bashar27

fix the collect ...

Asked: bashar27 55 Product: Maple 18

September 11 2019

1 1

restart;
T := mu+lambda*H(xi)+(v-1)*H(xi)^2;
2
mu + lambda H(xi) + (v - 1) H(xi)
u[0] := a[0]+a[1]*(d+H(xi))+a[2]/(d+H(xi))+a[3]*(d+H(xi))^2+a[4]/(d+H(xi))^2;
a[2] 2
a[0] + a[1] (d + H(xi)) + --------- + a[3] (d + H(xi))
d + H(xi)

a[4]
+ ------------
2
(d + H(xi))
diff(u[0], xi);
/ d \
a[2] |---- H(xi)|
/ d \ \ dxi /
a[1] |---- H(xi)| - -----------------
\ dxi / 2
(d + H(xi))

/ d \
2 a[4] |---- H(xi)|
/ d \ \ dxi /
+ 2 a[3] (d + H(xi)) |---- H(xi)| - -------------------
\ dxi / 3
(d + H(xi))
collect(%, diff(H(xi), xi));
/ a[2] 2 a[4] \ / d
|a[1] - ------------ + 2 a[3] (d + H(xi)) - ------------| |---- H(xi
| 2 3| \ dxi
\ (d + H(xi)) (d + H(xi)) /

\
)|
/
d[1] := (a[1]-a[2]/(d+H(xi))^2+2*a[3]*(d+H(xi))-2*a[4]/(d+H(xi))^3)*T;
/ a[2] 2 a[4] \ /
|a[1] - ------------ + 2 a[3] (d + H(xi)) - ------------| \mu
| 2 3|
\ (d + H(xi)) (d + H(xi)) /

2\
+ lambda H(xi) + (v - 1) H(xi) /
diff(d[1], xi);
/ / d \ / d \\
|2 a[2] |---- H(xi)| 6 a[4] |---- H(xi)||
| \ dxi / / d \ \ dxi /|
|------------------- + 2 a[3] |---- H(xi)| + -------------------|
| 3 \ dxi / 4 |
\ (d + H(xi)) (d + H(xi)) /

/ 2\ / a[2]
\mu + lambda H(xi) + (v - 1) H(xi) / + |a[1] - ------------
| 2
\ (d + H(xi))

2 a[4] \ / / d \
+ 2 a[3] (d + H(xi)) - ------------| |lambda |---- H(xi)|
3| \ \ dxi /
(d + H(xi)) /

/ d \\
+ 2 (v - 1) H(xi) |---- H(xi)||
\ dxi //
collect(%, diff(H(xi), xi));
// 2 a[2] 6 a[4] \ /
||------------ + 2 a[3] + ------------| \mu + lambda H(xi)
|| 3 4|
\\(d + H(xi)) (d + H(xi)) /

2\ / a[2]
+ (v - 1) H(xi) / + |a[1] - ------------ + 2 a[3] (d + H(xi))
| 2
\ (d + H(xi))

2 a[4] \ \ / d \
- ------------| (lambda + 2 (v - 1) H(xi))| |---- H(xi)|
3| | \ dxi /
(d + H(xi)) / /
d[2] := ((2*a[2]/(d+H(xi))^3+2*a[3]+6*a[4]/(d+H(xi))^4)*(mu+lambda*H(xi)+(v-1)*H(xi)^2)+(a[1]-a[2]/(d+H(xi))^2+2*a[3]*(d+H(xi))-2*a[4]/(d+H(xi))^3)*(lambda+(2*(v-1))*H(xi)))*T;
// 2 a[2] 6 a[4] \ /
||------------ + 2 a[3] + ------------| \mu + lambda H(xi)
|| 3 4|
\\(d + H(xi)) (d + H(xi)) /

2\ / a[2]
+ (v - 1) H(xi) / + |a[1] - ------------ + 2 a[3] (d + H(xi))
| 2
\ (d + H(xi))

2 a[4] \ \ /
- ------------| (lambda + 2 (v - 1) H(xi))| \mu + lambda H(xi)
3| |
(d + H(xi)) / /

