Standalone Mac Lane 1.7.5

Stable version of the Mac Lane infrastructure for discrete (pseudo-)valuations which should work on an unmodified Sage 7.4 or later.

To use, download the attached archive and

$ tar zxf mac_lane-1.7.5.tgz
$ mv mac_lane-mac_lane-1.7.5 mac_lane
$ sage
sage: from mac_lane import *
sage: pAdicValuation(QQ, 2)
2-adic valuation

The code heavily uses assert statements. These checks can be quite expensive. To disable them, start sage as PYTHONOPTIMIZE=yes sage.

Changes in this version

• Comparison of limit valuations:

sage: R.<x> = QQ[]
sage: F = (x^2 + 7) * (x^2 + 9)
sage: G = (x^2 + 7)
sage: V = pAdicValuation(QQ, 2).mac_lane_approximants(F, require_incomparability=True); V
[[ Gauss valuation induced by 2-adic valuation, v(x + 1) = 2 ],
 [ Gauss valuation induced by 2-adic valuation, v(x + 1) = 1/2, v(x^2 + 2*x + 3) = 3/2 ],
 [ Gauss valuation induced by 2-adic valuation, v(x + 3) = 3 ]]
sage: LimitValuation(V[0], F) >= LimitValuation(V[1], F)
False
sage: LimitValuation(V[0], F) >= LimitValuation(V[0], G)
True