diff --git a/src/doc/en/reference/references/index.rst b/src/doc/en/reference/references/index.rst index eefbaf1f4d2..190915f9c82 100644 --- a/src/doc/en/reference/references/index.rst +++ b/src/doc/en/reference/references/index.rst @@ -2392,6 +2392,10 @@ REFERENCES: toric varieties defined by atomic lattices*. Inventiones Mathematicae. **155** (2004), no. 3, pp. 515-536. +.. [FZ2001] \S. Fomin and A. Zelevinsky. *Cluster algebras I. Foundations*, + \J. Amer. Math. Soc. **15** (2002), no. 2, pp. 497-529. + :arxiv:`math/0104151` (2001). + .. [FZ2007] \S. Fomin and \A. Zelevinsky, *Cluster algebras IV. Coefficients*, Compos. Math. 143 (2007), no. 1, 112-164. diff --git a/src/doc/en/thematic_tutorials/geometry/polyhedra_tutorial.rst b/src/doc/en/thematic_tutorials/geometry/polyhedra_tutorial.rst index bf6ff21766b..d657d0cb2af 100644 --- a/src/doc/en/thematic_tutorials/geometry/polyhedra_tutorial.rst +++ b/src/doc/en/thematic_tutorials/geometry/polyhedra_tutorial.rst @@ -791,17 +791,17 @@ polytope is already defined! Bibliography ============= -.. [Bro1983] Brondsted, A., An Introduction to Convex Polytopes, volume 90 - of Graduate Texts in Mathematics. Springer-Verlag, New York, 1983. ISBN - 978-1-4612-7023-2 +.. [Bro1983] \A. Brondsted, An Introduction to Convex Polytopes, volume 90 + of Graduate Texts in Mathematics. Springer-Verlag, New York, 1983. + ISBN 978-1-4612-7023-2 -.. [Goo2004] J.E. Goodman and J. O'Rourke, editors, CRC Press LLC, Boca Raton, FL, 2004. +.. [Goo2004] \J. E. Goodman and J. O'Rourke, editors, CRC Press LLC, Boca Raton, FL, 2004. ISBN 978-1584883012 (65 chapters, xvii + 1539 pages). -.. [Gru1967] Grünbaum, B., Convex polytopes, volume 221 of Graduate Texts in - Mathematics. Springer-Verlag, New York, 2003. ISBN - 978-1-4613-0019-9 +.. [Gru1967] \B. Grünbaum, Convex polytopes, volume 221 of Graduate Texts in + Mathematics. Springer-Verlag, New York, 2003. + ISBN 978-1-4613-0019-9 -.. [Zie2007] Ziegler, G. M., Lectures on polytopes, volume 152 of Graduate +.. [Zie2007] \G. M. Ziegler, Lectures on polytopes, volume 152 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2007. ISBN 978-0-387-94365-7 diff --git a/src/sage/coding/self_dual_codes.py b/src/sage/coding/self_dual_codes.py index 132eb9b10cc..ca7f80cfc4f 100644 --- a/src/sage/coding/self_dual_codes.py +++ b/src/sage/coding/self_dual_codes.py @@ -68,7 +68,7 @@ SD codes not of this form will be called (for the purpose of documenting the code below) "exceptional". Except when n is "small", most sd codes are exceptional (based on a counting -argument and table 9.1 in the Huffman+Pless [HP2003], page 347). +argument and table 9.1 in the Huffman+Pless [HP2003]_, page 347). +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ @@ -78,12 +78,11 @@ REFERENCES: -- [HP2003] W. C. Huffman, V. Pless, Fundamentals of +- [HP2003] \W. C. Huffman, V. Pless, Fundamentals of Error-Correcting Codes, Cambridge Univ. Press, 2003. -- [P] V. Pless, - "A classification of self-orthogonal codes over GF(2)", Discrete - Math 3 (1972) 209-246. +- [P] \V. Pless, "A classification of self-orthogonal codes over GF(2)", + Discrete Math 3 (1972) 209-246. """ from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF @@ -270,7 +269,7 @@ def self_dual_binary_codes(n): 22, 22, 30, 