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site/index.markdown

@@ -6,14 +6,88 @@ description: Symtegration is a Haskell library for symbolic integration.
 
 Symtegration is a Haskell library intended to support symbolic integration of mathematical expressions.
 
+It offers the following:
+
+*   Symbolic integration of mathematical expressions.
+
+    *   Integration of polynomials.
+
+    *   Integration of trigonometric functions.
+
+    *   Integration of exponential and logarithmic functions.
+
+    *   Partial support for integrating ratios of two polynomials.
+
+    *   Integration by substitution.
+
+*   Symbolic representation of mathematical expressions.
+
+*   Utility functions to make it easier to read the mathematical expressions.
+    For example, deriving equivalent Haskell code for a mathematical expression,
+    and some support for simplifying symbolic representations.
+
+## Integration {#integration}
+
+Mathematical expressions with either numeric coefficients or symbolic coefficients
+can be integrated.  For example:
+
 ```haskell
->>> :load Symtegration
+>>> import Symtegration
 >>> toHaskell <$> integrate "x" (4 * "x" **3 + 1)
 Just "x + (x ** 4)"
 >>> toHaskell <$> integrate "x" (1 / (1 + "x" ** 2))
 Just "atan x"
 ```
 
+Concrete numbers can also be computed from these integrals.  For example:
+
+```haskell
+>>> import Symtegration
+>>> let (Just p) = integrate "x" (4 * "x" ** 3 + 1)
+>>> fractionalEvaluate p (\case "x" -> Just (3 / 7 :: Rational))
+Just (1110 % 2401)
+```
+
+### Symbolic integration in GHCi {#ghci}
+
+With Symtegration, symbolic integration can be done within [GHCi].
+When executing GHCi within the Symtegration project, it is best
+to load only the `Symtegration` module to avoid name collisions,
+so start GHCi without loading any modules.
+
+```shell
+$ stack ghci --no-load
+```
+
+Within GHCi, explicitly load the `Symtegration` module.
+You can then proceed to symbolically integrate mathematical expressions
+and compute approximate or exact values from these integrals.
+
+```haskell
+>>> :load Symtegration
+>>> toHaskell <$> integrate "x" ("a" * "x" ** 4 + "x" + "b")
+Just "b * x + (1 / 2) * (x ** 2) + a * ((x ** 5) / 5)"
+>>>
+>>> let (Just p) = integrate "x" ("x" ** 2)
+>>> evaluate p (\case "x" -> Just 1)
+Just 0.3333333333333333
+>>>
+>>> fractionalEvaluate p (\case "x" -> Just (1 :: Rational))
+Just (1 % 3)
+```
+
+[GHCi]: https://downloads.haskell.org/ghc/latest/docs/users_guide/ghci.html
+
+### Symblic integration in IHaskell {#ihaskell}
+
+Symtegration can also be used in [IHaskell] to do symbolic integration.
+Its use can be seen in an [example IHaskell notebook],
+which you try out by [running on mybinder.org].
+
+[IHaskell]: https://github.com/IHaskell/IHaskell
+[example IHaskell notebook]: https://github.com/chungyc/haskell-notebooks/blob/main/Symtegration.ipynb
+[running on mybinder.org]: https://mybinder.org/v2/gh/chungyc/ihaskell/custom?urlpath=git-pull%3Frepo%3Dhttps%253A%252F%252Fgithub.heygears.com%252Fchungyc%252Fhaskell-notebooks%26urlpath%3Dlab%252Ftree%252Fhaskell-notebooks%252FSymtegration.ipynb%26branch%3Dmain
+
 ## Project information {#information}
 
 *   [Source repository](https://github.com/symtegration/symtegration)

site/style/default.lhs

@@ -108,7 +108,7 @@ listsStyle = do
 \begin{code}
 codeStyle :: Css
 codeStyle = do
-  div # ".sourceCode" ? do
+  div # ".sourceCode" <> pre # ".shell" ? do
     borderStyle solid
     borderWidth $ px 1
     marginTop $ em 1
@@ -147,6 +147,9 @@ lightColorScheme = do
 
   a # link ? color blue
   a # visited ? color purple
+
+  h1 ? do
+    color $ rgb 0 0 125
 \end{code}
 
 \begin{code}
@@ -158,4 +161,7 @@ darkColorScheme = do
 
   a # link ? color cyan
   a # visited ? color pink
+
+  h1 ? do
+    color $ rgb 255 255 125
 \end{code}

site/template/default.html

@@ -48,7 +48,7 @@ <h1>$title$</h1>
     </main>
 
     <footer>
-      <p>Content licensed under the <a href="/LICENSE">Apache-2.0 license</a></p>
+      <p>Content licensed under the <a href="/LICENSE">Apache-2.0 license</a>.</p>
     </footer>
   </body>
 </html>