Coercion of multivariate polynomials over padics

[edgarcosta]

sage:PolynomialRing(Qp(2), 3, 'x')({(0,0,0):O(2)}).dict()
{}

instead of {(0,0,0):O(2)}

As a side effect substitution and addition is also broken:

sage: R.<x,y,z> = Qp(2)[]
sage: f = x  + y + z - 1
sage: f.dict()
{(0, 0, 0): 1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + 2^9 + 2^10 + 2^11 + 2^12 + 2^13 + 2^14 + 2^15 + 2^16 + 2^17 + 2^18 + 2^19 + O(2^20),
 (0, 0, 1): 1 + O(2^20),
 (0, 1, 0): 1 + O(2^20),
 (1, 0, 0): 1 + O(2^20)}
sage: f.substitute(x=Qp(2)(1).add_bigoh(1)).dict()
{(0, 0, 1): 1 + O(2^20), (0, 1, 0): 1 + O(2^20)}
sage: f((Qp(2)(1).add_bigoh(1),y,z)).dict()
{(0, 0, 1): 1 + O(2^20), (0, 1, 0): 1 + O(2^20)}

While I would expect: {(0, 0, 1): 1 + O(2^20), (0, 1, 0): 1 + O(2^20), (0,0,0): O(2)} and

sage: (f + (1 + O(2))).dict()
{(1, 0, 0): 1 + O(2^20), (0, 0, 1): 1 + O(2^20), (0, 1, 0): 1 + O(2^20)}

Alex Best, pointed out that most likely this has to do with a key removal being done with if blah == 0: instead of if blah.is_zero()

[alexjbest]

The problem is in the PolyDict? add function calls the PolyDict? constructor with zero=K.zero() and remove_zeroes=True, this is quite awkward as it makes it hard to fix this while maintaining that variables with exact zero coefficient removed. Maybe this should be changed so that if PolyDict? constructor is called with remove_zeroes=True then the base ring .is_zero() method is called. Possibly this is a performance hit though?

the offending lines are

if pdict[k] == zero:
    del pdict[k]

in sage/rings/polynomial/polydict.pyx

As for the constructor issue, it is the same with line x = polydict.PolyDict(x, parent.base_ring()(0), remove_zero=True) in sage/rings/polynomial/multi_polynomial_element.py that does it.

[edgarcosta]

Alex asked today about this ticket at the p-adics meeting on zulip.

Essentially the issue is that O(2) == 0 is true and a notion of exact zero should be used instead, I notice that there is a function _is_exact_zero but also x.is_zero(absprec=Infinity) for p-adic elements, are either of these suitable for a fix?

Julian mentioned there's at least one more ticket about this somewhere

On side a note, univariate polynomials seem to do the right thing:

sage: f = PolynomialRing(Qp(2),'a')([O(2),O(2^3)])
sage: f
O(2^3)*a + O(2)

[embray]

Ticket retargeted after milestone closed

[mkoeppe]

Batch modifying tickets that will likely not be ready for 9.1, based on a review of the ticket title, branch/review status, and last modification date.

[mkoeppe]

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.