sage.{matrix,modules,probability,stats,quadratic_forms,tensor}: Update # needs, modularization fixes

src/sage/features/sagemath.py

@@ -392,13 +392,67 @@ def __init__(self):
                               PythonModule('sage.interfaces.gap')])
 
 
+class sage__libs__linbox(JoinFeature):
+    r"""
+    A :class:`sage.features.Feature` describing the presence of :mod:`sage.libs.linbox`
+    and other modules depending on Givaro, FFLAS-FFPACK, LinBox.
+
+    In addition to the modularization purposes that this tag serves,
+    it also provides attribution to the upstream project.
+
+    TESTS::
+
+        sage: from sage.features.sagemath import sage__libs__linbox
+        sage: sage__libs__linbox().is_present()                                         # needs sage.libs.linbox
+        FeatureTestResult('sage.libs.linbox', True)
+    """
+    def __init__(self):
+        r"""
+        TESTS::
+
+            sage: from sage.features.sagemath import sage__libs__linbox
+            sage: isinstance(sage__libs__linbox(), sage__libs__linbox)
+            True
+        """
+        JoinFeature.__init__(self, 'sage.libs.linbox',
+                             [PythonModule('sage.rings.finite_rings.element_givaro')],
+                             spkg='sagemath_linbox', type='standard')
+
+
+class sage__libs__m4ri(JoinFeature):
+    r"""
+    A :class:`sage.features.Feature` describing the presence of Cython modules
+    depending on the M4RI and/or M4RIe libraries.
+
+    In addition to the modularization purposes that this tag serves,
+    it also provides attribution to the upstream project.
+
+    TESTS::
+
+        sage: from sage.features.sagemath import sage__libs__m4ri
+        sage: sage__libs__m4ri().is_present()                                           # needs sage.libs.m4ri
+        FeatureTestResult('sage.libs.m4ri', True)
+    """
+    def __init__(self):
+        r"""
+        TESTS::
+
+            sage: from sage.features.sagemath import sage__libs__m4ri
+            sage: isinstance(sage__libs__m4ri(), sage__libs__m4ri)
+            True
+        """
+        JoinFeature.__init__(self, 'sage.libs.m4ri',
+                             [PythonModule('sage.matrix.matrix_gf2e_dense')],
+                             spkg='sagemath_m4ri', type='standard')
+
+
 class sage__libs__ntl(JoinFeature):
     r"""
     A :class:`sage.features.Feature` describing the presence of :mod:`sage.libs.ntl`
-    and other modules depending on NTL and arb.
+    and other modules depending on NTL.
 
-    In addition to the modularization purposes that this tag serves, it also provides attribution
-    to the upstream project.
+    In addition to the modularization purposes that this tag serves,
+    it also provides attribution to the upstream project.
 
     TESTS::
 
@@ -423,11 +477,12 @@ class sage__libs__pari(JoinFeature):
     r"""
     A :class:`~sage.features.Feature` describing the presence of :mod:`sage.libs.pari`.
 
-    SageMath uses the :ref:`PARI <spkg_pari>` library (via :ref:`cypari2 <spkg_cypari>`) for numerous purposes.
-    Doctests that involves such features should be marked ``# needs sage.libs.pari``.
+    SageMath uses the :ref:`PARI <spkg_pari>` library (via :ref:`cypari2
+    <spkg_cypari>`) for numerous purposes.  Doctests that involves such features
+    should be marked ``# needs sage.libs.pari``.
 
-    In addition to the modularization purposes that this tag serves, it also provides attribution
-    to the upstream project.
+    In addition to the modularization purposes that this tag serves, it also
+    provides attribution to the upstream project.
 
     EXAMPLES::
 
@@ -1005,6 +1060,8 @@ def all_features():
             sage__libs__ecl(),
             sage__libs__flint(),
             sage__libs__gap(),
+            sage__libs__linbox(),
+            sage__libs__m4ri(),
             sage__libs__ntl(),
             sage__libs__pari(),
             sage__libs__singular(),

src/sage/homology/homology_group.py

@@ -165,6 +165,8 @@ def HomologyGroup(n, base_ring, invfac=None):
         Multiplicative Abelian group isomorphic to Z x Z x Z x Z
         sage: HomologyGroup(4, ZZ)
         Z x Z x Z x Z
+
+        sage: # needs sage.libs.flint (otherwise timeout)
         sage: HomologyGroup(100, ZZ)
         Z^100
     """

src/sage/matrix/action.pyx

@@ -209,23 +209,23 @@ cdef class MatrixMatrixAction(MatrixMulAction):
 
