Items tagged with equations equations Tagged Items Feed

hi....how i can extract Coefficients  (i.e. {f1[2],f2[2],f2[3],f3[2],.....f3[6]}) from every algebric equations and create matrix A ,in form AX=0, (X are f1[2],f2[2],f2[3],f3[2],.....f3[6] ) then the determinant of the matrix of coefficients (A) set to zero for obtaining unknown parameter omega.?

Note that  if m=3 then 6 equations is appeare and if m=4 then 9 equations is appeare.thus i need a procedure that works for every arbitary value of ''m''.

in attached file below m=4 thus we have 9 equations, i.e. 3 for eq1[k_] and 3 for eq2[k_] and so on...

also we should use boundary conditions for some amount of fi[j] (i=1,2,3 and j=2,3,...,7)

be extacting above Coefficients for example from first equation ,

''**:= (1/128)*f1[2]*omega^2-(1/4)*f2[2]-(1/2)*f2[3]+(1/4)*f2[4]+(1/4)*f3[2]-(1/2)*f3[3]+(1/4)*f3[4]+140*f1[2]-80*f1[3]+20*f1[4]'''

must compute

coeff(**, f1[2]); coeff(**, f2[2]) and so on...

 

 

 

 

 

fdm-maple.mw

 

 ############################Define some parameters

 

 
restart; Digits := 15; A1 := 10; A2 := 10; A3 := 10; A4 := 1; A5 := 1; A6 := 1; A7 := 1; A8 := 1; A9 := 1; A10 := 1; A11 := 1; B1 := 10; B2 := 10; B3 := 10; B4 := 1; B5 := 1; B6 := 1; B7 := 1; B8 := 1; B9 := 1; B10 := 1; B11 := 1; C1 := 10; C2 := 10; C3 := 10; C4 := 1; C5 := 1; C6 := 1; C7 := 1; C8 := 1; C9 := 1; C10 := 1; C11 := 1; C12 := 1; C13 := 1; C14 := 1; C15 := 1; C16 := 1; A12 := 1; B12 := 1; C18 := 1; C17 := 1; C19 := 1; n := 1; U := proc (x, theta) options operator, arrow; f1(x)*cos(n*theta) end proc; V := proc (x, theta) options operator, arrow; f2(x)*sin(n*theta) end proc; W := proc (x, theta) options operator, arrow; f3(x)*cos(n*theta) end proc; n := 1; m := 4; len := 1; h := len/m; nn := m+1
 ############################Define some equation

eq1[k_] := -2*f1[k]*(-A11*n^4+A10*n^2+A12*omega^2)*h^4+(A6*(f2[k-1]-f2[k+1])*n^3+A9*(f3[k-1]-f3[k+1])*n^2-A5*(f2[k-1]-f2[k+1])*n-A8*(f3[k-1]-f3[k+1]))*h^3+(4*(f1[k]-(1/2)*f1[k-1]-(1/2)*f1[k+1]))*(A3*n^2-A2)*h^2+(-A4*(f2[k-2]-2*f2[k-1]+2*f2[k+1]-f2[k+2])*n-A7*(f3[k-2]-2*f3[k-1]+2*f3[k+1]-f3[k+2]))*h+12*A1*(f1[k]+(1/6)*f1[k-2]-(2/3)*f1[k-1]-(2/3)*f1[k+1]+(1/6)*f1[k+2]):
  ``

 

 

 

 

                                     ######################################  APPLY BOUNDARY CONDITIONS

f1[nn+1] := f1[m]:
 

for k from 2 to m do eq1[k_]; eq2[k_]; eq3[k_] end do

-(1/64)*f2[4]+(1/128)*f2[3]+(1/64)*(f3[4]-(1/2)*f3[3])*(omega^2-1)-(1/64)*f1[2]+(1/32)*f1[3]+(1/64)*f1[4]-280*f3[4]-120*f3[2]+300*f3[3]+20*f3[7]

(1)

``



Download fdm-maple.mw

 

hi...how i can convert 3 couple equations to 1 equation with Placement each other?

thanks...

