solving a equation...

friends ,

i want to solve an equation but maple result is " Root of .. " term , how can i get rid of that

eqqq.mw

thanks

Solve and RootOf(allvalues)...

I want to solve the problem described below. I tried using two methods as shown below, each method has been runing for days without solving it. I will really appreciate your help.

Det1 := (1/256)*(Aiso*(c+t)^2*(a^2+b^2)*(mu-1)*Pi^2-4*a^2*b^2*c*Gc)*(16*Aiso^2*Do^2*(c+t)^4*(a^2+b^2)^6*Pi^12+10*(a^2+b^2)^5*((c+t)^2*Aiso+4*Do)*Gc*(c+t)^2*c*a^2*Do*b^2*Aiso*Pi^10+(a^2+b^2)^4*((c+t)^2*Aiso+4*Do)^2*Gc^2*c^2*a^4*b^4*Pi^8-(1024/81)*a^6*Aiso^2*b^6*Tcr^2*(c+t)^4*(a^2+b^2)^2*Pi^4-(2560/81)*a^8*Aiso*b^8*c*Gc*Tcr^2*(c+t)^2*(a^2+b^2)*Pi^2-(1024/81)*a^10*b^10*c^2*Gc^2*Tcr^2)*(Aiso*(c+t)^2*(a^2+4*b^2)*(mu-1)*Pi^2-4*a^2*b^2*c*Gc)*(Aiso*(c+t)^2*(a^2+b^2)*(mu-1)*Pi^2-a^2*b^2*c*Gc)*(16*(c+t)^4*(a^2+(1/4)*b^2)^3*Do^2*(a^2+4*b^2)^3*Aiso^2*Pi^12+(10*(a^2+b^2))*((c+t)^2*Aiso+4*Do)*Gc*(c+t)^2*(a^2+(1/4)*b^2)^2*c*a^2*Do*(a^2+4*b^2)^2*b^2*Aiso*Pi^10+((c+t)^2*Aiso+4*Do)^2*Gc^2*(a^2+(1/4)*b^2)^2*c^2*a^4*(a^2+4*b^2)^2*b^4*Pi^8-(1024/81)*(c+t)^4*(a^2+(1/4)*b^2)*Tcr^2*a^6*(a^2+4*b^2)*b^6*Aiso^2*Pi^4-(2560/81)*a^8*Aiso*b^8*c*Gc*Tcr^2*(c+t)^2*(a^2+b^2)*Pi^2-(1024/81)*a^10*b^10*c^2*Gc^2*Tcr^2)*((mu-1)*(c+t)^2*(a^2+(1/4)*b^2)*Aiso*Pi^2-a^2*b^2*c*Gc)/(b^20*a^20*(c+t)^16) = 0;

# method 1;
EQN := RootOf(Det1, Tcr);

EQN_2 := allvalues(EQN);

# method 2;

EQN := solve(Det1, Tcr);

Is it possible get a solution of this equation without RoofOf in form explicit?

Simplify RootOf() expression...

Hi!

I have a question here. Is there any way to simplify a complicated number expressed in terms of RootOf() forms?

I got numbers like

c:=(3/128)*RootOf(3*_Z^4-20*_Z^3+50*_Z^2-20*_Z+3)^3-(5/32)*RootOf(3*_Z^4-20*_Z^3+50*_Z^2-20*_Z+3)^2+(1/64)*sqrt(4+6*sqrt(6))+(25/64)*RootOf(3*_Z^4-20*_Z^3+50*_Z^2-20*_Z+3)-(3/128)*RootOf(3+3*_Z^2+(-3*RootOf(3*_Z^4-20*_Z^3+50*_Z^2-20*_Z+3)^3+20*RootOf(3*_Z^4-20*_Z^3+50*_Z^2-20*_Z+3)^2-47*RootOf(3*_Z^4-20*_Z^3+50*_Z^2-20*_Z+3))*_Z)-5/64

I am quite sure this number is 0:
evalf(c, 100) gives:
0.+1.*10^(-101)*I

However, I tried simplify(c) and convert( c, 'radical' ) and some other choices of simplify() function. None of them can output 0. Is there any maple functions that can help me to simplify this kind of expressions?

