More docsssss

docs/src/man/manual.md

@@ -34,12 +34,13 @@ maxima>
 
 # Maxima Expressions
 
-Maxima.jl revolves around the Maxima expression type: `MExpr`. Maxima expressions can be constructed using a constructor or a string macro. 
+Maxima.jl revolves around the Maxima expression type: `MExpr`. Maxima expressions can be constructed using a constructor or a string macro and evaluated with `mcall`. 
 
 ```@repl
 using Maxima # hide
 MExpr("sin(x)/x")
 m"integrate(1 + x^2, x)"
+mcall(ans)
 ```
 
 Maxima expressions don't neccessarily need to be valid Maxima, but a warning will be printed when the expression is printed and an error will be thrown if the expression is evaluated. 
@@ -52,19 +53,39 @@ m"1/0"
 mcall(ans)
 ```
 
-Maxima expressions can be evaluated using `mcall`.
+Maxima.jl also allows for translation between Maxima and Julia expressions. 
+
+```julia
+julia> g = m"atan(%i*%pi*y)"
+
+ %i atanh(%pi y)
+
+julia> parse(g)
+:(im * atanh(y * π))
+
+julia> exp = :(sin(π*im))
+:(sin(π * im))
+
+julia> mexp = MExpr(exp)
+
+ %i sinh(%pi)
 
-```@repl
-using Maxima # hide
-m"integrate(1/(1+x^2), x)"
-mcall(ans)
-mcall(m"1+")
 ```
 
-#  
+# Basic Library
 
+Maxima.jl wraps many of the basic Maxima functions for convenience and these functions may be applied to Maxima expressions, Julia expressions or basic strings. By convention, the return type of these functions is determined by the most important input type. For instance, the `integrate` function returns the type of the integrand. 
 
+```julia
+julia> integrate("sin(x)", :x)
+"-cos(x)"
 
+julia> integrate(:(sin(x)), "x")
+:(-cos(x))
 
+julia> integrate(m"sin(x)", 'x')
 
+ - cos(x)
 
+```
+As you can see, the basic library functions are very flexible about their argument types. Basically, as long as the argument string interpolates to the thing you want then it will work. For a list of all the functions that are wrapped take a look through the library reference section of the documentation.