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## [Axiom-developer] [WesterProblemSet] pdf, ps, and dvi are now available

 From: Bill Page Subject: [Axiom-developer] [WesterProblemSet] pdf, ps, and dvi are now available Date: Tue, 31 Jan 2006 20:04:24 -0600

```Changes http://wiki.axiom-developer.org/WesterProblemSet/diff
--

??changed:
-[[1, 2, 4, 5], [1, 4, 2, 3]]
-
-
-   (7)  [[1,2,4,5],[1,4,2,3]]
@[[1, 2, 4, 5], [1, 4, 2, 3]]

(7)  @[[1,2,4,5],[1,4,2,3]]

??changed:
-x:= matrix([[41, 27, 22], [79, 53, 78]]);
x:= matrix(@[[41, 27, 22], [79, 53, 78]]);

??changed:
-t:= [[3.33, 3.25, 3.92, 3.50,  4.33,  4.92,  6.08,  7.42,  8.33,  8.00,  9.25,
_
t:= @[[3.33, 3.25, 3.92, 3.50,  4.33,  4.92,  6.08,  7.42,  8.33,  8.00,  9.25,
_

??changed:
-[[37, 45, 38, 42, 31], [4, 0, 5, 2, 4], [31200, 26800, 35000, 30300, 25400]];
@[[37, 45, 38, 42, 31], [4, 0, 5, 2, 4], [31200, 26800, 35000, 30300, 25400]];

??changed:
-[[80, 80, 75, 62, 62, 62, 62, 62, 58, 58, 58, 58, 58, 58, 50, 50, 50, 50, 50, _
@[[80, 80, 75, 62, 62, 62, 62, 62, 58, 58, 58, 58, 58, 58, 50, 50, 50, 50, 50, _

??changed:
-[[  0,   4,   7,   7,  11,  18,  24,  30,  32,  43,  46,  60,  64,  70,  71, _
@[[  0,   4,   7,   7,  11,  18,  24,  30,  32,  43,  46,  60,  64,  70,  71, _

??changed:
-   (5)  [[x= 1,y= 2]]
(5)  @[[x= 1,y= 2]]

??changed:
-   (48)  [[x= - %DW + 4,y= 2,z= %DW]]
(48)  @[[x= - %DW + 4,y= 2,z= %DW]]

??changed:
-   [[x= 1,y= 1,z= 1], [x= - 1,y= 1,z= 1],
@[[x= 1,y= 1,z= 1], [x= - 1,y= 1,z= 1],

??changed:
--- Company, 1981, p. 104 => [[0 1 2 1], [0 -1 1 -1], [2 1 0 -1]]^T
-[transpose(matrix([[0, 1, 2, 1]])), transpose(matrix([[0, 1, 3, 1]])), _
- transpose(matrix([[1, 1, 1, 0]])), transpose(matrix([[1, 3, 6, 2]]))]
-- Company, 1981, p. 104 => @[[0 1 2 1], [0 -1 1 -1], [2 1 0 -1]]^T
[transpose(matrix(@[[0, 1, 2, 1]])), transpose(matrix(@[[0, 1, 3, 1]])), _
transpose(matrix(@[[1, 1, 1, 0]])), transpose(matrix(@[[1, 3, 6, 2]]))]

??changed:
-matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
matrix(@[[1, 2, 3], [4, 5, 6], [7, 8, 9]]);

??changed:
--- (2, 3)-minor => [[1, 2], [7, 8]]
---minor(matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]), 2, 3)
-- (2, 3)-minor => @[[1, 2], [7, 8]]
--minor(matrix(@[[1, 2, 3], [4, 5, 6], [7, 8, 9]]), 2, 3)

??changed:
-   [matrix([[a, 1],[0, a]]), b, matrix([[c, 1, 0],[0, c, 1],[0, 0, c]])])
@[matrix([[a, 1],[0, a]]), b, matrix([[c, 1, 0],[0, c, 1],[0, 0, c]])])

??changed:
--- => [[1 1], [1 0]]
-- => @[[1 1], [1 0]]

??changed:
--- => [[-cos t, -sin t], [sin t, -cos t]]
-matrix([[cos(t), sin(t)], [-sin(t), cos(t)]])
-- => @[[-cos t, -sin t], [sin t, -cos t]]
matrix(@[[cos(t), sin(t)], [-sin(t), cos(t)]])

??changed:
