@@ -3525,7 +3525,8 @@ cdef class Matrix(Matrix1):
35253525 cdef Py_ssize_t i, j, m, n, r
35263526 n = self._nrows
35273527
3528- tm = verbose("Computing Hessenberg Normal Form of %sx%s matrix"%(n, n))
3528+ tm = verbose(f"Computing Hessenberg Normal Form of {n}x{n} matrix",
3529+ level=2)
35293530
35303531 if not self.is_square():
35313532 raise TypeError("self must be square")
@@ -3576,7 +3577,8 @@ cdef class Matrix(Matrix1):
35763577 # column m, and we're only worried about column m-1 right now.
35773578 # Add u*column_j to column_m.
35783579 self.add_multiple_of_column_c(m, j, u, 0)
3579- verbose("Finished Hessenberg Normal Form of %sx%s matrix"%(n, n), tm)
3580+ verbose(f"Finished Hessenberg Normal Form of {n}x{n} matrix",
3581+ level=2, t=tm)
35803582
35813583 def _charpoly_hessenberg(self, var):
35823584 """
@@ -3769,12 +3771,12 @@ cdef class Matrix(Matrix1):
37693771 [0 0 1]
37703772 """
37713773 from sage.matrix.matrix_space import MatrixSpace
3772- tm = verbose("computing right kernel matrix over a number field for %sx%s matrix" % (self.nrows(), self.ncols()), level=1 )
3774+ tm = verbose("computing right kernel matrix over a number field for %sx%s matrix" % (self.nrows(), self.ncols()), level=2 )
37733775 basis = self.__pari__().matker()
37743776 # Coerce PARI representations into the number field
37753777 R = self.base_ring()
37763778 basis = [[R(x) for x in row] for row in basis]
3777- verbose("done computing right kernel matrix over a number field for %sx%s matrix" % (self.nrows(), self.ncols()), level=1 , t=tm)
3779+ verbose("done computing right kernel matrix over a number field for %sx%s matrix" % (self.nrows(), self.ncols()), level=2 , t=tm)
37783780 return 'pivot-pari-numberfield', MatrixSpace(R, len(basis), ncols=self._ncols)(basis)
37793781
37803782 def _right_kernel_matrix_over_field(self, *args, **kwds):
@@ -3828,7 +3830,7 @@ cdef class Matrix(Matrix1):
38283830 [0 0 1]
38293831 """
38303832 from sage.matrix.matrix_space import MatrixSpace
3831- tm = verbose("computing right kernel matrix over an arbitrary field for %sx%s matrix" % (self.nrows(), self.ncols()), level=1 )
3833+ tm = verbose("computing right kernel matrix over an arbitrary field for %sx%s matrix" % (self.nrows(), self.ncols()), level=2 )
38323834 E = self.echelon_form(*args, **kwds)
38333835 pivots = E.pivots()
38343836 pivots_set = set(pivots)
@@ -3857,7 +3859,7 @@ cdef class Matrix(Matrix1):
38573859 basis.append(v)
38583860 M = MS(basis, coerce=False)
38593861 tm = verbose("done computing right kernel matrix over an arbitrary field for %sx%s matrix"
3860- % (self.nrows(), self.ncols()), level=1 , t=tm)
3862+ % (self.nrows(), self.ncols()), level=2 , t=tm)
38613863 return 'pivot-generic', M
38623864
38633865 def _right_kernel_matrix_over_domain(self):
@@ -3915,15 +3917,15 @@ cdef class Matrix(Matrix1):
39153917 [0 0 1]
39163918 """
39173919 tm = verbose("computing right kernel matrix over a domain for %sx%s matrix"
3918- % (self.nrows(), self.ncols()), level=1 )
3920+ % (self.nrows(), self.ncols()), level=2 )
39193921 d, _, v = self.smith_form()
39203922 basis = []
39213923 cdef Py_ssize_t i, nrows = self._nrows
39223924 for i in range(self._ncols):
39233925 if i >= nrows or d[i, i] == 0:
39243926 basis.append(v.column(i))
39253927 verbose("done computing right kernel matrix over a domain for %sx%s matrix"
3926- % (self.nrows(), self.ncols()), level=1 , t=tm)
3928+ % (self.nrows(), self.ncols()), level=2 , t=tm)
39273929 return 'computed-smith-form', self.new_matrix(nrows=len(basis), ncols=self._ncols, entries=basis)
39283930
39293931 def _right_kernel_matrix_over_integer_mod_ring(self):
@@ -4077,16 +4079,16 @@ cdef class Matrix(Matrix1):
40774079 ....: sparse=False)
40784080 sage: B = copy(A).sparse_matrix()
40794081 sage: from sage.misc.verbose import set_verbose
4080- sage: set_verbose(1 )
4082+ sage: set_verbose(2 )
40814083 sage: D = A.right_kernel(); D
4082- verbose 1 (<module>) computing a right kernel for 4x5 matrix over Rational Field
4084+ verbose 2 (<module>) computing a right kernel for 4x5 matrix over Rational Field
40834085 ...
