dsol := dsolve([eq2=diff(s(t),t), eq3=diff(s(t),t), eq4=diff(s(t),t)], [a(t),b(t),c(t)]);
eval(subs(t(t)=t,subs(_C1(t) = _C1, subs(_C2(t) = _C2, subs(_C3(t) = _C3, sol1)))));

after subs t(t) = t , it still  have t(t)

_C1, _C2, _C3 are constant, how to set them constant, to make diff(_C2) = 0 etc

eval(simplify(subs(a=_C1,subs(b=1/(diff(c(t), t)),subs(c=_C2+_C3*exp(-t),eq2)))));

(diff(_C2(t), t)+(diff(_C3(t), t))*(exp(-t))(t)+_C3(t)*(diff((exp(-t))(t), t)))*(-(diff(_C1(t), t))*(diff(diff((c(t))(t), t), t))/(diff((c(t))(t), t))^2+(diff(s(t), t))/(diff((c(t))(t), t)))
a

1.

with(RegularChains):
with(ConstructibleSetTools):
source1 := PolynomialRing([a,b,c]);
target1 := PolynomialRing([e1,e2,e3,e4]);
source1list := [eq2a, eq3a,eq4a];
target1list := [eq2b, eq3b, eq4b,eq5b];
cs := PolynomialMapPreimage(target1list, source1list, source1, target1);

Error, (in RegularChains:-ConstructibleSetTools:-PolynomialMapPreimage) number of map functions is different from number of variables in target space

in maple 15 do not have error, however now it has error for the code below

with(RegularChains): with(RegularChains): with(ConstructibleSetTools): 

source1 := PolynomialRing([e1, e2, e3]);
target1 := PolynomialRing([a, b, c]);
source1list := [-1*e1+2*e2+*e3, -1*e1+2*e2+*e3, -1*e1+2*e2+*e3];
target1list := [.....]; cs :=
PolynomialMapPreimage(target1list, source1list, source1, target1);

Error, invalid product/quotient

http://www.maplesoft.com/support/help/Maple/view.aspx?path=GroupTheory/SylowSubgroup

P2:=SylowSubgroup(2,G);

P2;

in above example, it can show a permutation group

G:=AlternatingGroup(5);

P2:=SylowSubgroup(3,G);

a permutation group on .... letters

but in some example such as above, it only show a statement a permutation group on .... letters

how to show what it is?

in harmonic ocillator version, why it has error after it dsolve?

with(Physics[Vectors]):
with(SumTools):
Setup(mathematicalnotation = true):

Qs is Qss*cos(m*t+phi);

H := 1/(8*Pi*c^2)*Summation(Commutator(diff(Qs*cos(w*t+phi),t)*diff(conjugate(Qs*cos(w*t+phi)),t)+w^2*Qs*cos(w*t+phi)*conjugate(Qs*cos(w*t+phi))),ks=1..3)-1/c*(Summation(conjugate(Qs*cos(w*t+phi)),ks=1..3));

or

H := 1/(8*Pi*c^2)*Summation(Commutator(diff(Qs,t)*diff(conjugate(Qs),t)+w^2*Qs*conjugate(Qs)),ks=1..3);

#Qs = p, Ps := Pss*sin(m*t+phi) Ps = qs

i use

H := 1/(8*Pi*c^2)*Summation(Commutator(diff(Qs*cos(w*t+phi),t)*diff(conjugate(Qs*cos(w*t+phi)),t)+w^2*Qs*cos(w*t+phi)*conjugate(Qs*cos(w*t+phi))),ks=1..3)-1/c*(Summation(conjugate(Qs*cos(w*t+phi)),ks=1..3));

 HJ := subs(Qs= diff(f(q,P,t), q), H);

H:=subs( f(q,P,t) = f1(q) + f2(t), HJ);
sol:=dsolve({rhs(H)=E,lhs(H)=E});
S:=rhs(sol[1][1]+sol[1][2]);
p:=diff(S,q);
Q:=diff(S,E);