Advanced Search

Maple 2021 Questions and Posts

These are Posts and Questions associated with the product, Maple 2021
View unanswered posts
Maple 2021 Questions and Posts Feed

Peoblem with animation...

Asked by: JAMET 420
animation plotting geometry
November 23 2024
0  6

On considère un cercle fixe O et un point fixe A extérieur. Une sécante variable BC à ce cercle passe par un point fixe J.
Démontrer que le cercle ABC passe par un second point fixe P.
restart;
Proc := proc(m)
local xA, yA, xB, yB, xC, yC, xJ, yJ, tx, dr, Oo, c1, r, eqBJ, eq1, sol;
_EnvHorizontalName := 'x'; _EnvVerticalName := 'y';
xJ := 5; yJ := 1; geometry:-point(A, 2, 4); geometry:-point(J, xJ, yJ); geometry:-point(Oo, 0, 0);
r := 3; c1 := plottools[geometry:-circle]([0, 0], r, color = blue);
eqBJ := y = m*(x - xJ) + yJ; geometry:-line(BJ, eqBJ, [x, y]);
eq1 := x^2 + y^2 = r^2; sol := solve({eqBJ, eq1}, {x, y}, explicit);
xB := subs(sol[1], x); yB := subs(sol[1], y);
geometry:-point(B, xB, yB); xC := subs(sol[2], x); yC := subs(sol[2], y);
geometry:-point(C, xC, yC); geometry:-circle(c2, [A, B, C]); geometry:-line(AB, [A, B]); geometry:-line(AC, [A, C]);
eqBJ := y = m*(x - xJ) + yJ; geometry:-line(BJ, eqBJ, [x, y]);
eq1 := x^2 + y^2 = r^2; sol := solve({eqBJ, eq1}, {x, y},explicit);
xB := subs(sol[1], x); yB := subs(sol[1], y); geometry:-point(B, xB, yB);
xC := subs(sol[2], x); yC := subs(sol[2], y); geometry:-point(C, xC, yC);
geometry:-circle(c2, [A, B, C]); geometry:-line(AB, [A, B]); geometry:-line(AC, [A, C]);
tx := plots:-textplot([[geometry:-coordinates(A)[], "A"], [geometry:-coordinates(B)[], "B"], [geometry:-coordinates(C)[], "C"], [geometry:-coordinates(J)[], "J"]], font = [times, bold, 16], align = [above, right]);
dr := geometry:-draw([AB(color = black), c2(color = magenta), A(color = blue, symbol = solidcircle, symbolsize = 16),
B(color = red, symbol = solidcircle, symbolsize = 16), C(color = red, symbol = solidcircle, symbolsize = 16),
J(color = red, symbol = solidcircle, symbolsize = 16)]); plots:-display([dr, c1, tx], axes = normal, view = [-5 .. 6, -4 .. 6], scaling = constrained);
end proc;
plots:-animate(Proc, [m], m = -0.9 .. 0.2*Pi, frames = 50);
Error, (in plots/animate) two lists or Vectors of numerical values expected
NULL;
I am trying to find out point P; Thank you for your help.

Source Codes for "Gaps Between Integers Having...

by: fosuwxb 25 Maple 2021
integer divisors
November 09 2024
0  2

Here are the source codes for the paper  "Gaps Between Integers Having a Common Divisor with an Odd Semi-prime"


 

gg := proc (x, y) return abs(x-y)-1 end proc

proc (x, y) return abs(x-y)-1 end proc

 (1)

CopyArrayElem := proc (x, n) local y, i; y := Array(1 .. n); for i to n do y(i) := x(i) end do; return y end proc

proc (x, n) local y, i; y := Array(1 .. n); for i to n do y(i) := x(i) end do; return y end proc

 (2)

PrintArray := proc (x, n) local i; for i to n do printf("%d, ", x(i)); if i = (1/2)*n then printf("|,") end if end do; printf("\n") end proc

proc (x, n) local i; for i to n do printf("%d, ", x(i)); if i = (1/2)*n then printf("|,") end if end do; printf(" ") end proc

 (3)

GapArray := proc (x, n) local i, y; y := Array(1 .. n-1); for i to n-1 do y(i) := gg(x(i), x(i+1)) end do; return y end proc

proc (x, n) local i, y; y := Array(1 .. n-1); for i to n-1 do y(i) := gg(x(i), x(i+1)) end do; return y end proc

 (4)

ShiftArrayElem := proc (x, n, d) local i, y; y := Array(1 .. n); for i to n do y(i) := x(i)+d end do; return y end proc

proc (x, n, d) local i, y; y := Array(1 .. n); for i to n do y(i) := x(i)+d end do; return y end proc

 (5)

NULL

"chost:=proc(p,q) local i,j,m; local Hpq,hh; Hpq:=Array(1..p+q-2); hh:=Array(1..p+q-2); for i from 1 to q-1 do Hpq(i):=i*p; od; for j from 1 to p-1 do; Hpq(i++):=j*q; od; hh:=sort(Hpq); return hh; end proc "

proc (p, q) local i, j, m, Hpq, hh; Hpq := Array(1 .. p+q-2); hh := Array(1 .. p+q-2); for i to q-1 do Hpq(i) := i*p end do; for j to p-1 do Hpq(`++`(i)) := j*q end do; hh := sort(Hpq); return hh end proc

 (6)

nGroup := proc (p, m) local j, n, ar; ar := Array(1 .. m); for j from 0 to m-1 do n := ceil((j+1)*p/m)-floor(j*p/m)-1; ar(j+1) := n end do; return ar end proc

proc (p, m) local j, n, ar; ar := Array(1 .. m); for j from 0 to m-1 do n := ceil((j+1)*p/m)-floor(j*p/m)-1; ar(j+1) := n end do; return ar end proc

