Relevance of Landau's Algorithm for Denesting Radicals
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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 Jan 1 at 15:18
Manfred WeisManfred Weis
4,59721442
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add a comment |
$begingroup$
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 Jan 1 at 15:18
Manfred WeisManfred Weis
4,59721442
$endgroup$
add a comment |
$begingroup$
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 Jan 1 at 15:18
Manfred WeisManfred Weis
4,59721442
$endgroup$
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 Jan 1 at 15:18
Manfred WeisManfred Weis
4,59721442
asked Jan 1 at 15:18
Manfred WeisManfred Weis
4,59721442
asked Jan 1 at 15:18
Manfred WeisManfred Weis
4,59721442
asked Jan 1 at 15:18
Manfred WeisManfred Weis
4,59721442
asked Jan 1 at 15:18
Manfred WeisManfred Weis
4,59721442
4,59721442
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 Jan 1 at 16:31
LSpice
2,83822627
answered Jan 1 at 16:28
Carlo BeenakkerCarlo Beenakker
77.6k9182286
$endgroup$
$begingroup$
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.
$endgroup$
– LSpice
Jan 1 at 16:31
$begingroup$
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.
$endgroup$
– LSpice
Jan 1 at 16:32
add a comment |
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1 Answer
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active
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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 Jan 1 at 16:31
LSpice
2,83822627
answered Jan 1 at 16:28
Carlo BeenakkerCarlo Beenakker
77.6k9182286
$endgroup$
$begingroup$
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.
$endgroup$
– LSpice
Jan 1 at 16:31
$begingroup$
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.
$endgroup$
– LSpice
Jan 1 at 16:32
add a comment |
$begingroup$
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 Jan 1 at 16:31
LSpice
2,83822627
answered Jan 1 at 16:28
Carlo BeenakkerCarlo Beenakker
77.6k9182286
$endgroup$
$begingroup$
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.
$endgroup$
– LSpice
Jan 1 at 16:31
$begingroup$
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.
$endgroup$
– LSpice
Jan 1 at 16:32
add a comment |
$begingroup$
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 Jan 1 at 16:31
LSpice
2,83822627
answered Jan 1 at 16:28
Carlo BeenakkerCarlo Beenakker
77.6k9182286
$endgroup$
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 Jan 1 at 16:31
LSpice
2,83822627
answered Jan 1 at 16:28
Carlo BeenakkerCarlo Beenakker
77.6k9182286
edited Jan 1 at 16:31
LSpice
2,83822627
edited Jan 1 at 16:31
LSpice
2,83822627
edited Jan 1 at 16:31
LSpice
2,83822627
2,83822627
answered Jan 1 at 16:28
Carlo BeenakkerCarlo Beenakker
77.6k9182286
answered Jan 1 at 16:28
Carlo BeenakkerCarlo Beenakker
77.6k9182286
answered Jan 1 at 16:28
Carlo BeenakkerCarlo Beenakker
77.6k9182286
77.6k9182286
$begingroup$
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.
$endgroup$
– LSpice
Jan 1 at 16:31
$begingroup$
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.
$endgroup$
– LSpice
Jan 1 at 16:32
add a comment |
$begingroup$
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.
$endgroup$
– LSpice
Jan 1 at 16:31
$begingroup$
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.
$endgroup$
– LSpice
Jan 1 at 16:32
$begingroup$
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.
$endgroup$
– LSpice
Jan 1 at 16:31
$begingroup$
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.
$endgroup$
– LSpice
Jan 1 at 16:31
$begingroup$
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.
$endgroup$
– LSpice
Jan 1 at 16:32
$begingroup$
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.
$endgroup$
– LSpice
Jan 1 at 16:32
add a comment |
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