Relevance of Landau's Algorithm for Denesting Radicals












3














I just came across a Wikipedia article Nested Radicals that mentions Landau's Algorithm for deciding, whether a nested radical can be denested, but that Wikipedia article is just a stub.
Googling "Landau's Algorithms" produces references to the Wang and Landau Algorithm.




Question:



What role does Landau's Algorithm play in mathematical research, i.e. did it pave the way for further progress, e.g. towards a deterministic algorithm for denesting radicals, or did it "just" solve an isolated problem?



I am asking because the original article is freely accessible online, but isn't described in the omniscient Wikipedia.

Is my impression right, that because Ramanujan provided some examples of denested radicals, that the topic is of some relevance?







algebraic-number-theory algorithms







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    3














    I just came across a Wikipedia article Nested Radicals that mentions Landau's Algorithm for deciding, whether a nested radical can be denested, but that Wikipedia article is just a stub.
    Googling "Landau's Algorithms" produces references to the Wang and Landau Algorithm.




    Question:



    What role does Landau's Algorithm play in mathematical research, i.e. did it pave the way for further progress, e.g. towards a deterministic algorithm for denesting radicals, or did it "just" solve an isolated problem?



    I am asking because the original article is freely accessible online, but isn't described in the omniscient Wikipedia.

    Is my impression right, that because Ramanujan provided some examples of denested radicals, that the topic is of some relevance?







    algebraic-number-theory algorithms







    share|cite|improve this question

























      3












      3








      3







      I just came across a Wikipedia article Nested Radicals that mentions Landau's Algorithm for deciding, whether a nested radical can be denested, but that Wikipedia article is just a stub.
      Googling "Landau's Algorithms" produces references to the Wang and Landau Algorithm.




      Question:



      What role does Landau's Algorithm play in mathematical research, i.e. did it pave the way for further progress, e.g. towards a deterministic algorithm for denesting radicals, or did it "just" solve an isolated problem?



      I am asking because the original article is freely accessible online, but isn't described in the omniscient Wikipedia.

      Is my impression right, that because Ramanujan provided some examples of denested radicals, that the topic is of some relevance?







      algebraic-number-theory algorithms







      share|cite|improve this question













      I just came across a Wikipedia article Nested Radicals that mentions Landau's Algorithm for deciding, whether a nested radical can be denested, but that Wikipedia article is just a stub.
      Googling "Landau's Algorithms" produces references to the Wang and Landau Algorithm.




      Question:



      What role does Landau's Algorithm play in mathematical research, i.e. did it pave the way for further progress, e.g. towards a deterministic algorithm for denesting radicals, or did it "just" solve an isolated problem?



      I am asking because the original article is freely accessible online, but isn't described in the omniscient Wikipedia.

      Is my impression right, that because Ramanujan provided some examples of denested radicals, that the topic is of some relevance?







      algebraic-number-theory algorithms




      algebraic-number-theory algorithms






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      asked 2 hours ago









      Manfred Weis

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          This 2017 article Gkioulekas - On the denesting of nested square roots summarizes the status of this topic. Landau's algorithm is not a "final" solution because it runs in exponential time with respect to the depth of the expression that one is attempting to denest. To find a general algorithm that runs in polynomial time remains an open problem. See also this related MSE posting.






          share|cite|improve this answer























          • Maybe it's just me, but I thought I remembered a massive re-organisation that rendered all ResearchGate links pointing to the wrong place. (Maybe I'm thinking of CiteSeer.) Anyway, though it can probably rot even more easily, here's a link to the article on the author's home page: Gkioulekas - On the de-nesting of nested square roots.
            – LSpice
            1 hour ago










          • Also, I edited to add the name of the author of the paper, but apparently did so while you were making your own edit, with the result that the system thought I was deleting your edit. I apologise, and think I have restored your intended edit.
            – LSpice
            1 hour ago











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          1 Answer
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          active

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          2














          This 2017 article Gkioulekas - On the denesting of nested square roots summarizes the status of this topic. Landau's algorithm is not a "final" solution because it runs in exponential time with respect to the depth of the expression that one is attempting to denest. To find a general algorithm that runs in polynomial time remains an open problem. See also this related MSE posting.