 

3-1.mw

pd1 := A1*(diff(U(x, theta), x, x, x, x))+A2*(diff(U(x, theta), x, x))+A3*(diff(U(x, theta), x, x, theta, theta))+A4*(diff(V(x, theta), x, x, x, theta))+A5*(diff(V(x, theta), x, theta))+A6*(diff(V(x, theta), x, theta, theta, theta))+A7*(diff(W(x, theta), x, x, x))+A8*(diff(W(x, theta), x))+A9*(diff(W(x, theta), x, theta, theta))+A10*(diff(U(x, theta), theta, theta))+A11*(diff(U(x, theta), theta, theta, theta, theta))-A12*omega^2*U(x, theta)

A1*(diff(diff(diff(diff(U(x, theta), x), x), x), x))+A2*(diff(diff(U(x, theta), x), x))+A3*(diff(diff(diff(diff(U(x, theta), theta), theta), x), x))+A4*(diff(diff(diff(diff(V(x, theta), theta), x), x), x))+A5*(diff(diff(V(x, theta), theta), x))+A6*(diff(diff(diff(diff(V(x, theta), theta), theta), theta), x))+A7*(diff(diff(diff(W(x, theta), x), x), x))+A8*(diff(W(x, theta), x))+A9*(diff(diff(diff(W(x, theta), theta), theta), x))+A10*(diff(diff(U(x, theta), theta), theta))+A11*(diff(diff(diff(diff(U(x, theta), theta), theta), theta), theta))-A12*omega^2*U(x, theta)

(1)

pd2 := B1*(diff(V(x, theta), x, x, x, x))+B2*(diff(V(x, theta), x, x))+B3*(diff(V(x, theta), theta, theta, theta, theta))+B4*(diff(V(x, theta), theta, theta))+B5*(diff(V(x, theta), x, x, theta, theta))+B6*(diff(U(x, theta), x, x, x, theta))+B7*(diff(U(x, theta), x, theta, theta, theta))+B8*(diff(U(x, theta), x, theta))+B9*(diff(W(x, theta), x, x, theta))+B10*(diff(W(x, theta), theta, theta, theta))+B11*(diff(W(x, theta), theta))-B12*omega^2*V(x, theta)

B1*(diff(diff(diff(diff(V(x, theta), x), x), x), x))+B2*(diff(diff(V(x, theta), x), x))+B3*(diff(diff(diff(diff(V(x, theta), theta), theta), theta), theta))+B4*(diff(diff(V(x, theta), theta), theta))+B5*(diff(diff(diff(diff(V(x, theta), theta), theta), x), x))+B6*(diff(diff(diff(diff(U(x, theta), theta), x), x), x))+B7*(diff(diff(diff(diff(U(x, theta), theta), theta), theta), x))+B8*(diff(diff(U(x, theta), theta), x))+B9*(diff(diff(diff(W(x, theta), theta), x), x))+B10*(diff(diff(diff(W(x, theta), theta), theta), theta))+B11*(diff(W(x, theta), theta))-B12*omega^2*V(x, theta)

(2)

pd3 := C1*(diff(W(x, theta), x, x, x, x, x, x))+C2*(diff(W(x, theta), x, x, x, x))+C3*(diff(W(x, theta), x, x, x, x, theta, theta))+C4*(diff(W(x, theta), x, x))+C5*(diff(W(x, theta), x, x, theta, theta))+C6*(diff(W(x, theta), x, x, theta, theta, theta, theta))+C7*(diff(U(x, theta), x, x, x))+C8*(diff(U(x, theta), x))+C9*(diff(U(x, theta), x, theta, theta))+C10*(diff(V(x, theta), x, x, theta))+C11*(diff(V(x, theta), theta))+C12*(diff(V(x, theta), theta, theta, theta))+C13*W(x, theta)+C14*(diff(W(x, theta), theta, theta))+C15*(diff(W(x, theta), theta, theta, theta, theta))+C16*(diff(W(x, theta), theta, theta, theta, theta, theta, theta))-C19*omega^2*W(x, theta)-C18*omega^2*(diff(W(x, theta), theta, theta))-C17*omega^2*(diff(W(x, theta), x, x))

