remove most references to Arb as an independent library

COPYING.txt

@@ -31,7 +31,6 @@ the licenses of the components of Sage are included below as well.
 
 SOFTWARE                    LICENSE
 -----------------------------------------------------------------------
-arb                         GPLv2+
 boehm_gc                    MIT-like license (see below)
 backports_ssl_match_hostname  Python License
 boost_cropped               Boost Software License (see below)

build/bin/sage-package

@@ -15,7 +15,6 @@
 #
 #   $ sage-package list
 #   4ti2
-#   arb
 #   autotools
 #   [...]
 #   zlib

build/sage_bootstrap/app.py

@@ -57,18 +57,18 @@ def list_cls(self, *package_classes, **filters):
 
         $ sage --package list
         4ti2
-        arb
-        autotools
+        _bootstrap
+        _develop
         [...]
         zlib
 
         $ sage -package list --has-file=spkg-configure.m4 :experimental:
         perl_term_readline_gnu
 
         $ sage -package list --has-file=spkg-configure.m4 --has-file=distros/debian.txt
-        arb
-        boost_cropped
-        brial
+        4ti2
+        _develop
+        _prereq
         [...]
         zlib
         """

build/sage_bootstrap/cmdline.py

@@ -70,14 +70,11 @@
 
     $ sage --package list
     4ti2
-    arb
-    autotools
     [...]
     zlib
 
     $ sage --package list :standard:
-    arb
-    backports_ssl_match_hostname
+    _prereq
     [...]
     zlib
 """

src/doc/en/developer/portability_testing.rst

@@ -243,21 +243,22 @@ At the end of the ``./configure`` run, Sage issued a message like the
 following::
 
   configure: notice: the following SPKGs did not find equivalent system packages:
-                     arb boost_cropped bzip2 ... zeromq zlib
+                     boost_cropped bzip2 ... zeromq zlib
   checking for the package system in use... debian
   configure: hint: installing the following system packages is recommended and
                    may avoid building some of the above SPKGs from source:
-  configure:   $ sudo apt-get install libflint-arb-dev ... libzmq3-dev libz-dev
+  configure:   $ sudo apt-get install ... libzmq3-dev libz-dev
   configure: After installation, re-run configure using:
   configure:   $ make reconfigure
 
 This information comes from Sage's database of equivalent system
 packages.  For example::
 
-  root@39d693b2a75d:/sage# ls build/pkgs/arb/distros/
-  arch.txt	conda.txt	debian.txt	gentoo.txt
-  root@39d693b2a75d:/sage# cat build/pkgs/arb/distros/debian.txt
-  libflint-arb-dev
+  $ ls build/pkgs/flint/distros/
+  alpine.txt  cygwin.txt  fedora.txt   gentoo.txt    macports.txt  opensuse.txt  void.txt
+  conda.txt   debian.txt  freebsd.txt  homebrew.txt  nix.txt       repology.txt
+  $ cat build/pkgs/flint/distros/debian.txt
+  libflint-dev
 
 Note that these package equivalencies are based on a current stable or
 testing version of the distribution; the packages are not guaranteed
@@ -885,7 +886,7 @@ an isolated copy of Homebrew with all prerequisites for bootstrapping::
   checking for a BSD-compatible install... /usr/bin/install -c
   checking whether build environment is sane... yes
   ...
-  configure: notice: the following SPKGs did not find equivalent system packages: arb cbc cliquer ... tachyon xz zeromq
+  configure: notice: the following SPKGs did not find equivalent system packages: cbc cliquer ... tachyon xz zeromq
   checking for the package system in use... homebrew
   configure: hint: installing the following system packages is recommended and may avoid building some of the above SPKGs from source:
   configure:   $ brew install cmake gcc gsl mpfi ninja openblas gpatch r readline xz zeromq
@@ -1085,7 +1086,7 @@ Scrolling down in the right pane shows "Annotations":
 
        docker (fedora-31, standard)
        artifacts/logs-commit-8ca1c2df8f1fb4c6d54b44b34b4d8320ebecb164-tox-docker-fedora-31-standard/config.log#L1
-       configure: notice: the following SPKGs did not find equivalent system packages: arb cbc cddlib cmake eclib ecm fflas_ffpack flint fplll givaro gp
+       configure: notice: the following SPKGs did not find equivalent system packages: cbc cddlib cmake eclib ecm fflas_ffpack flint fplll givaro gp
 
