Support univariate Laurent divisibility over non-domains - #42693
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This implements the univariate phase of #41318. It is a narrower alternative
to #41327: multivariate Laurent polynomial rings over non-integral domains keep
their existing guard.
For a coefficient ring
A, the implementation uses the standard isomorphismbetween
A[x, x^-1]andA[x, y]/(xy - 1). Before embedding an element in the cover, itremoves its overall Laurent monomial factor, which is a unit. This keeps
Groebner-basis work independent of a harmless global exponent shift.
The change:
paths;
dividesand ideal membership over supportednon-integral domains through the polynomial cover;
extended ideal;
work;
NotImplementedErrorfor unsupported polynomial backends instead ofsilently returning a false negative.
Performance
Measured against the compiled
developbaseline on one pinned CPU,alternating variants across four fresh processes (nine inner rounds each):
developdivides, falsedivides, trueZmod(8)cover divisibility10^1210^12Zmod(8)ideal, cold / hotTests
./sage -t --warn-long 5.0 src/sage/rings/polynomial/laurent_polynomial.pyx src/sage/rings/polynomial/laurent_polynomial_ideal.py src/sage/rings/polynomial/laurent_polynomial_ring_base.py-- 767 tests passed.
Zmod(4),Zmod(6),Zmod(8), andZmod(12): 180 membership cases and 180 knownmultiples passed.
git diff --checkpassed.Fixes #41318.
📝 Checklist
⌛ Dependencies
None.