2\
+ (v - 1) H(xi) /

eq := (2*k*k)*w*beta*d[2]-(2*alpha*k*k)*d[1]-2*w*u[0]+k*u[0]*u[0];
2 // 2 a[2] 6 a[4] \ /
2 k w beta ||------------ + 2 a[3] + ------------| \mu
|| 3 4|
\\(d + H(xi)) (d + H(xi)) /

2\ / a[2]
+ lambda H(xi) + (v - 1) H(xi) / + |a[1] - ------------
| 2
\ (d + H(xi))

2 a[4] \
+ 2 a[3] (d + H(xi)) - ------------| (lambda + 2 (v - 1) H(xi)
3|
(d + H(xi)) /

\ / 2\ 2 /
)| \mu + lambda H(xi) + (v - 1) H(xi) / - 2 alpha k |a[1]
| |
/ \

a[2] 2 a[4] \ /
- ------------ + 2 a[3] (d + H(xi)) - ------------| \mu
2 3|
(d + H(xi)) (d + H(xi)) /

2\ /
+ lambda H(xi) + (v - 1) H(xi) / - 2 w |a[0]
|
\

a[2] 2
+ a[1] (d + H(xi)) + --------- + a[3] (d + H(xi))
d + H(xi)

a[4] \ / a[2]
+ ------------| + k |a[0] + a[1] (d + H(xi)) + ---------
2| | d + H(xi)
(d + H(xi)) / \

2 a[4] \
+ a[3] (d + H(xi)) + ------------|^2
2|
(d + H(xi)) /
value(%);
2 // 2 a[2] 6 a[4] \ /
2 k w beta ||------------ + 2 a[3] + ------------| \mu
|| 3 4|
\\(d + H(xi)) (d + H(xi)) /

2\ / a[2]
+ lambda H(xi) + (v - 1) H(xi) / + |a[1] - ------------
| 2
\ (d + H(xi))

2 a[4] \
+ 2 a[3] (d + H(xi)) - ------------| (lambda + 2 (v - 1) H(xi)
3|
(d + H(xi)) /

\ / 2\ 2 /
)| \mu + lambda H(xi) + (v - 1) H(xi) / - 2 alpha k |a[1]
| |
/ \

a[2] 2 a[4] \ /
- ------------ + 2 a[3] (d + H(xi)) - ------------| \mu
2 3|
(d + H(xi)) (d + H(xi)) /

2\ /
+ lambda H(xi) + (v - 1) H(xi) / - 2 w |a[0]
|
\

a[2] 2
+ a[1] (d + H(xi)) + --------- + a[3] (d + H(xi))
d + H(xi)

a[4] \ / a[2]
+ ------------| + k |a[0] + a[1] (d + H(xi)) + ---------
2| | d + H(xi)
(d + H(xi)) / \

2 a[4] \
+ a[3] (d + H(xi)) + ------------|^2
2|
(d + H(xi)) /
expr := simplify(%);
Error, (in simplify) too many levels of recursion
temp := algsubs(d+H(xi) = freeze(d+H(xi)), numer(expr));
expr
thaw(collect(temp, freeze(d+H(xi)))/denom(expr));
expr
collect(%, H(xi));

fix simplify problem...

Asked: bashar27 55 Product: Maple 18

September 09 2019

2 0

restart;
lambda := 1;
1
mu := 1;
1
v := 2;
2
r := lambda*(v-1);
1
g := mu*(v-1);
1
a[2] := 0;
0

omega := -(1/2)*alpha*l[1]*l[2]*lambda^2+2*alpha*l[1]*l[2]*mu*v-2*alpha*l[1]*l[2]*mu-alpha*h[1]*h[2];
3
- alpha l[1] l[2] - alpha h[1] h[2]
2
a[0] := -(1/2)*(2*d*v-2*d-lambda)*alpha*l[1]*l[2]/(h[1]*beta*(sqrt(h[1]*beta*alpha*l[1]*l[2])/(h[1]*beta)));
(2 d - 1) alpha l[1] l[2]
- ----------------------------------
(1/2)
2 (h[1] beta alpha l[1] l[2])
a[1] := sqrt(h[1]*beta*alpha*l[1]*l[2])*(v-1)/(beta*h[1]);
(1/2)
(h[1] beta alpha l[1] l[2])
--------------------------------
beta h[1]

