Wrong basic interval arithmetic in PolynomialRing

[sagetrac-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:

• attachment: trac_13760_interval_polynomial_fix.patch
• attachment: trac_13760_regression_tests.patch
• attachment: trac_7712_regression_tests_for_13760_fix.patch
• attachment: trac_13760_documentation_fix.patch

CC: @burcin @mwhansen @malb @zimmermann6

Component: basic arithmetic

Keywords: interval, polynomial, multivariate

Author: Guillaume Moroz

Reviewer: Paul Zimmermann

Merged: sage-5.6.beta1

Issue created by migration from https://trac.sagemath.org/ticket/13760

[sagetrac-gmoroz]

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

[sagetrac-gmoroz]

comment:2

Attachment: trac_13760_interval_polynomial_fix.patch.gz

[sagetrac-gmoroz]

Author: gmoroz

[zimmermann6]

comment:5

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

Paul

[zimmermann6]

Work Issues: add non-regression test

[zimmermann6]

comment:7

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

Paul

[sagetrac-gmoroz]

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

[zimmermann6]

comment:8

Attachment: trac_13760_regression_tests.patch.gz

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

Paul

[zimmermann6]

comment:9

all tests pass with the regression tests.

Paul

[sagetrac-gmoroz]

comment:10

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

[sagetrac-gmoroz]

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

[zimmermann6]

comment:12

Attachment: trac_7712_regression_tests_for_13760_fix.patch.gz

[zimmermann6]

Changed author from gmoroz to Guillaume Moroz

[zimmermann6]

Reviewer: Paul Zimmermann

[zimmermann6]

Changed work issues from add non-regression test to none

[jdemeyer]

comment:13

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

[zimmermann6]

comment:15

Replying to @jdemeyer:

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

Done.
Paul

[tscrim]

comment:16

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

[sagetrac-gmoroz]

comment:17

Replying to @tscrim:

One very minor documentation thing, there should be a blankline after any double colon :: (see line 514 in the attachment: 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]

Work Issues: docstrings

[tscrim]

comment:18

Replying to @sagetrac-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.

[sagetrac-gmoroz]

Attachment: trac_13760_documentation_fix.patch.gz

[sagetrac-gmoroz]

comment:20

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]

comment:21

Thanks for fixing this.

[jdemeyer]

Changed work issues from docstrings to none

[jdemeyer]

Merged: sage-5.6.beta1