40844086 Vector space of degree 5 and dimension 2 over Rational Field
40854087 Basis matrix:
40864088 [ 1 0 1 1/2 -1/2]
40874089 [ 0 1 -1/2 -1/4 -1/4]
40884090 sage: S = B.right_kernel(); S
4089- verbose 1 (<module>) computing a right kernel for 4x5 matrix over Rational Field
4091+ verbose 2 (<module>) computing a right kernel for 4x5 matrix over Rational Field
40904092 ...
40914093 Vector space of degree 5 and dimension 2 over Rational Field
40924094 Basis matrix:
@@ -4145,11 +4147,11 @@ cdef class Matrix(Matrix1):
41454147 sage: Q = QuadraticField(-7)
41464148 sage: a = Q.gen(0)
41474149 sage: A = matrix(Q, [[2, 5-a, 15-a, 16+4*a], [2+a, a, -7 + 5*a, -3+3*a]])
4148- sage: set_verbose(1 )
4150+ sage: set_verbose(2 )
41494151 sage: A.right_kernel(algorithm='default')
41504152 verbose ...
4151- verbose 1 (<module>) computing right kernel matrix over a number field for 2x4 matrix
4152- verbose 1 (<module>) done computing right kernel matrix over a number field for 2x4 matrix
4153+ verbose 2 (<module>) computing right kernel matrix over a number field for 2x4 matrix
4154+ verbose 2 (<module>) done computing right kernel matrix over a number field for 2x4 matrix
41534155 ...
41544156 Vector space of degree 4 and dimension 2 over
41554157 Number Field in a with defining polynomial x^2 + 7 with a = 2.645751311064591?*I
@@ -4209,11 +4211,11 @@ cdef class Matrix(Matrix1):
42094211 sage: A = matrix(GF(2), [[0, 1, 1, 0, 0, 0],
42104212 ....: [1, 0, 0, 0, 1, 1,],
42114213 ....: [1, 0, 0, 0, 1, 1]])
4212- sage: set_verbose(1 )
4214+ sage: set_verbose(2 )
42134215 sage: A.right_kernel(algorithm='default')
42144216 verbose ...
4215- verbose 1 (<module>) computing right kernel matrix over integers mod 2 for 3x6 matrix
4216- verbose 1 (<module>) done computing right kernel matrix over integers mod 2 for 3x6 matrix
4217+ verbose ... (<module>) computing right kernel matrix over integers mod 2 for 3x6 matrix
4218+ verbose ... (<module>) done computing right kernel matrix over integers mod 2 for 3x6 matrix
42174219 ...
42184220 Vector space of degree 6 and dimension 4 over Finite Field of size 2
42194221 Basis matrix:
@@ -4274,10 +4276,10 @@ cdef class Matrix(Matrix1):
42744276 sage: A = matrix(F, 3, 4, [[ 1, a, 1+a, a^3+a^5],
42754277 ....: [ a, a^4, a+a^4, a^4+a^8],
42764278 ....: [a^2, a^6, a^2+a^6, a^5+a^10]])
4277- sage: set_verbose(1 )
4279+ sage: set_verbose(2 )
42784280 sage: A.right_kernel(algorithm='default')
42794281 verbose ...
4280- verbose 1 (<module>) computing right kernel matrix over an arbitrary field for 3x4 matrix
4282+ verbose 2 (<module>) computing right kernel matrix over an arbitrary field for 3x4 matrix
42814283 ...
42824284 Vector space of degree 4 and dimension 2 over Finite Field in a of size 5^2
42834285 Basis matrix:
@@ -4339,23 +4341,23 @@ cdef class Matrix(Matrix1):
43394341 ....: [0, 3, 1, 2, 3, 6, 2]],
43404342 ....: sparse=False)
43414343 sage: B = copy(A).sparse_matrix()
4342- sage: set_verbose(1 )
4344+ sage: set_verbose(2 )
43434345 sage: D = A.right_kernel(); D
4344- verbose 1 (<module>) computing a right kernel for 4x7 matrix over Integer Ring
4345- verbose 1 (<module>) computing right kernel matrix over the integers for 4x7 matrix
4346+ verbose ... (<module>) computing a right kernel for 4x7 matrix over Integer Ring
4347+ verbose ... (<module>) computing right kernel matrix over the integers for 4x7 matrix
43464348 ...
