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what does it means and what it will do. Can some one help me for solving this

Shootlib := "C:/Shoot9"; libname := Shootlib, libname; with(Shoot);

while i m receiving the following message:

"Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received Shoot "

Full program is :

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;
 

HI

please help me for dsolve this nonlinear differential equations

thanls...

HAB.mw
 

restart; Digite := 100; Phi0 := 5; A := b*h; g13 := 31/250000000; g1 := 113/500000; f13 := 1/1000000000; c1 := 226000000000000; b := 10*10^(-9); J := (1/12)*b*h^3; h := 15*10^(-9); L := 100*10^(-9); E1 := (339/10000000000000000000000)*(diff(u(x), x, x, x, x))+(1017/10000000000000000000000)*(diff(w(x), x, x))*(diff(w(x), x, x, x))+(339/10000000000000000000000)*(diff(w(x), x, x, x, x))*(diff(w(x), x))-(339/10000)*(diff(u(x), x, x))-(339/10000)*(diff(w(x), x))*(diff(w(x), x, x)) = 0

E2 := -(1017/1600000000000000000000000000000000000000)*(diff(w(x), x, x, x, x, x, x))+(1589109/2500000000000000000000000)*(diff(w(x), x, x, x, x))-(339/10000*(diff(u(x), x, x)+(diff(w(x), x))*(diff(w(x), x, x))))*(diff(w(x), x))-(diff(w(x), x, x))*((339/10000)*(diff(u(x), x))+(339/20000)*(diff(w(x), x))^2+0.5824000000e-4)+(339/10000000000000000000000)*(diff(w(x), x, x))*(diff(u(x), x, x, x)+(diff(w(x), x, x))^2+(diff(w(x), x, x, x))*(diff(w(x), x)))+(339/10000000000000000000000)*(diff(w(x), x))*(diff(u(x), x, x, x, x)+3*(diff(w(x), x, x))*(diff(w(x), x, x, x))+(diff(w(x), x, x, x, x))*(diff(w(x), x)))-2 = 0:
 

E3 := -5.385803274*10^(-17)*(diff(Phi(x), x, x))+2.659881780*Phi(x)-5.125107476*10^(-20)*(diff(psi(x), x, x))+1.146681319*psi(x)+3.300000000*10^(-8)*(diff(w(x), x, x)) = 0:

E4 := -5.125107476*10^(-20)*(diff(Phi(x), x, x))+1.146681319*Phi(x)+(891/100000000000000)*(diff(psi(x), x, x))/Pi+34976.39822*psi(x)+0.4351500000e-5*(diff(w(x), x, x)) = 0:

dsys3 := {EQ1, EQ2, EQ3, EQ4, c1*J*((D@@2)(w))(0)+A*g13*((D@@2)(w))(0)-2*b*f13*Phi0-g1*J*((D@@4)(w))(0)+g1*A*(((D@@2)(u))(0)+((D@@1)(w))(0)*((D@@2)(w))(0))*((D@@1)(w))(0) = 0, c1*J*((D@@2)(w))(L)+A*g13*((D@@2)(w))(L)-2*b*f13*Phi0-g1*J*((D@@4)(w))(L)+g1*A*(((D@@2)(u))(L)+((D@@1)(w))(L)*((D@@2)(w))(L))*((D@@1)(w))(L) = 0, Phi(0) = 0, Phi(L) = 0, psi(0) = 0, psi(L) = 0, u(0) = 0, u(L) = 0, w(0) = 0, w(L) = 0, (D(u))(0) = 0, (D(u))(L) = 0, ((D@@2)(w))(0) = 0, ((D@@2)(w))(L) = 0}; dsolve(dsys3, numeric, initmesh = 3024, abserr = 0.1e-4)

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

 

``


 

Download HAB.mw

 

I uploaded this file AnimationTest.mw to the Maple Cloud. One a 3d animation and one just a 3d plot. When I open the file in the Maple Cloud from my browser,  I cannot rotate either plot with the mouse. Is there a way to change the worksheets so rotation from the browser will be possible?

