#13760: Wrong basic interval arithmetic in PolynomialRing
------------------------------------------------------+---------------------
Reporter: gmoroz | Owner:
AlexGhitza
Type: defect | Status:
positive_review
Priority: major | Milestone:
sage-5.6
Component: basic arithmetic | Resolution:
Keywords: interval, polynomial, multivariate | Work issues:
docstrings
Report Upstream: N/A | Reviewers: Paul
Zimmermann
Authors: Guillaume Moroz | Merged in:
Dependencies: | Stopgaps:
------------------------------------------------------+---------------------
Changes (by tscrim):
* status: needs_work => positive_review
Old description:
> 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, then
> trac_13760_regression_tests.patch, then
> trac_7712_regression_tests_for_13760_fix.patch, and finally
> trac_13760_documentation_fix.patch.
New description:
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]
--
Comment:
Thanks for fixing this.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13760#comment:21>
Sage <http://www.sagemath.org>
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