4347- verbose 1 (<module>) done computing right kernel matrix over the integers for 4x7 matrix
4349+ verbose ... (<module>) done computing right kernel matrix over the integers for 4x7 matrix
43484350 ...
43494351 Free module of degree 7 and rank 3 over Integer Ring
43504352 Echelon basis matrix:
43514353 [ 1 12 3 14 -3 -10 1]
43524354 [ 0 35 0 25 -1 -31 17]
43534355 [ 0 0 7 12 -3 -1 -8]
43544356 sage: S = B.right_kernel(); S
4355- verbose 1 (<module>) computing a right kernel for 4x7 matrix over Integer Ring
4356- verbose 1 (<module>) computing right kernel matrix over the integers for 4x7 matrix
4357+ verbose ... (<module>) computing a right kernel for 4x7 matrix over Integer Ring
4358+ verbose ... (<module>) computing right kernel matrix over the integers for 4x7 matrix
43574359 ...
4358- verbose 1 (<module>) done computing right kernel matrix over the integers for 4x7 matrix
4360+ verbose ... (<module>) done computing right kernel matrix over the integers for 4x7 matrix
43594361 ...
43604362 Free module of degree 7 and rank 3 over Integer Ring
43614363 Echelon basis matrix:
@@ -4399,11 +4401,11 @@ cdef class Matrix(Matrix1):
43994401 sage: R.<y> = QQ[]
44004402 sage: A = matrix(R, [[ 1, y, 1+y^2],
44014403 ....: [y^3, y^2, 2*y^3]])
4402- sage: set_verbose(1 )
4404+ sage: set_verbose(2 )
44034405 sage: A.right_kernel(algorithm='default', basis='echelon')
44044406 verbose ...
4405- verbose 1 (<module>) computing right kernel matrix over a domain for 2x3 matrix
4406- verbose 1 (<module>) done computing right kernel matrix over a domain for 2x3 matrix
4407+ verbose 2 (<module>) computing right kernel matrix over a domain for 2x3 matrix
4408+ verbose 2 (<module>) done computing right kernel matrix over a domain for 2x3 matrix
44074409 ...
44084410 Free module of degree 3 and rank 1 over
44094411 Univariate Polynomial Ring in y over Rational Field
@@ -4988,7 +4990,7 @@ cdef class Matrix(Matrix1):
49884990 return K
49894991
49904992 R = self.base_ring()
4991- tm = verbose(lazy_string("computing a right kernel for %sx%s matrix over %s", self.nrows(), self.ncols(), R), level=1 )
4993+ tm = verbose(lazy_string("computing a right kernel for %sx%s matrix over %s", self.nrows(), self.ncols(), R), level=2 )
49924994
49934995 # Sanitize basis format
49944996 # 'computed' is OK in right_kernel_matrix(), but not here
@@ -5010,7 +5012,7 @@ cdef class Matrix(Matrix1):
50105012 else:
50115013 K = ambient.submodule_with_basis(M.rows(), already_echelonized=False, check=False)
50125014
5013- verbose(lazy_string("done computing a right kernel for %sx%s matrix over %s", self.nrows(), self.ncols(), R), level=1 , t=tm)
5015+ verbose(lazy_string("done computing a right kernel for %sx%s matrix over %s", self.nrows(), self.ncols(), R), level=2 , t=tm)
50145016 self.cache('right_kernel', K)
50155017 return K
50165018
@@ -5162,10 +5164,10 @@ cdef class Matrix(Matrix1):
51625164 if K is not None:
51635165 return K
51645166
5165- tm = verbose("computing left kernel for %sx%s matrix" % (self.nrows(), self.ncols()), level=1 )
5167+ tm = verbose("computing left kernel for %sx%s matrix" % (self.nrows(), self.ncols()), level=2 )
51665168 K = self.transpose().right_kernel(*args, **kwds)
51675169 self.cache('left_kernel', K)
5168- verbose("done computing left kernel for %sx%s matrix" % (self.nrows(), self.ncols()), level=1 , t=tm)
5170+ verbose("done computing left kernel for %sx%s matrix" % (self.nrows(), self.ncols()), level=2 , t=tm)
51695171 return K
51705172
51715173 kernel = left_kernel
@@ -5680,7 +5682,7 @@ cdef class Matrix(Matrix1):
56805682 B = g(self)
56815683 t2 = verbose('decomposition -- raising g(self) to the power %s'%m, level=2)
56825684 B = B ** m
5683- verbose('done powering', t2)
5685+ verbose('done powering', level=2, t= t2)
56845686 t = verbose('decomposition -- done computing g(self)', level=2, t=t)
56855687 E.append((B.kernel(), m==1))
56865688 t = verbose('decomposition -- time to compute kernel', level=2, t=t)
@@ -5772,11 +5774,11 @@ cdef class Matrix(Matrix1):
57725774 if M.degree() != self.ncols():
57735775 raise ArithmeticError("M must be a subspace of an %s-dimensional space" % self.ncols())
57745776
5775- time = verbose(t=0)
5777+ time = verbose(level=2, t=0)
57765778
57775779 # 1. Restrict
57785780 B = self.restrict(M, check=check_restrict)
5779- time0 = verbose("decompose restriction -- ", time)
5781+ time0 = verbose("decompose restriction -- ", level=2, t= time)
57805782
57815783 # 2. Decompose restriction
57825784 D = B.decomposition(**kwds)
@@ -5791,13 +5793,13 @@ cdef class Matrix(Matrix1):
57915793 # combination of the basis of W, and these linear combinations
57925794 # define the corresponding subspaces of the ambient space M.