I Could Not Write An If Then Or Ifelse Statement. Please Help Me.

f := unapply(x^2-2, x); a := 1; b := 2; n := 10; Digits := 10;
      2    
x -> x  - 2
                               1
                               2
                               10
                               10
c := evalf(eval((a*f(b)-b*f(a))/(f(b)-f(a))));
                          1.333333333
if  f(c)*f(a)<0 then ;
          "      k:=evalf(eval(|(f(c))/(b-c)|)) and "

                          /(1 + k) a f(b) - b f(a)\
             x[i] := evalf|-----------------------|
                          \  (1 + k) f(b) - f(a)  /
            "     elif f(x[i])*f(a)<0 then b:=x[i]"
                 "     else b:=c and a:=x[i] "
                  "     if f(c)*f(a)>0 then "
                 "      k:=|(f(c))/(b-c)|and "

                          /a f(b) - b f(a) (1 + k)\
             x[i] := evalf|-----------------------|
                          \  f(b) - f(a) (1 + k)  /
            "     elif f(x[i])*f(a)>0 then a:=x[i]"
              "     else a:=c and b:=x[i] end if"

Error, unterminated 'if' statement
     Typesetting:-mambiguous(Typesetting:-mambiguous(

       if fApplyFunction(c)sdotfApplyFunction(a)lt0 then , 

       Typesetting:-merror("unterminated 'if' statement")))

Im trying to solve 12 equations with 12 variables but I can't solve. Please help and advise me to solve this problem. Iproject3.mw
project3.mw

 

 

 

Hi, I have a big system with 27 polynomial equations in 16 unknowns: f_1=...=f_27=0.  I can store these equations but I cannot calculate a Grobner basis of the ideal  J generated by my polynomials (allocation problem) - I use the library "with(FGb)"-  What interests me is whether my system is minimal in the following sense.

If, for example,  I remove f_1, is the ideal generated by (f_2,...f_27)  J again ? That is to say, is f_1 in the ideal generated by f_2,...,f_27 ? I would like to get an answer "yes" or "no" for each removed  f_i.

My question: can we solve the problem above  without calculating a Grobner basis of J?

Thanks in advance.

 

 

 

 

 


 

diff(Q(t), t) = k*A*(T__1s(t)-T__2s(t))/d

diff(Q(t), t) = h__1(t)*A*(T__1(t)-T__1s(t))

diff(Q(t), t) = h__2(t)*A*(T__2s(t)-T__2(t))

Q(t) = m__1*c__p*(T__1i-T__1(t))

Q(t) = m__2*c__p*(T__2(t)-T__2i)

h__1(t) = k(T__1(t), T__1s(t))*(.825+.387*(g*h^3*c__p*beta(T__1(t), T__1s(t))*rho(T__1(t), T__1s(t))^2*(T__1(t)-T__1s(t))/(k(T__1(t), T__1s(t))*mu(T__1(t), T__1s(t))))^(1/6)/(1+(.492*k(T__1(t), T__1s(t))/(c__p*mu(T__1(t), T__1s(t))))^(9/16))^(8/27))^2/h

h__2(t) = k(T__2(t), T__2s(t))*(.825+.387*(g*h^3*c__p*beta(T__2(t), T__2s(t))*rho(T__2(t), T__2s(t))^2*(T__2s(t)-T__2(t))/(k(T__2(t), T__2s(t))*mu(T__2(t), T__2s(t))))^(1/6)/(1+(.492*k(T__2(t), T__2s(t))/(c__p*mu(T__2(t), T__2s(t))))^(9/16))^(8/27))^2/h

 