-matrix([[x, y]]) * (a*matrix([[1, 3, 5], [2, 4, 6]]) _
matrix(@[[x, y]]) * (a*matrix(@[[1, 3, 5], [2, 4, 6]]) _

??changed:
-   [(2a - 8)y + (a + 7)x  (4a + 10)y + (3a - 9)x  (6a - 12)y + (5a + 11)x]
@[(2a - 8)y + (a + 7)x  (4a + 10)y + (3a - 9)x  (6a - 12)y + (5a + 11)x]

??changed:
-norm(matrix([[1, -2*%i], [-3*%i, 4]]), %plusInfinity)
norm(matrix(@[[1, -2*%i], [-3*%i, 4]]), %plusInfinity)

??changed:
-norm(matrix([[a/(b*c), 1/c, 1/b], [1/c, b/(a*c), 1/a], [1/b, 1/a, c/(a*b)]]), _
norm(matrix(@[[a/(b*c), 1/c, 1/b], [1/c, b/(a*c), 1/a], [1/b, 1/a, c/(a*b)]]), _

??changed:
--- Hermitian (complex conjugate transpose) => [[1, f(4 + 5 i)], [2 - 3 i, 6]]
-- Hermitian (complex conjugate transpose) => @[[1, f(4 + 5 i)], [2 - 3 i, 6]]

??changed:
-map('conjugate, transpose(matrix([[1, 2 + 3*%i], [f(4 - 5*%i), 6]])) _
map('conjugate, transpose(matrix(@[[1, 2 + 3*%i], [f(4 - 5*%i), 6]])) _

??changed:
-m:= matrix([[a, b], [1, a*b]])
m:= matrix(@[[a, b], [1, a*b]])

??changed:
--- => [[A_11^(-1), -A_11^(-1) A_12 A_22^(-1)], [0, A_22^(-1)]].
-- => @[[A_11^(-1), -A_11^(-1) A_12 A_22^(-1)], [0, A_22^(-1)]].

??changed:
-matrix([[A11, A12], [0, A22]])**(-1)
matrix(@[[A11, A12], [0, A22]])**(-1)

??changed:
--- => [[1 0 -1 0 2], [0 1 2 0 -1], [0 0 0 1 3], [0 0 0 0 0]]
-- => @[[1 0 -1 0 2], [0 1 2 0 -1], [0 0 0 1 3], [0 0 0 0 0]]

??changed:
-rank(matrix([[-1, 3, 7, -5], [4, -2, 1, 3], [2, 4, 15, -7]]))
rank(matrix(@[[-1, 3, 7, -5], [4, -2, 1, 3], [2, 4, 15, -7]]))

??changed:
-rank(matrix([[2*sqrt(2), 8], [6*sqrt(6), 24*sqrt(3)]]))
rank(matrix(@[[2*sqrt(2), 8], [6*sqrt(6), 24*sqrt(3)]]))

??changed:
-rank(matrix([[sin(2*t), cos(2*t)], _
rank(matrix(@[[sin(2*t), cos(2*t)], _

??changed:
--- Null space => [[2 4 1 0], [0 -3 0 1]]^T or variant   [Bradley, p. 207]
-nullSpace(matrix([[1, 0, -2, 0], [-2, 1, 0, 3], [-1, 2, -6, 6]]))
-
-
-   (21)  [[2,4,1,0],[0,- 3,0,1]]
-- Null space => @[[2 4 1 0], [0 -3 0 1]]^T or variant   [Bradley, p. 207]
nullSpace(matrix(@[[1, 0, -2, 0], [-2, 1, 0, 3], [-1, 2, -6, 6]]))

(21)  @[[2,4,1,0],[0,- 3,0,1]]

??changed:

??changed:
--- => lambda = {1, 1, 1}, eigenvectors = [[4 -1 4], [1 -1 2], [3 -1 3]]^T
-- => lambda = {1, 1, 1}, eigenvectors = @[[4 -1 4], [1 -1 2], [3 -1 3]]^T

??changed:

??changed:

??changed:
--- Jordan form => diag([[1 1],[0 1]], [[1 1],[0 1]], -1)   [Gantmacher, p. 172]
-- Jordan form => diag(@[[1 1],[0 1]], [[1 1],[0 1]], -1)   [Gantmacher, p. 172]

??changed:
--- Smith normal form => [[1, 0], [0, x^4 - x^2 + 1]]   [Cullen, p. 230]
-matrix([[x**2, x - 1], [x + 1, x**2]])
-- Smith normal form => @[[1, 0], [0, x^4 - x^2 + 1]]   [Cullen, p. 230]
matrix(@[[x**2, x - 1], [x + 1, x**2]])

??changed:
