
Re: Is there any efficient easy way to compare two lists with the same length with Mathematica?
Posted:
Jan 20, 2012 1:49 AM


Note however that == does not "thread" over lists. Equal is, of course, not Listable so {1,1}==1 is unevaluated
Thread[{1, 1} == 1]
{True, True}
Equality of lists (including matrices etc) is indeed implemented (but not through Listability) because the advantage of being able to use the same function Equal for all these different situations overrides the flexibility that you loose (like the one you point out). So I agree, but I simply don't think and equally good case can be made for Greater etc.
Andrzej
On 19 Jan 2012, at 17:24, Murray Eisenberg wrote:
> > > Yes, I understand the danger of having greater, etc., threading automatically over lists. > > But one might make the same argument as to whether == should thread automatically. For example, suppose you are modeling rational numbers as pairs of integers. Then you would want {a,b} == {c, d} to be True exacgly when a d == b c. > > On 1/19/12 5:10 AM, Andrzej Kozlowski wrote: >> I do not think I would like Mathematica to automatically thread Greater >> etc over lists or automatically return False or True. Comparisons such >> as {3, 4}>= {2, 5} do not have a canonical meaning and they may arise >> in programs where the fact that they are kept unevaluated can be >> convenient e.g this >> Min /@ ({3, 4}>= {2, 5}) is a convenient way to compare minima >> (Min@{3,5}>=Min@{2,5} is quite a lot longer...). >> In general, there has to be a balance between the sort of things >> Mathematica does automatically and the sort of things that Mathematica >> leaves unevaluated until you make your intention more clear (by using >> Thread, for instance). In this particular case I think the second choice >> is the right one. >> >> Andrzej Kozlowski >> >> >> >> On 18 Jan 2012, at 11:57, Murray Eisenberg wrote: >> >>> Over time more and more things like this have been extended to work >>> automatically on lists. But so far, as you discovered, not GreaterEqual >>> (nor Greater, etc.). Here's one way without explicitly using Table: >>> >>> a = RandomInteger[{0, 20}, 5]; >>> b = RandomInteger[{0, 20}, 5]; >>> And @@ MapThread[Greater, {a, b}] >>> >>> The key there is MapThread, which does what you (and I) would evidently >>> like Mathematica to do automatically  in effect, to make GreaterEqual >>> have Listable as an Attribute. >>> >>> On 1/17/12 3:34 AM, Rex wrote: >>>> Given two lists `A={a1,a2,a3,...an}` and `B={b1,b2,b3,...bn}`, I would >>>> say `A>=B` if and only if all `ai>=bi`. >>>> >>>> There is a builtin logical comparison of two lists, `A==B`, but no >>>> `A>B`. >>>> Do we need to compare each element like this >>>> >>>> And@@Table[A[[i]]>=B[[i]],{i,n}] >>>> >>>> Any better tricks to do this? >>>> >>> >>>  >>> Murray Eisenberg murray@math.umass.edu >>> Mathematics& Statistics Dept. >>> Lederle Graduate Research Tower phone 413 5491020 (H) >>> University of Massachusetts 413 5452859 (W) >>> 710 North Pleasant Street fax 413 5451801 >>> Amherst, MA 010039305 >>> >> >> > >  > Murray Eisenberg murray@math.umass.edu > Mathematics & Statistics Dept. > Lederle Graduate Research Tower phone 413 5491020 (H) > University of Massachusetts 413 5452859 (W) > 710 North Pleasant Street fax 413 5451801 > Amherst, MA 010039305