 

rho(T__1(t), T__1s(t)) = 999.9399+2.1082425*10^(-2)*(T__1(t)+T__1s(t))-1.77436275*10^(-3)*(T__1(t)+T__1s(t))^2+.438696375*10^(-5)*(T__1(t)+T__1s(t))^3-.6189861563*10^(-8)*(T__1(t)+T__1s(t))^4

beta(T__1(t), T__1s(t)) = -(4.216485*10^(-2)-7.097451*10^(-3)*(T__1(t)+T__1s(t))+2.63217825*10^(-5)*(T__1(t)+T__1s(t))^2-4.9518879*10^(-8)*(T__1(t)+T__1s(t))^3)/(999.9399+2.1082425*10^(-2)*(T__1(t)+T__1s(t))-1.77436275*10^(-3)*(T__1(t)+T__1s(t))^2+.438696375*10^(-5)*(T__1(t)+T__1s(t))^3-.6189861563*10^(-8)*(T__1(t)+T__1s(t))^4)
mu(T__1(t), T__1s(t)) = 2.414*10^(247.8/(.5*(T__1(t)+T__1s(t))+133)-5)

k(T__1(t), T__1s(t)) = -9.481411*10^(-6)*(T__1(t)+T__1s(t))^2+2.1356735*10^(-3)*(T__1(t)+T__1s(t))+.5599920949

 

 

rho(T__2(t), T__2s(t)) = 999.9399+2.1082425*10^(-2)*(T__2(t)+T__2s(t))-1.77436275*10^(-3)*(T__2(t)+T__2s(t))^2+.438696375*10^(-5)*(T__2(t)+T__2s(t))^3-.6189861563*10^(-8)*(T__2(t)+T__2s(t))^4

beta(T__2(t), T__2s(t)) = -(4.216485*10^(-2)-7.097451*10^(-3)*(T__2(t)+T__2s(t))+2.63217825*10^(-5)*(T__2(t)+T__2s(t))^2-4.9518879*10^(-8)*(T__2(t)+T__2s(t))^3)/(999.9399+2.1082425*10^(-2)*(T__2(t)+T__2s(t))-1.77436275*10^(-3)*(T__2(t)+T__2s(t))^2+.438696375*10^(-5)*(T__2(t)+T__2s(t))^3-.6189861563*10^(-8)*(T__2(t)+T__2s(t))^4)
mu(T__2(t), T__2s(t)) = 2.414*10^(247.8/(.5*(T__2(t)+T__2s(t))+133)-5)

k(T__2(t), T__2s(t)) = -9.481411*10^(-6)*(T__2(t)+T__2s(t))^2+2.1356735*10^(-3)*(T__2(t)+T__2s(t))+.5599920949

 

"`h__1`(t)=(-9.481411*10^(-6) (`T__1`(t)+`T__1s`(t))^(2)+2.1356735*10^(-3) (`T__1`(t)+`T__1s`(t))+0.5599920949)/(h) (0.825+(0.387 ((g h^(3) `c__p` (-(4.216485*10^(-2)-7.097451*10^(-3) (`T__1`(t)+`T__1s`(t))+2.63217825*10^(-5) (`T__1`(t)+`T__1s`(t))^(2)-4.9518879*10^(-8) (`T__1`(t)+`T__1s`(t))^(3))/(999.9399+2.1082425*10^(-2) (`T__1`(t)+`T__1s`(t))-1.77436275*10^(-3) (`T__1`(t)+`T__1s`(t))^(2)+0.438696375*10^(-5) (`T__1`(t)+`T__1s`(t))^(3)  -0.6189861563*10^(-8) (`T__1`(t)+`T__1s`(t))^(4))) (999.9399+2.1082425*10^(-2) (`T__1`(t)+`T__1s`(t))-1.77436275*10^(-3) (`T__1`(t)+`T__1s`(t))^(2)+0.438696375*10^(-5) (`T__1`(t)+`T__1s`(t))^(3)  -0.6189861563*10^(-8) (`T__1`(t)+`T__1s`(t))^(4))^(2) (`T__1`(t)-`T__1s`(t)))/((-9.481411*10^(-6) (`T__1`(t)+`T__1s`(t))^(2)+2.1356735*10^(-3) (`T__1`(t)+`T__1s`(t))+0.5599920949) 2.414*10^((247.8)/(0.5 (`T__1`(t)+`T__1s`(t))+133)-5)))^((1)/(6)))/((1+((0.492 (-9.481411*10^(-6) (`T__1`(t)+`T__1s`(t))^(2)+2.1356735*10^(-3) (`T__1`(t)+`T__1s`(t))+0.5599920949))/(`c__p` 2.414*10^((247.8)/(0.5 (`T__1`(t)+`T__1s`(t))+133)-5)))^((9)/(16)))^((8)/(27))))^(2)"