Omega := lambda^2-4*mu*v+4*mu;
-3
H := (-lambda+sqrt(-Omega)*{tan(sqrt(-Omega)*xi)+sec(sqrt(-Omega)*xi)})/(2*(v-1));
1 1 (1/2) / / (1/2) \ / (1/2) \\
- - + - 3 { tan\3 xi/ + sec\3 xi/ }
2 2 \ /

u := a[0]+a[1]*(d+H)+a[2]/(d+H);
(2 d - 1) alpha l[1] l[2] 1 /
- ---------------------------------- + --------- |
(1/2) beta h[1] \
2 (h[1] beta alpha l[1] l[2])

(1/2) / 1
(h[1] beta alpha l[1] l[2]) |d - -
\ 2

1 (1/2) / / (1/2) \ / (1/2) \\ \\
+ - 3 { tan\3 xi/ + sec\3 xi/ }||
2 \ / //
f := diff(u, xi);
/ //
1 | (1/2) (1/2) { |
----------- \(h[1] beta alpha l[1] l[2]) 3 \\1
2 beta h[1]

2\
/ (1/2) \ | (1/2)
+ tan\3 xi/ / 3

\ \
/ (1/2) \ / (1/2) \ (1/2) }|
+ sec\3 xi/ tan\3 xi/ 3 / /
S := diff(f, xi);
/ /
1 | (1/2) (1/2) { /
----------- \(h[1] beta alpha l[1] l[2]) 3 \6 tan\
2 beta h[1]

/ 2\
(1/2) \ | / (1/2) \ |
3 xi/ \1 + tan\3 xi/ /

2
/ (1/2) \ / (1/2) \
+ 3 sec\3 xi/ tan\3 xi/

/ 2\\ \
/ (1/2) \ | / (1/2) \ | }|
+ 3 sec\3 xi/ \1 + tan\3 xi/ // /

eq := -(alpha*h[1]*h[2]+omega)*u-(2*beta*h[1]*u*u)*u+alpha*l[1]*l[2]*S;
3 / (2 d - 1) alpha l[1] l[2]
- - alpha l[1] l[2] |- ---------------------------------- +
2 | (1/2)
\ 2 (h[1] beta alpha l[1] l[2])

1 / (1/2) / 1
--------- |(h[1] beta alpha l[1] l[2]) |d - -
beta h[1] \ \ 2

1 (1/2) / / (1/2) \ / (1/2) \\ \\\
+ - 3 { tan\3 xi/ + sec\3 xi/ }||| - 2 beta h[1
2 \ / //|
/

/ (2 d - 1) alpha l[1] l[2] 1 /
] |- ---------------------------------- + --------- |
| (1/2) beta h[1] \
\ 2 (h[1] beta alpha l[1] l[2])

(1/2) / 1
(h[1] beta alpha l[1] l[2]) |d - -
\ 2

1 (1/2) / / (1/2) \ / (1/2) \\ \\\
+ - 3 { tan\3 xi/ + sec\3 xi/ }|||^3 +
2 \ / //|
/

/
1 | (1/2)
----------- \alpha l[1] l[2] (h[1] beta alpha l[1] l[2])
2 beta h[1]

/ / 2\
(1/2) { / (1/2) \ | / (1/2) \ |
3 \6 tan\3 xi/ \1 + tan\3 xi/ /

2
/ (1/2) \ / (1/2) \
+ 3 sec\3 xi/ tan\3 xi/

/ 2\\ \
/ (1/2) \ | / (1/2) \ | }|
+ 3 sec\3 xi/ \1 + tan\3 xi/ // /
value(%);
3 / (2 d - 1) alpha l[1] l[2]
- - alpha l[1] l[2] |- ---------------------------------- +
2 | (1/2)
\ 2 (h[1] beta alpha l[1] l[2])

