.7291666666666666666666666666666666666667e-1*AA[7]-0.4209845712841021199545876524493439780765e-1*AA[8]-.2187500000000000000000000000000000000000*AA[10]-0.4209845712841021199545876524493439780765e-1*AA[11]-0.7291666666666666666666666666666666666667e-1*AA[13]-0.4209845712841021199545876524493439780765e-1*AA[14]-.2187500000000000000000000000000000000000*AA[16]-0.4209845712841021199545876524493439780765e-1*AA[17]-.3485026278705127084547018641802470265047 = 0

 

AA[4]+AA[34]-0.3125000000000000000000000000000000000000e-1*AA[19]-0.2706329386826370771136634908602925573348e-1*AA[20]-0.6987712429686842801278667714785238235753e-2*AA[21]-.2187500000000000000000000000000000000000*AA[22]-0.8118988160479112313409904725808776720045e-1*AA[23]-0.6987712429686842801278667714785238235753e-2*AA[24]-0.3125000000000000000000000000000000000000e-1*AA[25]-0.2706329386826370771136634908602925573348e-1*AA[26]-0.6987712429686842801278667714785238235753e-2*AA[27]-.2187500000000000000000000000000000000000*AA[28]-0.8118988160479112313409904725808776720045e-1*AA[29]-0.6987712429686842801278667714785238235753e-2*AA[30]-.4861359120657514230255804989470837145084 = 0

 

(1/2)*(AA[12]*5^(1/2)-2*AA[10])*2^(1/2)-2*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(5/2)*AA[6]^2 = 0

 

(1/2)*(AA[18]*5^(1/2)-2*AA[16])*2^(1/2)-2*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(5/2)*AA[36]^2 = 0

 

(1/2)*(AA[24]*5^(1/2)-2*AA[22])*2^(1/2)-2*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(5/2)*AA[6]^2 = 0

 

(1/2)*(AA[30]*5^(1/2)-2*AA[28])*2^(1/2)-2*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(5/2)*AA[36]^2 = 0

 

AA[5]+AA[35]-0.2706329386826370771136634908602925573348e-1*AA[7]-0.1562500000000000000000000000000000000000e-1*AA[8]-0.8118988160479112313409904725808776720045e-1*AA[10]-0.1562500000000000000000000000000000000000e-1*AA[11]-0.2706329386826370771136634908602925573348e-1*AA[13]-0.1562500000000000000000000000000000000000e-1*AA[14]-0.8118988160479112313409904725808776720045e-1*AA[16]-0.1562500000000000000000000000000000000000e-1*AA[17]-0.6706936200477749554587801633123274049430e-1 = 0

 

AA[5]+AA[35]-0.6014065304058601713636966463562056829663e-2*AA[19]-0.5208333333333333333333333333333333333333e-2*AA[20]-0.1344785884099797529576133819368888753762e-2*AA[21]-0.4209845712841021199545876524493439780765e-1*AA[22]-0.1562500000000000000000000000000000000000e-1*AA[23]-0.1344785884099797529576133819368888753762e-2*AA[24]-0.6014065304058601713636966463562056829663e-2*AA[25]-0.5208333333333333333333333333333333333333e-2*AA[26]-0.1344785884099797529576133819368888753762e-2*AA[27]-0.4209845712841021199545876524493439780765e-1*AA[28]-0.1562500000000000000000000000000000000000e-1*AA[29]-0.1344785884099797529576133819368888753762e-2*AA[30]-0.9355689989796860791725737785335001844313e-1 = 0

 

(1/18)*(-12*AA[11]*3^(1/2)-3*AA[12]*5^(1/2)-18*AA[10])*2^(1/2)+(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0

 

(1/18)*(-12*AA[17]*3^(1/2)-3*AA[18]*5^(1/2)-18*AA[16])*2^(1/2)+(8/3)*((1/6)*AA[36]*5^(1/2)+AA[34])*AA[35]*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0

