Please I am trying to get a compact result for this code in particular the lines assigne "a" and "b" respectively. I am sure the result shoud not be more than two lines. Can someone be of help? 

restart:
P:=a[0]+(a[1]*x)/(1+(a[2]*x)/(1+(a[3]*x))):
Q:=diff(P,x):
T:=diff(P,x,x):
e1:=simplify(eval(P, x=q))=y[n]:
e2:=simplify(eval(Q,x=q))=f[n]:
e3:=simplify(eval(Q,x=q+h))=f[n+1]:
e4:=simplify(eval(T,x=q+h))=g[n+1]:
var:=seq(a[i], i=0..3):
M:=e||(1..4):
Cc:=eval(<var>, solve(eval({M}),{var}) ):
for i from 1 to 4 do
	a[i-1]:=Cc[i]:
end do:
Cf:=P:
a:=y[n+1]=collect(simplify(eval(Cf, x=q+h)),[y[n], f[n], f[n+1],g[n+1]], recursive):
b:=map(eval@allvalues, [a]);

please how can I simplify the results of assigned K cum each of the coefficients further in the following code? the results are too large.

restart:
#k=2:
omega:=u/h:
psi:=v/h:
t:=(sum(a[j]*x^j,j=0..2)+a[3]*sin(omega*x)+a[4]*cos(omega*x)+a[5]*sin(psi*x)+a[6]*cos(psi*x)):
F:=diff(t,x):
G:=diff(t,x,x):
p1:=simplify(eval(t,x=q+h))=y[n+1]:
p2:=simplify(eval(F,x=q))=f[n]:
p3:=simplify(eval(F,x=q+h))=f[n+1]:
p4:=simplify(eval(F,x=q+2*h))=f[n+2]:
p5:=simplify(eval(G,x=q))=g[n]:
p6:=simplify(eval(G,x=q+h))=g[n+1]:
p7:=simplify(eval(G,x=q+2*h))=g[n+2]:
vars:= seq(a[i],i=0..6):
Cc:=eval(<vars>, solve({p||(1..7)}, {vars})):
for i from 1 to 7 do
	a[i-1]:=Cc[i]:
end do:
Cf:=t:

K:= collect(combine(simplify(eval(Cf,x=q+2*h),size),trig),{y[n+1],f[n],f[n+1],f[n+2],g[n],g[n+1],g[n+2]},factor):


alpha[1]=simplify(coeff(K,y[n+1]));
beta[0]=simplify(coeff(K,f[n]),size);
beta[1]=simplify(coeff(K,f[n+1]),size):
beta[2]=simplify(coeff(K,f[n+2]),size):
gamma[0]=simplify(coeff(K,g[n]),size):
gamma[1]=simplify(coeff(K,g[n+1]),size):
gamma[2]=simplify(coeff(K,g[n+2]),size):

Hello everyone.and complements

Please I am trying to obtain series expansion of the expression below in u but encounter difficulties particularly when b=0. I am very optimistic that when b=0 there will be a result not division by 0. Can I get help on the code?

Thank you in anticipation of your quick and positive responses and suggestions

# for k=2 CHEBY HYBRID WITH mu=(1-(1/2)*sqrt(2)))) AND v=(1+(1/2)*sqrt(2))))
restart:
omega:=u/h:
t:=(sum(a[j]*x^j,j=0..3)+a[4]*sin(omega*x)+a[5]*cos(omega*x)):
F:=diff(t,x):
G:=diff(t,x,x):
p1:=simplify(eval(t,x=q))=y[n]:
p2:=simplify(eval(t,x=q+(1-(1/2)*sqrt(2))*h))=y[n+mu]:
p3:=simplify(eval(t,x=q+h))=y[n+1]:
p4:=simplify(eval(t,x=q+(1+(1/2)*sqrt(2))*h))=y[n+v]:
p5:=simplify(eval(F,x=q+2*h))=f[n+2]:
p6:=simplify(eval(G,x=q+2*h))=g[n+2]:

vars:= seq(a[i],i=0..5):
Cc:=eval(<vars>, solve({p||(1..6)}, {vars})):
for i from 1 to 6 do
	a[i-1]:=Cc[i]:
end do:
Cf:=t:

