# Ticket #10952: trac_10952-reviewer-docs.patch

File trac_10952-reviewer-docs.patch, 2.8 KB (added by rbeezer, 10 years ago)
• ## doc/en/developer/conventions.rst

# HG changeset patch
# User Rob Beezer <beezer@ups.edu>
# Date 1313993715 25200
diff --git a/doc/en/developer/conventions.rst b/doc/en/developer/conventions.rst
 a 0.0511114082399688 -  If a line contains tol or tolerance, numerical results are only verified to the given tolerance. This may be prefixed by abs[olute verified to the given tolerance. This may be prefixed by abs[olute] or rel[ative] to specify whether to measure absolute or relative error; defaults to relative error except when the expected value is exactly zero: error; this defaults to relative error except when the expected value is exactly zero: :: sage: RDF(pi)                               # abs tol 1e-5 3.14159 sage: [10^n for n in [0.0 .. 4]]            # rel tol 2e-4 [0.9999, 10.001, 100.01, 999.9, 10001] sage: RDF(pi)                               # abs tol 1e-5 3.14159 sage: [10^n for n in [0.0 .. 4]]            # rel tol 2e-4 [0.9999, 10.001, 100.01, 999.9, 10001] This can be useful when the exact output is subject to rounding error and/or processor floating point arithmetic variation. and/or processor floating point arithmetic variation.  Here are some more examples. A singular value decomposition of a matrix will produce two unitary matrices.  Over the reals, this means the inverse of the matrix is equal to its transpose.  We test this result by applying the norm to a matrix difference.  The result will usually be a "small" number, distinct from zero. :: sage: A = matrix(RDF, 8, range(64)) sage: U, S, V = A.SVD() sage: (U.transpose()*U-identity_matrix(8)).norm()    # abs tol 1e-10 0.0 The 8-th cyclotomic field is generated by the complex number e^\frac{i\pi}{4}.  Here we compute a numerical approximation. :: sage: K = CyclotomicField(8) sage: g = K.gen(0); g zeta8 sage: N(zeta8)                             # absolute tolerance 1e-15 0.707106781186548 + 0.707106781186547*I A relative tolerance on a root of a polynomial. :: sage: p = (y - 10^16)*(y-10^(-13))*(y-2); p y^3 + (-1e+16)*y^2 + (2e+16)*y - 2000.0 sage: p.roots() sage: p.roots(multiplicities=False)     # relative tol 1e-10 10^16 -  If a line contains todo: not implemented, it is never tested. It is good to include lines like this to make clear what we