 Clicking on the annotations does not take you to a very useful
 place. To view details, click on one of the items in the pane. This

src/doc/en/reference/rings_numerical/index.rst

@@ -28,7 +28,7 @@ Interval Arithmetic
 -------------------
 
 Sage implements real and complex interval arithmetic using MPFI
-(RealIntervalField, ComplexIntervalField) and arb (RealBallField,
+(RealIntervalField, ComplexIntervalField) and FLINT (RealBallField,
 ComplexBallField).
 
 .. toctree::

src/sage/arith/misc.py

@@ -291,8 +291,10 @@ def bernoulli(n, algorithm='default', num_threads=1):
       - ``'default'`` -- use 'flint' for n <= 20000, then 'arb' for n <= 300000
         and 'bernmm' for larger values (this is just a heuristic, and not guaranteed
         to be optimal on all hardware)
-      - ``'arb'`` -- use the arb library
-      - ``'flint'`` -- use the FLINT library
+      - ``'arb'`` -- use the ``bernoulli_fmpq_ui`` function (formerly part of
+        Arb) of the FLINT library
+      - ``'flint'`` -- use the ``arith_bernoulli_number`` function of the FLINT
+        library
       - ``'pari'`` -- use the PARI C library
       - ``'gap'`` -- use GAP
       - ``'gp'`` -- use PARI/GP interpreter

src/sage/features/sagemath.py

@@ -360,7 +360,7 @@ def __init__(self):
 class sage__libs__flint(JoinFeature):
     r"""
     A :class:`sage.features.Feature` describing the presence of :mod:`sage.libs.flint`
-    and other modules depending on FLINT and arb.
+    and other modules depending on FLINT.
 
     In addition to the modularization purposes that this tag serves, it also provides attribution
     to the upstream project.

src/sage/matrix/matrix_complex_ball_dense.pxd

@@ -1,4 +1,4 @@
-from sage.libs.arb.types cimport acb_mat_t
+from sage.libs.flint.types cimport acb_mat_t
 from sage.matrix.matrix_dense cimport Matrix_dense
 from sage.matrix.matrix_generic_dense cimport Matrix_generic_dense
 from sage.structure.parent cimport Parent

src/sage/matrix/matrix_complex_ball_dense.pyx

@@ -1,14 +1,14 @@
 # distutils: libraries = flint
 r"""
-Arbitrary precision complex ball matrices using Arb
+Arbitrary precision complex ball matrices
 
 AUTHORS:
 
 - Clemens Heuberger (2014-10-25): Initial version.
 
-This is a rudimentary binding to the `Arb library
-<http://arblib.org>`_; it may be useful to refer to its
-documentation for more details.
+This is an incomplete interface to the `acb_mat module
+<https://flintlib.org/doc/acb_mat.html>`_ of FLINT; it may be useful to refer
+to its documentation for more details.
 
 TESTS::
 
@@ -36,8 +36,8 @@ from cpython.object cimport Py_EQ, Py_NE
 from cysignals.signals cimport sig_on, sig_str, sig_off
 
 from sage.arith.power cimport generic_power_pos
-from sage.libs.arb.acb cimport *
-from sage.libs.arb.acb_mat cimport *
+from sage.libs.flint.acb cimport *
+from sage.libs.flint.acb_mat cimport *
 from sage.libs.gmp.mpz cimport mpz_fits_ulong_p, mpz_get_ui
 from sage.matrix.constructor import matrix
 from sage.matrix.args cimport SparseEntry, MatrixArgs_init
@@ -120,7 +120,7 @@ cdef inline long prec(Matrix_complex_ball_dense mat) noexcept:
 cdef class Matrix_complex_ball_dense(Matrix_dense):
     """
     Matrix over a complex ball field. Implemented using the
-    ``acb_mat`` type of the Arb library.
+    ``acb_mat`` type of the FLINT library.
 