 (7)

Position := proc (ary, k) local i, pos; pos := 0; for i to k-1 do pos := pos+ary(i) end do; pos := pos+1; return pos end proc

proc (ary, k) local i, pos; pos := 0; for i to k-1 do pos := pos+ary(i) end do; pos := pos+1; return pos end proc

 (8)

groups := proc (p, q, lm, m) local k, j, x, r, ll, rr, ni, bl, br, i; i := 1; printf("______\n"); for k from 0 to m-2 do ll := floor(k*p/m); rr := floor((k+1)*p/m); ni := rr-ll; for j to ni do r := (j+ll)*m-k*p; printf("(%d: %d),", i, r); if j = ni then printf(" # %d p-hosts after q-host %d\n", lm+1, i*q) end if; i := i+1 end do; printf("\n") end do; ll := floor((m-1)*p/m); rr := p-1; ni := rr-ll; for j to ni do r := (j+ll)*m-k*p; printf("(%d: %d),", i, r); i := i+1 end do; printf("\n______\n") end proc

proc (p, q, lm, m) local k, j, x, r, ll, rr, ni, bl, br, i; i := 1; printf("______ "); for k from 0 to m-2 do ll := floor(k*p/m); rr := floor((k+1)*p/m); ni := rr-ll; for j to ni do r := (j+ll)*m-k*p; printf("(%d: %d),", i, r); if j = ni then printf(" # %d p-hosts after q-host %d ", lm+1, i*q) end if; i := i+1 end do; printf(" ") end do; ll := floor((m-1)*p/m); rr := p-1; ni := rr-ll; for j to ni do r := (j+ll)*m-k*p; printf("(%d: %d),", i, r); i := i+1 end do; printf(" ______ ") end proc

 (9)

idx := proc (p, m) local i, r, ri; for i to p-1 do r := i*m-floor(i*m/p)*p; if r = 1 or r = p-1 then ri := i end if; printf("%d, ", r) end do; printf("\n"); return ri end proc

proc (p, m) local i, r, ri; for i to p-1 do r := i*m-floor(i*m/p)*p; if r = 1 or r = p-1 then ri := i end if; printf("%d, ", r) end do; printf(" "); return ri end proc

 (10)

DoTest := proc (p, q) local k, i, j, x, y, r, ni, lambda, n, g, xx, ll, rr, w, pos, nj, hh, grp; n := p+q-2; g := Array(1 .. n-1); hh := chost(p, q); printf("Hosts of p and q are:\n"); PrintArray(hh, n); lambda := floor(q/p); r := q-lambda*p; printf("Lambda=%d\nr=%d\n", lambda, r); printf("The %d elements in S(r,p) are:\n", p-1); for i to p-1 do printf("%d,", i*r) end do; printf("\n"); printf("The %d elements in rZ(r,p) are:\n", p-1); for j to p-1 do x := j*r-floor(j*r/p)*p; printf("%d,", x) end do; printf("\n"); printf("The %d subsets are as follows:\n", r); groups(p, q, lambda, r); printf("The maximum gap is: %d \n", p-1); g := q-p-1; printf("Total number of maximum gaps is:%d\n", g); g := GapArray(hh, n); xx := CopyArrayElem(hh, n-1); dataplot(xx, g) end proc

proc (p, q) local k, i, j, x, y, r, ni, lambda, n, g, xx, ll, rr, w, pos, nj, hh, grp; n := p+q-2; g := Array(1 .. n-1); hh := chost(p, q); printf("Hosts of p and q are: "); PrintArray(hh, n); lambda := floor(q/p); r := q-lambda*p; printf("Lambda=%d r=%d ", lambda, r); printf("The %d elements in S(r,p) are: ", p-1); for i to p-1 do printf("%d,", i*r) end do; printf(" "); printf("The %d elements in rZ(r,p) are: ", p-1); for j to p-1 do x := j*r-floor(j*r/p)*p; printf("%d,", x) end do; printf(" "); printf("The %d subsets are as follows: ", r); groups(p, q, lambda, r); printf("The maximum gap is: %d ", p-1); g := q-p-1; printf("Total number of maximum gaps is:%d ", g); g := GapArray(hh, n); xx := CopyArrayElem(hh, n-1); dataplot(xx, g) end proc

 (11)

``

DoTest(3, 5)

  

DoTest(5, 7)

  

 

 

 

NULL

DoTest(7, 9)

  

DoTest(11, 13)

  

DoTest(7, 11)

  

NULL

DoTest(5, 23)

  

DoTest(11, 47)

  

DoTest(13, 71)

  

DoTest(17, 29)

  

DoTest(23, 31)

  

DoTest(13, 23)

  

DoTest(11, 17)

  

 

DoTest(11, 29)

  

DoTest(13, 27)

  

DoTest(13, 79)

  

DoTest(11, 45)

  

DoTest(41, 71)

  

DoTest(47, 97)

  

DoTest(53, 103)

  

DoTest(101, 199)

  

DoTest(101, 205)

  

DoTest(23, 45)

  

DoTest(13, 25)

  

DoTest(13, 77)

  

DoTest(23, 93)

  

DoTest(23, 91)

  

DoTest(13, 25)

  

DoTest(13, 77)

  

DoTest(47, 91)

  

DoTest(53, 109)

  

NULL


 

Download Hosts.mw

How change trigonometry to shorter trigonometric ?...

Asked by: salim-barzani 160
simplification trig
October 20 2024
0  10

How we can change identity like 1/sin(x)=csc(x) or 1/cos(x)=sec(x) sometime our function is beger than this and radical come in how i can do thus simplification?

> 

restart
> 

M := sin(x)/cos(x)

sin(x)/cos(x)

 (1)
> 

convert(M, trig)

sin(x)/cos(x)

 (2)
> 

tan(x)

tan(x)

 (3)
> 

simplify(M)

sin(x)/cos(x)

 (4)
> 

K := 1/sinh(x)

1/sinh(x)

 (5)
> 

simplify(convert(K, trig))

1/sinh(x)

 (6)
> 

csch(x)

csch(x)

 (7)
> 

Q := sqrt(beta[0]/(B[1]*cosh(xi*sqrt(-lambda))))

(beta[0]/(B[1]*cosh(xi*(-lambda)^(1/2))))^(1/2)

 (8)

(beta[0]/(B[1]*cosh(xi*(-lambda)^(1/2))))^(1/2)

 (9)
> 

simplify((beta[0]/(B[1]*cosh(xi*(-lambda)^(1/2))))^(1/2), 'trig')

(beta[0]/(B[1]*cosh(xi*(-lambda)^(1/2))))^(1/2)

 (10)
 

NULL

Download identity_change.mw

Fregier point of a point on an ellipsa...

Asked by: JAMET 420
animation plotting ellipse
October 20 2024
1  6

OneFrame := proc(k)
local Courbe, T, a, b, c, t, P, Q, NormM, F, Ell, sol, N1, N2, dr, tx;
a := 11; b := 7; c := sqrt(a^2 - b^2); t := 1/3*Pi;
Ell := x^2/a^2 + y^2/b^2 = 1;
geometry:-point(T, (a^2 - b^2)*cos(t)^3/a, -(a^2 - b^2)*sin(t)^3/b);
Courbe := plots:-implicitplot(Ell, x = -a - 10 .. a + 10, y = -b - 10 .. b + 10, scaling = constrained, color = blue);
NormM := plots:-implicitplot(y - b*sin(t) = a*sin(t)*(x - a*cos(t))/(b*cos(t)), x = -a - 5 .. a + 10, y = -b - 10 .. b + 10, color = orange); geometry:-line(Per, y - b*sin(t) = a*sin(t)*(x - a*cos(t))/(b*cos(t)), [x, y]);
geometry:-point(P, subs(y = 0
, geometry:-Equation(Per), 0));
geometry:-point(Q, 0, subs(x = 0, geometry:-Equation(Per)));
geometry:-point(M, a*cos(t), b*sin(t));
geometry:-point(N1, a*cos(k), b*sin(k));
geometry:-point(F, 2.329411765, -2.567510609);
geometry:-line(L, N1, F);
sol := solve({geometry:-Equation(L), Ell}, {x, y},explicit);
geometry:-point(N2, subs(sol[2], x), subs(sol[2], y));
geometry:-segment(sg, N1, N2);
tx := plots:-textplot([[geometry:-coordinates(M)[], "M"],
[geometry:-coordinates(N1)[], "N1"], [geometry:-coordinates(N2)[], "N2"],
[geometry:-coordinates(P)[], "P"],
[geometry:-coordinates(Q)[], "Q"],
[geometry:-coordinates(F)[], "F point de Frégier"],
[geometry:-coordinates(T)[], "T"]], font = [times, bold, 16], align = [above, left]);
dr := geometry:-draw([sg(color = magenta, linestyle = dash),
Per(color = black), P(color = red, symbol = solidcircle, symbolsize = 12),
Q(color = red, symbol = solidcircle, symbolsize = 12),
M(color = black, symbol = solidcircle, symbolsize = 12),
F(color = red, symbol = solidcircle, symbolsize = 12),
N1(color = black, symbol = solidcircle, symbolsize = 8),
N2(color = black, symbol = solidcircle, symbolsize = 8),
T(color = black, symbol = solidcircle, symbolsize = 8)]);
plots:-display(Courbe, tx, dr, scaling = constrained, axes = none); end proc;

plots:-animate(OneFrame, [k], k = Pi/3 .. Pi, frames = 50);
Error, (in plots/animate) wrong type of arguments
Why this animation does't work ? Thank you very much.
 

Can any one tell me why my equation not expanded t...

Asked by: salim-barzani 160
multiplication syntax 2dmath
October 18 2024
0  3

i use all code really sometime this is happen i can find each term seperatly without any factoring and collecting term i want all of them term by term i did all simplify code but i did't get result

> 

restart
> 

with(PDEtools)
> 

NULL
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

F := l((V(xi)^(1/(2*m)))^(4*m-2)*(V(xi)^(1/(2*m))*((1/4)*V(xi)^(1/(2*m))*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^(1/(2*m))*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^(1/(2*m))*(diff(V(xi), xi))^2/(m*V(xi)^2))+(1/4)*(4*m+l-1)*(V(xi)^(1/(2*m)))^2*(diff(V(xi), xi))^2/(m^2*V(xi)^2)))*a+4*m((V(xi)^(1/(2*m)))^(4*m-2)*(V(xi)^(1/(2*m))*((1/4)*V(xi)^(1/(2*m))*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^(1/(2*m))*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^(1/(2*m))*(diff(V(xi), xi))^2/(m*V(xi)^2))+(1/4)*(4*m+l-1)*(V(xi)^(1/(2*m)))^2*(diff(V(xi), xi))^2/(m^2*V(xi)^2)))*a+b[5]*(V(xi)^(1/(2*m)))^(8*m)+b[4]*(V(xi)^(1/(2*m)))^(6*m)+b[3]*(V(xi)^(1/(2*m)))^(6*m)+b[2]*(V(xi)^(1/(2*m)))^(4*m)+(1/2)*b[6]*(V(xi)^(1/(2*m)))^2*(diff(V(xi), xi))^2*(2*m-1)*(V(xi)^(1/(2*m)))^(-2+2*m)/(m*V(xi)^2)+2*(V(xi)^(1/(2*m)))^(2*m-1)*((1/4)*V(xi)^(1/(2*m))*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^(1/(2*m))*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^(1/(2*m))*(diff(V(xi), xi))^2/(m*V(xi)^2))*m*b[6]+b[1]*(V(xi)^(1/(2*m)))^(2*m)-l*lambda = 0

