gh-36569: `sage.matrix`, `sage.modules`: Update `# needs`
    
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URL: #36569
Reported by: Matthias Köppe
Reviewer(s): David Coudert

Author: Release Manager

src/sage/matrix/args.pyx

@@ -871,6 +871,7 @@ cdef class MatrixArgs:
 
         Check github issue #36065:
 
+            sage: # needs sage.rings.number_field
             sage: class MyAlgebraicNumber(sage.rings.qqbar.AlgebraicNumber):
             ....:     def __bool__(self):
             ....:         raise ValueError

src/sage/matrix/constructor.pyx

@@ -580,7 +580,7 @@ def matrix(*args, **kwds):
 
     Check :trac:`24459`::
 
-        sage: # needs sage.libs.flint
+        sage: # needs sage.libs.linbox
         sage: Matrix(ZZ, sys.maxsize, sys.maxsize)
         Traceback (most recent call last):
         ...

src/sage/matrix/matrix0.pyx

@@ -543,11 +543,11 @@ cdef class Matrix(sage.structure.element.Matrix):
 
         TESTS::
 
-            sage: class MyAlgebraicNumber(sage.rings.qqbar.AlgebraicNumber):            # needs sage.rings.number_fields
+            sage: class MyAlgebraicNumber(sage.rings.qqbar.AlgebraicNumber):            # needs sage.rings.number_field
             ....:     def __bool__(self):
             ....:         raise ValueError
-            sage: mat = matrix(1, 1, MyAlgebraicNumber(1))                              # needs sage.rings.number_fields
-            sage: bool(mat)                                                             # needs sage.rings.number_fields
+            sage: mat = matrix(1, 1, MyAlgebraicNumber(1))                              # needs sage.rings.number_field
+            sage: bool(mat)                                                             # needs sage.rings.number_field
             Traceback (most recent call last):
             ...
             ValueError
@@ -4898,7 +4898,7 @@ cdef class Matrix(sage.structure.element.Matrix):
         Over finite fields::
 
             sage: A = matrix(GF(59), 3, [10,56,39,53,56,33,58,24,55])
-            sage: A.multiplicative_order()                                              # needs sage.groups
+            sage: A.multiplicative_order()                                              # needs sage.libs.pari
             580
             sage: (A^580).is_one()
             True
@@ -4918,7 +4918,7 @@ cdef class Matrix(sage.structure.element.Matrix):
         Over `\ZZ`::
 
             sage: m = matrix(ZZ, 2, 2, [-1,1,-1,0])
-            sage: m.multiplicative_order()                                              # needs sage.groups
+            sage: m.multiplicative_order()                                              # needs sage.libs.pari
             3
 
             sage: m = posets.ChainPoset(6).coxeter_transformation()                     # needs sage.combinat sage.graphs
@@ -4930,10 +4930,10 @@ cdef class Matrix(sage.structure.element.Matrix):
             10
 
             sage: M = matrix(ZZ, 2, 2, [1, 1, 0, 1])
-            sage: M.multiplicative_order()                                              # needs sage.groups
+            sage: M.multiplicative_order()                                              # needs sage.libs.pari
             +Infinity
 
-            sage: for k in range(600):                                                  # needs sage.groups
+            sage: for k in range(600):                                                  # needs sage.groups sage.modular
             ....:     m = SL2Z.random_element()
             ....:     o = m.multiplicative_order()
             ....:     if o != Infinity and m**o != SL2Z.one():
@@ -4948,7 +4948,7 @@ cdef class Matrix(sage.structure.element.Matrix):
             ....:     else:
             ....:         return ZZ.random_element(-100,100)
             sage: rnd = matrix(ZZ, 8, 8, val)
-            sage: (rnd * m24 * rnd.inverse_of_unit()).multiplicative_order()            # needs sage.groups
+            sage: (rnd * m24 * rnd.inverse_of_unit()).multiplicative_order()            # needs sage.libs.pari
             24
 
         TESTS::
@@ -5827,9 +5827,9 @@ cdef class Matrix(sage.structure.element.Matrix):
 
         Tests for :trac:`28570`::
 
-            sage: P = posets.TamariLattice(7)                                           # needs sage.combinat sage.graphs
-            sage: M = P._hasse_diagram._leq_matrix                                      # needs sage.combinat sage.graphs
-            sage: M.inverse_of_unit()   # this was very slow, now 1s                    # needs sage.combinat sage.graphs
+            sage: P = posets.TamariLattice(7)                                           # needs sage.graphs
+            sage: M = P._hasse_diagram._leq_matrix                                      # needs sage.graphs
+            sage: M.inverse_of_unit()   # this was very slow, now 1s                    # needs sage.graphs
             429 x 429 sparse matrix over Integer Ring...
 
             sage: m = matrix(Zmod(2**2), 1, 1, [1], sparse=True)

src/sage/matrix/matrix1.pyx

@@ -103,7 +103,7 @@ cdef class Matrix(Matrix0):
             [ [ 0, 1, 2 ], [ 3, 4, 5 ], [ 6, 7, 8 ] ]
             sage: g.CharacteristicPolynomial()
             x_1^3-12*x_1^2-18*x_1
-            sage: A.characteristic_polynomial()
+            sage: A.characteristic_polynomial()                                         # needs sage.libs.pari
             x^3 - 12*x^2 - 18*x
             sage: matrix(QQ, g) == A
             True