update README to reflect its general applicability (#97)

* update README

* fix

* fix tests

README.md

@@ -1,6 +1,6 @@
 
 
-# Physical units and unit-aware mathematical system in JAX
+# ``BrainUnit``: physical units and unit-aware mathematical system for brain dynamics and AI4Science
 
 <p align="center">
   	<img alt="Header image of brainunit." src="https://github.com/chaobrain/brainunit/blob/main/docs/_static/brainunit.png" width=50%>
@@ -20,7 +20,56 @@
 </p>
 
 
-[``brainunit``](https://github.com/chaor/brainunit) provides physical units and unit-aware mathematical system in JAX for brain dynamics and AI4Science
+## Motivation
+
+
+[``brainunit``](https://github.com/chaobrain/brainunit) provides physical units and unit-aware mathematical system in JAX for brain dynamics and AI4Science. 
+
+It is initially designed to enable unit-aware computations in brain dynamics modeling (see our [ecosystem](https://ecosystem-for-brain-dynamics.readthedocs.io/)).
+
+However, its features and capacities can be applied to general domains for scientific computing and AI for science. 
+We also provide ample examples and tutorials to help users integrate ``brainunit`` into their projects 
+(see [Unit-aware computation ecosystem](#unit-aware-computation-ecosystem) in the below).
+
+
+## Features
+
+
+The uniqueness of ``Brainunit`` lies in that it brings physical units handling and AI-driven computation together in a seamless way:
+
+- It provides over 2,000 commonly used physical units and constants.
+- It implements over 500 unit-aware mathematical functions.
+- Its physical units and unit-aware functions are fully compatible with JAX, including autograd, JIT, vecterization, parallelization, and others.
+
+
+A quick example:
+
+```python
+
+import brainunit as u
+
+# Define a physical quantity
+x = 3.0 * u.meter
+x
+# [out] 3. * meter
+
+# autograd
+f = lambda x: x ** 3
+u.autograd.grad(f)(x)
+# [out] 27. * meter2 
+
+
+# JIT
+import jax
+jax.jit(f)(x)
+# [out] 27. * klitre
+
+# vmap
+jax.vmap(f)(u.math.arange(0. * u.mV, 10. * u.mV, 1. * u.mV))
+# [out]  ArrayImpl([  0.,   1.,   8.,  27.,  64., 125., 216., 343., 512., 729.],
+#                  dtype=float32) * mvolt3
+```
+
 
 
 ## Installation

brainunit/_base_test.py

@@ -30,6 +30,7 @@
 import jax.numpy as jnp
 import numpy as np
 import pytest
+from numpy.ma.core import indices
 from numpy.testing import assert_equal
 
 import brainunit as u
@@ -768,23 +769,23 @@ def test_deepcopy(self):
         assert d_copy["x"] == 2 * second
         assert d["x"] == 1 * second
 
-    def test_numpy_functions_indices(self):
+    def test_indices_functions(self):
         """
         Check numpy functions that return indices.
         """
         values = [np.array([-4, 3, -2, 1, 0]), np.ones((3, 3)), np.array([17])]
         units = [volt, second, siemens, mV, kHz]
 
         # numpy functions
-        keep_dim_funcs = [np.argmin, np.argmax, np.argsort, np.nonzero]
+        indice_funcs = [u.math.argmin, u.math.argmax, u.math.argsort, u.math.nonzero]
 
         for value, unit in itertools.product(values, units):
             q_ar = value * unit
-            for func in keep_dim_funcs:
+            for func in indice_funcs:
                 test_ar = func(q_ar)
                 # Compare it to the result on the same value without units
                 comparison_ar = func(value)
-                test_ar = np.asarray(test_ar)
+                test_ar = u.math.asarray(test_ar)
                 comparison_ar = np.asarray(comparison_ar)
                 assert_equal(
                     test_ar,