6 years, 8 days

## How can I merge these four pictures into...

Maple

 > restart:
 >
 >
 (1)
 > e_oredr := 1:
 > ode := subs(D = sum('e^(i-1)*D[i]', 'i' = 1 .. e_oredr+1), ode);
 (2)
 > u := sum('q[i]*e^i', 'i' = 0 .. e_oredr);
 (3)
 > ode := collect(ode, e):
 >
 >
 > ode:=simplify(%,{e^3=0,e^2=0});
 (4)
 >
 >
 >
 > for i from 0 to e_oredr do eq[i] := coeff(lhs(ode), e, i) = 0 end do;
 (5)
 >
 > eq[1]:=convert(eq[1](t1, t2), diff);
 (6)
 >
 > q[0] :=A(t2)*exp(I*t1)+b*exp(I*w*t1)+conjugate(A)(t2)*exp(-I*t1)+b*exp(-I*w*t1); convert(%, 'exp'); q[0] := unapply(%, (t1, t2)):  # Chage the value
 (7)
 >
 > expand(lhs(eq[1])):
 > eq:=combine(%, exp):
 > eq:=simplify(%, power):
 > eq:=combine(subs(w=1/3+e*sigma,%),exp):   ## substituting the detuning parameter
 > expand(%):
 > eq:=algsubs(t1*e=t2,%):
 >
 > eq:=collect(%, exp(I*t1)):
 >
 > coeff(%, exp(I*t1),1):
 > simplify(combine(%,exp));
 (8)
 > subs({A(t2)=a(t2)*exp(I*beta(t2))/2,conjugate(A)(t2)=a(t2)*exp(-I*beta(t2))/2},%);
 (9)
 > combine(%,exp);
 (10)
 > map(x->x*exp(-I*beta(t2)),%);
 (11)
 > simplify(%,exp);
 (12)
 > subs({3*sigma*t2-beta(t2)=C(t2),beta(t2)=3*sigma*t2-C(t2)},%);
 (13)
 > convert(%,trig);
 (14)
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 > cond1 := collect(coeff(%, I, 0), [diff(C(t2), t2), cos(C(t2))]);
 (15)
 > cond2 := collect(coeff(%%, I, 1), [diff(A(t2), t2), sin(C(t2))]);
 (16)
 > a(t2):= a; C(t2):=C; cond1 = 0; cond2 =0;
 (17)
 > alpha[1]:=unapply(alpha[1],[t1,t2]);alpha[2]:=unapply(alpha[2],[t1,t2]);
 (18)
 > remove(has, cond1, cos)^2+remove(has, cond2, sin)^2 = select(has, cond1, cos)^2+select(has, cond2, sin)^2;
 (19)
 > simplify(%,'trig');
 (20)
 >
 > af_eq:=%;
 (21)
 > ##
 >
 >
 > ##
 > b:=0.5*f0/(1-(1/3)^2);
 (22)
 > with(plots, implicitplot):
 > f0 :=1; alpha[1]:=0.0087;alpha[2]:=2.5871;   b:=0.5*f0/(1-(1/3)^2);#change the value
 (23)
 > af_eq; curve1,curve2:=solve(af_eq, sigma): A0:=2:
 (24)

 >
 >

 >

 > pu1:=implicitplot([sigma=curve2,sigma=curve1],sigma =-5..20, a = 0 .. A0,  numpoints = 200000, axes = box, axesfont=[SYMBOL, 14],labels = [sigma, a], labelfont = [SYMBOL, 16],color="red",tickmarks=[9,12],thickness=3,'view' = [-5 .. 20, 0 .. 6]): pu2:=implicitplot([sigma=curve2,sigma=curve1],sigma =-5..20, a = A0 .. 10,linestyle=[1,3],  numpoints = 20000, axes = box, axesfont=[SYMBOL, 14],labels = [sigma, a], labelfont = [SYMBOL, 16],color="red",tickmarks=[9,12],thickness=3,'view' = [-5 .. 20, 0 .. 6]):
 > A0:=-2:
 > pu3:=implicitplot([sigma=curve2,sigma=curve1],sigma =-5..20, a = -10 .. A0, linestyle=[3,1], numpoints = 200000, axes = box, axesfont=[SYMBOL, 14],labels = [sigma, a], labelfont = [SYMBOL, 16],color="red",tickmarks=[9,12],thickness=3,'view' = [-5 .. 20, -6 .. 0]): pu4:=implicitplot([sigma=curve2,sigma=curve1],sigma =-5..20, a = A0 .. 0,  numpoints = 20000, axes = box, axesfont=[SYMBOL, 14],labels = [sigma, a], labelfont = [SYMBOL, 16],color="red",tickmarks=[9,12],thickness=3,'view' = [-5 .. 20, -6 .. 0]):
 > pp1:=display([pu1,pu2,pu3,pu4]);
 (25)
 > How can I merge these pictures into one
 >
 >
 >
 >
 >

Like this one

## Anxious!! How to express the part of the...

Maple

How to express the part of  unstable curve with a dashline.   Hope someone can help me achieve this.

 >
 (13)
 > combine(%, 'exp');
 (14)
 > subs(I*B(t2)=I*sigma*t2-I*C(t2),B(t2)=sigma*t2-C(t2), %);
 (15)
 > conds := combine(%, 'exp');
 (16)
 > convert(conds, 'trig');
 (17)
 > cond1 := collect(coeff(%, I, 0), [diff(A(t2), t2), cos(C(t2))]);
 (18)
 > cond2 := collect(coeff(`%%`, I, 1), [diff(A(t2), t2), sin(C(t2)), cos(C(t2))]);
 (19)
 > A(t2):= A; C(t2):=C; cond1 = 0; cond2 =0;
 (20)
 > remove(has, cond1, cos)^2+remove(has, cond2, sin)^2 = simplify(select(has, cond1, cos)^2+select(has, cond2, sin)^2, 'trig');
 (21)
 > af_eq:=%;
 (22)
 > alpha[1]:=0.0087;alpha[2]:=2.5871;f0:=f[0]
 (23)
 >
 >
 >
 >
 > ##
 >
 >
 > e:='e':    f0:='f0':   alpha[1]:='alpha[1]':   alpha[2]:='alpha[2]':
 > cond1;
 (24)
 > cond2;
 (25)

 > linalg[jacobian]([-cond2,-cond1/A],[A,C]);
 (26)
 >

 > subs(cos(C)=solve(cond1,cos(C)),sin(C)=solve(cond2,sin(C)),%);
 (27)

 > map(simplify,%):

 > linalg[charpoly](%,lambda):

 > p:=collect(%,lambda);
 (28)
 >

 > coeff(p,lambda,0);
 (29)
 >

 > stab_cond:=%;
 (30)
 >

 > af_eq;
 (31)

 > with(plots, implicitplot,implicitplot3d):
 >
 > f0 :=0.1; alpha[1]:=0.0087;alpha[2]:=2.5871;
 (32)
 >

 > p1:=implicitplot(stab_cond,sigma = -1.2 .. 2, A = 0 .. 2,  numpoints = 20000, axes = box, axesfont=[SYMBOL, 14],labels = [sigma, A], labelfont = [SYMBOL, 16],color="Green",tickmarks=[9,12],thickness=2,linestyle=dash):

 > with(plots,textplot):    with(plots,display):

 > ps1:=textplot([0.75, 0.65, "Unstable region"], 'align' = {'above', 'right'},rotation = 0.6, font=[Times,bold,12]):

 > pu1:=implicitplot(af_eq,sigma = -1.2 .. 2, A = 0 .. 2,  numpoints = 20000, axes = box, axesfont=[SYMBOL, 14],labels = [sigma, A], labelfont = [SYMBOL, 16],color="red",tickmarks=[9,12],thickness=2):
 > pp1:=display({p1,ps1,pu1});
 > Like this picture.

## Why does the "textplot" command not work...

Maple 2018

Why does the "textplot" command not work? I just want to write

 >
 > af_eq := (3*alpha[2](t[1], t[2])*A^3*(1/8)-A*sigma)^2+(1/4)*alpha[1](t[1], t[2])^2*A^2 = (1/4)*f0^2
 (1)
 > alpha[1]:=0.0087;alpha[2]:=2.5871;f0:=f[0]
 (2)
 >
 > with(plots, implicitplot,implicitplot3d):
 > f0 :=0.1; alpha[1]:=0.0087;alpha[2]:=2.5871;
 (3)
 > p1:=implicitplot(af_eq, sigma = -1.2 .. 2, A = 0 .. 2,  numpoints = 20000, axes = box, axesfont=[SYMBOL, 14],labels = [sigma, A], labelfont = [SYMBOL, 16],color="Red",tickmarks=[9,12],thickness=2);
 >
 >
 >
 >
 (4)
 >

## How could I substitute the (t1*e) into t...

Maple 2018

How could I substitute the (t1*e) into t2 at the index of e?  I am trying many ways to do that, but it doesn't work. please help me.