Thanks!

William

Are these RootOf actually equivalent?...

While exploring a relatively simple sin equation, depending on how I process I get different forms of the root. Numerically, they appear to be the same, but I am having difficult figuring out how they could be, and would appreciate some guidance.

The more standard root is

21*arccos(RootOf(448*_Z^7+192*_Z^6-784*_Z^5-288*_Z^4+392*_Z^3+108*_Z^2-49*_Z-6, index = 2))/Pi

The less standard approach is

-(21*I)*ln(RootOf(7*_Z^14+6*_Z^13+6*_Z+7, index = 2))/Pi

Both of the RootOf appear to be irreducible, and it is not clear to me how you could transform the more complicated degree 7 polynomial into the simpler degree 14 polynomial while still retaining exactly the same roots?

If the equivalence holds up then it would be much easier for me to generalize the second form than the first.

I was, by the way, looking at minimizing sin(2/7*Pi*x) _+ sin(1/3*Pi*x) over its first complete cycle, as part of working up to a general rule for minimizing sum of sin of different amplitude and periods. diff(), then standard form is solve(), and less standard form is solve() of convert/exp() of the diff()

Solve Simple Equation...

Hi all,

Is there anyone who could help me with this error? I am sure there is at least one solution for the equation.

Thanks

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/EQ.mw .

RootOf expressions...

suppose one has a solution to a system of equations that returns results as RootOf(X) expressions. I would like to know if there is a procedure for extracting the "X" from the RootOf for the purpose of further algebraic analysis.

How do I get a better solution?...

Here is my code in Maple.

#Solve the initial-value problem using the technique of question 2. Find the implicit solution.
eqn3:=(exp(x)+y)*dx+(2+x+y*exp(y))*dy=0;
(exp(x) + y) dx + (2 + x + y exp(y)) dy = 0
#subject to y(0)=1.
M:=exp(x)+y; N:=2+x+y*exp(y);
exp(x) + y
2 + x + y exp(y)
int(M, x); int(N,y);
exp(x) + y x
y x + 2 y + y exp(y) - exp(y)
implicitsoln1 := exp(x)+y*x+2*y+y*exp(y)-exp(y)=C;
exp(x) + y x + 2 y + y exp(y) - exp(y) = C
y1 := solve(implicitsoln1,y);
RootOf(-exp(_Z) _Z - _Z x + C + exp(_Z) - 2 _Z - exp(x))
C:=subs({x=0,y=1},lhs(implicitsoln1));
exp(0) + 2
y1;

How do I get it to to not have "root of" and give me a more specific solution.

Is `evala/toprof` command in new Maple versions?...

Does `evala/toprof` still exist in newer Maple versions, or is there an equivalent?

Simplification of RootOf...

hi...how i can gain result for solve three equations,in which term '' Root of'' dont appear?

thanks

 (1)

 (2)

 (3)

 (4)

 (5)

Problem with dsolve...

Dear all,

I am trying to solve the following system of equations by using dsolve, but I get the error:  error, (in RootOf) expression independent of, _Z, could you please help me to solve it. Thank you.