         Respects compatible subdivisions::
 
-            sage: M = matrix(5, 5, prime_range(100))
-            sage: M.subdivide(2,3); M
+            sage: M = matrix(5, 5, prime_range(100))                                    # needs sage.libs.pari
+            sage: M.subdivide(2, 3); M                                                  # needs sage.libs.pari
             [ 2  3  5| 7 11]
             [13 17 19|23 29]
             [--------+-----]
             [31 37 41|43 47]
             [53 59 61|67 71]
             [73 79 83|89 97]
-            sage: N = matrix(5,2,[n^2 for n in range(10)])
-            sage: N.subdivide(3,1); N
+            sage: N = matrix(5, 2, [n^2 for n in range(10)])
+            sage: N.subdivide(3, 1); N
             [ 0| 1]
             [ 4| 9]
             [16|25]
             [--+--]
             [36|49]
             [64|81]
-            sage: M*N
+            sage: M*N                                                                   # needs sage.libs.pari
             [ 1048| 1388]
             [ 3056| 4117]
             [-----+-----]
@@ -235,7 +235,7 @@ cdef class MatrixMatrixAction(MatrixMulAction):
 
         Note that this is just like block matrix multiplication::
 
-            sage: M.subdivision(0,0) * N.subdivision(0,0) + M.subdivision(0,1) * N.subdivision(1,0)
+            sage: M.subdivision(0,0) * N.subdivision(0,0) + M.subdivision(0,1) * N.subdivision(1,0)                     # needs sage.libs.pari
             [1048]
             [3056]
 
@@ -249,7 +249,7 @@ cdef class MatrixMatrixAction(MatrixMulAction):
             [16|25]
             [36|49]
             [64|81]
-            sage: M*N
+            sage: M*N                                                                   # needs sage.libs.pari
             [ 1048  1388]
             [ 3056  4117]
             [ 5360  7303]

