(Numeric) should -7 % 5 = -2 ?

Discussion in 'Python' started by Stan Heckman, Jun 28, 2003.

  1. Stan Heckman

    Stan Heckman Guest

    Is the following behavior expected, or have I broken my Numeric
    installation somehow?

    $python
    Python 2.2.2 (#1, Mar 21 2003, 23:01:54)
    [GCC 3.2.3 20030316 (Debian prerelease)] on linux2
    Type "help", "copyright", "credits" or "license" for more information.
    >>> import Numeric
    >>> Numeric.__version__

    '23.0'
    >>> -7 % 5

    3
    >>> Numeric.array(-7) % 5

    -2
    >>> Numeric.remainder(-7, 5)

    -2

    --
    Stan
    Stan Heckman, Jun 28, 2003
    #1
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  2. Stan Heckman wrote:

    > Is the following behavior expected, or have I broken my Numeric
    > installation somehow?
    >
    > $ python
    > >>> import Numeric
    > >>> Numeric.__version__

    > '23.0'
    > >>> -7 % 5

    > 3
    > >>> Numeric.array(-7) % 5

    > -2
    > >>> Numeric.remainder(-7, 5)

    > -2


    looks like Numeric implements C semantics, which is different
    from how Python does it.

    </F>
    Fredrik Lundh, Jun 28, 2003
    #2
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  3. Stan Heckman

    Tim Roberts Guest

    "Louis M. Pecora" <> wrote:

    >Fredrik Lundh <> wrote:
    >
    >> > >>> -7 % 5
    >> > 3
    >> > >>> Numeric.array(-7) % 5
    >> > -2
    >> > >>> Numeric.remainder(-7, 5)
    >> > -2

    >>
    >> looks like Numeric implements C semantics, which is different
    >> from how Python does it.

    >
    >Hmmm... "remainder" makes sense. But "%" is mod, right. IIRC from my
    >abstract algebra days (only 30 yrs ago :) ) The "X mod n" function
    >maps onto the postive integers from 0 to n-1. So sounds like numeric
    >contradicts the math texts. Not good since it's a math module.


    That's a bit harsh. The problem is that there is no universal agreement in
    the world of computer science as to what the semantics of the modulo
    operator should be when presented with a negative operand. Contradicting
    Fredrik, something I do with great reluctance, the C standard specifies
    that the behavior is implementation-defined, so in fact BOTH answers
    "implement C semantics".

    Fortran, on the other hand, defines A mod P as A-INT(A/P)*P, which is
    exactly what Numeric produces. Since folks interested in numerical
    programming often have a strong Fortran background, it is not terribly
    surprising that Numeric should follow Fortran's lead.
    --
    - Tim Roberts,
    Providenza & Boekelheide, Inc.
    Tim Roberts, Jul 1, 2003
    #3
  4. "Tim Roberts" <> wrote in message news:...

    > Contradicting Fredrik, something I do with great reluctance, the C standard
    > specifies that the behavior is implementation-defined, so in fact BOTH answers
    > "implement C semantics".


    Only if you're looking at an old version of the standard; it's not implementation
    dependent in C99.
    Richard Brodie, Jul 1, 2003
    #4
  5. In article <>, Tim Roberts
    <> wrote:

    > >Hmmm... "remainder" makes sense. But "%" is mod, right. IIRC from my
    > >abstract algebra days (only 30 yrs ago :) ) The "X mod n" function
    > >maps onto the postive integers from 0 to n-1. So sounds like numeric
    > >contradicts the math texts. Not good since it's a math module.

    >
    > That's a bit harsh.


    You may be right. I got to work and checked my old Abstract Algebra
    book. The defintion is,

    We write a=b mod m if m divides (a-b) (i.e. no remeinder).

    The defintion does not say how to compute the mod, rather it is an
    expression of a relationship between a and b. Hence, writing -2=-7 mod
    5 appears to be OK.

