Fix spaces

sagemath · Aug 8, 2022 · ab725f2 · ab725f2
1 parent 3f1d1c3
commit ab725f2
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Showing 4 changed files with 23 additions and 32 deletions.
diff --git a/src/sage/homology/free_resolution.py b/src/sage/homology/free_resolution.py
@@ -16,9 +16,8 @@
 
  sage: from sage.homology.free_resolution import FreeResolution
  sage: S.<x,y,z,w> = PolynomialRing(QQ)
- sage: m1 = matrix(S, 1, [z^2 - y*w, y*z - x*w, y^2 - x*z]).transpose()
- sage: m2 = matrix(S, 3, [-y, x, z, -y, -w, z])
- sage: r = FreeResolution(m1, name='S')
+ sage: m = matrix(S, 1, [z^2 - y*w, y*z - x*w, y^2 - x*z]).transpose()
+ sage: r = FreeResolution(m, name='S')
  sage: r
  S^1 <-- S^3 <-- S^2 <-- 0
 
@@ -27,9 +26,6 @@
  sage: r
  S^1 <-- S^3 <-- S^2 <-- 0
 
- sage: FreeResolution(m2, name='S')
- S^2 <-- S^6 <-- S^5 <-- 0
-
 ::
 
  sage: from sage.homology.graded_resolution import GradedFreeResolution
@@ -57,6 +53,7 @@
 AUTHORS:
 
 - Kwankyu Lee (2022-05-13): initial version
+
 """
 
 # ****************************************************************************
@@ -83,17 +80,24 @@
 
 class FreeResolution_generic(SageObject):
  r"""
- Abstract base class of finite free resolutions.
+ Generic base class of finite free resolutions.
+
+ A subclass must provide a ``_maps`` attribute that contains a list of the
+ maps defining the resolution.
 
  The matrix at index `i` in the list defines the differential map from
- `(i+1)`-th free module to the `i`-th free module over the base ring by
+ `(i + 1)`-th free module to the `i`-th free module over the base ring by
  multiplication on the left. The number of matrices in the list is the
  length of the resolution. The number of rows and columns of the matrices
  define the ranks of the free modules in the resolution.
 
  Note that the first matrix in the list defines the differential map at
  homological index `1`.
 
+ A subclass can define ``_initial_differential`` attribute that
+ contains the `0`-th differential map whose codomain is the target
+ of the free resolution.
+
  EXAMPLES::
 
  sage: from sage.homology.free_resolution import FreeResolution
@@ -115,13 +119,6 @@ def __init__(self, base_ring, name='F'):
  """
  Initialize.
 
- Subclasses must provide a ``_maps`` attribute that contains the
- maps defining the resolution.
-
- A subclass can define ``_initial_differential`` attribute that
- contains the `0`-th differential map whose codomain is the target
- of the free resolution.
-
  INPUT:
 
  - ``base_ring`` -- a ring
@@ -421,7 +418,9 @@ class FreeResolution(FreeResolution_generic):
 
  - ``module`` -- a submodule of a free module `M` of rank `n` over `S` or
  an ideal of a multi-variate polynomial ring
+
  - ``name`` -- a string; name of the base ring
+
  - ``algorithm`` -- Singular algorithm to compute a resolution of ``ideal``
 
  OUTPUT: a minimal free resolution of the ideal

diff --git a/src/sage/homology/graded_resolution.py b/src/sage/homology/graded_resolution.py
@@ -60,6 +60,7 @@
 AUTHORS:
 
 - Kwankyu Lee (2022-05): initial version
+
 """
 
 # ****************************************************************************
@@ -92,12 +93,16 @@ class GradedFreeResolution(FreeResolution):
 
  - ``module`` -- a homogeneous submodule of a free module `M` of rank `n`
  over `S` or a homogeneous ideal of a multivariate polynomial ring `S`
+
  - ``degrees`` -- (default: a list with all entries `1`) a list of integers
  or integer vectors giving degrees of variables of `S`
+
  - ``shifts`` -- a list of integers or integer vectors giving shifts of
  degrees of `n` summands of the free module `M`; this is a list of zero
  degrees of length `n` by default
+
  - ``name`` -- a string; name of the base ring
+
  - ``algorithm`` -- Singular algorithm to compute a resolution of ``ideal``
 
  If ``module`` is an ideal of `S`, it is considered as a submodule of a
@@ -347,6 +352,7 @@ def betti(self, i, a=None):
  INPUT:
 
  - ``i`` -- nonnegative integer
+
  - ``a`` -- a degree; if ``None``, return Betti numbers in all degrees
 