restart;
Digits := 20;
with(plots);
Nr := .1; Nb := .3; Nt := .1; Rb := 0; Lb := 1; Le := 10; Pe := 1; ss := .2; aa := .1; bb := .2; cc := .3; nn := 1.5;
Eq1 := nn.(diff(f(eta), eta))^(nn-1).(diff(f(eta), `\$`(eta, 2)))-(nn+1)/(2.*nn+1).eta.(diff(theta(eta), eta)-Nr.(diff(h(eta), eta))-Rb.(diff(g(eta), eta))) = 0;
Eq2 := diff(theta(eta), `\$`(eta, 2))+nn/(2.*nn+1).f(eta).(diff(theta(eta), eta))+Nb.(diff(theta(eta), eta)).(diff(h(eta), eta))+Nt.((diff(theta(eta), eta))^2) = 0;
Eq3 := diff(h(eta), `\$`(eta, 2))+nn/(2.*nn+1).Le.f(eta).(diff(h(eta), eta))+Nt/Nb.(diff(theta(eta), `\$`(eta, 2))) = 0;
Eq4 := diff(g(eta), `\$`(eta, 2))+nn/(2.*nn+1).Lb.f(eta).(diff(g(eta), eta))-Pe.((diff(g(eta), eta)).(diff(h(eta), eta))+(diff(h(eta), `\$`(eta, 2))).g(eta)) = 0;
etainf := 10;
bcs := f(0) = ss/Le.(D(h))(0), theta(0) = lambda+aa.(D(theta))(0), h(0) = lambda+bb.(D(h))(0), g(0) = lambda+cc.(D(g))(0), (D(f))(etainf) = 0, theta(etainf) = 0, h(etainf) = 0, g(etainf) = 0;
dsys := {Eq1, Eq2, Eq3, Eq4, bcs};
dsol := dsolve(dsys, numeric, continuation = lambda, output = procedurelist);
Error, (in RootOf) expression independent of, _Z

Problem with symbolical solution...

Hi,

I have been trying to solve the following equation with respect to y, but I have not been successful. In fact, I always get answer RootOf(...). I should mention that all variables and parameters are real non-negative. I have also tested with "assume", but it did not help. Any suggestion would be appreciated.

 (1)

 (2)

 (3)

Thanks.

How to get rid of RootOf?...

hi.please see attached file below and help me for gain real or complex answer

with out show answer in root of manner

thanksroot_of....mw

Trouble with RootOf in set...

Hello everyone! I got some trouble in process a list. Hope you can help:

Assume i got a list like this:

{{k = k, l = RootOf(_Z^2+_Z*k+k^2-1), o = -k-RootOf(_Z^2+_Z*k+k^2-1)}, {k = k, l = RootOf(_Z^2+_Z*k+k^2+1), o = -k-RootOf(_Z^2+_Z*k+k^2+1)}, {k = 0, l = 1, o = -1}, {k = 0, l = -1, o = 1}, {k = 1, l = 0, o = -1}, {k = 1, l = -1, o = 0}, {k = -1, l = 0, o = 1}, {k = -1, l = 1, o = 0}, {k = RootOf(_Z^2+1), l = 0, o = -RootOf(_Z^2+1)}, {k = RootOf(_Z^2+1), l = -RootOf(_Z^2+1), o = 0}}

Now all i want is remove Complex and RootOf from this list, how can i do that?

Obtaining the splitting field...

I am trying to obtain the splitting field of New_polyq. evala@AFactor did not complete. Applying splitting sequentially produced independent extensions from the first 2 (3?) factors. evala@Indep did not complete for the union of all 4 extensions.

What libraries would handle this better?

restart; _EnvExplicit:=false;interface(labelwidth=200);
Rho_polys:=rho[3,1]^3-2, rho[3,2]^2+rho[3,2]*rho[3,1]+rho[3,1]^2, 2*rho[6,1]^3+rho[6,1]^6-2, rho[12,1]^2+rho[6,1]^2-1, 2*rho[12,2]^2-rho[6,1]^2*rho[3,2]*rho[3,1]^2-2*rho[6,1]^2-2;
New_poly:=1/16*(-rho[6,1]^4*rho[3,2]*rho[3,1]-2-rho[3,1]^2*rho[6,1]^4-2*rho[6,1]*rho[3,2]*rho[3,1]-2*rho[3,1]^2*rho[6,1]+2*lambda^2)*(rho[6,1]^4*rho[3,2]*rho[3,1]+2*rho[6,1]*rho[3,2]*rho[3,1]-2+2*lambda^2)*(-2+2*rho[3,1]^2*rho[6,1]+rho[3,1]^2*rho[6,1]^4+2*lambda^2)*(-2+rho[6,1]^2*rho[3,2]*rho[3,1]^2+2*lambda^2);
sol:=solve({Rho_polys});
alias(op(sol));
New_polyq:=subs(sol,New_poly);

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