30, 42, 42, 56, 56, 77, 77, 101, 101, 135, 135, 176, 176, 231] These numbers grow too slowly to account for all the sd codes (see Huffman+Pless' Table 9.1, referenced above). In fact, in - Table 9.10 of [HP2003], the number B_n of inequivalent sd binary codes + Table 9.10 of [HP2003]_, the number B_n of inequivalent sd binary codes of length n is given:: n 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 diff --git a/src/sage/combinat/rsk.py b/src/sage/combinat/rsk.py index 5e5ffa82526..9bc3f1d8720 100644 --- a/src/sage/combinat/rsk.py +++ b/src/sage/combinat/rsk.py @@ -138,7 +138,7 @@ .. [EG1987] Paul Edelman, Curtis Greene. *Balanced Tableaux*. Advances in Mathematics 63 (1987), pp. 42-99. - https://doi.org/10.1016/0001-8708(87)90063-6 + :doi:`10.1016/0001-8708(87)90063-6` .. [BKSTY06] \A. Buch, A. Kresch, M. Shimozono, H. Tamvakis, and A. Yong. *Stable Grothendieck polynomials and* `K`-*theoretic factor sequences*. @@ -147,7 +147,7 @@ .. [GR2018v5sol] Darij Grinberg, Victor Reiner. *Hopf Algebras In Combinatorics*, - :arXiv:`1409.8356v5`, available with solutions at + :arxiv:`1409.8356v5`, available with solutions at https://arxiv.org/src/1409.8356v5/anc/HopfComb-v73-with-solutions.pdf """ @@ -515,6 +515,7 @@ def _backward_format_output(self, lower_row, upper_row, output, "q must be standard to have a %s as valid output" %output) raise ValueError("invalid output option") + class RuleRSK(Rule): r""" Rule for the classical Robinson-Schensted-Knuth insertion. diff --git a/src/sage/groups/abelian_gps/abelian_group.py b/src/sage/groups/abelian_gps/abelian_group.py index 514f68fd629..5ae1a14a997 100644 --- a/src/sage/groups/abelian_gps/abelian_group.py +++ b/src/sage/groups/abelian_gps/abelian_group.py @@ -57,7 +57,7 @@ (4, f4, 4) Background on invariant factors and the Smith normal form -(according to section 4.1 of [C1]): An abelian group is a +(according to section 4.1 of [Cohen1]_): An abelian group is a group `A` for which there exists an exact sequence `\ZZ^k \rightarrow \ZZ^\ell \rightarrow A \rightarrow 1`, for some positive integers @@ -151,13 +151,13 @@ REFERENCES: -- [C1] H. Cohen Advanced topics in computational number theory, +.. [Cohen1] \H. Cohen, Advanced topics in computational number theory, Springer, 2000. -- [C2] ----, A course in computational algebraic number theory, +.. [Cohen2] \H. Cohen, A course in computational algebraic number theory, Springer, 1996. -- [R] J. Rotman, An introduction to the theory of +.. [Rotman] \J. Rotman, An introduction to the theory of groups, 4th ed, Springer, 1995. .. warning:: @@ -165,7 +165,6 @@ Many basic properties for infinite abelian groups are not implemented. - AUTHORS: - William Stein, David Joyner (2008-12): added (user requested) is_cyclic, diff --git a/src/sage/matrix/matrix0.pyx b/src/sage/matrix/matrix0.pyx index 88d9c2af4d0..41b8da5f415 100644 --- a/src/sage/matrix/matrix0.pyx +++ b/src/sage/matrix/matrix0.pyx @@ -1589,7 +1589,7 @@ cdef class Matrix(sage.structure.element.Matrix): ########################################################### def base_ring(self): """ - Returns the base ring of the matrix. + Return the base ring of the matrix. EXAMPLES:: @@ -2270,7 +2270,7 @@ cdef class Matrix(sage.structure.element.Matrix): def dimensions(self): r""" - Returns