"`h__2`(t)=(-9.481411*10^(-6) (`T__2`(t)+`T__2s`(t))^(2)+2.1356735*10^(-3) (`T__2`(t)+`T__2s`(t))+0.5599920949)/(h) (0.825+(0.387 ((g h^(3) `c__p` (-(4.216485*10^(-2)-7.097451*10^(-3) (`T__2`(t)+`T__2s`(t))+2.63217825*10^(-5) (`T__2`(t)+`T__2s`(t))^(2)-4.9518879*10^(-8) (`T__2`(t)+`T__2s`(t))^(3))/(999.9399+2.1082425*10^(-2) (`T__2`(t)+`T__2s`(t))-1.77436275*10^(-3) (`T__2`(t)+`T__2s`(t))^(2)+0.438696375*10^(-5) (`T__2`(t)+`T__2s`(t))^(3)  -0.6189861563*10^(-8) (`T__2`(t)+`T__2s`(t))^(4))) (999.9399+2.1082425*10^(-2) (`T__2`(t)+`T__2s`(t))-1.77436275*10^(-3) (`T__2`(t)+`T__2s`(t))^(2)+0.438696375*10^(-5) (`T__2`(t)+`T__2s`(t))^(3)  -0.6189861563*10^(-8) (`T__2`(t)+`T__2s`(t))^(4))^(2) (`T__2s`(t)-`T__2`(t)))/((-9.481411*10^(-6) (`T__2`(t)+`T__2s`(t))^(2)+2.1356735*10^(-3) (`T__2`(t)+`T__2s`(t))+0.5599920949) 2.414*10^((247.8)/(0.5 (`T__2`(t)+`T__2s`(t))+133)-5)))^((1)/(6)))/((1+((0.492 (-9.481411*10^(-6) (`T__2`(t)+`T__2s`(t))^(2)+2.1356735*10^(-3) (`T__2`(t)+`T__2s`(t))+0.5599920949))/(`c__p` 2.414*10^((247.8)/(0.5 (`T__2`(t)+`T__2s`(t))+133)-5)))^((9)/(16)))^((8)/(27))))^(2)"