    The "uniqueness" comes in when we recogize that mod m defines an
    equivalence relation on the integers and so for a given m every integer
    falls into a unique class (or subset of integers). The set of m
    subsets is equivalent to the positive integers 0 to m-1.

    So it appears that the translation between math and computer science is
    not as clear as I thought. In math (well, number theory) mod is a
    relation, not an operation. In computer science it is an operation.

    Waddayathink?

    --
    Lou Pecora
    - My views are my own.
    Louis M. Pecora, Jul 1, 2003
    #5
  6. Stan Heckman

    Bob Gailer Guest

    At 11:19 AM 7/1/2003 -0400, Louis M. Pecora wrote:

    >In article <>, Tim Roberts
    ><> wrote:
    >
    > > >Hmmm... "remainder" makes sense. But "%" is mod, right. IIRC from my
    > > >abstract algebra days (only 30 yrs ago :) ) The "X mod n" function
    > > >maps onto the postive integers from 0 to n-1. So sounds like numeric
    > > >contradicts the math texts. Not good since it's a math module.

    > >
    > > That's a bit harsh.

    >
    >You may be right. I got to work and checked my old Abstract Algebra
    >book. The defintion is,
    >
    >We write a=b mod m if m divides (a-b) (i.e. no remeinder).
    >
    >The defintion does not say how to compute the mod, rather it is an
    >expression of a relationship between a and b. Hence, writing -2=-7 mod
    >5 appears to be OK.
    >[snip]


    To quote from "Number Theory and its History" by Oystein Ore, page 213f:
    "When an integer a is divided by another m, one has
    a = km + r
    where the remainder is some positive integer less than m. Thus for any
    number a there exists a congruence
    a (is congruent to) r (mod m)
    where r is a unique one among the numbers 0, 2, 1, .... m-1"

    Bob Gailer

    303 442 2625


    ---
    Outgoing mail is certified Virus Free.
    Checked by AVG anti-virus system (http://www.grisoft.com).
    Version: 6.0.492 / Virus Database: 291 - Release Date: 6/24/2003
    Bob Gailer, Jul 1, 2003
    #6
  7. "Louis M. Pecora" wrote:

    > We write a=b mod m if m divides (a-b) (i.e. no remeinder).
    >
    > The defintion does not say how to compute the mod, rather it is an
    > expression of a relationship between a and b. Hence, writing -2=-7
    > mod
    > 5 appears to be OK.


    Right. Equivalences modulo m are really alternate numerical spaces in
    which arithmetic is done; in mathematics, the modulo is not strictly an
    operator. In those cases, you don't really have to pick a unique
    residue when doing arithmetic (mod m), since it's all equivalence
    relation anyway.

    In computer science, where modulo is an operator that must return a
    unique value, it's not really specified whether (-n % m) (m, n positive)
    should be negative or not. Some languages/systems chose negative, some
    don't. The choice is never "wrong" unless it's done inconsistently
    within a particular language/system.

    --
    Erik Max Francis && && http://www.alcyone.com/max/
    __ San Jose, CA, USA && 37 20 N 121 53 W && &tSftDotIotE
    / \ People are taught to be racists.
    \__/ Jose Abad
    Erik Max Francis, Jul 2, 2003
    #7
  8. In article <020720031459050258%>,
    Louis M. Pecora wrote:
    > In article <>, Bob
    > Gailer <> wrote:
    >
    >> "When an integer a is divided by another m, one has
    >> a = km + r
    >> where the remainder is some positive integer less than m.

    >
    > Maybe I'm misunderstanding this, but what about -7 divided by 5? We
    > get k=-1 and r=-2.


    -7 = (-2) * 5 + 3

    So actually, k = -2 and r = 3


    > m can be negative. Maybe your quote was for the positive integers only.


    True, that definition does not make sense when m is negative. When I came
    across the subject in introductory group theory they said "positive divisor".

    Julian
    Julian Tibble, Jul 3, 2003
    #8
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