C1*(diff(diff(diff(diff(diff(diff(W(x, theta), x), x), x), x), x), x))+C2*(diff(diff(diff(diff(W(x, theta), x), x), x), x))+C3*(diff(diff(diff(diff(diff(diff(W(x, theta), theta), theta), x), x), x), x))+C4*(diff(diff(W(x, theta), x), x))+C5*(diff(diff(diff(diff(W(x, theta), theta), theta), x), x))+C6*(diff(diff(diff(diff(diff(diff(W(x, theta), theta), theta), theta), theta), x), x))+C7*(diff(diff(diff(U(x, theta), x), x), x))+C8*(diff(U(x, theta), x))+C9*(diff(diff(diff(U(x, theta), theta), theta), x))+C10*(diff(diff(diff(V(x, theta), theta), x), x))+C11*(diff(V(x, theta), theta))+C12*(diff(diff(diff(V(x, theta), theta), theta), theta))+C13*W(x, theta)+C14*(diff(diff(W(x, theta), theta), theta))+C15*(diff(diff(diff(diff(W(x, theta), theta), theta), theta), theta))+C16*(diff(diff(diff(diff(diff(diff(W(x, theta), theta), theta), theta), theta), theta), theta))-C19*omega^2*W(x, theta)-C18*omega^2*(diff(diff(W(x, theta), theta), theta))-C17*omega^2*(diff(diff(W(x, theta), x), x))

(3)

``


Download 3-1.mw

Dear All,

I have a problem solving the attached nonlinear system of equations using shooting method.
I will be grateful if you could help me finding the solutions out.

 

restart; Shootlib := "C:/Shoot9"; libname := Shootlib, libname; with(Shoot);
with(plots);
N1 := 1.0; N2 := 2.0; N3 := .5; Bt := 6; Re_m := N1*Bt; gamma1 := 1;
FNS := {f(eta), fp(eta), fpp(eta), g(eta), gp(eta), m(eta), mp(eta), n(eta), np(eta), fppp(eta)};
ODE := {diff(f(eta), eta) = fp(eta), diff(fp(eta), eta) = fpp(eta), diff(fpp(eta), eta) = fppp(eta), diff(g(eta), eta) = gp(eta), diff(gp(eta), eta) = N1*(2.*g(eta)+(eta-2.*f(eta)).gp(eta)+2.*g(eta)*fp(eta)+2.*N2.N3.(m(eta).np(eta)-n(eta).mp(eta))), diff(m(eta), eta) = mp(eta), diff(mp(eta), eta) = Re_m.(m(eta)+(eta-2.*f(eta)).mp(eta)+2.*m(eta)*fp(eta)), diff(n(eta), eta) = np(eta), diff(np(eta), eta) = Re_m.(2.*n(eta)+(eta-2.*f(eta)).np(eta)+2.*N2/N3.m(eta).gp(eta)), diff(fppp(eta), eta) = N1*(3.*fpp(eta)+(eta-2.*f(eta)).fppp(eta)-2.*N2.N2.m(eta).(diff(mp(eta), eta)))};
blt := 1.0; IC := {f(0) = 0, fp(0) = 0, fpp(0) = alpha1, g(0) = 1, gp(0) = beta1, m(0) = 0, mp(0) = beta2, n(0) = 0, np(0) = beta3, fppp(0) = alpha2};
BC := {f(blt) = .5, fp(blt) = 0, g(blt) = 0, m(blt) = 1, n(blt) = 1};
infolevel[shoot] := 1;
S := shoot(ODE, IC, BC, FNS, [alpha1 = 1.425, alpha2 = .425, beta1 = -1.31, beta2 = 1.00, beta3 = 1.29]);
Error, (in isolate) cannot isolate for a function when it appears with different arguments
p := odeplot(S, [eta, fp(eta)], 0 .. 15);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
display(p);
Error, (in plots:-display) expecting plot structure but received: p
p2 := odeplot(S, [eta, theta(eta)], 0 .. 10);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
display(p2);
Error, (in plots:-display) expecting plot structure but received: p2

 

 

      General description of the method of solving underdetermined systems of equations. As a particular application of the idea proposed a universal method  kinematic analysis for all kinds of linkage (lever) mechanisms. With the description and examples.
      The method can be used for powerful CAD linkages.

Description: Calculation_method_of_linkages.pdf

Attachment:
figure_1.mw
figure_2.mw

Or all in one
Calculation_method_of_linkages_(with_attach.).pdf


        Some examples of a much larger number calculated by the proposed method. Examples gathered here not to look for them on the forum and opportunity to demonstrate the method.  Among the examples, I think, there are very complicated.