diff(Q(t), t) = k*A*(T__1s(t)-T__2s(t))/d, diff(Q(t), t) = A*(T__1(t)-T__1s(t))*(-9.481411*10^(-6)*(T__1(t)+T__1s(t))^2+2.1356735*10^(-3)*(T__1(t)+T__1s(t))+.5599920949)*(.825+.387*(((-g*h^3*c__p*(4.216485*10^(-2)-7.097451*10^(-3)*(T__1(t)+T__1s(t))+2.63217825*10^(-5)*(T__1(t)+T__1s(t))^2-4.9518879*10^(-8)*(T__1(t)+T__1s(t))^3)/(999.9399+2.1082425*10^(-2)*(T__1(t)+T__1s(t))-1.77436275*10^(-3)*(T__1(t)+T__1s(t))^2+.438696375*10^(-5)*(T__1(t)+T__1s(t))^3-.6189861563*10^(-8)*(T__1(t)+T__1s(t))^4))*((999.9399+2.1082425*10^(-2)*(T__1(t)+T__1s(t))-1.77436275*10^(-3)*(T__1(t)+T__1s(t))^2+.438696375*10^(-5)*(T__1(t)+T__1s(t))^3-.6189861563*10^(-8)*(T__1(t)+T__1s(t))^4)^2))*(T__1(t)-T__1s(t))/(2.414*10^(247.8/(.5*(T__1(t)+T__1s(t))+133)-5)*(-9.481411*10^(-6)*(T__1(t)+T__1s(t))^2+2.1356735*10^(-3)*(T__1(t)+T__1s(t))+.5599920949)))^(1/6)/(1+((.492*(-9.481411*10^(-6)*(T__1(t)+T__1s(t))^2+2.1356735*10^(-3)*(T__1(t)+T__1s(t))+.5599920949))/(2.414*c__p*10^(247.8/(.5*(T__1(t)+T__1s(t))+133)-5)))^(9/16))^(8/27))^2/h, diff(Q(t), t) = A*(T__2s(t)-T__2(t))*(-9.481411*10^(-6)*(T__2(t)+T__2s(t))^2+2.1356735*10^(-3)*(T__2(t)+T__2s(t))+.5599920949)*(.825+.387*(((-g*h^3*c__p*(4.216485*10^(-2)-7.097451*10^(-3)*(T__2(t)+T__2s(t))+2.63217825*10^(-5)*(T__2(t)+T__2s(t))^2-4.9518879*10^(-8)*(T__2(t)+T__2s(t))^3)/(999.9399+2.1082425*10^(-2)*(T__2(t)+T__2s(t))-1.77436275*10^(-3)*(T__2(t)+T__2s(t))^2+.438696375*10^(-5)*(T__2(t)+T__2s(t))^3-.6189861563*10^(-8)*(T__2(t)+T__2s(t))^4))*((999.9399+2.1082425*10^(-2)*(T__2(t)+T__2s(t))-1.77436275*10^(-3)*(T__2(t)+T__2s(t))^2+.438696375*10^(-5)*(T__2(t)+T__2s(t))^3-.6189861563*10^(-8)*(T__2(t)+T__2s(t))^4)^2))*(T__2s(t)-T__2(t))/(2.414*10^(247.8/(.5*(T__2(t)+T__2s(t))+133)-5)*(-9.481411*10^(-6)*(T__2(t)+T__2s(t))^2+2.1356735*10^(-3)*(T__2(t)+T__2s(t))+.5599920949)))^(1/6)/(1+((.492*(-9.481411*10^(-6)*(T__2(t)+T__2s(t))^2+2.1356735*10^(-3)*(T__2(t)+T__2s(t))+.5599920949))/(2.414*c__p*10^(247.8/(.5*(T__2(t)+T__2s(t))+133)-5)))^(9/16))^(8/27))^2/h, Q(t) = m__1*c__p*(T__1i-T__1(t)), Q(t) = m__2*c__p*(T__2(t)-T__2i)

diff(Q(t), t) = k*A*(T__1s(t)-T__2s(t))/d, diff(Q(t), t) = A*(T__1(t)-T__1s(t))*(-0.9481411000e-5*(T__1(t)+T__1s(t))^2+0.2135673500e-2*T__1(t)+0.2135673500e-2*T__1s(t)+.5599920949)*(.825+.387*(-.4142502071*g*h^3*c__p*(0.4216485000e-1-0.7097451000e-2*T__1(t)-0.7097451000e-2*T__1s(t)+0.2632178250e-4*(T__1(t)+T__1s(t))^2-0.4951887900e-7*(T__1(t)+T__1s(t))^3)*(999.9399+0.2108242500e-1*T__1(t)+0.2108242500e-1*T__1s(t)-0.1774362750e-2*(T__1(t)+T__1s(t))^2+0.4386963750e-5*(T__1(t)+T__1s(t))^3-0.6189861563e-8*(T__1(t)+T__1s(t))^4)*(T__1(t)-T__1s(t))/(10^(247.8/(.5*T__1(t)+.5*T__1s(t)+133)-5)*(-0.9481411000e-5*(T__1(t)+T__1s(t))^2+0.2135673500e-2*T__1(t)+0.2135673500e-2*T__1s(t)+.5599920949)))^(1/6)/(1+.4087338992*((-0.9481411000e-5*(T__1(t)+T__1s(t))^2+0.2135673500e-2*T__1(t)+0.2135673500e-2*T__1s(t)+.5599920949)/(c__p*10^(247.8/(.5*T__1(t)+.5*T__1s(t)+133)-5)))^(9/16))^(8/27))^2/h, diff(Q(t), t) = A*(T__2s(t)-T__2(t))*(-0.9481411000e-5*(T__2(t)+T__2s(t))^2+0.2135673500e-2*T__2(t)+0.2135673500e-2*T__2s(t)+.5599920949)*(.825+.387*(-.4142502071*g*h^3*c__p*(0.4216485000e-1-0.7097451000e-2*T__2(t)-0.7097451000e-2*T__2s(t)+0.2632178250e-4*(T__2(t)+T__2s(t))^2-0.4951887900e-7*(T__2(t)+T__2s(t))^3)*(999.9399+0.2108242500e-1*T__2(t)+0.2108242500e-1*T__2s(t)-0.1774362750e-2*(T__2(t)+T__2s(t))^2+0.4386963750e-5*(T__2(t)+T__2s(t))^3-0.6189861563e-8*(T__2(t)+T__2s(t))^4)*(T__2s(t)-T__2(t))/(10^(247.8/(.5*T__2(t)+.5*T__2s(t)+133)-5)*(-0.9481411000e-5*(T__2(t)+T__2s(t))^2+0.2135673500e-2*T__2(t)+0.2135673500e-2*T__2s(t)+.5599920949)))^(1/6)/(1+.4087338992*((-0.9481411000e-5*(T__2(t)+T__2s(t))^2+0.2135673500e-2*T__2(t)+0.2135673500e-2*T__2s(t)+.5599920949)/(c__p*10^(247.8/(.5*T__2(t)+.5*T__2s(t)+133)-5)))^(9/16))^(8/27))^2/h, Q(t) = m__1*c__p*(T__1i-T__1(t)), Q(t) = m__2*c__p*(T__2(t)-T__2i)