57935795
5794- verbose("decomposition -- ", time0)
5796+ verbose("decomposition -- ", level=2, t= time0)
57955797 C = M.basis_matrix()
57965798
57975799 D = [((W.basis_matrix() * C).row_module(self.base_ring()), is_irred) for W, is_irred in D]
57985800 D = decomp_seq(D)
57995801
5800- verbose(t=time)
5802+ verbose(level=2, t=time)
58015803 return D
58025804
58035805 def restrict(self, V, check=True):
@@ -6040,9 +6042,9 @@ cdef class Matrix(Matrix1):
60406042 raise ArithmeticError("self must be a square matrix")
60416043 n = self.nrows()
60426044 v = sage.modules.free_module.VectorSpace(self.base_ring(), n).gen(i)
6043- tm = verbose('computing iterates...')
6045+ tm = verbose('computing iterates...', level=2 )
60446046 cols = self.iterates(v, 2*n).columns()
6045- tm = verbose('computed iterates', tm)
6047+ tm = verbose('computed iterates', level=2, t= tm)
60466048 f = None
60476049 # Compute the minimal polynomial of the linear recurrence
60486050 # sequence corresponding to the 0-th entries of the iterates,
@@ -6052,9 +6054,9 @@ cdef class Matrix(Matrix1):
60526054 else:
60536055 R = [t]
60546056 for i in R:
6055- tm = verbose('applying berlekamp-massey')
6057+ tm = verbose('applying berlekamp-massey', level=2 )
60566058 g = berlekamp_massey.berlekamp_massey(cols[i].list())
6057- verbose('berlekamp-massey done', tm)
6059+ verbose('berlekamp-massey done', level=2, t= tm)
60586060 if f is None:
60596061 f = g
60606062 else:
@@ -8100,7 +8102,7 @@ cdef class Matrix(Matrix1):
81008102 if self.fetch('in_echelon_form'):
81018103 return self.fetch('pivots')
81028104
8103- _ = verbose('generic in-place Gauss elimination on %s x %s matrix using %s algorithm' % (self._nrows, self._ncols, algorithm))
8105+ _ = verbose('generic in-place Gauss elimination on %s x %s matrix using %s algorithm' % (self._nrows, self._ncols, algorithm), level=2 )
81048106 self.check_mutability()
81058107 cdef Matrix A
81068108
@@ -8852,7 +8854,7 @@ cdef class Matrix(Matrix1):
88528854 [ 0 0 0 0]
88538855 [ 0 0 0 0]
88548856 """
8855- tm = verbose('strassen echelon of %s x %s matrix'%(self._nrows, self._ncols))
8857+ tm = verbose('strassen echelon of %s x %s matrix'%(self._nrows, self._ncols), level=2 )
88568858
88578859 self.check_mutability()
88588860
@@ -8872,7 +8874,7 @@ cdef class Matrix(Matrix1):
88728874 from sage.matrix import strassen
88738875 pivots = strassen.strassen_echelon(self.matrix_window(), cutoff)
88748876 self.cache('pivots', pivots)
8875- verbose('done with strassen', tm)
8877+ verbose('done with strassen', level=2, t= tm)
88768878
88778879 cpdef matrix_window(self, Py_ssize_t row=0, Py_ssize_t col=0,
88788880 Py_ssize_t nrows=-1, Py_ssize_t ncols=-1,
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