bashar27

fix simplify problem...

Asked: bashar27 60 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 60 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 60 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 60 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/

fix simplify problem...

Asked: bashar27 60 Product: Maple 18

May 22 2019

1 1

restart;
lambda := 1;
1
mu := 1;
1
alpha := 1;
1
v := 2;
2
delta := 1;
1
m := 1;
1
d := 3;
3
l := 1;
1
omega := -(1/2)*a*lambda^2-a*m^2+2*a*mu*v-delta*l*m-(1/2)*delta*lambda^2+2*delta*mu*v-l^2*mu-(1/2)*lambda^2*mu+2*mu^2*v-2*a*mu-2*delta*mu-2*mu^2;
1
- a + 1
2
a[0] := ((2*d*v-2*d-lambda)*(1/2))*sqrt(2)*sqrt(gamma*(a+delta+mu))/gamma;
(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma
a[1] := 0;
0
a[2] := -(2*(1/2))*sqrt(2)*sqrt(gamma*(a+delta+mu))*(d^2*v-d^2-d*lambda+mu)/gamma;
(1/2) (1/2)
7 2 (gamma (a + 2))
- -----------------------------
gamma
Omega := lambda^2-4*mu*v+4*mu;
-3
H := (-lambda+sqrt(-Omega)*tan((1/2)*sqrt(-Omega)*xi))/(2*(v-1));
1 1 (1/2) /1 (1/2) \
- - + - 3 tan|- 3 xi|
2 2 \2 /
u := a[0]+a[1]*(d+H)+a[2]/(d+H);
(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma

(1/2) (1/2)
7 2 (gamma (a + 2))
- -------------------------------------
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 xi||
\2 2 \2 //

eta := -l*y-m*x+omega*t;
/1 \
-y - x + |- a + 1| t
\2 /
u := a[0]+a[1]*(d+H)+a[2]/(d+H);
(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma

(1/2) (1/2)
7 2 (gamma (a + 2))
- -------------------------------------
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 xi||
\2 2 \2 //

f := diff(u, xi);
/ 2\
(1/2) (1/2) |3 3 /1 (1/2) \ |
7 2 (gamma (a + 2)) |- + - tan|- 3 xi| |
\4 4 \2 / /
-------------------------------------------------------
2
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 xi||
\2 2 \2 //
S := diff(u, xi);
/ 2\
(1/2) (1/2) |3 3 /1 (1/2) \ |
7 2 (gamma (a + 2)) |- + - tan|- 3 xi| |
\4 4 \2 / /
-------------------------------------------------------
2
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 xi||
\2 2 \2 //
xi := x+y-(-2*alpha*m-delta*l-delta*m-2*l*mu)*t;
x + y + 6 t
eq := (-omega-a*m*m-delta*l*m-mu*l*l)*u-(gamma*u*u)*u+(a+delta+mu)*S;
/ (1/2) (1/2)
/ 3 \ |5 2 (gamma (a + 2))
|- - a - 3| |-----------------------------
\ 2 / | 2 gamma
|
\

(1/2) (1/2) \ /
7 2 (gamma (a + 2)) | |
- ------------------------------------------------| - gamma |
/5 1 (1/2) /1 (1/2) \\| |
gamma |- + - 3 tan|- 3 (x + y + 6 t)||| |
\2 2 \2 /// \

(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma

(1/2) (1/2) \
7 2 (gamma (a + 2)) |
- ------------------------------------------------|^3 +
/5 1 (1/2) /1 (1/2) \\|
gamma |- + - 3 tan|- 3 (x + y + 6 t)|||
\2 2 \2 ///

/
1 |
------------------------------------------------- |7 (a + 2)
2 \
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 (x + y + 6 t)||
\2 2 \2 //

/ 2
(1/2) (1/2) |3 3 /1 (1/2) \
2 (gamma (a + 2)) |- + - tan|- 3 (x + y + 6 t)|
\4 4 \2 /

\\
||
||
//
value(%);
/ (1/2) (1/2)
/ 3 \ |5 2 (gamma (a + 2))
|- - a - 3| |-----------------------------
\ 2 / | 2 gamma
|
\

(1/2) (1/2) \ /
7 2 (gamma (a + 2)) | |
- ------------------------------------------------| - gamma |
/5 1 (1/2) /1 (1/2) \\| |
gamma |- + - 3 tan|- 3 (x + y + 6 t)||| |
\2 2 \2 /// \

(1/2) (1/2)
5 2 (gamma (a + 2))
-----------------------------
2 gamma

(1/2) (1/2) \
7 2 (gamma (a + 2)) |
- ------------------------------------------------|^3 +
/5 1 (1/2) /1 (1/2) \\|
gamma |- + - 3 tan|- 3 (x + y + 6 t)|||
\2 2 \2 ///

/
1 |
------------------------------------------------- |7 (a + 2)
2 \
/5 1 (1/2) /1 (1/2) \\
gamma |- + - 3 tan|- 3 (x + y + 6 t)||
\2 2 \2 //

/ 2
(1/2) (1/2) |3 3 /1 (1/2) \
2 (gamma (a + 2)) |- + - tan|- 3 (x + y + 6 t)|
\4 4 \2 /

\\
||
||
//

simplify(%);
Error, (in simplify/tools/_zn) too many levels of recursion

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