(1)

"(->)"

``

``

``

i have a system with 5 dif equations and five unknows. i have told to maple to solve it numerically with interactively solve comand (right cilck button). the window open like it normally does and i put values to my parameters, with an initial condition for the system (Q(0)=0). then i press numerically solve and that's all, the program just keep evaluating with no answer. i wait for 15 min, which i think is too much time, and got any answer yet.

hope you can help with this

thanks.. 
 

Download propuesta_transfer.mw

I assigned

before an algebraic calculation so I would like to get  or have the program print the 70 digits of the answer and not just 10 digits. Because when I press ENTER, I get only 10 digits.

 

I am trying to implement Subresultant p.r.s. algorithm for calculating greatest common divisor. The algorithm decribed in the book:

My code return the correct GCD, however the sub-resultant terms are different from the result of the built-in function. The last term a[i-1] is huge and involves fractions. I think my implementation is same as the algorithm described in the textbook.

I have attached the file. Could anybody spot anything wrong in the code? Why do fractions still appear? In my code, "lsr" is last subresultant term returned from the built-in function, the second one is my result.

with(RegularChains);

[Chain, ChangeOfOrder, Construct, Cut, DahanSchostTransform, Dimension, Empty, EqualSaturatedIdeals, EquiprojectableDecomposition, Extend, ExtendedNormalizedGcd, IsAlgebraic, IsEmptyChain, IsInRadical, IsInSaturate, IsIncluded, IsPrimitive, IsStronglyNormalized, IsZeroDimensional, IteratedResultant, LastSubresultant, Lift, ListConstruct, NormalizeRegularChain, NumberOfSolutions, Polynomial, Regularize, RemoveRedundantComponents, SeparateSolutions, Squarefree, SquarefreeFactorization, SubresultantChain, SubresultantOfIndex, Under, Upper]

(1)

A42vlastsub := proc (f, g) local i, a, dt, bt, om; i := 1; if degree(f) < degree(g) then a[0] := primpart(g, x); a[1] := primpart(f, x) else a[0] := primpart(f, x); a[1] := primpart(g, x) end if; dt[0] := degree(a[0])-degree(a[1]); bt[2] := (-1)^(dt[0]+1); om[2] := -1; while a[i] <> 0 do a[i+1] := normal(prem(a[i-1], a[i], x)/bt[i+1]); dt[i] := degree(a[i])-degree(a[i+1]); i := i+1; om[i+1] := (-lcoeff(a[i-1]))^dt[i-2]*om[i]^(1-dt[i-2]); bt[i+1] := -lcoeff(a[i-1])*om[i+1]^dt[i-1] end do; return a[i-1] end proc;