 

(1/18)*(-12*AA[23]*3^(1/2)-3*AA[24]*5^(1/2)-18*AA[22])*2^(1/2)+(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0

 

(1/18)*(-12*AA[29]*3^(1/2)-3*AA[30]*5^(1/2)-18*AA[28])*2^(1/2)+(8/3)*((1/6)*AA[36]*5^(1/2)+AA[34])*AA[35]*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0

 

AA[6]+AA[36]-0.2329237476562280933759555904928412745252e-2*AA[7]-0.1344785884099797529576133819368888753762e-2*AA[8]-0.6987712429686842801278667714785238235753e-2*AA[10]-0.1344785884099797529576133819368888753762e-2*AA[11]-0.2329237476562280933759555904928412745252e-2*AA[13]-0.1344785884099797529576133819368888753762e-2*AA[14]-0.6987712429686842801278667714785238235753e-2*AA[16]-0.1344785884099797529576133819368888753762e-2*AA[17] = 0

 

AA[6]+AA[36] = 0

(3)

fsolve({seq}(EQQ[i],i=1..36),{seq}(AA[i],i=1..36));

fsolve({AA[3]+AA[33] = 0, AA[6]+AA[36] = 0, (1/2)*(AA[9]*5^(1/2)-2*AA[7])*2^(1/2)-2*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(5/2)*AA[3]^2 = 0, (1/2)*(AA[12]*5^(1/2)-2*AA[10])*2^(1/2)-2*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(5/2)*AA[6]^2 = 0, (1/2)*(AA[15]*5^(1/2)-2*AA[13])*2^(1/2)-2*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(5/2)*AA[33]^2 = 0, (1/2)*(AA[18]*5^(1/2)-2*AA[16])*2^(1/2)-2*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(5/2)*AA[36]^2 = 0, (1/2)*(AA[21]*5^(1/2)-2*AA[19])*2^(1/2)-2*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(5/2)*AA[3]^2 = 0, (1/2)*(AA[24]*5^(1/2)-2*AA[22])*2^(1/2)-2*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(5/2)*AA[6]^2 = 0, (1/2)*(AA[27]*5^(1/2)-2*AA[25])*2^(1/2)-2*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(5/2)*AA[33]^2 = 0, (1/2)*(AA[30]*5^(1/2)-2*AA[28])*2^(1/2)-2*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(5/2)*AA[36]^2 = 0, (1/18)*(-12*AA[8]*3^(1/2)-3*AA[9]*5^(1/2)-18*AA[7])*2^(1/2)+(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0, (1/18)*(12*AA[8]*3^(1/2)-3*AA[9]*5^(1/2)-18*AA[7])*2^(1/2)-(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0, (1/18)*(-12*AA[11]*3^(1/2)-3*AA[12]*5^(1/2)-18*AA[10])*2^(1/2)+(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0, (1/18)*(12*AA[11]*3^(1/2)-3*AA[12]*5^(1/2)-18*AA[10])*2^(1/2)-(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0, (1/18)*(-12*AA[14]*3^(1/2)-3*AA[15]*5^(1/2)-18*AA[13])*2^(1/2)+(8/3)*AA[32]*((1/6)*AA[33]*5^(1/2)+AA[31])*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0, (1/18)*(12*AA[14]*3^(1/2)-3*AA[15]*5^(1/2)-18*AA[13])*2^(1/2)-(8/3)*AA[32]*((1/6)*AA[33]*5^(1/2)+AA[31])*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0, (1/18)*(-12*AA[17]*3^(1/2)-3*AA[18]*5^(1/2)-18*AA[16])*2^(1/2)+(8/3)*AA[35]*((1/6)*AA[36]*5^(1/2)+AA[34])*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0, (1/18)*(12*AA[17]*3^(1/2)-3*AA[18]*5^(1/2)-18*AA[16])*2^(1/2)-(8/3)*AA[35]*((1/6)*AA[36]*5^(1/2)+AA[34])*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0, (1/18)*(-12*AA[20]*3^(1/2)-3*AA[21]*5^(1/2)-18*AA[19])*2^(1/2)+(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0, (1/18)*(12*AA[20]*3^(1/2)-3*AA[21]*5^(1/2)-18*AA[19])*2^(1/2)-(8/3)*((1/6)*AA[3]*5^(1/2)+AA[1])*AA[2]*3^(1/2)+(2/3)*AA[1]*AA[3]*5^(1/2)+2*AA[1]^2+(8/3)*AA[2]^2+(5/18)*AA[3]^2 = 0, (1/18)*(-12*AA[23]*3^(1/2)-3*AA[24]*5^(1/2)-18*AA[22])*2^(1/2)+(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0, (1/18)*(12*AA[23]*3^(1/2)-3*AA[24]*5^(1/2)-18*AA[22])*2^(1/2)-(8/3)*((1/6)*AA[6]*5^(1/2)+AA[4])*AA[5]*3^(1/2)+(2/3)*AA[4]*AA[6]*5^(1/2)+2*AA[4]^2+(8/3)*AA[5]^2+(5/18)*AA[6]^2 = 0, (1/18)*(-12*AA[26]*3^(1/2)-3*AA[27]*5^(1/2)-18*AA[25])*2^(1/2)+(8/3)*AA[32]*((1/6)*AA[33]*5^(1/2)+AA[31])*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0, (1/18)*(12*AA[26]*3^(1/2)-3*AA[27]*5^(1/2)-18*AA[25])*2^(1/2)-(8/3)*AA[32]*((1/6)*AA[33]*5^(1/2)+AA[31])*3^(1/2)+(2/3)*AA[31]*AA[33]*5^(1/2)+2*AA[31]^2+(8/3)*AA[32]^2+(5/18)*AA[33]^2 = 0, (1/18)*(-12*AA[29]*3^(1/2)-3*AA[30]*5^(1/2)-18*AA[28])*2^(1/2)+(8/3)*AA[35]*((1/6)*AA[36]*5^(1/2)+AA[34])*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0, (1/18)*(12*AA[29]*3^(1/2)-3*AA[30]*5^(1/2)-18*AA[28])*2^(1/2)-(8/3)*AA[35]*((1/6)*AA[36]*5^(1/2)+AA[34])*3^(1/2)+(2/3)*AA[34]*AA[36]*5^(1/2)+2*AA[34]^2+(8/3)*AA[35]^2+(5/18)*AA[36]^2 = 0, AA[3]+AA[33]-0.2329237476562280933759555904928412745252e-2*AA[7]-0.1344785884099797529576133819368888753762e-2*AA[8]-0.6987712429686842801278667714785238235753e-2*AA[10]-0.1344785884099797529576133819368888753762e-2*AA[11]-0.2329237476562280933759555904928412745252e-2*AA[13]-0.1344785884099797529576133819368888753762e-2*AA[14]-0.6987712429686842801278667714785238235753e-2*AA[16]-0.1344785884099797529576133819368888753762e-2*AA[17] = 0, AA[6]+AA[36]-0.2329237476562280933759555904928412745252e-2*AA[7]-0.1344785884099797529576133819368888753762e-2*AA[8]-0.6987712429686842801278667714785238235753e-2*AA[10]-0.1344785884099797529576133819368888753762e-2*AA[11]-0.2329237476562280933759555904928412745252e-2*AA[13]-0.1344785884099797529576133819368888753762e-2*AA[14]-0.6987712429686842801278667714785238235753e-2*AA[16]-0.1344785884099797529576133819368888753762e-2*AA[17] = 0, AA[1]+AA[31]-0.1041666666666666666666666666666666666667e-1*AA[7]-0.6014065304058601713636966463562056829663e-2*AA[8]-0.3125000000000000000000000000000000000000e-1*AA[10]-0.6014065304058601713636966463562056829663e-2*AA[11]-0.1041666666666666666666666666666666666667e-1*AA[13]-0.6014065304058601713636966463562056829663e-2*AA[14]-0.3125000000000000000000000000000000000000e-1*AA[16]-0.6014065304058601713636966463562056829663e-2*AA[17]-.1161675426235042361515672880600823421682 = 0, AA[2]+AA[32]-0.9021097956087902570455449695343085244494e-2*AA[7]-0.5208333333333333333333333333333333333333e-2*AA[8]-0.2706329386826370771136634908602925573348e-1*AA[10]-0.5208333333333333333333333333333333333333e-2*AA[11]-0.9021097956087902570455449695343085244494e-2*AA[13]-0.5208333333333333333333333333333333333333e-2*AA[14]-0.2706329386826370771136634908602925573348e-1*AA[16]-0.5208333333333333333333333333333333333333e-2*AA[17]-0.6706936200477749554587801633123274049430e-1 = 0, AA[4]+AA[34]-0.7291666666666666666666666666666666666667e-1*AA[7]-0.4209845712841021199545876524493439780765e-1*AA[8]-.2187500000000000000000000000000000000000*AA[10]-0.4209845712841021199545876524493439780765e-1*AA[11]-0.7291666666666666666666666666666666666667e-1*AA[13]-0.4209845712841021199545876524493439780765e-1*AA[14]-.2187500000000000000000000000000000000000*AA[16]-0.4209845712841021199545876524493439780765e-1*AA[17]-.3485026278705127084547018641802470265047 = 0, AA[5]+AA[35]-0.2706329386826370771136634908602925573348e-1*AA[7]-0.1562500000000000000000000000000000000000e-1*AA[8]-0.8118988160479112313409904725808776720045e-1*AA[10]-0.1562500000000000000000000000000000000000e-1*AA[11]-0.2706329386826370771136634908602925573348e-1*AA[13]-0.1562500000000000000000000000000000000000e-1*AA[14]-0.8118988160479112313409904725808776720045e-1*AA[16]-0.1562500000000000000000000000000000000000e-1*AA[17]-0.6706936200477749554587801633123274049430e-1 = 0, AA[1]+AA[31]-0.1041666666666666666666666666666666666667e-1*AA[19]-0.9021097956087902570455449695343085244494e-2*AA[20]-0.2329237476562280933759555904928412745252e-2*AA[21]-0.7291666666666666666666666666666666666667e-1*AA[22]-0.2706329386826370771136634908602925573348e-1*AA[23]-0.2329237476562280933759555904928412745252e-2*AA[24]-0.1041666666666666666666666666666666666667e-1*AA[25]-0.9021097956087902570455449695343085244494e-2*AA[26]-0.2329237476562280933759555904928412745252e-2*AA[27]-0.7291666666666666666666666666666666666667e-1*AA[28]-0.2706329386826370771136634908602925573348e-1*AA[29]-0.2329237476562280933759555904928412745252e-2*AA[30]-.1620453040219171410085268329823612381694 = 0, AA[2]+AA[32]-0.6014065304058601713636966463562056829663e-2*AA[19]-0.5208333333333333333333333333333333333333e-2*AA[20]-0.1344785884099797529576133819368888753762e-2*AA[21]-0.4209845712841021199545876524493439780765e-1*AA[22]-0.1562500000000000000000000000000000000000e-1*AA[23]-0.1344785884099797529576133819368888753762e-2*AA[24]-0.6014065304058601713636966463562056829663e-2*AA[25]-0.5208333333333333333333333333333333333333e-2*AA[26]-0.1344785884099797529576133819368888753762e-2*AA[27]-0.4209845712841021199545876524493439780765e-1*AA[28]-0.1562500000000000000000000000000000000000e-1*AA[29]-0.1344785884099797529576133819368888753762e-2*AA[30]-0.9355689989796860791725737785335001844313e-1 = 0, AA[4]+AA[34]-0.3125000000000000000000000000000000000000e-1*AA[19]-0.2706329386826370771136634908602925573348e-1*AA[20]-0.6987712429686842801278667714785238235753e-2*AA[21]-.2187500000000000000000000000000000000000*AA[22]-0.8118988160479112313409904725808776720045e-1*AA[23]-0.6987712429686842801278667714785238235753e-2*AA[24]-0.3125000000000000000000000000000000000000e-1*AA[25]-0.2706329386826370771136634908602925573348e-1*AA[26]-0.6987712429686842801278667714785238235753e-2*AA[27]-.2187500000000000000000000000000000000000*AA[28]-0.8118988160479112313409904725808776720045e-1*AA[29]-0.6987712429686842801278667714785238235753e-2*AA[30]-.4861359120657514230255804989470837145084 = 0, AA[5]+AA[35]-0.6014065304058601713636966463562056829663e-2*AA[19]-0.5208333333333333333333333333333333333333e-2*AA[20]-0.1344785884099797529576133819368888753762e-2*AA[21]-0.4209845712841021199545876524493439780765e-1*AA[22]-0.1562500000000000000000000000000000000000e-1*AA[23]-0.1344785884099797529576133819368888753762e-2*AA[24]-0.6014065304058601713636966463562056829663e-2*AA[25]-0.5208333333333333333333333333333333333333e-2*AA[26]-0.1344785884099797529576133819368888753762e-2*AA[27]-0.4209845712841021199545876524493439780765e-1*AA[28]-0.1562500000000000000000000000000000000000e-1*AA[29]-0.1344785884099797529576133819368888753762e-2*AA[30]-0.9355689989796860791725737785335001844313e-1 = 0}, {AA[1], AA[2], AA[3], AA[4], AA[5], AA[6], AA[7], AA[8], AA[9], AA[10], AA[11], AA[12], AA[13], AA[14], AA[15], AA[16], AA[17], AA[18], AA[19], AA[20], AA[21], AA[22], AA[23], AA[24], AA[25], AA[26], AA[27], AA[28], AA[29], AA[30], AA[31], AA[32], AA[33], AA[34], AA[35], AA[36]})