K:=collect(combine(simplify(eval(Cf,x=q+2*h),size),trig),{y[n],y[n+mu],y[n+1],y[n+v],f[n+2], g[n+2]},factor):


Num := numer(K):
Den := denom(K):

N := 20:   # order of expansion
Num_N :=(convert(series(Num, u, N),polynom)):
Den_N := (convert(series(Den, u, N),polynom)):
b:=y[n+2]=(convert(series(Num_N/Den_N, u, N),polynom)):

eval(b,u=0); 

Please can someone help with maple comand to obtain Jacobian elliptic functions particularly in code editing region?

Hello everyone.

Please I am trying to obtain series expansion of the expression below in u and v up to order 30 but encounter difficulties cum maple is slow to display solution. Can I get help on the code and what to do to optimize the displayed time of maple?

Thank you in anticipation of your quick and positive responses and suggestions.

convert(series(convert(series((y[n]+((-8 h u^2 v^2-4 u^3 sin(u) h+2 sin(2 u) h u^3+2 sin(2 v) h v^3-4 v^3 h sin(v)+2 v^3 h sin(2 u+v)+2 u^3 h sin(u-2 v)+2 u^3 h sin(u+2 v)-2 v^3 h sin(2 u-v)-u^3 h sin(2 u+2 v)-v^3 h sin(2 u+2 v)-u^3 h sin(2 u-2 v)+v^3 h sin(2 u-2 v)+4 h u^3 v^2 sin(2 u)+4 h u^2 v^3 sin(2 v)-4 h u^3 v^2 sin(u-v)+4 h u^2 v^3 sin(u-v)-4 h u^3 v^2 sin(u+v)-4 h u^2 v^3 sin(u+v)+4 h u^2 v^2 cos(u)+4 h u^2 v^2 cos(2 u)+4 h u^2 v^2 cos(2 v)+4 h u^2 v^2 cos(v)-4 h u^3 v cos(2 u-v)-2 h u^2 v^2 cos(2 u-v)+2 h u v^3 cos(2 u-v)+4 h u^3 v cos(2 u+v)-2 h u^2 v^2 cos(2 u+v)-2 h u v^3 cos(2 u+v)+2 h u^3 v cos(u-2 v)-2 h u^2 v^2 cos(u-2 v)-4 h u v^3 cos(u-2 v)-2 h u^3 v cos(u+2 v)-2 h u^2 v^2 cos(u+2 v)+4 h u v^3 cos(u+2 v)+4 h u^3 v cos(u-v)+4 h u v^3 cos(u-v)-4 h u^3 v cos(u+v)-4 h u v^3 cos(u+v)+4 u sin(u) v^2 h-2 sin(2 u) h u v^2-2 sin(2 v) h u^2 v+4 v h sin(v) u^2-2 v u^2 h sin(2 u+v)-2 u v^2 h sin(u-2 v)-2 u v^2 h sin(u+2 v)+2 v u^2 h sin(2 u-v)+v u^2 h sin(2 u+2 v)+u v^2 h sin(2 u+2 v)-v u^2 h sin(2 u-2 v)+u v^2 h sin(2 u-2 v)) f[n])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)+((-8 h u^2 v^2+8 u^3 sin(u) h-4 sin(2 u) h u^3-4 sin(2 v) h v^3+8 v^3 h sin(v)-4 v^3 h sin(2 u+v)-4 u^3 h sin(u-2 v)-4 u^3 h sin(u+2 v)+4 v^3 h sin(2 