1 / (1/2) / 1
--------- |(h[1] beta alpha l[1] l[2]) |d - -
beta h[1] \ \ 2

1 (1/2) / / (1/2) \ / (1/2) \\ \\\
+ - 3 { tan\3 xi/ + sec\3 xi/ }||| - 2 beta h[1
2 \ / //|
/

/ (2 d - 1) alpha l[1] l[2] 1 /
] |- ---------------------------------- + --------- |
| (1/2) beta h[1] \
\ 2 (h[1] beta alpha l[1] l[2])

(1/2) / 1
(h[1] beta alpha l[1] l[2]) |d - -
\ 2

1 (1/2) / / (1/2) \ / (1/2) \\ \\\
+ - 3 { tan\3 xi/ + sec\3 xi/ }|||^3 +
2 \ / //|
/

/
1 | (1/2)
----------- \alpha l[1] l[2] (h[1] beta alpha l[1] l[2])
2 beta h[1]

/ / 2\
(1/2) { / (1/2) \ | / (1/2) \ |
3 \6 tan\3 xi/ \1 + tan\3 xi/ /

2
/ (1/2) \ / (1/2) \
+ 3 sec\3 xi/ tan\3 xi/

/ 2\\ \
/ (1/2) \ | / (1/2) \ | }|
+ 3 sec\3 xi/ \1 + tan\3 xi/ // /
simplify(%);
Error, (in simplify/power) invalid input: ln expects its 1st argument, x, to be of type algebraic, but received {(sin(3^(1/2)*xi)+1)/cos(3^(1/2)*xi)}

how to get good 3d figure...

Asked: bashar27 55 Product: Maple 18

September 02 2019

1 0

restart;

K := -3;
-3
m := 1;
1
w := -4*K;
12
alpha[0] := -2;
-2
alpha[1] := 0;
0
a := 2;
2
b := 3;
3
1
beta[1] := (12*(m^2+K))/(a+b);
-24
---
5
xi := -t*w+x+y;
-12 t + x + y

F := -sqrt(-K)*tanh(sqrt(-K)*xi);
(1/2) / (1/2) \
-3 tanh\3 (-12 t + x + y)/
U := alpha[0]+alpha[1]*(m+F)+beta[1]/(m+F);
24
-2 - -------------------------------------------
/ (1/2) / (1/2) \\
5 \1 - 3 tanh\3 (-12 t + x + y)//
1
y := 0;
0

plot3d(U, x = -10 .. -10, t = -10 .. 10);

t := 0;
0
plot(U, x = -10 .. 10);

how to solve problem...

Asked: bashar27 55 Product: Maple 18

September 01 2019

1 0

RootOf(_Z^2*beta*h[1]-alpha*l[1]*l[2], label = _L2)

how to collect S(xi), R(xi) and S(xi)*R(...

Asked: bashar27 55 Product: Maple 18

July 02 2019

1 0

restart;
T := -S(xi)*S(xi)+mu*R(xi)-lambda;
2
-S(xi) + mu R(xi) - lambda
Q := -S(xi)*R(xi);
-S(xi) R(xi)
u := a[0]+a[1]*S(xi)+b[1]*R(xi);
a[0] + a[1] S(xi) + b[1] R(xi)
diff(u, xi);
/ d \ / d \
a[1] |---- S(xi)| + b[1] |---- R(xi)|
\ dxi / \ dxi /
Fr := Q*b[1]+T*a[1];
/ 2 \
-S(xi) R(xi) b[1] + \-S(xi) + mu R(xi) - lambda/ a[1]
diff(Fr, xi);
/ d \ / d \
-|---- S(xi)| R(xi) b[1] - S(xi) |---- R(xi)| b[1]
\ dxi / \ dxi /