l((V(xi)^((1/2)/m))^(4*m-2)*(V(xi)^((1/2)/m)*((1/4)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^((1/2)/m)*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m*V(xi)^2))+(1/4)*(4*m+l-1)*(V(xi)^((1/2)/m))^2*(diff(V(xi), xi))^2/(m^2*V(xi)^2)))*a+4*m((V(xi)^((1/2)/m))^(4*m-2)*(V(xi)^((1/2)/m)*((1/4)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^((1/2)/m)*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m*V(xi)^2))+(1/4)*(4*m+l-1)*(V(xi)^((1/2)/m))^2*(diff(V(xi), xi))^2/(m^2*V(xi)^2)))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)+b[4]*(V(xi)^((1/2)/m))^(6*m)+b[3]*(V(xi)^((1/2)/m))^(6*m)+b[2]*(V(xi)^((1/2)/m))^(4*m)+(1/2)*b[6]*(V(xi)^((1/2)/m))^2*(diff(V(xi), xi))^2*(2*m-1)*(V(xi)^((1/2)/m))^(-2+2*m)/(m*V(xi)^2)+2*(V(xi)^((1/2)/m))^(2*m-1)*((1/4)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^((1/2)/m)*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m*V(xi)^2))*m*b[6]+b[1]*(V(xi)^((1/2)/m))^(2*m)-l*lambda = 0

 (2)
> 

simplify(l((V(xi)^((1/2)/m))^(4*m-2)*(V(xi)^((1/2)/m)*((1/4)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^((1/2)/m)*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m*V(xi)^2))+(1/4)*(4*m+l-1)*(V(xi)^((1/2)/m))^2*(diff(V(xi), xi))^2/(m^2*V(xi)^2)))*a+4*m((V(xi)^((1/2)/m))^(4*m-2)*(V(xi)^((1/2)/m)*((1/4)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^((1/2)/m)*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m*V(xi)^2))+(1/4)*(4*m+l-1)*(V(xi)^((1/2)/m))^2*(diff(V(xi), xi))^2/(m^2*V(xi)^2)))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)+b[4]*(V(xi)^((1/2)/m))^(6*m)+b[3]*(V(xi)^((1/2)/m))^(6*m)+b[2]*(V(xi)^((1/2)/m))^(4*m)+(1/2)*b[6]*(V(xi)^((1/2)/m))^2*(diff(V(xi), xi))^2*(2*m-1)*(V(xi)^((1/2)/m))^(-2+2*m)/(m*V(xi)^2)+2*(V(xi)^((1/2)/m))^(2*m-1)*((1/4)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m^2*V(xi)^2)+(1/2)*V(xi)^((1/2)/m)*(diff(diff(V(xi), xi), xi))/(m*V(xi))-(1/2)*V(xi)^((1/2)/m)*(diff(V(xi), xi))^2/(m*V(xi)^2))*m*b[6]+b[1]*(V(xi)^((1/2)/m))^(2*m)-l*lambda = 0)

((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+((diff(diff(V(xi), xi), xi))*b[6]+V(xi)*b[1])*(V(xi)^((1/2)/m))^(2*m)+V(xi)*((b[3]+b[4])*(V(xi)^((1/2)/m))^(6*m)+l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)-l*lambda))/V(xi) = 0

 (3)
> 

simplify(((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+((diff(diff(V(xi), xi), xi))*b[6]+V(xi)*b[1])*(V(xi)^((1/2)/m))^(2*m)+V(xi)*((b[3]+b[4])*(V(xi)^((1/2)/m))^(6*m)+l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)-l*lambda))/V(xi) = 0)

((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+((diff(diff(V(xi), xi), xi))*b[6]+V(xi)*b[1])*(V(xi)^((1/2)/m))^(2*m)+V(xi)*((b[3]+b[4])*(V(xi)^((1/2)/m))^(6*m)+l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)-l*lambda))/V(xi) = 0

 (4)
> 

numer(lhs(((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+((diff(diff(V(xi), xi), xi))*b[6]+V(xi)*b[1])*(V(xi)^((1/2)/m))^(2*m)+V(xi)*((b[3]+b[4])*(V(xi)^((1/2)/m))^(6*m)+l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)-l*lambda))/V(xi) = 0))*denom(rhs(((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+((diff(diff(V(xi), xi), xi))*b[6]+V(xi)*b[1])*(V(xi)^((1/2)/m))^(2*m)+V(xi)*((b[3]+b[4])*(V(xi)^((1/2)/m))^(6*m)+l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)-l*lambda))/V(xi) = 0)) = numer(rhs(((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+((diff(diff(V(xi), xi), xi))*b[6]+V(xi)*b[1])*(V(xi)^((1/2)/m))^(2*m)+V(xi)*((b[3]+b[4])*(V(xi)^((1/2)/m))^(6*m)+l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)-l*lambda))/V(xi) = 0))*denom(lhs(((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+((diff(diff(V(xi), xi), xi))*b[6]+V(xi)*b[1])*(V(xi)^((1/2)/m))^(2*m)+V(xi)*((b[3]+b[4])*(V(xi)^((1/2)/m))^(6*m)+l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+b[5]*(V(xi)^((1/2)/m))^(8*m)-l*lambda))/V(xi) = 0))