 

(2)

f := (y^2-1)*((y+1)*x^4+(y^2-1)*x^3+(y^3-1)*x^2+(y^4-1)*x+y^5-1);

(y-1)*x^5+(y^2-1)*x^4+(y^3-1)*x^3+(y^4-1)*x^2+(y^5-1)*x+y^6-1

(3)

R := RegularChains:-PolynomialRing([y, x]);

subresultant_chain

(4)

lsr := LastSubresultant(src, R);

y^25+y^24+2*y^23+4*y^22+8*y^21+16*y^20+46*y^19+160*y^18+402*y^17+808*y^16+1384*y^15+2080*y^14+2932*y^13+3762*y^12+4406*y^11+4740*y^10+4720*y^9+4400*y^8+3810*y^7+2968*y^6+2102*y^5+1360*y^4+800*y^3+400*y^2+139*y+21

(5)

``

mylastsr := A42vlastsub(primpart(f, x), primpart(g, x));

-(35867/3794275180128377091639574036764685364535950857523710002444946112771297432041422848)*y^9-(10309/7588550360256754183279148073529370729071901715047420004889892225542594864082845696)*y^8-(2889061/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^10-(94304133/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^13-(35600337/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^12-(11265153/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^11-(4325932673/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^21-(3534515779/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^20-(2703789263/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^19-(1929251163/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^18-(1277273509/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^17-(778538921/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^16-(432069123/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^15-(215109057/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^14-(5255652033/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^25-(5374732281/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^23-(5474736805/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^24-(4971065401/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^22-(475/3794275180128377091639574036764685364535950857523710002444946112771297432041422848)*y^7-(21/3794275180128377091639574036764685364535950857523710002444946112771297432041422848)*y^6-(332387607/30354201441027016733116592294117482916287606860189680019559568902170379456331382784)*y^32-(1/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^49-(23/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^48-(251/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^47-(1735/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^46-(8571/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^45-(32463/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^44-(99205/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^43-(255999/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^42-(586005/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^41-(1263605/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^40-(2747253/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^39-(6322305/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^38-(15325169/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^37-(37286331/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^36-(86630947/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^35-(186556683/60708402882054033466233184588234965832575213720379360039119137804340758912662765568)*y^34-(92016457/15177100720513508366558296147058741458143803430094840009779784451085189728165691392)*y^33-(275974877/15177100720513508366558296147058741458143803430094840009779784451085189728165691392)*y^31-(847698927/30354201441027016733116592294117482916287606860189680019559568902170379456331382784)*y^30-(1210953247/30354201441027016733116592294117482916287606860189680019559568902170379456331382784)*y^29-(1616246617/30354201441027016733116592294117482916287606860189680019559568902170379456331382784)*y^28-(505494959/7588550360256754183279148073529370729071901715047420004889892225542594864082845696)*y^27-(2376326883/30354201441027016733116592294117482916287606860189680019559568902170379456331382784)*y^26

(6)

``


 

Download subresultant.mw

I resolved the coefficients to a 2nd order diff eq of the form:ay''+by'+cy=f(t)

I have included the .mw file for convenience at the link at the bottom of the page.  I resolved the coefficients in 2 different ways & they do not concur.  The 1st approach used the LaPlace transform & partial fraction decomposition.  The coefficient results are given by equations # 14 & 15.  The 2nd approach used undetermined coefficients where I assumed the particular solution and then applied the initial conditions to resolve the coefficients pertaining to the homogeneous solution which are given in the results listed in equation #23.  Noted in the 1st case the coeff's are A3 & A4 and for the 2nd approach the coeff's are A1 & A2.  I have worked this numerous times & do not understand why they do not concur.  So I thought I should get some fresh eyes on the problem to find where I may have gone wrong.

Any new perspective will be greatly apprecieated.

I had trouble uploading the .mw file so I have included an alternative link to retrieve the file if the code contents is illegible or you cannot dowlad the file drectly from the weblink  Download coeffs_of_homogen_soln_discrepancy.mw.  You should be able to download from the alternative link below once you paste the link into your browser.  If you cannot & wish for me to provide the file in some other fashion respond with some specific instructions & I will attempt to get the file to you.

https://unl.box.com/s/dywe90wwpy0t4ilkuxshkivz2z26mud8

Thanks 4 any help you can provide.

