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Matthias Koeppe
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Use more block tags, update # needs
1 parent ee025b0 commit 33f8c98

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‎src/sage/matrix/matrix1.pyx

Lines changed: 54 additions & 44 deletions
Original file line numberDiff line numberDiff line change
@@ -96,21 +96,22 @@ cdef class Matrix(Matrix0):
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EXAMPLES::
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sage: # needs sage.libs.gap
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sage: A = MatrixSpace(QQ,3,3)([0,1,2,3,4,5,6,7,8])
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sage: g = gap(A) # indirect doctest # needs sage.libs.gap
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sage: g # needs sage.libs.gap
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sage: g = gap(A) # indirect doctest
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sage: g
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[ [ 0, 1, 2 ], [ 3, 4, 5 ], [ 6, 7, 8 ] ]
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sage: g.CharacteristicPolynomial() # needs sage.libs.gap
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sage: g.CharacteristicPolynomial()
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x_1^3-12*x_1^2-18*x_1
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sage: A.characteristic_polynomial() # needs sage.libs.gap
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sage: A.characteristic_polynomial()
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x^3 - 12*x^2 - 18*x
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sage: matrix(QQ, g) == A # needs sage.libs.gap
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sage: matrix(QQ, g) == A
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True
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Particularly difficult is the case of matrices over cyclotomic
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fields and general number fields. See :trac:`5618` and :trac:`8909`::
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sage: # needs sage.rings.number_field
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sage: # needs sage.libs.gap sage.rings.number_field
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sage: K.<zeta> = CyclotomicField(8)
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sage: A = MatrixSpace(K, 2, 2)([0, 1+zeta, 2*zeta, 3])
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sage: g = gap(A); g
@@ -120,7 +121,7 @@ cdef class Matrix(Matrix0):
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sage: g.IsMatrix()
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true
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sage: # needs sage.rings.number_field
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sage: # needs sage.libs.gap sage.rings.number_field
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sage: x = polygen(ZZ, 'x')
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sage: L.<tau> = NumberField(x^3 - 2)
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sage: A = MatrixSpace(L, 2, 2)([0, 1+tau, 2*tau, 3])
@@ -157,7 +158,7 @@ cdef class Matrix(Matrix0):
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sage: libgap(identity_matrix(ZZ, 2)) # needs sage.libs.gap
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[ [ 1, 0 ], [ 0, 1 ] ]
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sage: libgap(matrix(GF(3), 2, 2, [4,5,6,7])) # needs sage.libs.gap sage.rings.finite_rings
161+
sage: libgap(matrix(GF(3), 2, 2, [4,5,6,7])) # needs sage.libs.gap
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[ [ Z(3)^0, Z(3) ], [ 0*Z(3), Z(3)^0 ] ]
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"""
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from sage.libs.gap.libgap import libgap
@@ -301,26 +302,28 @@ cdef class Matrix(Matrix0):
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We first coerce a square matrix. ::
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sage: # optional - magma
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sage: A = MatrixSpace(QQ,3)([1,2,3,4/3,5/3,6/4,7,8,9])
305-
sage: B = magma(A); B # (indirect doctest) optional - magma
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sage: B = magma(A); B # indirect doctest
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[ 1 2 3]
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[4/3 5/3 3/2]
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[ 7 8 9]
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sage: B.Type() # optional - magma
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sage: B.Type()
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AlgMatElt
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sage: B.Parent() # optional - magma
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sage: B.Parent()
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Full Matrix Algebra of degree 3 over Rational Field
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We coerce a non-square matrix over
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`\ZZ/8\ZZ`. ::
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sage: # optional - magma
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sage: A = MatrixSpace(Integers(8),2,3)([-1,2,3,4,4,-2])
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sage: B = magma(A); B # optional - magma
321+
sage: B = magma(A); B
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[7 2 3]
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[4 4 6]
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sage: B.Type() # optional - magma
324+
sage: B.Type()
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ModMatRngElt
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sage: B.Parent() # optional - magma
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sage: B.Parent()
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Full RMatrixSpace of 2 by 3 matrices over IntegerRing(8)
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sage: R.<x,y> = QQ[]
@@ -338,17 +341,17 @@ cdef class Matrix(Matrix0):
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We coerce a matrix over a cyclotomic field, where the generator