(V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+(V(xi)^((1/2)/m))^(2*m)*V(xi)*b[1]+(V(xi)^((1/2)/m))^(6*m)*V(xi)*b[3]+(V(xi)^((1/2)/m))^(6*m)*V(xi)*b[4]+V(xi)*l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*V(xi)*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+(V(xi)^((1/2)/m))^(8*m)*V(xi)*b[5]-V(xi)*l*lambda+(V(xi)^((1/2)/m))^(2*m)*(diff(diff(V(xi), xi), xi))*b[6] = 0

 (5)
> 

simplify((V(xi)^((1/2)/m))^(4*m)*V(xi)*b[2]+(V(xi)^((1/2)/m))^(2*m)*V(xi)*b[1]+(V(xi)^((1/2)/m))^(6*m)*V(xi)*b[3]+(V(xi)^((1/2)/m))^(6*m)*V(xi)*b[4]+V(xi)*l((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+4*V(xi)*m((1/4)*(V(xi)^((1/2)/m))^(4*m)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/(m^2*V(xi)^2))*a+(V(xi)^((1/2)/m))^(8*m)*V(xi)*b[5]-V(xi)*l*lambda+(V(xi)^((1/2)/m))^(2*m)*(diff(diff(V(xi), xi), xi))*b[6] = 0, 'symbolic')

V(xi)*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0

 (6)
> 

simplify(V(xi)*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0)

V(xi)*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0

 (7)
> 

normal(V(xi)*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0, ':-expanded')

V(xi)^3*b[2]+V(xi)^2*b[1]+V(xi)^4*b[3]+V(xi)^4*b[4]+V(xi)*l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+4*V(xi)*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+V(xi)^5*b[5]-V(xi)*l*lambda+V(xi)*(diff(diff(V(xi), xi), xi))*b[6] = 0

 (8)
> 

normal(V(xi)^3*b[2]+V(xi)^2*b[1]+V(xi)^4*b[3]+V(xi)^4*b[4]+V(xi)*l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+4*V(xi)*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+V(xi)^5*b[5]-V(xi)*l*lambda+V(xi)*(diff(diff(V(xi), xi), xi))*b[6] = 0)

V(xi)^3*b[2]+V(xi)^2*b[1]+V(xi)^4*b[3]+V(xi)^4*b[4]+V(xi)*l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+4*V(xi)*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+V(xi)^5*b[5]-V(xi)*l*lambda+V(xi)*(diff(diff(V(xi), xi), xi))*b[6] = 0

 (9)
> 

eval(4*%*m^2)

(4*V(xi)^3*b[2]+4*V(xi)^2*b[1]+4*V(xi)^4*b[3]+4*V(xi)^4*b[4]+4*V(xi)*l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+16*V(xi)*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+4*V(xi)^5*b[5]-4*V(xi)*l*lambda+4*V(xi)*(diff(diff(V(xi), xi), xi))*b[6])*m^2 = 0

 (10)
> 

simplify((4*V(xi)^3*b[2]+4*V(xi)^2*b[1]+4*V(xi)^4*b[3]+4*V(xi)^4*b[4]+4*V(xi)*l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+16*V(xi)*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+4*V(xi)^5*b[5]-4*V(xi)*l*lambda+4*V(xi)*(diff(diff(V(xi), xi), xi))*b[6])*m^2 = 0)

4*V(xi)*m^2*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0

 (11)
> 

simplify(4*V(xi)*m^2*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0, 'symbolic')

4*V(xi)*m^2*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0

 (12)
> 

normal(4*V(xi)*m^2*(l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+4*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(l+2*m)*(diff(V(xi), xi))^2)/m^2)*a+(diff(diff(V(xi), xi), xi))*b[6]+V(xi)^4*b[5]+(b[3]+b[4])*V(xi)^3+V(xi)^2*b[2]+V(xi)*b[1]-l*lambda) = 0, ':-expanded')

4*V(xi)^5*m^2*b[5]+4*V(xi)^4*m^2*b[3]+4*V(xi)^4*m^2*b[4]+4*V(xi)^3*m^2*b[2]+4*V(xi)*m^2*(diff(diff(V(xi), xi), xi))*b[6]+4*V(xi)^2*m^2*b[1]+4*V(xi)*m^2*l((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a+16*V(xi)*m^2*m((1/4)*(2*(diff(diff(V(xi), xi), xi))*V(xi)*m+(diff(V(xi), xi))^2*l+2*(diff(V(xi), xi))^2*m)/m^2)*a-4*V(xi)*m^2*l*lambda = 0

 (13)
 

NULL

Download simplify.mw

In exploring when number are come out are too long...

Asked by: salim-barzani 160
decimal
October 15 2024
0  5

When i want reploting with the parameter i make them shorter by hand, make a problem for me and give me the same graph how fixed this problem? there is any code write in begind and give me all number about 2 decimal?

> 

restart
> 

K := [alpha = .33101604, theta = -2.54098361, mu = 4.89071038, k = 5.0, A[1] = 2.70491803, a = 3.63387978]

[alpha = .33101604, theta = -2.54098361, mu = 4.89071038, k = 5.0, A[1] = 2.70491803, a = 3.63387978]

 (1)
> 

MapleTA:-Builtin:-decimal(2, 20.8571)

20.86

 (2)
> 

MapleTA:-Builtin:-decimal(2, K)

Error, (in MapleTA:-Builtin:-decimal) invalid input: round expects its 1st argument, a1, to be of type algebraic, but received [100*(alpha = .33101604), 100*(theta = -2.54098361), 100*(mu = 4.89071038), 100*(k = 5.0), 100*(A[1] = 2.70491803), 100*(a = 3.63387978)]

  
 

NULL

Download decimal.mw

How fix error in testing ode with condition?...

