Some list questions

*To*: mathgroup at smc.vnet.net*Subject*: [mg37132] Some list questions*From*: "flip" <flip_alpha at safebunch.com>*Date*: Sat, 12 Oct 2002 05:05:00 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hello (sorry for the long post), I have two seperate list questions that I was hoping to get help with. Question 1. I have a variable length list similar to that generated by FactorInteger, that is {number, exponent} pairs. An example follows. lista = {{2,3},{3,1},{5,1}} ... this is the number 2^3 * 3^1 * 5^1 I want to generate a list of "all" the products of numbers from this list. I can tell that I get a total (3+1)*(1+1)*(1+1) = 4*2*2 = 16, products and I want a list showing all of those. These would be: 2^3 can generate {2^0, 2^1, 2^2, 2^3} = {1, 2, 4 ,8} 3^1 can generate {3^0, 3^1} = {3} ... we dont care about the duplicate "1" 5^1 can generate {5^0, 5^1} = {5} ... we dont care about the duplicate "1" Hence the 4*2*2 = 16 (the product of one more of the exponents) above. Next we should get 16 products (from these lists), namely (I left them as products below to show what I am after): {1, 2, 4, 8, 1*3, 2*3, 4*3, 8*3, 1*5, 2 * 5, 4* 5, 8* 5, 1*3*5, 2*3*5, 4*3*5, 8*3*5} If the list were lista = {{2,4}, {3,2}, {5, 3},{7^5}}, we would have (4+1)(2+1)(3+1)(5+1) = 360 products, for example and the return values should be a single list showing all of those. Question 2. I have two lists and want to generate two new lists from them. These two lists are {number, exponent} pairs. In the first list, I want the "minimum intersection" of {number, exponent} pairs. In the second list, I want the "maximum union" of {number, exponent} pairs. Let me show an example: Input: list1 = {{2, 3}, {3, 4}, {5, 6}, {7, 2}, {17, 5}} list2 = {{2, 5}, {3, 2}, {5, 1}, {7, 3}} Output: minint = {{2, 3}, {3, 2}, {5, 1}, {7, 2}} Note: In this example we only kept those pairs where the intersection of the number exists and also keep the min power of those. maxint = {{2, 5}, {3, 4}, {5, 6}, {7, 3}, {17, 5}} Note: In this example we kept the union of lists and also keep the max power of each. Thank you so much to this newsgroup for being so helpful. Flip Note: remove the "_alpha" from the email given to email me.