Download coeffs_of_homogen_soln_discrepancy.mw

Dear all,

I'm investigating the vibration performance of timber beams. I have sample data from my test which shows the vibration of the beam. I want to determine the eigenfrequency from this data. The problem I face is that I'm not finding the probber eigenfrequency. I have two data rows; time and amplitude. I'm able to plot the amplitude with SignalPlot but not the time, therefore I have to adjust the samplerate. I have the same problem with the fourier analysis. Is it possible to include the time period as well?

Regards,

 

Maurits

 

Dear all,

I need to transforme these equation from time domain to frequency domain with fourier transforms and solve it in frequency domain but i received the flowing error

any helps

thank you !

 

``

restart:with(inttrans):

E:=1;L:=1;

1

 

1

(1)

 

equ := arccos(y(t)/R)*R*L*(diff(y(t), `$`(t, 1)))*abs(diff(y(t), `$`(t, 1)))+diff(y(t), `$`(t, 2))+m*sin(omega*t+k*R*sin(`&theta;l`))+arccos(y(t)/R);

arccos(y(t)/R)*R*(diff(y(t), t))*abs(diff(y(t), t))+diff(diff(y(t), t), t)+m*sin(omega*t+k*R*sin(`&theta;l`))+arccos(y(t)/R)

(2)

eq:=fourier(equ,t,omega);

((1/2)*I)*m*fourier(exp(-I*omega*t), t, omega)*exp(-(1/2)*k*R*exp(I*`&theta;l`)+(1/2)*k*R*exp(-I*`&theta;l`))-omega^2*fourier(y(t), t, omega)-((1/2)*I)*m*fourier(exp(I*omega*t), t, omega)*exp((1/2)*k*R*exp(I*`&theta;l`)-(1/2)*k*R*exp(-I*`&theta;l`))+R*fourier(arccos(y(t)/R)*(diff(y(t), t))*abs(diff(y(t), t)), t, omega)+fourier(arccos(y(t)/R), t, omega)

(3)

csi := y(0) = 0.2e-1, (D(y))(0) = 0;

y(0) = 0.2e-1, (D(y))(0) = 0

(4)

sol := dsolve({csi, eq}, numeric, maxfun = 1000000000)

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)

 

Error, (in solve) cannot solve expressions with fourier(arccos(Y[1]/R)*YP[1]*abs(YP[1]), t, omega) for YP[1]

 

Code :

Download Fourier_TRAns_MAPLEprime.mwFourier_TRAns_MAPLEprime.mw

Hi, I'm trying to use Maple to construct some examples of symmetry solutions for certain nonlinear PDE's.  As a warm up, however, I'm working through the commands just for the heat equation in 3d: u[t]-u[x,x]-u[y,y]-u[z,z]=0 

I've gotten Maple to produce both determining equations for the symmetry infinitesimal generators via the DeterminingPDE command.  I've also gotten the command Infinitesimals to work too.

However, when I next use PDETools Invariants command, it correctly outputs invariants for most of the generator output of Infinitesimals EXCEPT it won't output anything for the simple rotation generators yd[x]-xd[y].  It will, however, output invariants if the rotation is between an independent and the dependent coordinate.

An example:
with(PDETools)
S:=[_xi[x]=y, _xi[y]=-x, _eta[u]=0]
Invariants(S,u(x,y))

*Above returns nothing, But if you instead have _xi[x]=x and _xi[y]=y then it returns the right invariants.

Thanks in advance!

Hey, this is not the I've had this encounter. I want to open this saved document but when I open it and Maple starts up it just hits me with "A problem was encountered while opening the workbook. Database is not opened". How can I get to open it properly and see my math notes?

How can this be prevented?

When I try to upload the file in this message it says "Cant open a null file"

Any help?

 

Jacob

 

plz code and sole that this integral!!!!!!!!!!

!!!

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