Asked by: salim-barzani 160
solve pde simplification
October 12 2024
0  2

i found thus condition which if we substitute in equation must be equal to zero, i don't know  how i can get zero

test_pde1.mw

why get Error when do seperet real and imaginary o...

Asked by: salim-barzani 160
syntax 2dmath differential-equations
October 12 2024
0  4

each time i use this i did not have any problem but this equation not seperate any one know what is problem?

> 

restart
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

with(PDEtools)
> 

P := U(xi)^3*mu*C[2]*h[9]+(2*I)*(diff(U(xi), xi))*a*k*mu+4*(diff(U(xi), xi))*k*mu^3*C[2]*h[7]-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*C[2]*h[7]-U(xi)^3*mu*C[2]*h[8]+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*C[2]*h[7]+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[9]-(6*I)*(diff(diff(U(xi), xi), xi))*k^2*mu^2*C[2]*h[7]+I*U(xi)*mu^4*C[2]*h[7]-I*(diff(U(xi), xi))*v-U(xi)*w+b*U(xi)^3-U(xi)*a*mu^2+(diff(diff(U(xi), xi), xi))*a*k^2+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[8]+C[1](-U(xi)^3*mu^2*h[2]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[4]-(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[5]+(diff(U(xi), xi))^2*U(xi)*k^2*h[2]-U(xi)^3*mu^2*h[5]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[5]-(4*(diff(U(xi), xi))*I)*k*mu^3*h[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*h[1]*I+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[2]+h[6]*U(xi)^5-U(xi)^3*mu^2*h[4]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[4]+U(xi)*mu^4*h[1]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*h[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*h[1]+h[3](k^2*(diff(U(xi), xi))^2+2*(0+I)*(diff(U(xi), xi))*k*mu*U(xi)-mu^2*U(xi)^2)*U(xi)) = 0

U(xi)^3*mu*C[2]*h[9]+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[8]+4*(diff(U(xi), xi))*k*mu^3*C[2]*h[7]-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*C[2]*h[7]-U(xi)^3*mu*C[2]*h[8]+I*(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[9]-(6*I)*(diff(diff(U(xi), xi), xi))*k^2*mu^2*C[2]*h[7]+I*U(xi)*mu^4*C[2]*h[7]-I*(diff(U(xi), xi))*v+(2*I)*(diff(U(xi), xi))*a*k*mu-U(xi)*w+b*U(xi)^3-U(xi)*a*mu^2+(diff(diff(U(xi), xi), xi))*a*k^2+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*C[2]*h[7]+C[1](-U(xi)^3*mu^2*h[2]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[4]-(4*I)*(diff(U(xi), xi))*k*mu^3*h[1]+(diff(U(xi), xi))^2*U(xi)*k^2*h[2]-U(xi)^3*mu^2*h[5]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[5]+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*h[1]-(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[5]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[2]+h[6]*U(xi)^5-U(xi)^3*mu^2*h[4]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[4]+U(xi)*mu^4*h[1]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*h[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*h[1]+h[3](k^2*(diff(U(xi), xi))^2+(2*I)*(diff(U(xi), xi))*k*mu*U(xi)-mu^2*U(xi)^2)*U(xi)) = 0

 (2)
> 

Re(P)

Re(U(xi)^3*mu*C[2]*h[9]+4*(diff(U(xi), xi))*k*mu^3*C[2]*h[7]-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*C[2]*h[7]-U(xi)^3*mu*C[2]*h[8]-U(xi)*w+b*U(xi)^3-U(xi)*a*mu^2+(diff(diff(U(xi), xi), xi))*a*k^2+C[1](-U(xi)^3*mu^2*h[2]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[4]-(4*I)*(diff(U(xi), xi))*k*mu^3*h[1]+(diff(U(xi), xi))^2*U(xi)*k^2*h[2]-U(xi)^3*mu^2*h[5]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[5]+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*k^3*mu*h[1]-(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[5]+(2*I)*(diff(U(xi), xi))*U(xi)^2*k*mu*h[2]+h[6]*U(xi)^5-U(xi)^3*mu^2*h[4]+U(xi)^2*(diff(diff(U(xi), xi), xi))*k^2*h[4]+U(xi)*mu^4*h[1]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*h[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*h[1]+h[3](k^2*(diff(U(xi), xi))^2+(2*I)*(diff(U(xi), xi))*k*mu*U(xi)-mu^2*U(xi)^2)*U(xi)))-Im((diff(U(xi), xi))*U(xi)^2*k*C[2]*h[8]+(diff(U(xi), xi))*U(xi)^2*k*C[2]*h[9]-6*(diff(diff(U(xi), xi), xi))*k^2*mu^2*C[2]*h[7]+U(xi)*mu^4*C[2]*h[7]-(diff(U(xi), xi))*v+2*(diff(U(xi), xi))*a*k*mu+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k^4*C[2]*h[7]) = 0

 (3)
 

``

Download real_and_imaginary_.mw

Transformation of strange equation In PDE to ODE h...