     EXAMPLES::
 
@@ -143,7 +143,7 @@ cdef class Matrix_complex_ball_dense(Matrix_dense):
             sage: type(a)
             <class 'sage.matrix.matrix_complex_ball_dense.Matrix_complex_ball_dense'>
         """
-        sig_str("Arb exception")
+        sig_str("FLINT exception")
         acb_mat_init(self.value, self._nrows, self._ncols)
         sig_off()
 
@@ -695,7 +695,7 @@ cdef class Matrix_complex_ball_dense(Matrix_dense):
         There is currently no guarantee that the algorithm converges as the
         working precision is increased.
 
-        See the `Arb documentation <http://arblib.org/acb_mat.html#c.acb_mat_eig_multiple>`__
+        See the `FLINT documentation <https://flintlib.org/doc/acb_mat.html#c.acb_mat_eig_multiple>`__
         for more information.
 
         EXAMPLES::
@@ -764,7 +764,7 @@ cdef class Matrix_complex_ball_dense(Matrix_dense):
 
         No guarantees are made about the accuracy of the output.
 
-        See the `Arb documentation <http://arblib.org/acb_mat.html#c.acb_mat_approx_eig_qr>`__
+        See the `FLINT documentation <https://flintlib.org/doc/acb_mat.html#c.acb_mat_approx_eig_qr>`__
         for more information.
 
         EXAMPLES::
@@ -822,7 +822,7 @@ cdef class Matrix_complex_ball_dense(Matrix_dense):
         Additionally, there is currently no guarantee that the algorithm
         converges as the working precision is increased.
 
-        See the `Arb documentation <http://arblib.org/acb_mat.html#c.acb_mat_eig_simple>`__
+        See the `FLINT documentation <https://flintlib.org/doc/acb_mat.html#c.acb_mat_eig_simple>`__
         for more information.
 
         EXAMPLES::
@@ -882,7 +882,7 @@ cdef class Matrix_complex_ball_dense(Matrix_dense):
 
         No guarantees are made about the accuracy of the output.
 
-        See the `Arb documentation <http://arblib.org/acb_mat.html#c.acb_mat_approx_eig_qr>`__
+        See the `FLINT documentation <https://flintlib.org/doc/acb_mat.html#c.acb_mat_approx_eig_qr>`__
         for more information.
 
         EXAMPLES::
@@ -921,7 +921,7 @@ cdef class Matrix_complex_ball_dense(Matrix_dense):
         Additionally, there is currently no guarantee that the algorithm
         converges as the working precision is increased.
 
-        See the `Arb documentation <http://arblib.org/acb_mat.html#c.acb_mat_eig_simple>`__
+        See the `FLINT documentation <https://flintlib.org/doc/acb_mat.html#c.acb_mat_eig_simple>`__
         for more information.
 
         EXAMPLES::

src/sage/misc/package.py

@@ -24,7 +24,6 @@
     sage: sorted(pkgs.keys())  # optional - sage_spkg, random
     ['4ti2',
      'alabaster',
-     'arb',
      ...
      'zlib']
 
@@ -299,7 +298,6 @@ def list_packages(*pkg_types: str, pkg_sources: List[str] = ['normal', 'pip', 's
         sage: L = list_packages('standard')
         sage: sorted(L.keys())  # random
         ['alabaster',
-         'arb',
          'babel',
          ...
          'zlib']

src/sage/numerical/gauss_legendre.pyx

@@ -103,8 +103,8 @@ def nodes_uncached(degree, prec):
 
