How do I use relational operators on vectors?
{1, 2, 3} > {0, 1, 2} (*outputs {1, 2, 3} > {0, 1, 2}*) More generally, I want {a,b}>{c,d} to be equivalent to a>c && b>d. Or, I would want to say vars>0 where vars is a vector of my variables and that one constraint forces them all to be strictly positive. How might I achieve that?
And @@ Thread[{a, b} > {c, d}] (* a > c && b > d *) 
vars>0 example: And @@ Thread[vars > Flatten[ConstantArray[0, {Length[vars], 1}]]] works. $\endgroup$ Here is a new operator ( ⪢,alias \[NestedGreaterGreater] ) that is a generalisation of the built-in > :
NestedGreaterGreater[x___] := And @@ Thread[Greater[x]] This permits interesting operations :
{a, b} ⪢ {c, d} (a > c) && (b > d)
{a, b} ⪢ {c, d} ⪢ {e, f}(a > c > e) && (b > d > f)
{a, b} ⪢ c ⪢ {d, e}(a > c > d) && (b > c > e)
For clearity some parenthesis have been added in the previous results.
1>x>2 gives False (with x symbolic) $\endgroup$ You can also use the BoolEval package. You'd use it like this:
Needs["BoolEval`"] FreeQ[BoolEval[{1, 2, 3} > {0, 1, 2}], 0] (* True *) Or
Times @@ BoolEval[{1, 2, 3} > {0, 1, 2}] == 1 The point being that BoolEval returns a 1 or a 0 for each comparison, representing true or false. If there are no zeroes that means that all comparisons were true.
How do I use relational operators on vectors?
BoolEval is a general answer to this question.
If you want a more compact syntax you could implement BoolEvalAnd, BoolEvalOr etc. along the lines of the solution above.
