combinat::cartesian
--
cartesian product of sets (deprecated)
combinat::cartesian
(set1, set2, ..., setk)
computes the cartesian
product of the given sets set1
, set2
, ...,
setk
.
For every positive integer n, the set {1, ..., n}
may be denoted by n
, and 0
may be written instead of
the empty set.
combinat::cartesian(set1, set2, ..., setk)
set1, set2, ..., setk | - | Sets of domain type DOM_SET , or nonnegative integers. |
A set of domain type DOM_SET
containing k-tuples of
domain type DOM_LIST
, where k is the number of arguments.
set1
,
set2
is the set set1 x set2 x ... x setk of all k-tuples
[x1,x2,...,xk] with xn in setn
for each 1<=n<=k.combinat::cartesian
() is not commutative, as demonstrated in
example 3.Which cards exist, if you have the following suits and numbers available?
>> combinat::warnDeprecated(FALSE):
combinat::cartesian({Diamondsuit,Heartsuit,Spadesuit,Clubsuit},{7,8,9,10})
{[Clubsuit, 7], [Clubsuit, 8], [Clubsuit, 9], [Clubsuit, 10], [Spadesuit, 7], [Spadesuit, 8], [Spadesuit, 9], [Spadesuit, 10], [Diamondsuit, 7], [Diamondsuit, 8], [Diamondsuit, 9], [Diamondsuit, 10], [Heartsuit, 7], [Heartsuit, 8], [Heartsuit, 9], [Heartsuit, 10]}
The function combinat::cartesian
is deprecated:
>> old_val:=combinat::warnDeprecated(TRUE):
combinat::cartesian({Diamondsuit,Heartsuit,Spadesuit,Clubsuit},{7,8,9,10});
combinat::warnDeprecated(old_val):
Warning: combinat::cartesian(s1,s2,...) is obsolete. Please use 'combinat::cartesianProduct::list(s1,s2,...)' inste\ ad. [combinat::cartesian] {[Clubsuit, 7], [Clubsuit, 8], [Clubsuit, 9], [Clubsuit, 10], [Spadesuit, 7], [Spadesuit, 8], [Spadesuit, 9], [Spadesuit, 10], [Diamondsuit, 7], [Diamondsuit, 8], [Diamondsuit, 9], [Diamondsuit, 10], [Heartsuit, 7], [Heartsuit, 8], [Heartsuit, 9], [Heartsuit, 10]}
Here is the recommended replacement:
>> combinat::cartesianProduct::list({Diamondsuit,Heartsuit,Spadesuit,Clubsuit},{7,8,9,10})
[[Diamondsuit, 7], [Diamondsuit, 8], [Diamondsuit, 9], [Diamondsuit, 10], [Heartsuit, 7], [Heartsuit, 8], [Heartsuit, 9], [Heartsuit, 10], [Spadesuit, 7], [Spadesuit, 8], [Spadesuit, 9], [Spadesuit, 10], [Clubsuit, 7], [Clubsuit, 8], [Clubsuit, 9], [Clubsuit, 10]]
Note that the result is returned as a list.
The same as above, but with other numbers:
>> combinat::cartesian({Diamondsuit,Heartsuit,Spadesuit,Clubsuit},3)
{[Clubsuit, 1], [Clubsuit, 2], [Clubsuit, 3], [Spadesuit, 1], [Spadesuit, 2], [Spadesuit, 3], [Diamondsuit, 1], [Diamondsuit, 2], [Diamondsuit, 3], [Heartsuit, 1], [Heartsuit, 2], [Heartsuit, 3]}
Here is the recommended replacement:
>> combinat::cartesianProduct::list({Diamondsuit,Heartsuit,Spadesuit,Clubsuit},3)
[[Diamondsuit, 1], [Diamondsuit, 2], [Diamondsuit, 3], [Heartsuit, 1], [Heartsuit, 2], [Heartsuit, 3], [Spadesuit, 1], [Spadesuit, 2], [Spadesuit, 3], [Clubsuit, 1], [Clubsuit, 2], [Clubsuit, 3]]
The cartesian product isn't commutative:
>> combinat::cartesian({Diamondsuit},2); combinat::cartesian(2,{Diamondsuit})
{[Diamondsuit, 1], [Diamondsuit, 2]} {[1, Diamondsuit], [2, Diamondsuit]}
MuPAD Combinat, an open source algebraic combinatorics package