@vv 

so, what is the dorrect way to solve this?

@vv 

actually i have a equation which solve a very long time, it is like never end.

i observe the coefficient is so big, i do not know how to round this 

to make it faster, but i got error

how to solve these kind of big equation? 

https://drive.google.com/file/d/0Bxs_ao6uuBDUM25sR0VqWXotZnc/view?usp=sharing

read "C://Users//tester//Downloads//howtosolve.m":
Round := proc(x,n::integer:=1)
parse(sprintf(cat("%.",n,"f"),x));
end proc:

roundcoeffs1:=proc(p,x,n:=1) local t,c;
c:=map(Round, [coeffs(p,x,t)],n);
add(i, i = zip(`*`, c, [t]));
end:
roundcoeffs1(eigenvector1[1],[xx,x,y,z],3);
newvalue11 := solve(roundcoeffs1(eigenvector1[1],[xx,x,y,z],3) = newAB[1][1],xx):

@vv 

in maple 18 has error

Error, (in roundcoeffs1) invalid input: add expects 2 arguments, but received 1

@vv 

zip(`*`, [coeffs(p)], [seq(indets(p)[ii], ii=1..nops(indets(p)))])

indets is not suitable , because it is distinct and not original ordering

which way can have variable list that has original ordering

@vv 

when run in maple 18 got error, i would like to run in maple 15 and maple 18

if not use short code, what is normal way? 

Round := proc(x,n::integer:=1)
parse~(sprintf~(cat("%.",n,"f"),x));
end proc:

roundcoeffs:=proc(p,x)
local t;
add(Round~([coeffs(p,x,t)]) *~ [t]);
end:

p:=3.5*x^2+3.2*x-6.5+88.3*x*y-y^3+a*y:
roundcoeffs(p,[x,y]);

Error, (in roundcoeffs) invalid input: add expects 2 arguments, but received 1

@Carl Love 

first time to see that eliminate to use in this purpose.

@Kitonum 

i feel very excited. it is my first time to see this technique.

@Preben Alsholm 

Eigenvector has error true or false error when there is variable in matrix, when complex number, 

i have posted this error before, i still have not solved this problem yet

@Carl Love 

After thinking, i think your definition is correct

@Carl Love

what is the command simplify(fnormal~(B.B^*), zero); in maple 15?

my book use definition

G.[i].G[j] = 1 where i <> j

is this definition equivalent to the command simplify(fnormal~(B.B^*), zero); ?

tesleft@@Carl Love 

what is the syntax of simplify(fnormal~(B.B^*), zero);  in maple 15 ?

my book use

G[i].G[j]  = 1 where i <> j

is this definition same as the command simplify(fnormal~(B.B^*), zero); ?

@Kitonum 

if these are a set of harmonic oscillators c in summation(c*u)

will these harmonic oscillators change w and phi itself ?

i got questions about

1. they are invariant forever ?

2. they kept invariant over a fixed period time and change periodically ?

3. they always change for example time t and t+1 , w and phi already different ?

@Mac Dude 

it seems easy, i hope t1 and t2 are consecutively number 1 and 2, but actually it can be 3 and 4

these number can influence w and phi

how to choose these time number in better way in order to make w and phi time invariant?

@Doug Meade 

i mean from F = k*x

it can be written into four kinds of solutions

x(t) = A*sin(w*t+phi)

x(t) = alpha*cos(w*t) + beta*sin(w*t)

x(t) = exp(lambda*t)

x(t) = A*exp(i*w*t) - B*exp(-i*w*t)

but only x(t) = alpha*cos(w*t) + beta*sin(w*t)

and x(t) = A*sin(w*t+phi)

can be ploted into wave form

so, i am confused.

how to use maple to solve F=k*x into wave form solution?

as i see that dsolve solution expressed into exponential form

how to convert to cos(w*t)+i*sin(w*t), but this is only circle in complexplot

how can maple solve to 

x(t) = A*sin(w*t+phi)

and

x(t) = alpha*cos(w*t) + beta*sin(w*t) ?

@acer

the document i googled with mechanics-maple.pdf

http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CCMQFjAAahUKEwjZ95CK_fDIAhUhrKYKHQ-UDGI&url=http%3A%2F%2Futf.mff.cuni.cz%2F~scholtz%2Fdata%2Fmechanics-maple.pdf&usg=AFQjCNF8rEOSUNv1goQPjQdI4FB-UGarIg

after run some example from pdf , have one error and one of result is not the same as mentioned in document

Mechanics := module()
export SetVariables, LagrangeEqs, GeneralSol, SetMomenta, Hamiltonian, HamiltonEqs, GeneralHSol;
option package;
local subst1, subst2, substP, substPInv, varN, t, VarNames, Momenta;

SetVariables := proc (vars::list, time)
local i;
t := time;
VarNames := vars;
varN := nops(vars);
subst1 := {}; subst2 := {}; substP := {}; substPInv := {};
Momenta := NULL;
for i to varN do
subst1 := subst1 union {diff(vars[i](t), t) = v[i], vars[i](t) = q[i]};
subst2 := subst2 union {q[i] = vars[i](t), v[i] = diff(vars[i](t), t)};
substP := substP union {p[i](t) = p[i]};
substPInv := substPInv union {p[i] = p[i](t)};
Momenta := p[i], Momenta;
end do;
Momenta := [Momenta];
NULL;
end proc;