     .. TODO::
 
-        It may be worth testing if using the Arb algorithm for finding the
-        nodes and weights in ``arb/acb_calc/integrate_gl_auto_deg.c`` has better
+        It may be worth testing if using the FLINT/Arb algorithm for finding the
+        nodes and weights in ``src/acb_calc/integrate_gl_auto_deg.c`` has better
         performance.
     """
     cdef long j,j1,n

src/sage/rings/complex_arb.pxd

@@ -1,4 +1,4 @@
-from sage.libs.arb.acb cimport acb_t
+from sage.libs.flint.acb cimport acb_t
 from sage.rings.complex_interval cimport ComplexIntervalFieldElement
 from sage.rings.real_arb cimport RealBall
 from sage.structure.element cimport RingElement

src/sage/rings/complex_arb.pyx

@@ -1,30 +1,30 @@
 # -*- coding: utf-8
 r"""
-Arbitrary precision complex balls using Arb
+Arbitrary precision complex balls
 
-This is a binding to the `Arb library <http://arblib.org>`_; it
-may be useful to refer to its documentation for more details.
+This is an incomplete interface to the `acb module of FLINT <https://flintlib.org/doc/acb.html>`_;
+it may be useful to refer to its documentation for more details.
 
-Parts of the documentation for this module are copied or adapted from
-Arb's own documentation, licenced under the GNU General Public License
-version 2, or later.
+Parts of the documentation for this module are copied or adapted from Arb's
+(now FLINT's) own documentation, licenced at the time under the GNU General
+Public License version 2, or later.
 
 .. SEEALSO::
 
-    - :mod:`Real balls using Arb <sage.rings.real_arb>`
+    - :mod:`Real balls <sage.rings.real_arb>`
     - :mod:`Complex interval field (using MPFI) <sage.rings.complex_interval_field>`
     - :mod:`Complex intervals (using MPFI) <sage.rings.complex_interval>`
 
 Data Structure
 ==============
 
 A :class:`ComplexBall` represents a complex number with error bounds. It wraps
-an Arb object of type ``acb_t``, which  consists of a pair of real number balls
+an object of type ``acb_t``, which  consists of a pair of real number balls
 representing the real and imaginary part with separate error bounds. (See the
 documentation of :mod:`sage.rings.real_arb` for more information.)
 
 A :class:`ComplexBall` thus represents a rectangle `[m_1-r_1, m_1+r_1] +
-[m_2-r_2, m_2+r_2] i` in the complex plane. This is used in Arb instead of a
+[m_2-r_2, m_2+r_2] i` in the complex plane. This is used instead of a
 disk or square representation (consisting of a complex floating-point midpoint
 with a single radius), since it allows implementing many operations more
 conveniently by splitting into ball operations on the real and imaginary parts.
@@ -43,7 +43,7 @@ Comparison
 
 .. WARNING::
 
-    In accordance with the semantics of Arb, identical :class:`ComplexBall`
+    In accordance with the semantics of FLINT/Arb, identical :class:`ComplexBall`
     objects are understood to give permission for algebraic simplification.
     This assumption is made to improve performance. For example, setting ``z =
     x*x`` sets `z` to a ball enclosing the set `\{t^2 : t \in x\}` and not the
@@ -161,16 +161,16 @@ from cpython.complex cimport PyComplex_FromDoubles
 from sage.ext.stdsage cimport PY_NEW
 