https://vk.com/doc242471809_408704758
https://vk.com/doc242471809_408704572
https://vk.com/doc242471809_376439263
https://vk.com/doc242471809_402619761
https://vk.com/doc242471809_402610228
https://vk.com/doc242471809_401188803
https://vk.com/doc242471809_400465891
https://vk.com/doc242471809_400711315
https://vk.com/doc242471809_387358164
https://vk.com/doc242471809_380837279
https://vk.com/doc242471809_379935473
https://vk.com/doc242471809_380217387
https://vk.com/doc242471809_363266817
https://vk.com/doc242471809_353980472
https://vk.com/doc242471809_375452868
https://vk.com/doc242471809_353988163 
https://vk.com/doc242471809_353986884 
https://vk.com/doc242471809_353987119
https://vk.com/doc242471809_324249241
https://vk.com/doc242471809_324102889
https://vk.com/doc242471809_322219275
https://vk.com/doc242471809_437298137
https://vk.com/doc242471809_437308238
https://vk.com/doc242471809_437308241
https://vk.com/doc242471809_437308243
https://vk.com/doc242471809_437308245
https://vk.com/doc242471809_437308246
https://vk.com/doc242471809_437401651
https://vk.com/doc242471809_437664558

 

 

hello every one.please help me with solving this equations.i can not solve this and i need it.thanks


eq1 := (cos(beta2)-1)*w11-sin(beta2)*w12+(cos(alpha2)-1)*z11-sin(alpha2)*z12-cos(delta2) = 0; eq2 := (cos(beta2)-1)*w12+sin(beta2)*w11+(cos(alpha2)-1)*z12+sin(alpha2)*z11-2*sin(delta2) = 0; eq3 := (cos(beta3)-1)*w11-sin(beta3)*w12+(cos(alpha3)-1)*z11-sin(alpha3)*z12-3*cos(delta3) = 0; eq4 := (cos(beta3)-1)*w12+sin(beta3)*w11+(cos(alpha3)-1)*z12+sin(alpha3)*z11-4*sin(delta3) = 0; eq5 := (cos(beta4)-1)*w11-sin(beta4)*w12+(cos(alpha4)-1)*z11-sin(alpha4)*z12-5*cos(delta4) = 0; eq6 := (cos(beta4)-1)*w12+sin(beta4)*w11+(cos(alpha4)-1)*z12+sin(alpha4)*z11-6*sin(delta4) = 0; eq7 := (cos(beta5)-1)*w11-sin(beta5)*w12+(cos(alpha5)-1)*z11-sin(alpha5)*z12-7*cos(delta5) = 0; eq8 := (cos(beta5)-1)*w12+sin(beta5)*w11+(cos(alpha5)-1)*z12+sin(alpha5)*z11-8*sin(delta5) = 0; alpha2 := -20; alpha3 := -45; alpha4 := -75; alpha5 := -90; delta2 := 15.5; delta3 := -15.9829; delta4 := -13.6018; delta5 := -16.7388; P21 = .5217; P31 = 1.3421; P41 = 2.3116; P51 = 3.1780;

Hi,

I have attached a Maple file. My problem is that the solve for the simultaneous equation does not give me understandable results. I even simplified my equations by saying some parameters are zero although my final goal is to find an expression for a and varphi. Any idea how to solve this analytically? I know how to do it numerically. I need an analytical expression.

Thanks,

Baharm31

 

how i can calculate roots of the characteristic polynomial equations {dsys and dsys2}
and dsolve them with arbitrary initial condition for differennt amont of m and n?
thanks
Kr.mw

restart; a := 1; b := 2; Number := 10; q := 1; omega := 0.2e-1
``

Q1 := besselj(0, xi*b)*(eval(diff(bessely(0, xi*r), r), r = a))-(eval(diff(besselj(0, xi*r), r), r = a))*bessely(0, xi*b):

J := 0:

m := 0:

U1 := (int(r*K1[m]*(diff(K_01[m], r)+K_01[m]/r), r = a .. b))/(int(r*K1[m]^2, r = a .. b)); -1; U2 := -(int(r*K_01[m]*(diff(K1[m], r)), r = a .. b))/(int(r*K_01[m]^2, r = a .. b)); -1; U3 := (int(r^2*omega^2*K_01[m], r = a .. b))/(int(r*K_01[m]^2, r = a .. b))

0.6222222222e-3/K_01[12]

(1)

Q2 := besselj(1, eta*b)*(eval(diff(bessely(1, eta*r), r), r = a))-(eval(diff(besselj(1, eta*r), r), r = a))*bessely(1, eta*b):

E2 := unapply(Q2, eta):

m := 0:

 
dsys := {diff(S_mn(t), t, t, t)+xi[m]^2*(diff(S_mn(t), t, t))+(-U1*U2+eta__n^2)*(diff(S_mn(t), t))+xi[m]^2*eta__n^2*S_mn(t) = -(2*U2*b_m/(Pi*xi[m])*(-besselj(0, xi[m]*b)/besselj(1, xi[m]*a)))*q+xi[m]^2*U3}; 1; dsolve(dsys)