u-v)+2 u^3 h sin(2 u+2 v)+2 v^3 h sin(2 u+2 v)+2 u^3 h sin(2 u-2 v)-2 v^3 h sin(2 u-2 v)+8 h u^3 v^2 sin(u)+8 h u^2 v^3 sin(v)-4 h u^3 v^2 sin(2 u+v)+4 h u^2 v^3 sin(2 u+v)+4 h u^3 v^2 sin(u-2 v)+4 h u^2 v^3 sin(u-2 v)+4 h u^3 v^2 sin(u+2 v)-4 h u^2 v^3 sin(u+2 v)-4 h u^3 v^2 sin(2 u-v)-4 h u^2 v^3 sin(2 u-v)+8 h u^2 v^2 cos(u)+8 h u^2 v^2 cos(v)+4 h u^3 v cos(2 u-v)-4 h u^2 v^2 cos(2 u-v)-8 h u v^3 cos(2 u-v)-4 h u^3 v cos(2 u+v)-4 h u^2 v^2 cos(2 u+v)+8 h u v^3 cos(2 u+v)-8 h u^3 v cos(u-2 v)-4 h u^2 v^2 cos(u-2 v)+4 h u v^3 cos(u-2 v)+8 h u^3 v cos(u+2 v)-4 h u^2 v^2 cos(u+2 v)-4 h u v^3 cos(u+2 v)-2 h u^3 v cos(2 u+2 v)+4 h u^2 v^2 cos(2 u+2 v)-2 h u v^3 cos(2 u+2 v)+2 h u^3 v cos(2 u-2 v)+4 h u^2 v^2 cos(2 u-2 v)+2 h u v^3 cos(2 u-2 v)-8 u sin(u) v^2 h+4 sin(2 u) h u v^2+4 sin(2 v) h u^2 v-8 v h sin(v) u^2+4 v u^2 h sin(2 u+v)+4 u v^2 h sin(u-2 v)+4 u v^2 h sin(u+2 v)-4 v u^2 h sin(2 u-v)-2 v u^2 h sin(2 u+2 v)-2 u v^2 h sin(2 u+2 v)+2 v u^2 h sin(2 u-2 v)-2 u v^2 h sin(2 u-2 v)) f[n+1])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)+((-8 h u^2 v^2-4 u^3 sin(u) h+2 sin(2 u) h u^3+2 sin(2 v) h v^3-4 v^3 h sin(v)+2 v^3 h sin(2 u+v)+2 u^3 h sin(u-2 v)+2 u^3 h sin(u+2 v)-2 v^3 h sin(2 u-v)-u^3 h sin(2 u+2 v)-v^3 h sin(2 u+2 v)-u^3 h sin(2 u-2 v)+v^3 h sin(2 u-2 v)+4 h u^3 v^2 sin(2 u)+4 h u^2 v^3 sin(2 v)-4 h u^3 v^2 sin(u-v)+4 h u^2 v^3 sin(u-v)-4 h u^3 v^2 sin(u+v)-4 h u^2 v^3 sin(u+v)+4 h u^2 v^2 cos(u)+4 h u^2 v^2 cos(2 u)+4 h u^2 v^2 cos(2 v)+4 h u^2 v^2 cos(v)-4 h u^3 v cos(2 u-v)-2 h u^2 v^2 cos(2 u-v)+2 h u v^3 cos(2 u-v)+4 h u^3 v cos(2 u+v)-2 h u^2 v^2 cos(2 u+v)-2 h u v^3 cos(2 u+v)+2 h u^3 v cos(u-2 v)-2 h u^2 v^2 cos(u-2 v)-4 h u v^3 cos(u-2 v)-2 h u^3 v cos(u+2 v)-2 h u^2 v^2 cos(u+2 v)+4 h u v^3 cos(u+2 v)+4 h u^3 v cos(u-v)+4 h u v^3 cos(u-v)-4 h u^3 v cos(u+v)-4 h u v^3 cos(u+v)+4 u sin(u) v^2 h-2 sin(2 u) h u v^2-2 sin(2 v) h u^2 v+4 v h sin(v) u^2-2 v u^2 h sin(2 u+v)-2 u v^2 h sin(u-2 v)-2 u v^2 h sin(u+2 v)+2 v u^2 h sin(2 u-v)+v u^2 h sin(2 u+2 v)+u v^2 h sin(2 u+2 v)-v u^2 h sin(2 u-2 v)+u v^2 h sin(2 u-2 