Update README.md

README.md

@@ -43,7 +43,7 @@ Filled box refers to implemented or interfaced code.
  - [x] [Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures](https://arxiv.org/abs/2306.03801) provides fast representations of multiparameter persistence modules, by using their signed barcodes decompositions, and encoding it into signed measures. Implemented decompositions : Euler surfaces, Hilbert function, rank invariant (i.e. rectangles). It also provides representation technics for Machine Learning, i.e., Sliced Wasserstein kernels, Vectorizations.
  - [x] [A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions](https://arxiv.org/abs/2306.11170) Provides a vectorization framework for interval decomposable modules, for Machine Learning. Currently implemented as an extension of MMA.
  - [x] [Filtration-Domination in Bifiltered Graphs](https://doi.org/10.1137/1.9781611977561.ch3) Allows for 2-parameter edge collapses for 1-critical clique complexes. **Very useful** to speed up, e.g., Rips-Codensity bifiltrations. 
- - [x] [Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology](https://arxiv.org/abs/1902.05708) Minimal presentation of multiparameter persistence modules, using [mpfree](https://bitbucket.org/mkerber/mpfree/src/master/). Hilbert Decomposition Signed Measures can be computed using the mpfree backend.
+ - [x] [Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology](https://arxiv.org/abs/1902.05708) Minimal presentation of multiparameter persistence modules, using [mpfree](https://bitbucket.org/mkerber/mpfree/src/master/). Hilbert Decomposition Signed Measures, and MMA decompositions can be computed using the mpfree backend.
  - [ ] [Projected distances for multi-parameter persistence modules](https://arxiv.org/abs/2206.08818) Provides a strategy to estimate the convolution distance between multiparameter persistence module using projected barcodes. Implementation is a WIP.
  - [ ] [Delaunay Bifiltrations of Functions on Point Clouds](https://arxiv.org/abs/2310.15902) Provides an alternative to function rips bifiltrations, using Delaunay complexes.
  - [ ] [Efficient Two-Parameter Persistence Computation via Cohomology](https://doi.org/10.4230/LIPIcs.SoCG.2023.15) Minimal presentations for 2-parameter persistence clique complexes.
@@ -72,19 +72,26 @@ Due to the clang compiler, one may have to disable a compilator optimization to
 ```
 line in the `extra_compile_args` list. You should have should end up with something like the following.
 ```python
-extensions = [Extension(f"multipers.{module}",
-	sources=[f"multipers/{module}.pyx"],
-	language='c++',
-	extra_compile_args=[
-		"-Ofast",
-		"-std=c++20",
-		"-fno-aligned-new",
-		'-ltbb',
-		"-Wall",
-	],
-	extra_link_args=['-ltbb'],
-	define_macros=[("NPY_NO_DEPRECATED_API", "NPY_1_7_API_VERSION")],
-) for module in cython_modules]
+extensions = [
+    Extension(
+        f"multipers.{module}",
+        sources=[
+            f"multipers/{module}.pyx",
+        ],
+        language="c++",
+        extra_compile_args=[
+            "-Ofast",
+            "-std=c++20",
+            "-fno-aligned-new", # Uncomment this if you have trouble compiling on macos.
+            "-Wall",
+        ],
+        include_dirs=cpp_dirs,
+        define_macros=[("NPY_NO_DEPRECATED_API", "NPY_1_7_API_VERSION")],
+        libraries=["tbb", "tbbmalloc"],
+        library_dirs=library_dirs,
+    )
+    for module in cython_modules
+]
 ```
 #### Alternatives
 One may try to use the `clang` compiler provided by conda or brew. If you have a simpler alternative, please let me know ;)