Asked by: salim-barzani 160
pde differential-equations
October 11 2024
0  0

I have  a big problem in transformation How we can do suh transformation in  type of  procure  without use any hand work for example in physic abs|-| remove the exponential term how the maple remove that term automatically and collect all term and do my transformation this example is really hard one which is must do a lot by hand and mixed them which maybe a week take my time to get results and how i reach the results without spending that time i have a result of this equation and i am try to get but i don't know the results of this person is correct or not but i will share in here,  i did some try i will share in here too if in DEchange add U(xi) it will work and give me the other step but i need something more effective, when q^* is conjugate of q =exp(-ipsi(x,t))U(xi)

> 

NULL
> 

restart
> 

with(PDEtools)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)

 

 
> 

tr := {t = tau, x = xi/k+v*tau^alpha/(k*alpha)+theta, u(x, t) = U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)), u[1](x, t) = U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))}

{t = tau, x = xi/k+v*tau^alpha/(k*alpha)+theta, u(x, t) = U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)), u[1](x, t) = U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))}

 (2)
> 

pde := I*(I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)-mu*tau+theta))*w-exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))*v)+a*(diff(u(x, t), `$`(x, 2)))+b*U(xi)^2*u(x, t)+C[1](h[1]*(diff(u(x, t), `$`(x, 4)))+h[2]*(diff(u(x, t), x))^2*u[1](x, t)+h[3]*abs(diff(u(x, t), x))^2*u(x, t)+h[4]*U(xi)^2*(diff(u(x, t), `$`(x, 2)))+h[5]*u(x, t)^2*(diff(u[1](x, t), `$`(x, 2)))+h[6]*U(xi)^4*u(x, t))+I*C[2]*(h[7]*(diff(u(x, t), `$`(x, 4)))+h[8]*U(xi)^2*(diff(u(x, t), x))+h[9]*u(x, t)^2*(diff(u[1](x, t), x))) = 0

I*(I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)-mu*tau+theta))*w-exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))*v)+a*(diff(diff(u(x, t), x), x))+b*U(xi)^2*u(x, t)+C[1](h[1]*(diff(diff(diff(diff(u(x, t), x), x), x), x))+h[2]*(diff(u(x, t), x))^2*u[1](x, t)+h[3]*abs(diff(u(x, t), x))^2*u(x, t)+h[4]*U(xi)^2*(diff(diff(u(x, t), x), x))+h[5]*u(x, t)^2*(diff(diff(u[1](x, t), x), x))+h[6]*U(xi)^4*u(x, t))+I*C[2]*(h[7]*(diff(diff(diff(diff(u(x, t), x), x), x), x))+h[8]*U(xi)^2*(diff(u(x, t), x))+h[9]*u(x, t)^2*(diff(u[1](x, t), x))) = 0

 (3)
> 

``
> 

PDEtools:-dchange(tr, pde, [xi, tau, U, U(xi)])

I*(I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)-mu*tau+theta))*w-exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))*v)+a*((2*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))-U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^2)*k^2+b*U(xi)^3*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))+C[1](h[1]*(-(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k^3-6*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))/k^2+(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(U(xi), xi), xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^4)*k^4+h[2]*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))+I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)^2*k^2*U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))+h[3]*abs((exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))+I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)*k)^2*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))+h[4]*U(xi)^2*((2*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))-U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^2)*k^2+h[5]*U(xi)^2*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)))^2*((diff(diff(U(xi), xi), xi))*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))-(2*I)*(diff(U(xi), xi))*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k-U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^2)*k^2+h[6]*U(xi)^5*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)))+I*C[2]*(h[7]*(-(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))/k^3-6*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(U(xi), xi), xi))/k^2+(4*I)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(U(xi), xi), xi), xi))/k+exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k^4)*k^4+h[8]*U(xi)^2*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))*(diff(U(xi), xi))+I*U(xi)*exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)*k+h[9]*U(xi)^2*(exp(I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta)))^2*((diff(U(xi), xi))*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))-I*U(xi)*exp(-I*(xi/k+v*tau^alpha/(k*alpha)+mu*tau+theta))/k)*k) = 0

 (4)
 

NULL


Download find_ODE.mw

Please help; research example...

Asked by: MichaelVio 40
ode differential-equations
October 10 2024
1  4

@Rouben Rostamian  

Dear Sir Professor Rostamian my name is Viorel Popescu from the Polytechnic University of Bucharest if you remember in the summer of 2019 you helped me to solve the equation: rH''(r)+H'(r)+(rk^2-r^2*b^2/R^2)H(r)=0 where k, b, and R are real constants positive number, with condition H(R)=0 and H'(1/R)=R. I appreciate it very much, please I'm in a similarly embarrassing situation to beg you for an answer. I want to find the equation of audion and complete the experiment http://www.michaelvio.byethost8.com/Audion.pdf

My account in Maple Primes is the same michaelvio (35) as the email michaelvio@yahoo.com and also @gmail.com it's an experiment that I want to make for my PhD. Practically I suppose that the energy can be approx. as a series of power of frequency t from I selected severaral terms Ea := 0.00762014687*t + a*t^2 + b*t^3 + c*t^4 + d*t^5 and I guess that satisfies an equation as in the document. The case of photons is beyond my possibility, but a little help from a distinguished Professor as you should cheer me up Audion1.mw

Audion.docx

Please help! 

3D plot, Matlab export...

Asked by: salim-barzani 160
October 05 2024
1  20

Hi

How merge or combine two or more 3D plot together ? and How many 3D plot exist for describe graph ? and how we can transfer this combine plot to another program like matlab?

Maple is  good for decribe plot  and very faster from other program but for visualization and some other stuff we need other language program, so how we can combine the plot and how we transfer this plot another program like matlab i know the matlab have special template for this kind plot but i didn't have the template if any one have it it will be  awesome?

Download combine_graph.mw

Double Sigma for Matrix entries...

Asked by: mahmood1800 260
sum add incomplete-question
October 03 2024
0  4

Hi all
I have a simple problem with the following matrix entries. I probably have a problem with the indices. Because the matrix is ​​not calculated correctly. Anyone have suggestion?

Plot of integral doesn't succeed...