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must be named during the coercion. ::
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sage: K = CyclotomicField(9); z = K.0 # needs sage.rings.number_field
342-
sage: M = matrix(K, 3, 3, [0,1,3,z,z**4,z-1,z**17,1,0]) # needs sage.rings.number_field
343-
sage: M # needs sage.rings.number_field
344+
sage: # optional - magma, needs sage.rings.number_field
345+
sage: K = CyclotomicField(9); z = K.0
346+
sage: M = matrix(K, 3, 3, [0,1,3,z,z**4,z-1,z**17,1,0]); M
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[ 0 1 3]
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[ zeta9 zeta9^4 zeta9 - 1]
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[-zeta9^5 - zeta9^2 1 0]
347-
sage: magma(M) # optional - magma
350+
sage: magma(M)
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[ 0 1 3]
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[ zeta9 zeta9^4 zeta9 - 1]
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[-zeta9^5 - zeta9^2 1 0]
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sage: magma(M**2) == magma(M)**2 # optional - magma
354+
sage: magma(M**2) == magma(M)**2
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True
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One sparse matrix::
@@ -438,15 +441,15 @@ cdef class Matrix(Matrix0):
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EXAMPLES::
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sage: m = matrix(ZZ, [[1,2],[3,4]])
441-
sage: macaulay2(m) #optional - macaulay2 (indirect doctest)
444+
sage: macaulay2(m) # indirect doctest # optional - macaulay2
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| 1 2 |
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| 3 4 |
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::
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sage: R.<x,y> = QQ[]
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sage: m = matrix([[x,y],[1+x,1+y]])
449-
sage: macaulay2(m) #optional - macaulay2
452+
sage: macaulay2(m) # optional - macaulay2
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| x y |
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| x+1 y+1 |
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@@ -462,9 +465,9 @@ cdef class Matrix(Matrix0):
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Check that degenerate matrix dimensions are handled correctly
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(:trac:`28591`)::
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sage: macaulay2(matrix(QQ, 2, 0)).numrows() # optional - macaulay2
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sage: macaulay2(matrix(QQ, 2, 0)).numrows() # optional - macaulay2
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2
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sage: macaulay2(matrix(QQ, 0, 2)).numcols() # optional - macaulay2
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sage: macaulay2(matrix(QQ, 0, 2)).numcols() # optional - macaulay2
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2
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"""
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if macaulay2 is None:
@@ -516,7 +519,7 @@ cdef class Matrix(Matrix0):
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[1 2 3]
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[4 5 6]
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[7 8 9]
519-
sage: b = scilab(a); b # optional - scilab (indirect doctest)
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sage: b = scilab(a); b # indirect doctest # optional - scilab
520523
1. 2. 3.
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4. 5. 6.
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7. 8. 9.
@@ -577,14 +580,15 @@ cdef class Matrix(Matrix0):
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Symbolic matrices are supported::
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sage: M = matrix([[sin(x), cos(x)], [-cos(x), sin(x)]]); M # needs sage.symbolic
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sage: # needs sympy sage.symbolic
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sage: M = matrix([[sin(x), cos(x)], [-cos(x), sin(x)]]); M
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[ sin(x) cos(x)]
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[-cos(x) sin(x)]
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sage: sM = M._sympy_(); sM # needs sympy sage.symbolic
587+
sage: sM = M._sympy_(); sM
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Matrix([
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[ sin(x), cos(x)],
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[-cos(x), sin(x)]])
587-
sage: sM.subs(x, pi/4) # needs sympy sage.symbolic
591+
sage: sM.subs(x, pi/4)
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Matrix([
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[ sqrt(2)/2, sqrt(2)/2],
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[-sqrt(2)/2, sqrt(2)/2]])
@@ -680,20 +684,21 @@ cdef class Matrix(Matrix0):
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EXAMPLES::
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sage: # needs numpy
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sage: a = matrix(3, range(12))
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sage: a.numpy() # needs numpy
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sage: a.numpy()
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array([[ 0, 1, 2, 3],
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[ 4, 5, 6, 7],
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[ 8, 9, 10, 11]])
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sage: a.numpy('f') # needs numpy
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sage: a.numpy('f')
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array([[ 0., 1., 2., 3.],
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[ 4., 5., 6., 7.],
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[ 8., 9., 10., 11.]], dtype=float32)
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sage: a.numpy('d') # needs numpy
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sage: a.numpy('d')
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array([[ 0., 1., 2., 3.],
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[ 4., 5., 6., 7.],
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[ 8., 9., 10., 11.]])