 from sage.libs.mpfr cimport MPFR_RNDU, MPFR_RNDD, MPFR_PREC_MIN, mpfr_get_d_2exp
-from sage.libs.arb.types cimport ARF_RND_NEAR, arf_t, mag_t
-from sage.libs.arb.arb cimport *
-from sage.libs.arb.acb cimport *
-from sage.libs.arb.acb_calc cimport *
-from sage.libs.arb.acb_hypgeom cimport *
-from sage.libs.arb.acb_elliptic cimport *
-from sage.libs.arb.acb_modular cimport *
-from sage.libs.arb.acb_poly cimport *
-from sage.libs.arb.arf cimport arf_init, arf_get_d, arf_get_mpfr, arf_clear, arf_set, arf_is_nan
-from sage.libs.arb.mag cimport (mag_init, mag_clear, mag_set_d,
+from sage.libs.flint.types cimport ARF_RND_NEAR, arf_t, mag_t
+from sage.libs.flint.arb cimport *
+from sage.libs.flint.acb cimport *
+from sage.libs.flint.acb_calc cimport *
+from sage.libs.flint.acb_hypgeom cimport *
+from sage.libs.flint.acb_elliptic cimport *
+from sage.libs.flint.acb_modular cimport *
+from sage.libs.flint.acb_poly cimport *
+from sage.libs.flint.arf cimport arf_init, arf_get_d, arf_get_mpfr, arf_clear, arf_set, arf_is_nan
+from sage.libs.flint.mag cimport (mag_init, mag_clear, mag_set_d,
         MAG_BITS, mag_zero, mag_set_ui_2exp_si,
         mag_mul_2exp_si)
 from sage.libs.flint.fmpz cimport fmpz_t, fmpz_init, fmpz_get_mpz, fmpz_set_mpz, fmpz_clear
@@ -371,7 +371,7 @@ class ComplexBallField(UniqueRepresentation, sage.rings.abc.ComplexBallField):
             sage: CBF.base_ring()
             Real ball field with 53 bits of precision
 
-        There are direct coercions from ZZ and QQ (for which arb provides
+        There are direct coercions from ZZ and QQ (for which FLINT provides
         construction functions)::
 
             sage: CBF.coerce_map_from(ZZ)
@@ -1029,7 +1029,7 @@ class ComplexBallField(UniqueRepresentation, sage.rings.abc.ComplexBallField):
           the ball field) -- absolute accuracy goal
 
         Additionally, the following optional parameters can be used to control
-        the integration algorithm. See the `Arb documentation <http://arblib.org/acb_calc.html>`_
+        the integration algorithm. See the `FLINT documentation <https://flintlib.org/doc/acb_calc.html>`_
         for more information.
 
         - ``deg_limit`` -- maximum quadrature degree for each
@@ -1150,8 +1150,8 @@ class ComplexBallField(UniqueRepresentation, sage.rings.abc.ComplexBallField):
 
         ALGORITHM:
 
-        Uses the `acb_calc <http://arblib.org/acb_calc.html>`_ module of the Arb
-        library.
+        Uses the `acb_calc <https://flintlib.org/doc/acb_calc.html>`_ module of
+        the FLINT library.
 
         TESTS::
 
@@ -1256,7 +1256,7 @@ class ComplexBallField(UniqueRepresentation, sage.rings.abc.ComplexBallField):
 
 cdef inline bint _do_sig(long prec) noexcept:
     """
-    Whether signal handlers should be installed for calls to arb.
+    Whether signal handlers should be installed for calls to FLINT.
     """
     return (prec > 1000)
 
@@ -1298,8 +1298,7 @@ cdef inline real_ball_field(ComplexBall ball) noexcept:
 
 cdef class ComplexBall(RingElement):
     """
-    Hold one ``acb_t`` of the `Arb library
-    <http://arblib.org>`_
+    Hold one ``acb_t`` of the `FLINT library <https://flintlib.org>`_
 
     EXAMPLES::
 

src/sage/rings/number_field/number_field_element_quadratic.pxd

@@ -1,5 +1,5 @@
 from sage.libs.gmp.types cimport mpz_t
-from sage.libs.arb.types cimport arb_t
+from sage.libs.flint.types cimport arb_t
 from sage.rings.integer cimport Integer
 from sage.rings.rational cimport Rational
 from sage.rings.number_field.number_field_element cimport NumberFieldElement, NumberFieldElement_absolute