v)) f[n+2])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)+((-6 u^2 h^2-6 v^2 h^2-4 cos(2 u) h^2 u^2 v^2-4 cos(2 v) h^2 u^2 v^2+8 v^2 u^2 h^2 cos(u-v)+8 v^2 u^2 h^2 cos(u+v)+8 u sin(u) v^2 h^2+8 sin(2 u) h^2 u v^2+8 sin(2 v) h^2 u^2 v+8 v h^2 sin(v) u^2+4 v u^2 h^2 sin(2 u+v)-4 u v^2 h^2 sin(2 u+v)+8 v u^2 h^2 sin(u-v)-8 sin(u-v) h^2 u v^2-8 v u^2 h^2 sin(u+v)-8 sin(u+v) h^2 u v^2+4 v u^2 h^2 sin(u-2 v)+4 u v^2 h^2 sin(u-2 v)-4 v u^2 h^2 sin(u+2 v)+4 u v^2 h^2 sin(u+2 v)-4 v u^2 h^2 sin(2 u-v)-4 u v^2 h^2 sin(2 u-v)-4 u v h^2 cos(2 u-v)+4 u v h^2 cos(2 u+v)-4 u v h^2 cos(u-2 v)+4 u v h^2 cos(u+2 v)-2 u v h^2 cos(2 u+2 v)+2 u v h^2 cos(2 u-2 v)+8 cos(u-v) h^2 u v-8 cos(u+v) h^2 u v-8 v^2 u^2 h^2+8 h^2 cos(u) u^2-2 cos(2 u) h^2 u^2+6 cos(2 u) h^2 v^2+6 cos(2 v) h^2 u^2-2 cos(2 v) h^2 v^2+8 h^2 cos(v) v^2-4 v^2 h^2 cos(2 u-v)-4 v^2 h^2 cos(2 u+v)-4 u^2 h^2 cos(u-2 v)-4 u^2 h^2 cos(u+2 v)+u^2 h^2 cos(2 u+2 v)+v^2 h^2 cos(2 u+2 v)+u^2 h^2 cos(2 u-2 v)+v^2 h^2 cos(2 u-2 v)) g[n])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)+((6 u^2 h^2+6 v^2 h^2+4 cos(2 u) h^2 u^2 v^2+4 cos(2 v) h^2 u^2 v^2-8 v^2 u^2 h^2 cos(u-v)-8 v^2 u^2 h^2 cos(u+v)-8 u sin(u) v^2 h^2-8 sin(2 u) h^2 u v^2-8 sin(2 v) h^2 u^2 v-8 v h^2 sin(v) u^2-4 v u^2 h^2 sin(2 u+v)+4 u v^2 h^2 sin(2 u+v)-8 v u^2 h^2 sin(u-v)+8 sin(u-v) h^2 u v^2+8 v u^2 h^2 sin(u+v)+8 sin(u+v) h^2 u v^2-4 v u^2 h^2 sin(u-2 v)-4 u v^2 h^2 sin(u-2 v)+4 v u^2 h^2 sin(u+2 v)-4 u v^2 h^2 sin(u+2 v)+4 v u^2 h^2 sin(2 u-v)+4 u v^2 h^2 sin(2 u-v)+4 u v h^2 cos(2 u-v)-4 u v h^2 cos(2 u+v)+4 u v h^2 cos(u-2 v)-4 u v h^2 cos(u+2 v)+2 u v h^2 cos(2 u+2 v)-2 u v h^2 cos(2 u-2 v)-8 cos(u-v) h^2 u v+8 cos(u+v) h^2 u v+8 v^2 u^2 h^2-8 h^2 cos(u) u^2+2 cos(2 u) h^2 u^2-6 cos(2 u) h^2 v^2-6 cos(2 v) h^2 u^2+2 cos(2 v) h^2 v^2-8 h^2 cos(v) v^2+4 v^2 h^2 cos(2 u-v)+4 v^2 h^2 cos(2 u+v)+4 u^2 h^2 cos(u-2 v)+4 u^2 h^2 cos(u+2 v)-u^2 h^2 cos(2 u+2 v)-v^2 h^2 cos(2 u+2 v)-u^2 h^2 cos(2 u-2 v)-v^2 h^2 cos(2 u-2 v)) g[n+2])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)),u=0,32),polynom),v=0,32),polynom);