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sage: a.numpy('B') # needs numpy
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sage: a.numpy('B')
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array([[ 0, 1, 2, 3],
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[ 4, 5, 6, 7],
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[ 8, 9, 10, 11]], dtype=uint8)
@@ -712,15 +717,16 @@ cdef class Matrix(Matrix0):
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the magic :meth:`__array__` method) to convert Sage matrices
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to numpy arrays::
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715-
sage: import numpy # needs numpy
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sage: b = numpy.array(a); b # needs numpy
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sage: # needs numpy
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sage: import numpy
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sage: b = numpy.array(a); b
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array([[ 0, 1, 2, 3],
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[ 4, 5, 6, 7],
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[ 8, 9, 10, 11]])
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sage: b.dtype # needs numpy
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sage: b.dtype
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dtype('int32') # 32-bit
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dtype('int64') # 64-bit
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sage: b.shape # needs numpy
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sage: b.shape
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(3, 4)
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"""
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import numpy
@@ -762,7 +768,7 @@ cdef class Matrix(Matrix0):
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EXAMPLES::
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sage: M = Matrix(Integers(7), 2, 2, [5, 9, 13, 15]) ; M
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sage: M = Matrix(Integers(7), 2, 2, [5, 9, 13, 15]); M
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[5 2]
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[6 1]
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sage: M.lift()
@@ -806,7 +812,7 @@ cdef class Matrix(Matrix0):
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EXAMPLES::
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809-
sage: M = Matrix(Integers(8), 2, 4, range(8)) ; M
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sage: M = Matrix(Integers(8), 2, 4, range(8)); M
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[0 1 2 3]
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[4 5 6 7]
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sage: L = M.lift_centered(); L
@@ -1106,7 +1112,8 @@ cdef class Matrix(Matrix0):
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sage: c = a.dense_columns(); c
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[(x, 2/3*x), (x^2, x^5 + 1)]
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sage: parent(c[1])
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Ambient free module of rank 2 over the principal ideal domain Univariate Polynomial Ring in x over Rational Field
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Ambient free module of rank 2 over the principal ideal domain
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Univariate Polynomial Ring in x over Rational Field
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TESTS:
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@@ -1640,7 +1647,8 @@ cdef class Matrix(Matrix0):
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[ 1 2/3]
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[ y y^2]
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sage: C.parent()
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Full MatrixSpace of 2 by 2 dense matrices over Univariate Polynomial Ring in y over Rational Field
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Full MatrixSpace of 2 by 2 dense matrices over
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Univariate Polynomial Ring in y over Rational Field
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Stacking a dense matrix atop a sparse one returns a sparse
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matrix::
@@ -1911,7 +1919,8 @@ cdef class Matrix(Matrix0):
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sage: C = B.augment(A); C
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[ y y^2 1 2]
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sage: C.parent()
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Full MatrixSpace of 1 by 4 dense matrices over Univariate Polynomial Ring in y over Rational Field
1922+
Full MatrixSpace of 1 by 4 dense matrices over
1923+
Univariate Polynomial Ring in y over Rational Field
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sage: D = A.augment(B)
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Traceback (most recent call last):
@@ -1922,7 +1931,8 @@ cdef class Matrix(Matrix0):
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sage: F = E.augment(B); F
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[ 1 2 y y^2]
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sage: F.parent()
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Full MatrixSpace of 1 by 4 dense matrices over Univariate Polynomial Ring in y over Rational Field
1934+
Full MatrixSpace of 1 by 4 dense matrices over
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Univariate Polynomial Ring in y over Rational Field
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AUTHORS:
19281938
@@ -2098,8 +2108,8 @@ cdef class Matrix(Matrix0):
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INPUT:
21002110
2101-
* ``drows`` - list of indices of rows to be deleted from self.
2102-
* ``check`` - checks whether any index in ``drows`` is out of range. Defaults to ``True``.
2111+
* ``drows`` -- list of indices of rows to be deleted from ``self``.
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* ``check`` -- (boolean, default: ``True``); whether to check if any index in ``drows`` is out of range.
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.. SEEALSO::
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@@ -2161,7 +2171,7 @@ cdef class Matrix(Matrix0):
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21622172
def matrix_from_rows_and_columns(self, rows, columns):
21632173
"""
2164-
Return the matrix constructed from self from the given rows and
2174+
Return the matrix constructed from ``self`` from the given rows and
21652175
columns.
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EXAMPLES::

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