 > restart:
 >
 >
 >
 > (1/8)*alpha[2](t[1], t[2])*b^3*exp((3*I)*omega*t[1])+(1/8)*alpha[2](t[1], t[2])*b^3*exp(-(3*I)*omega*t[1])+(1/8)*alpha[2](t[1], t[2])*A(t[2])^3*exp((3*I)*t[1])+(1/8)*alpha[2](t[1], t[2])*A(t[2])^3*exp(-(3*I)*t[1])+3*alpha[2](t[1], t[2])*b^3*exp(-I*omega*t[1])*(1/8)+3*alpha[2](t[1], t[2])*b^3*exp(I*omega*t[1])*(1/8)-I*alpha[1](t[1], t[2])*A(t[2])*exp(-I*t[1])*(1/2)+3*alpha[2](t[1], t[2])*A(t[2])^2*b*exp(-I*omega*t[1])*(1/4)-I*(diff(A(t[2]), t[2]))*exp(-I*t[1])+3*alpha[2](t[1], t[2])*A(t[2])*exp(-I*t[1])*b^2*(1/4)-I*alpha[1](t[1], t[2])*b*omega*exp(-I*omega*t[1])*(1/2)+I*alpha[1](t[1], t[2])*b*omega*exp(I*omega*t[1])*(1/2)+3*alpha[2](t[1], t[2])*A(t[2])^3*exp(-I*t[1])*(1/8)+I*(diff(A(t[2]), t[2]))*exp(I*t[1])+3*alpha[2](t[1], t[2])*A(t[2])*b^2*exp(-I*t[1]-(2*I)*omega*t[1])*(1/8)+3*alpha[2](t[1], t[2])*A(t[2])*b^2*exp(-I*t[1]+(2*I)*omega*t[1])*(1/8)+q[1](t[1], t[2])+3*alpha[2](t[1], t[2])*A(t[2])^2*b*exp(-(2*I)*t[1]-I*omega*t[1])*(1/8)+3*alpha[2](t[1], t[2])*A(t[2])^3*exp(I*t[1])*(1/8)+3*alpha[2](t[1], t[2])*A(t[2])^2*b*exp(-(2*I)*t[1]+I*omega*t[1])*(1/8)+3*alpha[2](t[1], t[2])*A(t[2])*b^2*exp(I*t[1]-(2*I)*omega*t[1])*(1/8)+3*alpha[2](t[1], t[2])*A(t[2])*b^2*exp(I*t[1]+(2*I)*omega*t[1])*(1/8)+diff(q[1](t[1], t[2]), t[1], t[1])+3*alpha[2](t[1], t[2])*A(t[2])^2*b*exp((2*I)*t[1]-I*omega*t[1])*(1/8)+3*alpha[2](t[1], t[2])*A(t[2])^2*b*exp((2*I)*t[1]+I*omega*t[1])*(1/8)+I*alpha[1](t[1], t[2])*A(t[2])*exp(I*t[1])*(1/2)+3*alpha[2](t[1], t[2])*A(t[2])^2*b*exp(I*omega*t[1])*(1/4)+3*alpha[2](t[1], t[2])*A(t[2])*exp(I*t[1])*b^2*(1/4);
 (1)
 >
 >
 > eq:=combine(subs(w=3+e*sigma,%),exp);
 (2)
 > expand(%);
 (3)
 > eq:=combine(subs({e^(t1*e)=e^t2},%),exp);
 (4)
 > How could I substitute the (t1*e) into t2 at the index of e?  I am trying many ways to do that, but it doesn't work. please help me.   (t1*e)=t2

## Help me extracting the data from the Map...

Maple 2018

Help me extracting the data from the Maple figure. I was used the 'implicitplod3D' command to draw the figure.  I want to save the parameters of sigma, A  and f0 in Exce

 > af_eq := (3*alpha[2](t[1], t[2])*A^3*(1/8)-A*sigma)^2+(1/4)*alpha[1](t[1], t[2])^2*A^2 = (1/4)*f0^2
 (1)
 > with(plots, implicitplot,implicitplot3d):
 > alpha[1]:=0.1;alpha[2]:=0.1299;
 (2)
 > ##3D
 > implicitplot3d(af_eq, sigma = -1.5 .. 1.5,f0 =0..0.5, A = 0 .. 5,numpoints = 20000,style=surfacecontour,contours = 15);
 >
 >