f := 5*sin(t);
g := piecewise(t < 0, 1/(Diff(f,t$2)*Diff(x(f),t$2)+2/(Diff(f,t))*Diff(x(f),t)+10*x(f), t > 0), 1/(Diff(f,t$2))*Diff(x(f),t$2)-2*(1/Diff(f,t))*Diff(x(f),t)+10*x(f));
dsolve({f,g});

i updated equation by chain rules,

goal is to describe horizontal motion is moving from left to right and then right to the left, a 
repeat motion, vertical motion is just to describe the y axis

it is simple to understand.

is it possible to make dsolve has solution

f := 5*sin(t);
g := piecewise(t < 0, 1/(Diff(f,t$2)*Diff(x(f),t$2)+2/(Diff(f,t))*Diff(x(f),t)+10*x(f), t > 0), 1/(Diff(f,t$2))*Diff(x(f),t$2)-2*(1/Diff(f,t))*Diff(x(f),t)+10*x(f));
dsolve({f,g});

i updated equation by chain rules,

goal is to describe horizontal motion is moving from left to right and then right to the left, a 
repeat motion, vertical motion is just to describe the y axis

it is simple to understand.

is it possible to make dsolve has solution

https://skydrive.live.com/redir?resid=E0ED7271C68BE47C!344
https://skydrive.live.com/redir?resid=E0ED7271C68BE47C!342
https://skydrive.live.com/redir?resid=E0ED7271C68BE47C!343

when look above links' picture,

would like to do the following operation in maple

first input a permutation group

1 2 3 4 5

1 2 3 4 5

five rotation is to shift the second to the left

1 2 3 4 5

2 3 4 5 1

until getting the rest four

then

for reflection choose first rotation, divide second row into two group

[1], [2, 3, 4, 5] then symmetric exchange them, [1],[5, 4, 3,2] to become second row of first reflection

second reflection choose second rotation, divide second into two group

this time first group first two value, [2,3],[4,5,1] , then symmetric exchange them then [3,2],[1, 5, 4]

until get 5 rotation permutation group

then

do cycle factorization as doing in the table

first rotation 1 -> 1, 2-> 2 , so become [1] o [2] ...

second rotation 1->2->3->4->5-> so become [1,2,3,,4,5]  etc

first reflection 1->1, 2->5->2, 3->4->3 so become [1],[2,5],[3,4]  etc

then count number of [] in each cycle factorization, for first reflection has 3

if question is asking 5 colors, then C(f) become 5^3, which is (number of color)^(#(f))

for the type of permutation is in form of (a,b,c,d,e) as number of different value has 5

a means number of only 1 item  in [],

b means number of only 2 items in [],

c means number of only 3 items in [] , etc

for first rotation type is (5,0,0,0,0)

for first reflection type is (1,2,0,0,0)

https://skydrive.live.com/redir?resid=E0ED7271C68BE47C!344
https://skydrive.live.com/redir?resid=E0ED7271C68BE47C!342
https://skydrive.live.com/redir?resid=E0ED7271C68BE47C!343

when look above links' picture,

would like to do the following operation in maple

first input a permutation group

1 2 3 4 5

1 2 3 4 5

five rotation is to shift the second to the left

1 2 3 4 5

2 3 4 5 1

until getting the rest four

then

for reflection choose first rotation, divide second row into two group

[1], [2, 3, 4, 5] then symmetric exchange them, [1],[5, 4, 3,2] to become second row of first reflection

second reflection choose second rotation, divide second into two group

this time first group first two value, [2,3],[4,5,1] , then symmetric exchange them then [3,2],[1, 5, 4]

until get 5 rotation permutation group

then

do cycle factorization as doing in the table

first rotation 1 -> 1, 2-> 2 , so become [1] o [2] ...

second rotation 1->2->3->4->5-> so become [1,2,3,,4,5]  etc

first reflection 1->1, 2->5->2, 3->4->3 so become [1],[2,5],[3,4]  etc

then count number of [] in each cycle factorization, for first reflection has 3

if question is asking 5 colors, then C(f) become 5^3, which is (number of color)^(#(f))

for the type of permutation is in form of (a,b,c,d,e) as number of different value has 5

a means number of only 1 item  in [],

b means number of only 2 items in [],

c means number of only 3 items in [] , etc

for first rotation type is (5,0,0,0,0)

for first reflection type is (1,2,0,0,0)

Great! hope moving the graph can make it positive when t < 1

Great! hope moving the graph can make it positive when t < 1

@Carl Love 

goal is to find complex root which has conjugate too

have to find complex number first

after return complex number, then check whether real part the same or complex root the same

after add Vector(roo[i]) success

after add Vector(roo[i]) success

@Markiyan Hirnyk 

this is it

very useful command, thank you

@Markiyan Hirnyk 

this is it

very useful command, thank you

it works

what is the difference between VectorCalculus and Differential Geometry package?

as i do not know which them should be used when see divergence

finally i choose VectorCalculus

it works

what is the difference between VectorCalculus and Differential Geometry package?

as i do not know which them should be used when see divergence

finally i choose VectorCalculus

http://www.maplesoft.com/support/help/Maple/view.aspx?path=Groebner/Basis_details

Not understand the example above

as i see that it use seq, it is the same as [Vector([x+y, x, y]), Vector([x, x+y, y]), Vector([x, y, x+y])];

M := [seq(Vector(subsop(i+1=1, [F[i], 0, 0, 0])), i=1..3)];

restart;
with(Groebner):
with(Ore_algebra);
A := poly_algebra(x,y,z,s);
T := MonomialOrder(A, lexdeg([s], [x,y,z]), {s});
M := [Vector([x+y, x, y]), Vector([x, x+y, y]), Vector([x, y, x+y])];
G := Groebner[Basis](M, T);

got error, Error, (in Groebner:-Basis) the first argument must be a list or set of polynomials or a PolynomialIdeal

what is the correct way to pass a correct format of module

http://www.maplesoft.com/support/help/Maple/view.aspx?path=Groebner/Basis_details

Not understand the example above

as i see that it use seq, it is the same as [Vector([x+y, x, y]), Vector([x, x+y, y]), Vector([x, y, x+y])];

M := [seq(Vector(subsop(i+1=1, [F[i], 0, 0, 0])), i=1..3)];

restart;
with(Groebner):
with(Ore_algebra);
A := poly_algebra(x,y,z,s);
T := MonomialOrder(A, lexdeg([s], [x,y,z]), {s});
M := [Vector([x+y, x, y]), Vector([x, x+y, y]), Vector([x, y, x+y])];
G := Groebner[Basis](M, T);

got error, Error, (in Groebner:-Basis) the first argument must be a list or set of polynomials or a PolynomialIdeal

what is the correct way to pass a correct format of module