{S_mn(t) = (3111111111/5000000000000)/(K_01[12]*eta__n^2)+_C1*cos(eta__n*t)+_C2*sin(eta__n*t)+_C3*exp(-xi[12]^2*t)}

(2)

dsys2 := {diff(Q_mn(t), t, t, t)+xi[m]^2*(diff(Q_mn(t), t, t))+(-U1*U2+eta__n^2)*(diff(Q_mn(t), t))+xi[m]^2*eta__n^2*Q_mn(t) = -2*besselj(0, xi[m]*b)*U1*U2*b_m*(1-exp(-xi[m]^2*t))/(besselj(1, xi[m]*a)*Pi*xi[m]^3)}; 1; dsolve(dsys2)

{Q_mn(t) = _C1*exp(-xi[12]^2*t)+_C2*sin(eta__n*t)+_C3*cos(eta__n*t)}

(3)

``

 

``



Download Kr.mw

 

I have been working on a general solution to motion analysis and seem to be going backwards.  I have an numerical solution in Octave I use for comparison.  I have reduced the problem to a small example that exhibits the problem.

I posted a question similar to this, but, without a set of known values.

I am doing something wrong, but, what?

Tom Dean

## bearing.mpl, solve the target motion problem with bearings only.
##
## Consider a sensor platform moving through points (x,y) at times
## t[1..4] with the target bearings, Brg[1..4] taken at times t[1..4]
## with the target proceeding along a constant course and speed.
##
## time t, bearing line slope m, sensor position (x,y) are known
## values.
##
## Since this is a generated problem the target position at time t is
## provided to compare with the results.
##
#########################################################################
##
restart;
##
genKnownValues := proc()
    description "set the known values",
    "t - relative time",
    "x - sensor x location at time t[i]",
    "y - sensor y location at time t[i]",
    "m - slope of the bearing lines at time t[i]",
    "tgtPosit - target position at time t[i]";
    global t, m, x, y, tgtPosit;
    local dt, Cse, Spd, Brg, A, B, C, R, X;
    local tgtX, tgtY, tgtRange, tgtCse, tgtSpd;
## relative and delta time
    t := [0, 1+1/2, 3, 3+1/2];
    dt := [0, seq(t[idx]-t[idx-1],idx=2..4)];
## sensor motion
    Cse := [90, 90, 90, 50] *~ Pi/180; ## true heading
    Spd := [15, 15, 15, 22];  ## knots
## bearings to the target at time t
    Brg := [10, 358, 340, 330] *~ (Pi/180);
## slope of the bearing lines
    m:=map(tan,Brg);
## calculate the sensor position vs time
    x := ListTools[PartialSums](dt *~ Spd *~ map(cos, Cse));
    y := ListTools[PartialSums](dt *~ Spd *~ map(sin, Cse));
## target values  start the target at a known (x,y) position at a
## constant course and speed
    tgtRange := 95+25/32; ## miles at t1, match octave value...
    tgtCse := 170 * Pi/180; ## course
    tgtSpd := 10; ## knots
    tgtX := tgtRange*cos(Brg[1]);
    tgtX := tgtX +~ ListTools[PartialSums](dt *~ tgtSpd *~ cos(tgtCse));
    tgtY := tgtRange*sin(Brg[1]);
    tgtY := tgtY +~ ListTools[PartialSums](dt *~ tgtSpd *~ sin(tgtCse));
## return target position vs time as a matrix
    tgtPosit:=Matrix(4,2,[seq([tgtX[idx],tgtY[idx]],idx=1..4)]);
end proc:
##
#########################################################################
## t[], m[], x[], and y[] are known values
##
## equation of the bearing lines
eq1 := tgtY[1] - y[1]    = m[1]*(tgtX[1]-x[1]):
eq2 := tgtY[2] - y[2]    = m[2]*(tgtX[2]-x[2]):
eq3 := tgtY[3] - y[3]    = m[3]*(tgtX[3]-x[3]):
eq4 := tgtY[4] - y[4]    = m[4]*(tgtX[4]-x[4]):
## target X motion along the target line
eq5 := tgtX[2] - tgtX[1] = tgtVx*(t[2]-t[1]):
eq6 := tgtX[3] - tgtX[2] = tgtVx*(t[3]-t[2]):
eq7 := tgtX[4] - tgtX[3] = tgtVx*(t[4]-t[3]):
## target Y motion along the target line
eq8 := tgtY[2] - tgtY[1] = tgtVy*(t[2]-t[1]):
eq9 := tgtY[3] - tgtY[2] = tgtVy*(t[3]-t[2]):
eq10:= tgtY[4] - tgtY[3] = tgtVy*(t[4]-t[3]):
##
#########################################################################
##
## solve the equations
eqs  := {eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10}:

Sol:= solve(eqs, {tgtVx, tgtVy, seq([tgtX[k], tgtY[k]][], k= 1..4)}):
##

genKnownValues():
## these values are very close to Octave
evalf(t);evalf(m);evalf(x);evalf(y);evalf(tgtPosit);
## The value of tgtX[] and tgtY[] should equal the respective tgtPosit values
seq(evalf(eval([tgtX[idx],tgtY[idx]], Sol)),idx=1..4);

 


Dear all,

I wold like to find the solution of the next system of two equations with three unknowns but we assume that the unknows are positive integers. How the following code can work. Many thanks

 

 

 

> restart;
> assume(J, integer, J >= 0);
> assume(A, integer, A >= 0);
> assume(T, integer, T >= 0);
> eq1 := J+10*A+50*T=500;
   eq2 := J+A+T = 100;
  solve( {eq1,eq2},{J,A,T});

     Example of the equidistant surface at a distance of 0.25 to the surface
x3
-0.1 * (sin (4 * x1) + sin (3 * x2 + x3) + sin (2 * x2)) = 0
Constructed on the basis of universal parameterization of surfaces.

equidistant_surface.mw 


Hello,

I cant find solution how to create matrix form from equations of motion. Equations looks like this:

My equations ar much more complicated and one of them looks something like this:

 http://i63.tinypic.com/21c5ctk.png

and I want form like this:

I tried to do it using the Generate Matrix but it does not work as I expected. How can you get this form?

 For solving polynomial systems I used RootFinding[Isolate]. But after discussing the question http://www.mapleprimes.com/questions/211774-Roots-Of--Expz--1
I decided to compare Isolate and evalf(solve ([...], [...])). It seemed to me that solve some convenient. The only if in the equation there are integers as a real, they should be recorded with a decimal point. (For real solutions of this procedure should be used with (RealDomain).)  Examples:

SOLVE_ISOLATE.mw

I wonder why then the need Root Finding [Isolate]?

Hello,

 

I have a complex set of non linear diff eqns in the form :

y1'' = f(y1',y1,y2'',y2',y2,y3'',y3',y3,y4'',....,y6'',y6',y6,u1,u2,u3,u4) ;

y2'' = f(y1'',y1',y1,y2',y2,y3'',y3',y3,y4'',....,y6'',y6',y6,u1,u2,u3,u4)

and so on ... y6''=(...)

As I want to resolve this coupled systeme in matlab using @ODE45... I wanted the equations in the form : y1''=f(y1',y1,y2',y2,....) and so on ... => X'[] = f(X[],U[])

 

How can I force maple to rearrange a system of coupled eqns with only the variables i want ?

 

I know this is possible beacause it is a nonlinear state space model but maple do not work with nonlinear state space model... It give me error when I tried to create statespace model with my non linear diff eqns.

 

Thanks a lot !

I have a system of 16 polynomial equations in 15 variables. Independently I know there is at least a one parameter familiy of solutions to this system, so there is reason to think at least two of the equations are redundent. I would like to use Maple to decipher which of the equations are redundent, but I am unsure how to proceed.

So far I have looked at the Groebner package, and it seems like the Reduce and InterReduce commands will be useful. Say I call the set of 16 polynomials X and define a lexicographical order T on the variables. I then ask maple to compute

Reduce(X,X,T)

and receive a list with 7 zeroes and 9 polynomials. What exactly is this telling me? Does this mean that maple has used polynomial division and found that 7 of the equations are redundent?

Thanks for your help!

Hi everybody;

In the following attached file, I am trying to solve a system of nonlinear equations with one equality constraint. I have 9 equations and 9 unknowns. Attached file has composed of 3 main parts, first is input data, second is the 9 nonlinear equations from E_1 to E_9 and finally third part is constraint equation called C_1. My unknowns are "phi, theta, p, q, r, T, L, M and N". My question is that: Can Maple solve this problem?? Is there any solution to this problem or I have to change input data?? If Maple can solve this problem, how can I do that?? 

I appreciate your help in advance.

NL.mw

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