better example in README

Author: videlec

README.rst

@@ -51,7 +51,26 @@ setup.py install`` will produce an error.
 Usage
 -----
 
-Here is an example of some PARI/GP computations in Python
+The interface as been kept as close as possible from PARI/GP. The following
+computation in GP
+
+::
+
+    ? zeta(2)
+    %1 = 1.6449340668482264364724151666460251892
+
+    ? p = x^3 + x^2 + x - 1;
+    ? modulus = t^3 + t^2 + t - 1;
+    ? fq = factorff(p, 3, modulus);
+    ? centerlift(lift(fq))
+    %5 =
+    [            x - t 1]
+
+    [x + (t^2 + t - 1) 1]
+
+    [   x + (-t^2 - 1) 1]
+
+translates into
 
 ::
 
@@ -61,12 +80,11 @@ Here is an example of some PARI/GP computations in Python
     >>> pari(2).zeta()
     1.64493406684823
 
-    >>> pari(2197).ispower(3)
-    (3, 13)
-
-    >>> K = pari("bnfinit(x^3 - 2)")
-    >>> K.bnfunit()
-    [x - 1]
+    >>> p = pari("x^3 + x^2 + x - 1")
+    >>> modulus = pari("t^3 + t^2 + t - 1")
+    >>> fq = p.factorff(3, modulus)
+    >>> fq.lift().centerlift()
+    [x - t, 1; x + (t^2 + t - 1), 1; x + (-t^2 - 1), 1]
 
 The object **pari** above is the object for the interface and acts as a
 constructor. It can be called with basic Python objects like integer
@@ -76,9 +94,27 @@ the corresponding string is interpreted as if it was executed in a GP shell.
 Beyond the interface object **pari** of type **Pari**, any object you get a
 handle on is of type **Gen** (that is a wrapper around the **GEN** type from
 libpari). All PARI/GP functions are then available in their original names as
-*methods* like **zeta**, **ispower** or **bnfunit** above.
+*methods* like **zeta**, **factorff**, **lift** or **centerlift** above.
+
+Alternatively, the pari functions are accessible as methods of **pari**. The
+same computations be done via
+
+::
+
+    >>> import cypari2
+    >>> pari = cypari2.Pari()
+
+    >>> pari.zeta(2)
+    1.64493406684823
+
+    >>> p = pari("x^3 + x^2 + x - 1")
+    >>> modulus = pari("t^3 + t^2 + t - 1")
+    >>> fq = pari.factorff(p, 3, modulus)
+    >>> pari.centerlift(pari.lift(fq))
+    [x - t, 1; x + (t^2 + t - 1), 1; x + (-t^2 - 1), 1]
 
-The complete documentation is available at http://cypari2.readthedocs.io
+The complete documentation of cypari2 is available at http://cypari2.readthedocs.io and
+the PARI/GP documentation at http://pari.math.u-bordeaux.fr/doc.html
 
 Contributing
 ------------