Add free resolutions

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
 ----------------------------------------------

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.
 
@@ -4296,6 +4296,9 @@ 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
 
@@ -5370,7 +5373,7 @@ 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

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/resolutions/free
+   sage/resolutions/graded
+
+.. include:: ../footer.txt

src/sage/interfaces/singular.py

@@ -1,31 +1,6 @@
 r"""
 Interface to Singular
 
-AUTHORS:
-
-- David Joyner and William Stein (2005): first version
-
-- Martin Albrecht (2006-03-05): code so singular.[tab] and x =
-  singular(...), x.[tab] includes all singular commands.
-
-- Martin Albrecht (2006-03-06): This patch adds the equality symbol to
-  singular. Also fix a problem in which " " as prompt means comparison
-  will break all further communication with Singular.
-
-- Martin Albrecht (2006-03-13): added current_ring() and
-  current_ring_name()
-
-- William Stein (2006-04-10): Fixed problems with ideal constructor
-
-- Martin Albrecht (2006-05-18): added sage_poly.
-
-- Simon King (2010-11-23): Reduce the overhead caused by waiting for
-  the Singular prompt by doing garbage collection differently.
-
-- Simon King (2011-06-06): Make conversion from Singular to Sage more flexible.
-
-- Simon King (2015): Extend pickling capabilities.
-
 Introduction
 ------------
 
@@ -37,7 +12,6 @@
 your computer; this should be the case, since Singular is included
 with Sage. The interface offers three pieces of functionality:
 
-
 #. ``singular_console()`` - A function that dumps you
    into an interactive command-line Singular session.
 
@@ -238,10 +212,6 @@
 An Important Concept
 --------------------
 
-AUTHORS:
-
-- Neal Harris
-
 The following illustrates an important concept: how Sage interacts
 with the data being used and returned by Singular. Let's compute a
 Groebner basis for some ideal, using Singular through Sage.
@@ -325,6 +295,34 @@
     [Ideal (z) of Multivariate Polynomial Ring in x, z over Number Field in p with defining polynomial p^2 - p - 1]
     sage: [ J.gens() for J in I.primary_decomposition("gtz")]
     [[z]]
+
+AUTHORS:
+
+- David Joyner and William Stein (2005): first version
+
+- Neal Harris (unknown): perhaps added "An Important Concept"
+
+- Martin Albrecht (2006-03-05): code so singular.[tab] and x =
+  singular(...), x.[tab] includes all singular commands.
+
+- Martin Albrecht (2006-03-06): This patch adds the equality symbol to
+  singular. Also fix a problem in which " " as prompt means comparison
+  will break all further communication with Singular.
+
+- Martin Albrecht (2006-03-13): added current_ring() and
+  current_ring_name()
+
+- William Stein (2006-04-10): Fixed problems with ideal constructor
+
+- Martin Albrecht (2006-05-18): added sage_poly.
+
+- Simon King (2010-11-23): Reduce the overhead caused by waiting for
+  the Singular prompt by doing garbage collection differently.
+
+- Simon King (2011-06-06): Make conversion from Singular to Sage more flexible.
+
+- Simon King (2015): Extend pickling capabilities.
+
 """
 
 # ****************************************************************************
@@ -1496,8 +1494,6 @@ def __bool__(self):
         P = self.parent()
         return P.eval('%s == 0' % self.name()) == '0'
 
-
-
     def sage_polystring(self):
         r"""
         If this Singular element is a polynomial, return a string
@@ -2069,7 +2065,6 @@ def set_ring(self):
         """
         self.parent().set_ring(self)
 
-
     def sage_flattened_str_list(self):
         """
         EXAMPLES::
@@ -2596,6 +2591,7 @@ def flush(self):
         """
         sys.stdout.flush()
 
+
 class SingularGBDefaultContext:
     """
     Within this context all Singular Groebner basis calculations are

src/sage/libs/singular/decl.pxd

@@ -1134,8 +1134,16 @@ cdef extern from "singular/kernel/GBEngine/kstd1.h":
     cdef extern int Kstd1_deg   # degBound, default 0
     cdef extern int Kstd1_mu    # multBound, default 0
 
+cdef extern from "singular/kernel/ideals.h":
+    ctypedef ideal * resolvente
+
 cdef extern from "singular/kernel/GBEngine/syz.h":
     ctypedef struct syStrategy "ssyStrategy":
+        resolvente fullres;
+        resolvente minres;
+        int length;
+        int regularity;
+        short list_length;
         short references
 
 cdef extern from "singular/polys/ext_fields/transext.h":

src/sage/libs/singular/function.pxd

@@ -19,6 +19,7 @@ from sage.libs.singular.decl cimport leftv, idhdl, syStrategy, matrix, poly, ide
 from sage.libs.singular.decl cimport ring as singular_ring
 from sage.rings.polynomial.multi_polynomial_libsingular cimport MPolynomialRing_libsingular, MPolynomial_libsingular
 
+cdef new_sage_polynomial(ring,  poly *p)
 cdef poly* access_singular_poly(p) except <poly*> -1
 cdef singular_ring* access_singular_ring(r) except <singular_ring*> -1