  EXAMPLES::

diff --git a/src/sage/libs/singular/function.pyx b/src/sage/libs/singular/function.pyx
@@ -56,15 +56,10 @@ TESTS::
 AUTHORS:
 
 - Michael Brickenstein (2009-07): initial implementation, overall design
-
 - Martin Albrecht (2009-07): clean up, enhancements, etc
-
 - Michael Brickenstein (2009-10): extension to more Singular types
-
 - Martin Albrecht (2010-01): clean up, support for attributes
-
 - Simon King (2011-04): include the documentation provided by Singular as a code block
-
 - Burcin Erocal, Michael Brickenstein, Oleksandr Motsak, Alexander Dreyer, Simon King (2011-09): plural support
 
 """
@@ -757,7 +752,7 @@ cdef class Converter(SageObject):
 
  for j from 0 <= j < IDELEMS(i):
  p = self.to_sage_vector_destructive(i.m[j], free_module)
- i.m[j]=NULL # save it from getting freed
+ i.m[j] = NULL # save it from getting freed
  l.append( p )
 
  return Sequence(l, check=False, immutable=True)

diff --git a/src/sage/libs/singular/singular.pyx b/src/sage/libs/singular/singular.pyx
@@ -750,6 +750,7 @@ cpdef tuple si2sa_resolution_graded(Resolution res, tuple degrees):
  INPUT:
 
  - ``res`` -- Singular resolution
+
  - ``degrees`` -- list of integers or integer vectors
 
  The procedure is destructive, and ``res`` is not usable afterward.
@@ -868,7 +869,6 @@ cdef number *sa2si_QQ(Rational r, ring *_ring):
 
  - ``_ ring`` - a (pointer to) a singular ring, where the resul will live
 
-
  OUTPUT:
 
  - A (pointer to) a singular number
@@ -899,7 +899,6 @@ cdef number *sa2si_GFqGivaro(int quo, ring *_ring):
 
  - ``_ ring`` - a (pointer to) a singular ring, where the resul will live
 
-
  OUTPUT:
 
  - A (pointer to) a singular number
@@ -908,7 +907,6 @@ cdef number *sa2si_GFqGivaro(int quo, ring *_ring):
  generator. In this case, ``quo`` is the integer resulting from evaluating
  that polynomial in the characteristic of the field.
 
-
  TESTS::
 
  sage: F = FiniteField(5^2)
@@ -969,7 +967,6 @@ cdef number *sa2si_GFqNTLGF2E(FFgf2eE elem, ring *_ring):
 
  - ``_ ring`` - a (pointer to) a singular ring, where the resul will live
 
-
  OUTPUT:
 
  - A (pointer to) a singular number
@@ -1035,7 +1032,6 @@ cdef number *sa2si_GFq_generic(object elem, ring *_ring):
 
  - ``_ ring`` - a (pointer to) a singular ring, where the resul will live
 
-
  OUTPUT:
 
  - A (pointer to) a singular number
@@ -1102,7 +1098,6 @@ cdef number *sa2si_transext_QQ(object elem, ring *_ring):
 
  - ``_ ring`` - a (pointer to) a singular ring, where the resul will live
 
-
  OUTPUT:
 
  - A (pointer to) a singular number
@@ -1150,7 +1145,6 @@ cdef number *sa2si_transext_QQ(object elem, ring *_ring):
  sage: R(f)
  x + y + 1
  """
-
  cdef int j
  cdef number *n1
  cdef number *a
@@ -1255,7 +1249,6 @@ cdef number *sa2si_transext_FF(object elem, ring *_ring):
 
  - ``_ ring`` - a (pointer to) a singular ring, where the resul will live
 
-
  OUTPUT:
 
  - A (pointer to) a singular number
@@ -1357,7 +1350,6 @@ cdef number *sa2si_NF(object elem, ring *_ring):
 
  - ``_ ring`` - a (pointer to) a singular ring, where the resul will live
 
-
  OUTPUT:
 
  - A (pointer to) a singular number
@@ -1449,7 +1441,6 @@ cdef number *sa2si_ZZ(Integer d, ring *_ring):
 
  - ``_ ring`` - a (pointer to) a singular ring, where the resul will live
 
-
  OUTPUT:
 
  - A (pointer to) a singular number
@@ -1659,7 +1650,7 @@ cdef object si2sa_intvec(intvec *v):
 
  INPUT:
 
- - ``v`` - a (pointer to) a singular intvec
+ - ``v`` -- a (pointer to) a singular intvec
 
  OUTPUT: