Re: [math-fun] binary operation seeks symbol, name
I agree with Erich that "smin" and "smax" are fun to say, but I think I will follow Joerg's suggestion and write the operations as min^- and max^+ (and not give them names at all). As for Henry's request
Tell us more about the interesting properties of these operators.
the operations come up in the following context: Suppose we know that m and n are distinct integers, where m lies in the interval [a,b] and n lies in the interval [c,d]. Then max(m,n) lies in the interval [max^+(a,c), max(b,d)] while min(m,n) lies in the interval [min(a,c), min^-(b,d)]. Jim
I was curious about abstract algebraic properties like associativity, distributivity over ???, etc. At 11:31 AM 7/24/2009, James Propp wrote:
I agree with Erich that "smin" and "smax" are fun to say, but I think I will follow Joerg's suggestion and write the operations as min^- and max^+ (and not give them names at all). As for Henry's request
Tell us more about the interesting properties of these operators.
the operations come up in the following context: Suppose we know that m and n are distinct integers, where m lies in the interval [a,b] and n lies in the interval [c,d]. Then max(m,n) lies in the interval [max^+(a,c), max(b,d)] while min(m,n) lies in the interval [min(a,c), min^-(b,d)].
Jim
I would suspect a name exists. The max-or-increment version comes up when trying to compile an expression using one accumulator and the minimum number of temporary variables. Assume # is commutative but not associative. # requires one instruction, Sharp X, which performs accum <= accum # X. Then compile (A#B) # (C # (D#E)): When the two subexpressions on either side of # require an unequal number of temps, then the cost of the expression is just the larger of the two subexpr costs. But if the two sides both require K temps, the cost of the whole expression is 1 extra temp. Rich ------------- Quoting Henry Baker <hbaker1@pipeline.com>:
I was curious about abstract algebraic properties like associativity, distributivity over ???, etc.
At 11:31 AM 7/24/2009, James Propp wrote:
I agree with Erich that "smin" and "smax" are fun to say, but I think I will follow Joerg's suggestion and write the operations as min^- and max^+ (and not give them names at all). As for Henry's request
Tell us more about the interesting properties of these operators.
the operations come up in the following context: Suppose we know that m and n are distinct integers, where m lies in the interval [a,b] and n lies in the interval [c,d]. Then max(m,n) lies in the interval [max^+(a,c), max(b,d)] while min(m,n) lies in the interval [min(a,c), min^-(b,d)].
Jim
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