Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: C = SymmetricGroup(5).character_table()
sage: C.base_ring()
Cyclotomic Field of order 1 and degree 1
sage: P, L, U = C.LU(pivot=’partial’)
sage: C == P*L*U
True
AUTHOR:
•Rob Beezer (2011-04-26)
N(prec=None, digits=None)
Return a numerical approximation of self as either a real or complex number with at least the requested
number of bits or digits of precision.
INPUT:
•prec - an integer: the number of bits of precision
•digits - an integer: digits of precision
OUTPUT: A matrix coerced to a real or complex field with prec bits of precision.
EXAMPLES:
sage: d = matrix([[3, 0],[0,sqrt(2)]]) ;
sage: b = matrix([[1, -1], [2, 2]]) ; e = b * d * b.inverse();e
[ 1/2*sqrt(2) + 3/2 -1/4*sqrt(2) + 3/4]
[ -sqrt(2) + 3 1/2*sqrt(2) + 3/2]
sage: e.numerical_approx(53)
[ 2.20710678118655 0.396446609406726]
[ 1.58578643762690 2.20710678118655]
sage: e.numerical_approx(20)
[ 2.2071 0.39645]
[ 1.5858 2.2071]
sage: (e-I).numerical_approx(20)
[2.2071 - 1.0000*I 0.39645]
[ 1.5858 2.2071 - 1.0000*I]
sage: M=matrix(QQ,4,[i/(i+1) for i in range(12)]);M
[ 0 1/2 2/3]
[ 3/4 4/5 5/6]
[ 6/7 7/8 8/9]
[ 9/10 10/11 11/12]
sage: M.numerical_approx()
[0.000000000000000 0.500000000000000 0.666666666666667]
[0.750000000000000 0.800000000000000 0.833333333333333]
[0.857142857142857 0.875000000000000 0.888888888888889]
[0.900000000000000 0.909090909090909 0.916666666666667]
sage: matrix(SR, 2, 2, range(4)).n()
[0.000000000000000 1.00000000000000]
[ 2.00000000000000 3.00000000000000]
sage: numerical_approx(M)
[0.000000000000000 0.500000000000000 0.666666666666667]
[0.750000000000000 0.800000000000000 0.833333333333333]
126 Chapter 7. Base class for matrices, part 2