SetMomenta := proc (mom::list)
local i;
substP := {}; substPInv := {};
for i to varN do
substP := substP union {mom[i](t) = p[i]};
substPInv := substPInv union {p[i] = mom[i](t)};
end do;
Momenta := mom;
NULL;
end proc;

LagrangeEqs := proc (L)
local i, l1, term1, term2;
l1 := subs(subst1, L):
for i to varN do
term1 := [seq(diff(subs(subst2, diff(l1, v[i])), t), i = 1..varN)]:
term2 := [seq(subs(subst2, diff(l1, q[i])), i = 1..varN)]:
end do;
[ seq(simplify(term1[i]-term2[i]) = 0, i = 1..varN) ];
end proc;

RayleighEqs := proc(L, R)
local i, l1, r1, term1, term2, term3;
l1 := subs( subst1, L ):
r1 := subs( subst1, R ):
for i from 1 to varN do
term1:=[seq(diff(subs(subst2, diff(l1, v[i])), t), i=1..varN)]:
term2:=[seq(subs(subst2, diff(l1, q[i])), i=1..varN)]:
term3:=[seq(subs(subst2, diff(r1, v[i])), i=1..varN)]:
end do:
[ seq(simplify(term1[i]-term2[i]+term3[i]), i=1..varN) ];
end proc;

LagrEqsII := proc( L, Q::list )
local i, l1, term1, term2;
l1 := subs(subst1, L):
for i to varN do
term1 := [seq(diff(subs(subst2, diff(l1, v[i])), t), i = 1 .. varN)]:
term2 := [seq(subs(subst2, diff(l1, q[i])), i = 1 .. varN)]:
end do;
[seq(simplify(term1[i]-term2[i]) = Q[i], i = 1 .. varN)];
end proc;

LagrEqsIII := proc (L, R, Q::list)
local i, l1, r1, term1, term2, term3;
l1 := subs(subst1, L):
r1 := subs(subst1, R):
for i to varN do
term1 := [seq(diff(subs(subst2, diff(l1, v[i])), t), i = 1 .. varN)]:
term2 := [seq(subs(subst2, diff(l1, q[i])), i = 1 .. varN)]:
term3 := [seq(subs(subst2, diff(r1, v[i])), i = 1 .. varN)]:
end do;
[seq(simplify(term1[i]-term2[i]+term3[i]) = Q[i], i = 1 .. varN)];
end proc;

GeneralSol := proc (eqs::list)
local i, initconds, eqs2;
initconds := NULL:
eqs2 := eqs[][]:
for i to varN do
initconds:=VarNames[i](0)=q[i], (D(VarNames[i]))(0)=v[i], initconds:
end do;
dsolve({initconds, eqs2});
end proc;

Hamiltonian := proc (L)
local l1, momenta, H, subst3, i;
l1 := subs(subst1, L);
momenta := [seq(diff(l1, v[j]), j = 1 .. varN)];
subst3 := {seq(v[i] = solve(momenta[i] = p[i], v[i]), i = 1 .. varN)};
H := simplify(subs(subst3, sum(p[j]*v[j], j = 1 .. varN)-l1));
for i to varN do
H := subs({p[i] = Momenta[i](t), q[i] = VarNames[i](t)}, H)
end do;
H;
end proc;

HamiltonEqs := proc (H)
local i, eqs, h, s;
eqs := NULL;
h := subs(subst1, subs(substP, H));
s := subst2 union substPInv;
for i to varN do
eqs := eqs, diff(VarNames[i](t), t) = subs(s, diff(h, p[i])),
diff(Momenta[i](t), t) = -subs(s, diff(h, q[i]));
end do;
[eqs];
end proc;

GeneralHSol := proc( eqs ::list)
local i, initconds, eqs2;
initconds := NULL:
eqs2 := eqs[]:
for i from 1 to varN do
initconds :=VarNames[i](0)=VarNames[i][0],
Momenta[i](0)=Momenta[i][0],initconds:
end do;
dsolve( {eqs2, initconds} );
end proc;
end module;

with(LibraryTools):
LibLocation := cat("c:\\Temp");
Save(Mechanics, LibLocation);
with(FileTools):
march('list',"c:\\Temp\\Mechanics.lib");
save(Mechanics, "c:\\Temp\\Mechanics.m");
read "c:\\Temp\\Mechanics.m";

restart;
read "c:\\Temp\\Mechanics.m";
with(Mechanics);
SetVariables([x], t);
SetMomenta([p]);
H := p(t)^2/(2*m)+(1/2)*m*omega^2*x(t)^2;
eqs := HamiltonEqs(H);
sol := GeneralHSol(eqs);

restart;
read "c:\\Temp\\Mechanics.m";
with(Mechanics):
SetVariables([x], t);
L := (1/2)*m*diff(x(t), t)^2 - (1/2)*m*omega^2 * x(t)^2;
eqs := LagrangeEqs(L);
sol := GeneralSol( eqs );
X := unapply( rhs(sol), t );

1.

Error, (in dsolve) not a system with respect to the unknowns {x(0)}
Error, invalid input: rhs received sol, which is not valid for its 1st argument, expr

restart;
read "c:\\Temp\\Mechanics.m";
with(Mechanics):
SetVariables([theta], t):
SetMomenta([p]);
L := (1/2)*diff( theta(t), t )^2 + cos(theta);
H := Hamiltonian(L);
eqs := HamiltonEqs(H);

2. this example is not diff(p(t), t) = -sin(theta);