src/sage/matrix/args.pyx

@@ -83,7 +83,7 @@ cdef class SparseEntry:
         sage: from sage.matrix.args import SparseEntry
         sage: SparseEntry(123, 456, "abc")
         SparseEntry(123, 456, 'abc')
-        sage: SparseEntry(1/3, 2/3, x)
+        sage: SparseEntry(1/3, 2/3, x)                                                  # needs sage.symbolic
         Traceback (most recent call last):
         ...
         TypeError: unable to convert rational 1/3 to an integer
@@ -176,8 +176,10 @@ cdef class MatrixArgs:
         <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices over Real Double Field; typ=SCALAR; entries=3.141592653589793>
         [3.141592653589793               0.0]
         [              0.0 3.141592653589793]
-        sage: ma = MatrixArgs(2, 2, entries=pi); ma.finalized(); ma.matrix()
-        <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices over Symbolic Ring; typ=SCALAR; entries=pi>
+        sage: ma = MatrixArgs(2, 2, entries=pi); ma.finalized()                         # needs sage.symbolic
+        <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices
+         over Symbolic Ring; typ=SCALAR; entries=pi>
+        sage: ma.matrix()                                                               # needs sage.symbolic
         [pi  0]
         [ 0 pi]
         sage: ma = MatrixArgs(ZZ, 2, 2, entries={(0,0):7}); ma.finalized(); ma.matrix()
@@ -192,18 +194,27 @@ cdef class MatrixArgs:
         <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices over Integer Ring; typ=SEQ_FLAT; entries=(1, 2, 3, 4)>
         [1 2]
         [3 4]
-        sage: ma = MatrixArgs(QQ, entries=pari("[1,2;3,4]")); ma.finalized(); ma.matrix()
-        <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices over Rational Field; typ=SEQ_FLAT; entries=[1, 2, 3, 4]>
+
+        sage: # needs sage.libs.pari
+        sage: ma = MatrixArgs(QQ, entries=pari("[1,2;3,4]")); ma.finalized()
+        <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices
+         over Rational Field; typ=SEQ_FLAT; entries=[1, 2, 3, 4]>
+        sage: ma.matrix()
         [1 2]
         [3 4]
-        sage: ma = MatrixArgs(QQ, 2, 2, entries=pari("[1,2,3,4]")); ma.finalized(); ma.matrix()
-        <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices over Rational Field; typ=SEQ_FLAT; entries=[1, 2, 3, 4]>
+        sage: ma = MatrixArgs(QQ, 2, 2, entries=pari("[1,2,3,4]")); ma.finalized()
+        <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices
+         over Rational Field; typ=SEQ_FLAT; entries=[1, 2, 3, 4]>
+        sage: ma.matrix()
         [1 2]
         [3 4]
-        sage: ma = MatrixArgs(QQ, 2, 2, entries=pari("3/5")); ma.finalized(); ma.matrix()
-        <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices over Rational Field; typ=SCALAR; entries=3/5>
+        sage: ma = MatrixArgs(QQ, 2, 2, entries=pari("3/5")); ma.finalized()
+        <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices
+         over Rational Field; typ=SCALAR; entries=3/5>
+        sage: ma.matrix()
         [3/5   0]
         [  0 3/5]
+
         sage: ma = MatrixArgs(entries=matrix(2,2)); ma.finalized(); ma.matrix()
         <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices over Integer Ring; typ=MATRIX; entries=[0 0]
         [0 0]>
@@ -217,26 +228,37 @@ cdef class MatrixArgs:
         <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices over Integer Ring; typ=CALLABLE; entries=<function ...>>
         [1 2]
         [3 4]
+
+        sage: # needs numpy
         sage: from numpy import array
-        sage: ma = MatrixArgs(array([[1,2],[3,4]])); ma.finalized(); ma.matrix()
-        <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices over Integer Ring; typ=SEQ_SEQ; entries=array([[1, 2],
-               [3, 4]])>
+        sage: ma = MatrixArgs(array([[1,2],[3,4]])); ma.finalized()
+        <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices
+         over Integer Ring; typ=SEQ_SEQ; entries=array([[1, 2], [3, 4]])>
+        sage: ma.matrix()
         [1 2]
         [3 4]
-        sage: ma = MatrixArgs(array([[1.,2.],[3.,4.]])); ma.finalized(); ma.matrix()
-        <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices over Real Double Field; typ=MATRIX; entries=[1.0 2.0]
-        [3.0 4.0]>
+        sage: ma = MatrixArgs(array([[1.,2.],[3.,4.]])); ma.finalized()
+        <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices
+         over Real Double Field; typ=MATRIX; entries=[1.0 2.0]
+                                                     [3.0 4.0]>
+        sage: ma.matrix()
         [1.0 2.0]
         [3.0 4.0]
-        sage: ma = MatrixArgs(RealField(20), array([[1.,2.],[3.,4.]])); ma.finalized(); ma.matrix()
-        <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices over Real Field with 20 bits of precision; typ=MATRIX; entries=[1.0 2.0]
-        [3.0 4.0]>
+        sage: ma = MatrixArgs(RealField(20), array([[1.,2.],[3.,4.]])); ma.finalized()
+        <MatrixArgs for Full MatrixSpace of 2 by 2 dense matrices over Real Field
+         with 20 bits of precision; typ=MATRIX; entries=[1.0 2.0]
+                                                        [3.0 4.0]>
+        sage: ma.matrix()
         [1.0000 2.0000]
         [3.0000 4.0000]
-        sage: ma = MatrixArgs(graphs.CycleGraph(3)); ma.finalized(); ma.matrix()
-        <MatrixArgs for Full MatrixSpace of 3 by 3 dense matrices over Integer Ring; typ=MATRIX; entries=[0 1 1]
-        [1 0 1]
-        [1 1 0]>
+
+        sage: # needs sage.graphs
+        sage: ma = MatrixArgs(graphs.CycleGraph(3)); ma.finalized()
+        <MatrixArgs for Full MatrixSpace of 3 by 3 dense matrices
+         over Integer Ring; typ=MATRIX; entries=[0 1 1]
+                                                [1 0 1]
+                                                [1 1 0]>
+        sage: ma.matrix()
         [0 1 1]
         [1 0 1]
         [1 1 0]
@@ -458,8 +480,8 @@ cdef class MatrixArgs:
 
         Sparse examples::
 
