Relevance of Landau's Algorithm for Denesting Radicals
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
asked 2 hours ago
Manfred Weis
4,44521339
add a comment |
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
asked 2 hours ago
Manfred Weis
4,44521339
add a comment |
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
asked 2 hours ago
Manfred Weis
4,44521339
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
asked 2 hours ago
Manfred Weis
4,44521339
asked 2 hours ago
Manfred Weis
4,44521339
asked 2 hours ago
Manfred Weis
4,44521339
asked 2 hours ago
Manfred Weis
4,44521339
asked 2 hours ago
Manfred Weis
4,44521339
4,44521339
add a comment |
add a comment |
1 Answer
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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.
edited 1 hour ago
LSpice
2,82322627
answered 1 hour ago
Carlo Beenakker
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
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
edited 1 hour ago
LSpice
2,82322627
answered 1 hour ago
Carlo Beenakker
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
add a comment |
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.
edited 1 hour ago
LSpice
2,82322627
answered 1 hour ago
Carlo Beenakker
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
add a comment |
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.
edited 1 hour ago
LSpice
2,82322627
answered 1 hour ago
Carlo Beenakker
73.3k9165274
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.
edited 1 hour ago
LSpice
2,82322627
answered 1 hour ago
Carlo Beenakker
73.3k9165274
edited 1 hour ago
LSpice
2,82322627
edited 1 hour ago
LSpice
2,82322627
edited 1 hour ago
LSpice
2,82322627
2,82322627
answered 1 hour ago
Carlo Beenakker
73.3k9165274
answered 1 hour ago
Carlo Beenakker
73.3k9165274
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
add a comment |
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
add a comment |
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