Asked by: MichaelVio 40
integration numeric incomplete-question
October 02 2024
0  12

I want a plot of the function & the approx. calculus of integral:

E0 := evalf(int(T2, x = x0 .. x0 + 1.542976947*10^(-13))); it doesn't compute in in normal time...Audion.mw

in the program:

restart;
a := -1.44670357887361*10^(-7);
b := -1.049267156*10^(-9);
c := 1.890440485*10^(-12);
d := -6.233924848*10^(-16);
Ea := 0.00762014687*t + a*t^2 + b*t^3 + c*t^4 + d*t^5;
E1 := diff(Ea, t);
E2 := subs(t = 435, Ea);
E3 := subs(t = 528, Ea);
E4 := subs(t = 2860, Ea);
 

When i do substitute in equation two parameter con...

Asked by: salim-barzani 160
ode substitution differential-equations
September 30 2024
1  4

how fixed this for ode test

> 

restart
> 

with(PDEtools)
> 

with(Physics)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

``
> 

pde := -I*(diff(U(xi), xi))*gamma*k*mu+I*gamma*(diff(U(xi), xi))*sigma*w+(diff(diff(U(xi), xi), xi))*gamma*k*w+U(xi)*gamma*mu*sigma+(2*I)*(diff(U(xi), xi))*k*sigma+2*alpha*U(xi)^3+(diff(diff(U(xi), xi), xi))*k^2-I*(diff(U(xi), xi))*w-U(xi)*sigma^2-U(xi)*mu

-I*gamma*(diff(U(xi), xi))*k*mu+I*gamma*(diff(U(xi), xi))*sigma*w+gamma*(diff(diff(U(xi), xi), xi))*k*w+gamma*U(xi)*mu*sigma+(2*I)*(diff(U(xi), xi))*k*sigma+2*alpha*U(xi)^3+(diff(diff(U(xi), xi), xi))*k^2-I*(diff(U(xi), xi))*w-U(xi)*sigma^2-U(xi)*mu

 (2)
> 

case1 := [mu = -(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1), A[0] = 0, A[1] = -RootOf(_Z^2*alpha+gamma*k*w+k^2), B[1] = RootOf(_Z^2*alpha+gamma*k*w+k^2), w = (gamma*k*mu-2*k*sigma)/(gamma*sigma-1)]

[mu = -(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1), A[0] = 0, A[1] = -RootOf(_Z^2*alpha+gamma*k*w+k^2), B[1] = RootOf(_Z^2*alpha+gamma*k*w+k^2), w = (gamma*k*mu-2*k*sigma)/(gamma*sigma-1)]

 (3)
> 

G1 := U(xi) = 2*RootOf(_Z^2*alpha+gamma*k*w+k^2)/sinh(2*xi)

U(xi) = 2*RootOf(_Z^2*alpha+gamma*k*w+k^2)/sinh(2*xi)

 (4)
> 

pde1 := subs(case1, pde)

I*gamma*(diff(U(xi), xi))*k*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)+I*gamma*(diff(U(xi), xi))*sigma*(gamma*k*mu-2*k*sigma)/(gamma*sigma-1)+gamma*(diff(diff(U(xi), xi), xi))*k*(gamma*k*mu-2*k*sigma)/(gamma*sigma-1)-gamma*U(xi)*(4*gamma*k*w+4*k^2-sigma^2)*sigma/(gamma*sigma-1)+(2*I)*(diff(U(xi), xi))*k*sigma+2*alpha*U(xi)^3+(diff(diff(U(xi), xi), xi))*k^2-I*(diff(U(xi), xi))*(gamma*k*mu-2*k*sigma)/(gamma*sigma-1)-U(xi)*sigma^2+U(xi)*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)

 (5)
> 

pde2 := subs(case1, pde1)

I*gamma*(diff(U(xi), xi))*k*(4*gamma*(gamma*k*mu-2*k*sigma)*k/(gamma*sigma-1)+4*k^2-sigma^2)/(gamma*sigma-1)+I*gamma*(diff(U(xi), xi))*sigma*(-gamma*k*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)-2*k*sigma)/(gamma*sigma-1)+gamma*(diff(diff(U(xi), xi), xi))*k*(-gamma*k*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)-2*k*sigma)/(gamma*sigma-1)-gamma*U(xi)*(4*gamma*(gamma*k*mu-2*k*sigma)*k/(gamma*sigma-1)+4*k^2-sigma^2)*sigma/(gamma*sigma-1)+(2*I)*(diff(U(xi), xi))*k*sigma+2*alpha*U(xi)^3+(diff(diff(U(xi), xi), xi))*k^2-I*(diff(U(xi), xi))*(-gamma*k*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)-2*k*sigma)/(gamma*sigma-1)-U(xi)*sigma^2+U(xi)*(4*gamma*(gamma*k*mu-2*k*sigma)*k/(gamma*sigma-1)+4*k^2-sigma^2)/(gamma*sigma-1)

 (6)
> 

odetest(G1, pde2)
 

NULL

Download test_sol_for_PDE1.mw

Approximate solution for exponential equation...

Asked by: MichaelVio 40
exponential regression plotting
September 27 2024
0  11

I must approximate the coefficients a, b, c, and d in an exponential equation. Is it possible to plot?

Please help!

Ea := 0.00762014687*t + a*t^2 + b*t^3 + c*t^4 + d*t^5;
E1 := diff(Ea, t);
E2 := subs(t = 435, Ea);
E3 := subs(t = 528, Ea);
E4 := subs(t = 33168, Ea);

E1 = 5.012764943*10^(-24)*Ea/(exp(Ea/(4.100527530*10^(-21))) - 1)

Aph1.mw

1 2 3 4 5 6 7 Last Page 1 of 40