Wrong basic interval arithmetic in PolynomialRing

[gmoroz]

Some multiplications in multivariate polynomial rings over RIF or CIF are wrong:

sage: R.<x,y> = PolynomialRing(RIF,2)
sage: RIF(-2,1)*x
0

More tests

sage: R.<x,y> = PolynomialRing(RIF,2)
sage: RIF(-2,1)          # OK
0.?e1
sage: RIF(-2,1)*x        # Wrong
0
sage: RIF(-2,1)*x == 0   # Wrong
True
sage: cmp(RIF(-2,1)*x,0) # Wrong
0
sage: RIF(2,5)*x         # OK
1.?e1*x
sage: RIF(2,5)*x == 0    # OK
False

Code digging

The problem comes from the coercion:

sage: R(RIF(-2,1))
0
sage: R(RIF(-2,1)) == 0
True

This in turn comes from the creation (in __init__ of class MPolynomial_polydict in sage.rings.polynomial.multi_polynomial_element) of a PolyDict? object (defined in sage.rings.polynomial.polydict) with the option remove_zero == True.

from sage.rings.polynomial.polydict import PolyDict
sage: PolyDict({(0,0):1}, remove_zero=True) # OK
PolyDict with representation {(0, 0): 1}
sage: PolyDict({(0,0):0}, remove_zero=True) # OK
PolyDict with representation {}
sage: PolyDict({(0,0):RIF(-1,1)}, remove_zero=True) # Wrong
PolyDict with representation {}

To check if x is different from 0, PolyDict? uses the test x != 0, which actually checks for disjointness in interval field:

sage: RIF(-2,1) != 0
False

Possible correction

This bug might be corrected by replacing in PolyDict? the tests x != zero by one of:

• cmp(x,zero) != 0
• not x.is_zero()
• not x == zero

Apply:

• trac_13760_interval_polynomial_fix.patch
• trac_13760_regression_tests.patch
• trac_7712_regression_tests_for_13760_fix.patch
• trac_13760_documentation_fix.patch

[gmoroz]

A patch changing x != zero by not x == zero.

[zimmerma]

Guillaume, a non-regression test is missing (also for #7712).

Paul

[zimmerma]

all tests pass on top of 5.4.1, just waiting for a non-regression test.

Paul

[gmoroz]

add regression tests (to be applied after the fix patch)

[zimmerma]

Guillaume, why didn't you add as regression tests the examples in the description of #7712 and this ticket?

Paul

[zimmerma]

all tests pass with the regression tests.

Paul

[gmoroz]

I attached the patch with regression tests with user level examples on #7712 (this choice was quite random).

[gmoroz]

Includes regression tests for #7712 and #13760 (same patch as in #7712, moved here for convenience)

[jdemeyer]

Please indicate which patch(es) need to be applied.

[zimmerma]

Replying to jdemeyer:

Please indicate which patch(es) need to be applied.

Done. Paul

[tscrim]

One very minor documentation thing, there should be a blankline after any double colon :: (see line 514 in the trac_13760_regression_tests.patch ). Thanks.

[gmoroz]

Replying to tscrim:

One very minor documentation thing, there should be a blankline after any double colon :: (see line 514 in the trac_13760_regression_tests.patch ). Thanks.

It seems that I cannot attach a new patch for that. Is it because of the positive review status?

[tscrim]

Replying to gmoroz:

It seems that I cannot attach a new patch for that. Is it because of the positive review status?

Strange...I don't think so, but I'll set this to needs work and try it then.

[gmoroz]

Replying to tscrim:

Strange...I don't think so, but I'll set this to needs work and try it then.

My bad, it appears that my file didn't have permissions to be read.

[tscrim]

Thanks for fixing this.