/ / d \ / d \\
+ |-2 S(xi) |---- S(xi)| + mu |---- R(xi)|| a[1]
\ \ dxi / \ dxi //
d := -T*R(xi)*b[1]-S(xi)*Q*b[1]+(-2*S(xi)*T+mu*Q)*a[1];
/ 2 \ 2
-\-S(xi) + mu R(xi) - lambda/ R(xi) b[1] + S(xi) R(xi) b[1]

/ / 2 \ \
+ \-2 S(xi) \-S(xi) + mu R(xi) - lambda/ - mu S(xi) R(xi)/ a[

1]
diff(d, xi);
/ / d \ / d \\
-|-2 S(xi) |---- S(xi)| + mu |---- R(xi)|| R(xi) b[1]
\ \ dxi / \ dxi //

/ 2 \ / d \
- \-S(xi) + mu R(xi) - lambda/ |---- R(xi)| b[1]
\ dxi /

/ d \ 2 / d \ /
+ 2 S(xi) R(xi) b[1] |---- S(xi)| + S(xi) |---- R(xi)| b[1] + |
\ dxi / \ dxi / \
/ d \ / 2 \
-2 |---- S(xi)| \-S(xi) + mu R(xi) - lambda/
\ dxi /

/ / d \ / d \\
- 2 S(xi) |-2 S(xi) |---- S(xi)| + mu |---- R(xi)||
\ \ dxi / \ dxi //

/ d \ / d \\
- mu |---- S(xi)| R(xi) - mu S(xi) |---- R(xi)|| a[1]
\ dxi / \ dxi //
h := -(-2*S(xi)*T+mu*Q)*R(xi)*b[1]-(-S(xi)^2+mu*R(xi)-lambda)*Q*b[1]+2*S(xi)*R(xi)*b[1]*T+S(xi)^2*Q*b[1]+(-2*T*(-S(xi)^2+mu*R(xi)-lambda)-2*S(xi)*(-2*S(xi)*T+mu*Q)-mu*T*R(xi)-mu*S(xi)*Q)*a[1];
/ / 2 \ \
-\-2 S(xi) \-S(xi) + mu R(xi) - lambda/ - mu S(xi) R(xi)/ R(xi)

/ 2 \
b[1] + 3 \-S(xi) + mu R(xi) - lambda/ S(xi) R(xi) b[1]

/ 2
3 | / 2 \
- S(xi) R(xi) b[1] + \-2 \-S(xi) + mu R(xi) - lambda/ - 2 S(xi

/ / 2 \ \
) \-2 S(xi) \-S(xi) + mu R(xi) - lambda/ - mu S(xi) R(xi)/

\
/ 2 \ 2 |
- mu \-S(xi) + mu R(xi) - lambda/ R(xi) + mu S(xi) R(xi)/ a[

1]
collect(expand(h+3*Fr*Fr+(4*omega+3)*Fr), S(xi), R(xi));
/ 2 \ 4
R(xi)\3 a[1] - 6 a[1]/ S(xi)

3 /
+ R(xi)(6 R(xi) a[1] b[1] - 6 b[1] R(xi)) S(xi) + R(xi)\3

2 2 2
R(xi) b[1] - 6 R(xi) mu a[1] + 12 a[1] mu R(xi)

2 \
+ 6 lambda a[1] - 8 a[1] lambda - 4 omega a[1] - 3 a[1]/

2 / 2 2
S(xi) + R(xi)\-6 R(xi) mu a[1] b[1] + 6 R(xi) mu b[1]

+ 6 R(xi) lambda a[1] b[1] - 5 R(xi) lambda b[1]

\ / 2 2
- 4 R(xi) omega b[1] - 3 b[1] R(xi)/ S(xi) + R(xi)\3 a[1] mu

2 2 2 2
R(xi) - 3 a[1] mu R(xi) - 6 a[1] mu R(xi) lambda

+ 5 a[1] mu R(xi) lambda + 4 omega a[1] mu R(xi)

2 2 2
+ 3 a[1] lambda + 3 a[1] mu R(xi) - 2 a[1] lambda

\
- 4 omega a[1] lambda - 3 a[1] lambda/

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fix simplify problem...

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