Thanks a lot. Now how to locate vertex and focus of the parabola in the base (O,i,j) ?

Very good for the order of the coefficients but there is still a confusion between parabola and ellipse. How to avoid it ? Thank you.

Thank you very much. Without Geometry.

In fact I have the point K of coordinates are X, Y and I look for the place when m varies; Can you help me ? Thank you.

points:=seq(seq([xt[i][j], yt[i][j]], j=0..zt-1), i=1..2*n-1):
  p_cross:= pointplot([points], connect=true,scaling = constrained, color = black,linestyle=solid, filled=[yellow]):
  polygonplot([points], color = yellow, scaling = constrained):
  NULL:
  display([p_cross]); This drawing is obviously not suitable. How to amend it? Thabk you very much.

How to move the oscillating bar (B,C,P in the bar) or move point B

restart;

with(plots):

with(plottools):

R := 1: # length of OA

L := 5*R: # horizontal distance between O and C

H := 3*R: # vertical distance between O and C

a := 1.3*H: # length of AB

b := L - R:   # length of BC

A := R*<cos(t), sin(t)>:

B := A + a*<cos(s(t)), sin(s(t))>:  # s(t) is the angle of AB relative to the horizontal

C := [L, a]:

                         C := [5, 3.9]

# derive a differential equation for s(t)

B -~ C:

%^+ . % = b^2:

diff(%, t):

isolate(%, diff(s(t),t)):

de := simplify(%):

ic := s(0)=Pi/2:

dsol := dsolve({de,ic}, numeric, output=operator):

Head := translate(rotate(scale(polygonplot([[-60, 24], [63, -17], [60, -55.5], seq([84*cos(k1*Pi/100), 84*sin(k1*Pi/100)], k1 = -24 .. 7), [82, 18], [78, 20], [64, -3], [-46.5, 35]], scaling = constrained, color = "Gold"), 0.049, 0.03), 0.211, [0, 0]), 0, -0.3);

#Head := scale(polygonplot([ [-16,-1], [10, -1], [13,-5], [12,1], [-12,1]], scaling=constrained, color="Gold"), 0.4,#0.3):

Crank := scale(polygonplot([[-8, 6], [-7, 20], [-6, 38], [6, 38], [7, 20], [8, 6], [-10, 6], [-16, 6], [-25, 0], [-17, -8], [-8, -8], [-8, -17], [8, -17], [8, -8], [17, -8], [25, 0], [16, 6]], scaling = constrained, color = "Aquamarine"), 0.06, 0.04);

frame := proc(t)  # 0 <= t <= 2*Pi

local A, B, P, u;

uses plottools;

A := R*[cos(t), sin(t)];

A + [a*cos(s(t)), a*sin(s(t))];

B := eval(%, dsol);

P := 2*C - B;

C -~ B;

u := arctan(%[2],%[1]);  # angle of rotation of BC

        display(

circle([0,0], R),

plot([ [0,0], A, B, C, P ], style=pointline, symbol=solidcircle, symbolsize=20),

textplot([ [0,0,"O"], [A[],"A"], [B[],"B"], [C[],"C"], [P[],"P"] ], align={above}, font=[Times, bold, 18]),

translate(rotate(Head, u), C[1], C[2]),

                rotate(Crank,t-Pi/2),

                plot([A,B],color=red,thickness=8),

NULL, scaling=constrained);

end proc:

nframes := 60:

frames := seq(frame(2*Pi*i/nframes), i=0..nframes-1):

display(frames, insequence,size=[600,600]):

Thank you very much.

Thanks a lot for this animation. Now how to set "Head" on the skeleton ? Thank you. Head:=proc(k) local r,poly,k1,tC,tD,tE,DikC,DikD,DikE: global C,D,E: r:=84: C:=[-55,17]:D:=[0,0]:E:=[84,0]: poly:=[[-60,24],[63,-17],[60,-55.5],seq([r*cos((k*Pi)/(100)),r*sin((k*Pi)/(100))],k1=-24..7),[82,18],[78,20],[64,-3],[-46.5,35]] : tC:= textplot([C[], "C"], align={above, right}, font=[Times, bold, 18]): tD:=textplot([D[], "D"], align={above, left}, font=[Times, bold, 18]): tE:=textplot([E[], "E"], align={above, left}, font=[Times, bold, 18]): DikC:=disk(C,1,color=black): DikD:=disk(D,1,color=black): DikE:=disk(E,1,color=black): if 0<= k and k<=0.579 then display( polygon(poly,color=yellow), tC,tD,tE,DikC,DikD,DikE,scaling=constrained):rotate(`%`,k,D) elif -0.68<= k and k<=0 then display( polygon(poly,color=yellow), tC,tD,tE,DikC,DikD,DikE,scaling=constrained):rotate(`%`,k,D) fi

Bravo your rods are not elastic...Thank you.

The BC and BD rods do not retain the same length, so there is a difficult error to detect in the program.

How to shaw that any element of R² is a linear combination of (1,1) and (1,2), this decomposition is unique. The family is free and generates R². Thank you.

How to know if 2 pairs of vectors generate the same vector space ?
The 2 pairs of vectors are <1,0-1>  and <0,1,0> for une part, <2,1,-2> and <-1,2,,1> for the other. Thank you.

Sorry, I don't understand what are M, V, and sys.
How to get a base line of the linear application image ? Thank you.

Iam trying my own procedure taylor on sin(t) for t=0

f := t -> diff(sin(t), t);
f := proc (t) options operator, arrow; diff(sin(t), t) end proc

L := [seq(diff(f(t), [t $ i]), i = 1 .. 9)];
L := [-sin(t), -cos(t), sin(t), cos(t), -sin(t), -cos(t), sin(t), 

  cos(t), -sin(t)]

t := 0;
L;
                             t := 0

                 [0, -1, 0, 1, 0, -1, 0, 1, 0]

for k to 8 do
    -L[k + 1]*'t'^k/k!;
end do;
                               t

                               0

                               1  3
                             - - t 
                               6   

                               0

                              1   5
                             --- t 
                             120   

                               0

                              1    7
                           - ---- t 
                             5040   

                               0
How to get the sum ? Thank you very much.

On the model : t := 't';
taylor(sin(t), t = 0, 9);
                  1  3    1   5    1    7    / 9\
              t - - t  + --- t  - ---- t  + O\t /
                  6      120      5040           

with(LibraryTools);
LibLocation := cat(kernelopts(mapledir), "/lib/myLib.mla");
   LibLocation := "C:\Program Files\Maple 2018/lib/myLib.mla"
Create(LibLocation);
Error, (in march) archive data file could not be created
a := 10;
Save('a', LibLocation);
Error, (in LibraryTools:-Save) could not open `C:\Program Files\Maple 2018/lib/myLib.mla\a.m` for
Why this Library can't be created ? Thank ypo.

I get these messages. How to correct them ? Thank you.
Error, (in march) archive data file could not be created
Error, (in LibraryTools:-Save) could not open `C:/tmp/test.mla\MyPackage.m` for writing
Error, (in march) there is no existing archive in "C:/tmp/test.mla"
Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received MyPackage