the dimensions of this matrix as the tuple (nrows, ncols). + Return the dimensions of this matrix as the tuple (nrows, ncols). EXAMPLES:: @@ -2293,7 +2293,7 @@ cdef class Matrix(sage.structure.element.Matrix): ################################################### def act_on_polynomial(self, f): """ - Returns the polynomial f(self\*x). + Return the polynomial f(self\*x). INPUT: @@ -3599,8 +3599,7 @@ cdef class Matrix(sage.structure.element.Matrix): REFERENCES: - - [FZ2001] S. Fomin, A. Zelevinsky. *Cluster Algebras 1: Foundations*, - :arxiv:`math/0104151` (2001). + - [FZ2001]_ """ cdef Py_ssize_t i, j, _ cdef list pairs, k0_pairs, k1_pairs @@ -3707,8 +3706,7 @@ cdef class Matrix(sage.structure.element.Matrix): REFERENCES: - - [FZ2001] S. Fomin, A. Zelevinsky. *Cluster Algebras 1: Foundations*, - :arxiv:`math/0104151` (2001). + - [FZ2001]_ """ cdef dict d = {} cdef list queue = list(xrange(self._ncols)) @@ -3905,7 +3903,7 @@ cdef class Matrix(sage.structure.element.Matrix): def is_symmetric(self): """ - Returns True if this is a symmetric matrix. + Return True if this is a symmetric matrix. A symmetric matrix is necessarily square. @@ -4311,8 +4309,7 @@ cdef class Matrix(sage.structure.element.Matrix): REFERENCES: - - [FZ2001] S. Fomin, A. Zelevinsky. *Cluster Algebras 1: Foundations*, - :arxiv:`math/0104151` (2001). + - [FZ2001]_ """ if self._ncols != self._nrows: raise ValueError("The matrix is not a square matrix") @@ -4363,8 +4360,7 @@ cdef class Matrix(sage.structure.element.Matrix): REFERENCES: - - [FZ2001] S. Fomin, A. Zelevinsky. *Cluster Algebras 1: Foundations*, - :arxiv:`math/0104151` (2001). + - [FZ2001]_ """ if self._ncols != self._nrows: raise ValueError("The matrix is not a square matrix") @@ -4372,7 +4368,7 @@ cdef class Matrix(sage.structure.element.Matrix): def is_dense(self): """ - Returns True if this is a dense matrix. + Return True if this is a dense matrix. In Sage, being dense is a property of the underlying representation, not the number of nonzero entries. @@ -4470,7 +4466,7 @@ cdef class Matrix(sage.structure.element.Matrix): def is_singular(self): r""" - Returns ``True`` if ``self`` is singular. + Return ``True`` if ``self`` is singular. OUTPUT: @@ -4679,7 +4675,7 @@ cdef class Matrix(sage.structure.element.Matrix): def _nonzero_positions_by_row(self, copy=True): """ - Returns the list of pairs ``(i,j)`` such that ``self[i,j] != 0``. + Return the list of pairs ``(i,j)`` such that ``self[i,j] != 0``. It is safe to change the resulting list (unless you give the option ``copy=False``). @@ -4708,7 +4704,7 @@ cdef class Matrix(sage.structure.element.Matrix): def _nonzero_positions_by_column(self, copy=True): """ - Returns the list of pairs ``(i,j)`` such that ``self[i,j] != 0``, but + Return the list of pairs ``(i,j)`` such that ``self[i,j] != 0``, but sorted by columns, i.e., column ``j=0`` entries occur first, then column ``j=1`` entries, etc. @@ -4963,14 +4959,12 @@ cdef class Matrix(sage.structure.element.Matrix): ################################################### cdef _vector_times_matrix_(self, Vector v): """ - Returns the vector times matrix product. + Return the vector times matrix product. INPUT: - - ``v`` - a free module element. - OUTPUT: The vector times matrix product v\*A. EXAMPLES::