Maple 15 Questions and Posts

These are Posts and Questions associated with the product, Maple 15

I have two polynomials f(x,y,z) and g(x,y,z) and ask MAPLE to find conditions on the coefficients of f and g such that the Jacobian determinant in x and y is purely a polynomial in z. MAPLE finds 4 solutions, one of which is g=0, but does not find the solution f=0. I attach the relevant MAPLE worksheet.

The mechanism of transport of the material of the sewing machine M 1022 class: mathematical animation. 

Hi, currently im using maple 15

the coding did work but it is not the same with the answer
here, i attach the coding with the answer

derivation := proc (A, n)
local i, j, k, t, s1, s2, m, D, sols, eqns, Andre;
eqns := {};
D := matrix(n, n);
Andre := matrix(n, n);
for i to n-1 do
for j from i+1 to n do
for m to n do
s1 := sum(A[i, j, k]*D[m, k], k = 1 .. n);
s2 := sum(A[k, j, m]*D[k, i]+A[i, k, m]*D[k, j], k = 1 .. n);
eqns := `union`(eqns, {s1 = s2})
end do end do end do;
sols := [solve(eqns)];
t := nops(sols);
for i to t do
for j to n do
for k to n do
Andre[k, j] := subs(sols[i], D[k, j])
end do end do;
end do end proc

the maple result showing:

> AS1 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 2) = 1]);

> derivation(AS1, 2);
[D11 0]
[D21 D22]

> AS2 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1, (1, 2, 2) = 1]);
> derivation(AS2, 2);
[0 D12]
[D21 D22]

the maple should showing

> derivation(AS1, 2);
[D11 0]
[D21 2D11]

> AS2 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1, (1, 2, 2) = 1]);
> derivation(AS2, 2);
[0 0]
[D21 D22]

please help., thank you

how to field plot this system?

eq2 := ...;
eq3 := ...;
eq4 := ...;
sys := DiffEquation([eq2 = t, eq3 = t], inputvariable = [b(t)], outputvariable = [a(t), c(t)]);
ts := .1;
in_t := t;
sol := Simulate(sys, [in_t]);


  One way to get rolling without slipping animation in 3d. The trajectory and circle are divided into segments of equal length. In the next segment of the trajectory we construct circle, taking into account the fact that it turned on one segment. Rolling sphere or cylinder can be simulated, if we take plottools templates of the same radius, and replace them on the site of our circle.


not the same ordering every time of monomials after determinant and map sign positive and op in maple 15

sometimes i need to use Reverse or Rotate List to adjust.

why ordering is different in list of monomials?

is it caused by virus?


Spiral (equidistant) around the curve.  In this case, a spiral around the spiral.
So without any sense. 
If we re-save the animation with the program Easy GIF Animator, its size is reduced by about 10 times, and sometimes much more.

Imitation coloring both sides of the polygon in 3d.  We  build a new polygon in parallel with our polygon on a very short distance t. (We need any three points on the polygon plane, do not lie on a straight line.) This place in the program is highlighted in blue.

Paint the polygons are in different colors.

In a post of April 15, 2013 by Kitonum, the procedure named Picture accepts a list of polygon segments, creates a plot of these as a 2D polygon's boundaries and fills the polygon with a color.

The code below attempts to modify Picture to produce a 3D filled polygon in a plane parallel to the xy plane.

When invoked by the code below the procedure, the filling color conforms to the straight line boundaries but overflows the curved, parabolic boundary. How can this be corrected?

Picture:=proc(L, C, N::posint:=100, Boundary::list:=[linestyle=1])

 local i, var, var1, var2,e, e1, e2,e3, P, h ;

 global Q,Border;

 for i to nops(L) do    

#` set P`[i] = list of points for each segment.    

#` for a segment defined as a list of points, P[i] = the segment's definition`

#` for a curve definition, approximate it with a list of [x,y] points of its function evaluated at N even intervals in its

# range`  

  if type(L[i],listlist(algebraic))  then P[i]:=op(L[i]);   else  

  #` for curve def'n, set var = def'n and h= `(variable range)/(2)

  var:=lhs(L[i,2]);  var1:=lhs(rhs(L[i,2]));  var2:= rhs(rhs(L[i,2])); h:=(var2-var1)/(N);

  #` for function def'n, set e=function`

 if type(L[i,1], algebraic) then  e:=L[i,1];

  #` for polar function r=f(t) create N values of the [cos*r,sin*r] i.e. the equivalent [x,y] values for r valued at N even

  # divisions of its range`  

 if nops(L[i])=3 then P[i]:=seq(subs(var=var1+h*i,[e*cos(var), e*sin(var)]), i=0..N);  else

    #` for non-polar function y=f(x) create N values of [x,y] for x values at N even divisions of its range`  

 P[i]:=seq([var1+h*i, subs(var=var1+h*i,e)], i=0..N)  fi;  else

 #` for parametric function [f`(t),g(t)] create N values of [f(t),g(t)] for t values at N even divisions of its range.

     e1:=L[i,1,1];  e2:=L[i,1,2];

#` P`[i]:=seq(subs(var=var1+i*h,[e1, e2]), i=0..N):

 P[i]:=seq([subs(var=var1+i*h,e1), subs(var=var1+i*h,e2),0], i=0..N) fi; fi; od;  #`  MODIFIED FOR 3 D `[f(t), g(t), 0] 

  Q:=[seq(P[i], i=1..nops(L))];

 Border:=plottools[curve]([op(Q), Q[1]],  op(Boundary));

     #` the shaded figure is a polygon whose vertices are Q, whose interior color is C`  

 #` return a list of the polygon and its border`

   [plottools[polygon](Q, C),  Border];

 end proc: 

L := [[[0, 0, 0], [0, 1, 0]], [[x, x^2+1, 0], x = 0 .. 2], [[2, 5, 0], [2, 2, 0]], [[x, x, 0], x = 2 .. 0]]:

plots[display](Picture(L, color = yellow), axes = normal, scaling = constrained)

I seperate the variables in Real and Imigneray parts,  as follows:

------------------------- Defining the nature of the variables used ----------------------

t0:=0.0:tN:=30.0: M1:=5000;:th:=evalf((tN-t0)/M1):
ini1:=u(0)=Re(y(0)), v(0)=Im(z(0)),w(0)=x(0);
u(0) = 1, v(0) = 0, w(0) = -1
dsys1 :=diff(w(t),t)=-(N1+M*cos(2*omega*t))*w(t)-1+2*u(t)*cos(2*omega*t)+2*v(t)*sin(2*omega*t), diff(u(t),t)=-N1*u(t)+Delta*v(t)-2*M+(2*M*u(t)-N1-w(t))*cos(2*omega*t)-2*M*v(t)*sin(2*omega*t), diff(v(t),t)=-N1*v(t)-Delta*u(t)-2*M+(2*M*u(t)-N1-w(t))*sin(2*omega*t)+2*M*v(t)*cos(2*omega*t):
dsol1 :=dsolve({dsys1,ini1},var,numeric, output=listprocedure, abserr=1e-9, relerr=1e-8,range=0..1,maxfun=5000):
Warning, cannot evaluate the solution further right of .46544244e-3, maxfun limit exceeded (see ?dsolve,maxfun for details)
t1:=array(0..M1,[]): u1:=array(0..M1,[]): v1:=array(0..M1,[]): w1:=array(0..M1,[]): pt1:=array(0..M1,[]):pt2:=array(0..M1,[]):pt3:=array(0..M1,[]): 
for i from 0 to M1 do t1[i]:=evalf(th*i):u1[i]:=evalf(dsolu(t1[i]));v1[i]:=evalf(dsolv(t1[i])):w1[i]:=evalf(dsolw(t1[i])):pt1[i]:=[t1[i],u1[i]]:pt2[i]:=[t1[i],v1[i]]:pt3[i]:=[t1[i],w1[i]]:od:
Error, (in dsolu) cannot evaluate the solution further right of 0.46544244e-3, maxfun limit exceeded (see ?dsolve,maxfun for details)

plot(mytab3,t=0..5,tickmarks=[6, 6],axes=boxed);

but I got an error

I have downloaded the zip file for CalcP7, unzipped it, and can access its commands in a worksheet after issuing the command with(CalcP7), but "No Matches Found" displays when entering the command ?CalcP7. The download included a file named "aplication" (one "p") of type HDB, but Maple15 can't seem to access its contents.

Are CalcP7's help pages displayable? If so, what is necessary to access them?

I have had no trouble downloading the user package DirectSearch and accessing both its commands and its help pages.

I tried to load my document containing some notes, but then I got the message "There were problems during the loading process, Your worksheet may become incomplete", and as the message said my worksheet were incomplete. Is there a way to restore the document? I have tried following this and added the line it suggested:

But it didn't work.

I have attached the file.

plots[implicitplot3d](max(-x+y+z, x-y+z, x+y-z) = 1.0, x = 0 .. 1, y = 0 .. 1, z = 0 .. 1);

The help page for max does not explain or show an example of max(sequence of expressions)= a constant.

Please let me know if this link correctly accesses my worksheet. If not, I will copy its contents into this question.

Which ODE in the worksheet, if any, provides the correct answer?


f := proc (x) local t; if not type(evalf(x), 'numeric') then ('procname')(x) else evalf(Int(exp(-(1/10)*t^2), t = 0 .. x)) end if end proc

solA := dsolve({diff(y(x), x) = y(x)+f(x), y(0) = 0}, numeric, known = f)


[x = 1., y(x) = HFloat(0.7081492947996167)]


f2 := evalf(Int(exp(-(1/10)*t^2), t = 0 .. 1)); f(1)





solB := dsolve({diff(y(x), x) = y(x)+f2, y(0) = 0}, numeric, output = listprocedure)


[x(1) = 1., (y(x))(1) = HFloat(1.6626837619970016)]


YinSolB := subs(solB, y(x))

YinSolBeval := solve(YinSolB(a) = .7081, a); solB(YinSolBeval)



[x(.5491485953) = .5491485953, (y(x))(.5491485953) = HFloat(0.7081000000284681)]




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