-            sage: ma = MatrixArgs(3, 3, pi)
-            sage: list(ma.iter(sparse=True))
+            sage: ma = MatrixArgs(3, 3, pi)                                             # needs sage.symbolic
+            sage: list(ma.iter(sparse=True))                                            # needs sage.symbolic
             [SparseEntry(0, 0, pi), SparseEntry(1, 1, pi), SparseEntry(2, 2, pi)]
             sage: ma = MatrixArgs(2, 3)
             sage: list(ma.iter(sparse=True))
@@ -819,11 +841,11 @@ cdef class MatrixArgs:
         EXAMPLES::
 
             sage: from sage.matrix.args import MatrixArgs
-            sage: MatrixArgs(pi).finalized()
+            sage: MatrixArgs(pi).finalized()                                            # needs sage.symbolic
             Traceback (most recent call last):
             ...
             TypeError: the dimensions of the matrix must be specified
-            sage: MatrixArgs(RR, pi).finalized()
+            sage: MatrixArgs(RR, pi).finalized()                                        # needs sage.symbolic
             Traceback (most recent call last):
             ...
             TypeError: the dimensions of the matrix must be specified
@@ -1222,6 +1244,7 @@ cdef class MatrixArgs:
 
         Check that :trac:`26655` is fixed::
 
+            sage: # needs sage.rings.finite_rings
             sage: F.<a> = GF(9)
             sage: M = MatrixSpace(F, 2, 2)
             sage: A = M([[1, a], [0, 1]])
@@ -1232,11 +1255,11 @@ cdef class MatrixArgs:
         Constructing a matrix from a PARI ``t_VEC`` or ``t_COL`` with
         ``t_VEC`` or ``t_COL`` elements is currently not supported::
 
-            sage: M(pari([1, a, 0, 1]))
+            sage: M(pari([1, a, 0, 1]))                                                 # needs sage.libs.pari sage.rings.finite_rings
             Traceback (most recent call last):
             ...
             NameError: name 'a' is not defined
-            sage: M(pari([[1, a], [0, 1]]))
+            sage: M(pari([[1, a], [0, 1]]))                                             # needs sage.libs.pari sage.rings.finite_rings
             Traceback (most recent call last):
             ...
             NameError: name 'a' is not defined
@@ -1351,7 +1374,7 @@ cpdef MatrixArgs MatrixArgs_init(space, entries):
 
         sage: from sage.matrix.args import MatrixArgs_init
         sage: S = MatrixSpace(GF(2), 2, 4)
-        sage: ma = MatrixArgs_init(S, {(1,3):7})
+        sage: ma = MatrixArgs_init(S, {(1, 3): 7})
         sage: M = ma.matrix(); M
         [0 0 0 0]
         [0 0 0 1]

src/sage/matrix/benchmark.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.flint
 """
 Benchmarks for matrices
 
@@ -18,13 +19,14 @@
 """
 
 from .constructor import random_matrix, Matrix
+from sage.misc.lazy_import import lazy_import
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.misc.timing import cputime
 from cysignals.alarm import AlarmInterrupt, alarm, cancel_alarm
 
-from sage.interfaces.magma import magma
+lazy_import('sage.interfaces.magma', 'magma')
 
 verbose = False
 

src/sage/matrix/berlekamp_massey.py

@@ -55,11 +55,11 @@ def berlekamp_massey(a):
         sage: from sage.matrix.berlekamp_massey import berlekamp_massey
         sage: berlekamp_massey([1,2,1,2,1,2])
         x^2 - 1
-        sage: berlekamp_massey([GF(7)(1),19,1,19])
+        sage: berlekamp_massey([GF(7)(1), 19, 1, 19])
         x^2 + 6
         sage: berlekamp_massey([2,2,1,2,1,191,393,132])
         x^4 - 36727/11711*x^3 + 34213/5019*x^2 + 7024942/35133*x - 335813/1673
-        sage: berlekamp_massey(prime_range(2,38))
+        sage: berlekamp_massey(prime_range(2, 38))                                      # needs sage.libs.pari
         x^6 - 14/9*x^5 - 7/9*x^4 + 157/54*x^3 - 25/27*x^2 - 73/18*x + 37/9
 
     TESTS::

src/sage/matrix/compute_J_ideal.py

@@ -1,3 +1,4 @@
+# sage.doctest: needs sage.libs.pari       (for charpoly, minimal_polynomial in __init__)
 r"""
 `J`-ideals of matrices