(4)

``


 

Download ttttt33.mw

I am trying to do fsolve in a range (-7..14), however, it gives no solution.

But when I solve the same equations with solve (after removing all the Imaginary solutions), I get two results, one of them is in the range (-7..14). 

I even expanded the range of fsolve, say (-10..20), but still got no solution...

This is just getting weirder and weirder. Attached kindly find the Maple file, note that the first solve takes about 1 minute (on my laptop: CPU i7 + MEM 8G + SSD).

fsolve_In_Range.mw

Hi everybody,

I have to solve a system  of 3 equations in 3 unknowns.
One equation is linear while the others are not because of some  sinh(cste*unknown) term.
More of this the unknowns must verify some constraints of inequality type (but always very simple ; for instance “unknown <= value”).

solve fails because of the sinh terms
fsolve fails due to the inequalities


What Maple procedure do you advise me to use to solve this system ?
(at this stage I think advices could be sufficient ; if I keep coming up against the problem I will submit you a more detailed question)


Thanks in advance

 

With the following command I can plot two spheres and plot them.

f1 := x^2+y^2+z^2 = 1

f2 := x+y+z = 1

with(plottools);

with(plots);

S1 := implicitplot3d(f1, x = -1 .. 1, y = -1 .. 1, z = -1 .. 1, style = patchnogrid, color = blue, scaling = constrained, axes = boxed)

S2 := implicitplot3d(f2, x = -1 .. 1, y = -1 .. 1, z = -1 .. 1, style = patchnogrid, color = gold, scaling = constrained, axes = boxed)

dispaly(S1,S2)

My questions are:

1- How can I display (highlight) the circle which is the intersection between these two sphere on the same figure?

2- How can I find the equation of this circle?

Thank you.

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