--- Matrix exponential => e [[cos 2, -sin 2], [sin 2, cos 2]]
-exp(matrix([[1, -2], [2, 1]]))
-- Matrix exponential => e @[[cos 2, -sin 2], [sin 2, cos 2]]
exp(matrix(@[[1, -2], [2, 1]]))

??changed:
--- Sine of a Jordan matrix => diag([[sin a, cos a],[0, sin a]], sin b,
--- [[sin c, cos c, -sin(c)/2],[0, sin c, cos c],[0, 0, sin c]])
-- Sine of a Jordan matrix => diag(@[[sin a, cos a],[0, sin a]], sin b,
-- @[[sin c, cos c, -sin(c)/2],[0, sin c, cos c],[0, 0, sin c]])

??changed:
--- Sine of a matrix => [[1 0 0], [0 1 0], [0 0 1]]   [Cullen, p. 261]
-%pi/2*matrix([[2, 1, 1], [2, 3, 2], [1, 1, 2]]);
-- Sine of a matrix => @[[1 0 0], [0 1 0], [0 0 1]]   [Cullen, p. 261]
%pi/2*matrix(@[[2, 1, 1], [2, 3, 2], [1, 1, 2]]);

??changed:
--- Matrix square root => {+-[[3 1], [1 4]], +-1/sqrt(5) [[-1 7], [7 6]]}
-matrix([[10, 7], [7, 17]])
-- Matrix square root => address@hidden 1], [1 4]], +-1/sqrt(5) [[-1 7], [7 6]]}
matrix(@[[10, 7], [7, 17]])

??changed:
--- => [[e, (e - n) v w + e/2, (n - e) v], [0, e, 0], [0, (e - n) w, n]
-- => @[[e, (e - n) v w + e/2, (n - e) v], [0, e, 0], [0, (e - n) w, n]

??changed:
-matrix([[1, 1, 0], [0, 1, 0], [0, 0, 1]]);
matrix(@[[1, 1, 0], [0, 1, 0], [0, 0, 1]]);

??changed:
--- => [[0 a b], [0 0 0], [0 1/b 0]] for arbitrary a and b
-matrix([[0, 1, 0], [0, 0, 0], [0, 0, 0]]);
-- => @[[0 a b], [0 0 0], [0 1/b 0]] for arbitrary a and b
matrix(@[[0, 1, 0], [0, 0, 0], [0, 0, 0]]);

??changed:
-matrix([[1, 1], [2, 2], [3, 3]])
matrix(@[[1, 1], [2, 2], [3, 3]])

??changed:
--- Hessian of r^2 sin t => [[2 sin t, 2 r cos t], [2 r cos t, -r^2 sin t]]
-- Hessian of r^2 sin t => @[[2 sin t, 2 r cos t], [2 r cos t, -r^2 sin t]]

??changed:
--- Wronskian of (cos t, sin t) => [[cos t, sin t], [-sin t, cos t]]
-- Wronskian of (cos t, sin t) => @[[cos t, sin t], [-sin t, cos t]]

??changed:
--- Jacobian of (r cos t, r sin t) => [[cos t, -r sin t], [sin t, r cos t]]
-MYjacobian(e, v) == matrix([[D(f, x) for x in v] for f in e])
-- Jacobian of (r cos t, r sin t) => @[[cos t, -r sin t], [sin t, r cos t]]
MYjacobian(e, v) == matrix(@[[D(f, x) for x in v] for f in e])

??changed:
--- Hessian of r^2 sin t => [[2 sin t, 2 r cos t], [2 r cos t, -r^2 sin t]]
-- Hessian of r^2 sin t => @[[2 sin t, 2 r cos t], [2 r cos t, -r^2 sin t]]

??changed:
-   matrix([[D(f, [x . i, x . j]) for j in 1..n] for i in 1..n])
matrix(@[[D(f, [x . i, x . j]) for j in 1..n] for i in 1..n])

??changed:
-   matrix([[D(f . j, x, i-1) for j in 1..n] for i in 1..n])
matrix(@[[D(f . j, x, i-1) for j in 1..n] for i in 1..n])

??changed:
-a:= matrix([[1, -2], [3, 4]]);
a:= matrix(@[[1, -2], [3, 4]]);

??changed:
-b:= matrix([[5, 6], [-7, 8]]);
b:= matrix(@[[5, 6], [-7, 8]]);

--