Trac #33950: Add free and multigraded free resolutions with libSingul…

…ar backend Sage lacks free resolution computation. We add free and multigraded free resolutions pulling libSingular's resolutions. This will be a ground work for further commutative algebra and algebraic geometry computations. URL: https://trac.sagemath.org/33950 Reported by: klee Ticket author(s): Kwankyu Lee, Travis Scrimshaw Reviewer(s): Travis Scrimshaw, Kwankyu Lee
sagemath · Aug 29, 2022 · 8f6d1ac · 8f6d1ac
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diff --git a/src/doc/en/reference/index.rst b/src/doc/en/reference/index.rst
@@ -92,18 +92,22 @@ Discrete Mathematics
 * :doc:`Symbolic Logic <logic/index>`
 * :doc:`SAT solvers <sat/index>`
 
-Geometry, Topology, and Homological Algebra
--------------------------------------------
+Geometry and Topology
+---------------------
 
 * :doc:`Euclidean Spaces and Vector Calculus <euclidean_spaces/index>`
 * :doc:`Combinatorial and Discrete Geometry <discrete_geometry/index>`
-* :doc:`Cell Complexes, Simplicial Complexes, and
-  Simplicial Sets <topology/index>`
+* :doc:`Cell Complexes, Simplicial Complexes, and Simplicial Sets <topology/index>`
 * :doc:`Manifolds and Differential Geometry <manifolds/index>`
 * :doc:`Hyperbolic Geometry <hyperbolic_geometry/index>`
 * :doc:`Parametrized Surfaces <riemannian_geometry/index>`
 * :doc:`Knot Theory <knots/index>`
+
+Homological Algebra
+-------------------
+
 * :doc:`Chain Complexes and their Homology <homology/index>`
+* :doc:`Resolutions <resolutions/index>`
 
 Number Fields, Function Fields, and Valuations
 ----------------------------------------------

diff --git a/src/doc/en/reference/references/index.rst b/src/doc/en/reference/references/index.rst
@@ -95,7 +95,7 @@ REFERENCES:
              graphs and isoperimetric inequalities*, The Annals of Probability
              32 (2004), no.  3A, 1727-1745.
 
-.. [ASV2020] Federico Ardila, Mariel Supina, and Andrés R. Vindas-Meléndez, 
+.. [ASV2020] Federico Ardila, Mariel Supina, and Andrés R. Vindas-Meléndez,
          *The Equivariant Ehrhart Theory of the Permutahedron*,
          Proc. Amer. Math. Soc. Volume 148, Number 12, 2020, pp. 5091--5107.
 
@@ -4342,6 +4342,9 @@ REFERENCES:
              polynomials*. Trans. Amer. Math. Soc., 245 (1978),
              89-118.
 
+.. [MilStu2005] Ezra Miller and Bernd Sturmfels, *Combinatorial Commutative Algebra*,
+                GTM Vol. 227, Springer Science & Business Media, 2005.
+
 .. [Mil2004] Victor S. Miller, "The Weil pairing, and its
              efficient calculation", J. Cryptol., 17(4):235-261, 2004
 
@@ -5430,7 +5433,7 @@ REFERENCES:
 .. [St1986] Richard Stanley. *Two poset polytopes*,
             Discrete Comput. Geom. (1986), :doi:`10.1007/BF02187680`
 
-.. [Stap2011] Alan Stapledon. *Equivariant Ehrhart Theory*. 
+.. [Stap2011] Alan Stapledon. *Equivariant Ehrhart Theory*.
               Advances in Mathematics 226 (2011), no. 4, 3622-3654
 
 .. [Sta1973] \H. M. Stark, Class-Numbers of Complex Quadratic

diff --git a/src/doc/en/reference/resolutions/conf.py b/src/doc/en/reference/resolutions/conf.py
@@ -0,0 +1 @@
+../conf_sub.py
diff --git a/src/doc/en/reference/resolutions/index.rst b/src/doc/en/reference/resolutions/index.rst
@@ -0,0 +1,13 @@
+Resolutions
+===========
+
+Free and graded resolutions are tools for commutative algebra and algebraic
+geometry.
+
+.. toctree::
+   :maxdepth: 2
+
+   sage/homology/free_resolution
+   sage/homology/graded_resolution
+
+.. include:: ../footer.txt