update readme and code comment

README.md

@@ -20,7 +20,7 @@ Related Package: [MathieuFunctions.jl](https://github.com/BBN-Q/MathieuFunctions
 nu,ck=MathieuExponent(a,q)
 ```
 where `nu` is the characteristic exponent and vector `ck` is the Fourier coefficients of the eigenfunction with `norm(ck)≈1`.
-Note that `nu` is reduced to the interval `[0,2]` and `c0` corresponds to `ck[(length(ck)-1)÷2]` with the reduced `nu`.
+Note that `nu` is reduced to the interval `[0,2]` and `c0` corresponds to `ck[(length(ck)-1)÷2]` with the reduced `nu`. (For `nu` is real, the procedure actually reduces `nu` into `[0,1]`).
 
 ```julia
 W=MathieuWron(nu,ck::Vector,index::Int)
@@ -33,10 +33,22 @@ nu,ck=MathieuExponent(a,q)
 idx=(length(ck)-1)÷2+1
 W=MathieuWron(nu,ck,idx)
 ```
+In some cases, `W` could be negative. One can replace `nu` with `-nu` and reverse `ck`, i.e., `reverse!(ck)`, to get a positive `W`.
+If one prefers a positive `nu`, one can further shift `nu` with `nu+=2`. 
+In this case, `idx` should be `idx+=1`.
+Code example:
+```julia
+nu=2-nu
+reverse!(ck)
+idx=idx+=1
+W_new=MathieuWron(nu,ck,idx)
+```
+It can be verified that `W_new==-W`.
 
 If one knows `nu` (not reduced) and `q`, one can use
 ```julia
 W=MathieuWron(nu,q)
 ```
+During my test, the result is positive with such method.
 
 

src/char-coeff-new-indexing.jl

@@ -118,19 +118,21 @@ function MathieuCharVecWronλ(ν::Real,q::Real)
 end
 
 """
+`W=MathieuWron(ν,q)` or `W=MathieuWron(ν,C_k,index)`.
+
 Return the Wronskian.
 
 For Mathieu's equation
 
-y'' + (B_ν - 2 q cos( 2z )) y = 0,
+y'' + (a- 2 q cos( 2z )) y = 0,
 
 the Wronskian is defined by 
 
 ```math
 \\frac{\\dot{f} f^*-f \\dot{f^*}}{2i}
 ```
 
-where ``f=e^{i\\nu z}\\sum_k{C_{2k}e^{i2kz}}`` with ``\\sum_k{C_{2k}^2}=1`` is the solution of the Mathieu equation and ``f^*`` is its complex conjugate. 
+where ``f=e^{i\\nu z}\\sum_k{C_{k}e^{i2kz}}`` with ``\\sum_k{C_{k}^2}=1`` is the solution of the Mathieu equation and ``f^*`` is its complex conjugate. 
 """
 function MathieuWron(ν,q)
     _,C_2k,index=MathieuCharVecλ(ν,q)