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Mathematics

Listing objects under conditions

Richard KAUSCH
Posted 11 years ago

Hello, I cannot find how I could list all the 3-uples of integers {a,b,c} such that 0 < a ? b ? c < a+b and for instance c ? 10. I tried the condition command (/;) , Select, Cases,and other commands given in the Wolfram Documentation without any result. My goal is to let a discrete function act on those 3-uples that match the given condition. Could You please see the attached notebook and help me to find the correct coding to obtain ONLY the solutions and get rid of the useless "Null" .

That you very much for help.

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POSTED BY: Richard KAUSCH
7 Replies
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Paul Cleary
Paul Cleary
Posted 11 years ago
POSTED BY: Paul Cleary
Richard KAUSCH
Richard KAUSCH
Posted 11 years ago
POSTED BY: Richard KAUSCH
Richard KAUSCH
Richard KAUSCH
Posted 11 years ago

Thank you . I do not master properly the language. In your code ,I tried to change # + #2 into #1 +#2 and that changes nothing, (??) The initial condition a ? b ? c < a+b is not fullfilled by the function LessEqual but if this one is replaced by Less, we loose all cases where a = b or b = c. What I absolutely do not see is the way your code gives a ? b ? c, because the function which operates seems to give only that every composant is less than the sum of the two others. (# ? #1 + #2) In my diophantine problem,I have in fact c necessarily even. I cannot add this condition because the third composant c is not identified with the symbol #. Do not waste your patience if my questions are childish. Thank you for your help if you take time to teach.

Best regards
POSTED BY: Richard KAUSCH
Kuba Podkalicki
Kuba Podkalicki
Posted 11 years ago

Sorry, I missed that the last condition is indeed <. Moreover, # is the same as #1 that is why there was no differenc after your change. Is this ok now? Don't hesitate to ask if something is still not clear.

POSTED BY: Kuba Podkalicki
Richard KAUSCH
Richard KAUSCH
Posted 11 years ago

The only question that puzzles me is that I may read the code erroneously because the condition a ? b ? c is not visible ( I understand that the code gives a ? b+c, b ? c+a , c ? a+b ). This reading must be wrong.

POSTED BY: Richard KAUSCH
Kuba Podkalicki
Kuba Podkalicki
Posted 11 years ago

Select applies function in second argument to each triple {a,b,c}. When we have # < #3 & @@ #& it means we check if a&lt;c in that triple. You can write it #[[1]] < #[[3]] & to skip function composition.

Ok, now in our code we are doing a<=b<=c<a+b check which checks those conditions simultaneuosly, like e.g. 1 <= 2 <= 3 < 4.
POSTED BY: Kuba Podkalicki
Kuba Podkalicki
Kuba Podkalicki
Posted 11 years ago

Semi automatic, brute force approach, but works for less memory consuming examples:

Select[Tuples[Range[10], {3}], # <= #2 <= #3 < # + #2 & @@ # &   ]
POSTED BY: Kuba Podkalicki
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