          share|cite|improve this answer























          • Maybe it's just me, but I thought I remembered a massive re-organisation that rendered all ResearchGate links pointing to the wrong place. (Maybe I'm thinking of CiteSeer.) Anyway, though it can probably rot even more easily, here's a link to the article on the author's home page: Gkioulekas - On the de-nesting of nested square roots.
            – LSpice
            1 hour ago










          • Also, I edited to add the name of the author of the paper, but apparently did so while you were making your own edit, with the result that the system thought I was deleting your edit. I apologise, and think I have restored your intended edit.
            – LSpice
            1 hour ago
















          2














          This 2017 article Gkioulekas - On the denesting of nested square roots summarizes the status of this topic. Landau's algorithm is not a "final" solution because it runs in exponential time with respect to the depth of the expression that one is attempting to denest. To find a general algorithm that runs in polynomial time remains an open problem. See also this related MSE posting.






          share|cite|improve this answer























          • Maybe it's just me, but I thought I remembered a massive re-organisation that rendered all ResearchGate links pointing to the wrong place. (Maybe I'm thinking of CiteSeer.) Anyway, though it can probably rot even more easily, here's a link to the article on the author's home page: Gkioulekas - On the de-nesting of nested square roots.
            – LSpice
            1 hour ago










          • Also, I edited to add the name of the author of the paper, but apparently did so while you were making your own edit, with the result that the system thought I was deleting your edit. I apologise, and think I have restored your intended edit.
            – LSpice
            1 hour ago














          2












          2








          2






          This 2017 article Gkioulekas - On the denesting of nested square roots summarizes the status of this topic. Landau's algorithm is not a "final" solution because it runs in exponential time with respect to the depth of the expression that one is attempting to denest. To find a general algorithm that runs in polynomial time remains an open problem. See also this related MSE posting.






          share|cite|improve this answer














          This 2017 article Gkioulekas - On the denesting of nested square roots summarizes the status of this topic. Landau's algorithm is not a "final" solution because it runs in exponential time with respect to the depth of the expression that one is attempting to denest. To find a general algorithm that runs in polynomial time remains an open problem. See also this related MSE posting.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited 1 hour ago









          LSpice

          2,82322627




          2,82322627










          answered 1 hour ago









          Carlo Beenakker

          73.3k9165274




          73.3k9165274












          • Maybe it's just me, but I thought I remembered a massive re-organisation that rendered all ResearchGate links pointing to the wrong place. (Maybe I'm thinking of CiteSeer.) Anyway, though it can probably rot even more easily, here's a link to the article on the author's home page: Gkioulekas - On the de-nesting of nested square roots.
            – LSpice
            1 hour ago










          • Also, I edited to add the name of the author of the paper, but apparently did so while you were making your own edit, with the result that the system thought I was deleting your edit. I apologise, and think I have restored your intended edit.
            – LSpice
            1 hour ago


















          • Maybe it's just me, but I thought I remembered a massive re-organisation that rendered all ResearchGate links pointing to the wrong place. (Maybe I'm thinking of CiteSeer.) Anyway, though it can probably rot even more easily, here's a link to the article on the author's home page: Gkioulekas - On the de-nesting of nested square roots.
            – LSpice
            1 hour ago










          • Also, I edited to add the name of the author of the paper, but apparently did so while you were making your own edit, with the result that the system thought I was deleting your edit. I apologise, and think I have restored your intended edit.
            – LSpice
            1 hour ago
















          Maybe it's just me, but I thought I remembered a massive re-organisation that rendered all ResearchGate links pointing to the wrong place. (Maybe I'm thinking of CiteSeer.) Anyway, though it can probably rot even more easily, here's a link to the article on the author's home page: Gkioulekas - On the de-nesting of nested square roots.
          – LSpice
          1 hour ago




          Maybe it's just me, but I thought I remembered a massive re-organisation that rendered all ResearchGate links pointing to the wrong place. (Maybe I'm thinking of CiteSeer.) Anyway, though it can probably rot even more easily, here's a link to the article on the author's home page: Gkioulekas - On the de-nesting of nested square roots.
          – LSpice
          1 hour ago












          Also, I edited to add the name of the author of the paper, but apparently did so while you were making your own edit, with the result that the system thought I was deleting your edit. I apologise, and think I have restored your intended edit.
          – LSpice
          1 hour ago




          Also, I edited to add the name of the author of the paper, but apparently did so while you were making your own edit, with the result that the system thought I was deleting your edit. I apologise, and think I have restored your intended edit.
          – LSpice
          1 hour ago


















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