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In each of these decision problems, do we know whether an answer can be obtained in polynomial time?
(1) Given a bivariate polynomial equation of degree n with numerical coefficients, is the corresponding curve closed?
(2) Given a bivariate polynomial equation of degree n with numerical coefficients, with corresponding curve known to be closed, does the curve enclose a convex region?
(3) Given a bivariate polynomial equation of degree n with numerical coefficients, is the corresponding curve self-intersecting?
Thanks in advance! Loraof ( talk) 19:51, 30 April 2017 (UTC)
Does a curve of constant width necessarily enclose a convex region? Our article describes it as convex in the first sentence, implying that this is either a necessary property or a definitional feature, but is it really necessary? (Certainly the width is defined for non-convex shapes, as shown in the diagram in the lead of Mean width.) Thanks. Loraof ( talk) 19:59, 30 April 2017 (UTC)
Mathematics desk | ||
---|---|---|
< April 29 | << Mar | April | May >> | May 1 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
In each of these decision problems, do we know whether an answer can be obtained in polynomial time?
(1) Given a bivariate polynomial equation of degree n with numerical coefficients, is the corresponding curve closed?
(2) Given a bivariate polynomial equation of degree n with numerical coefficients, with corresponding curve known to be closed, does the curve enclose a convex region?
(3) Given a bivariate polynomial equation of degree n with numerical coefficients, is the corresponding curve self-intersecting?
Thanks in advance! Loraof ( talk) 19:51, 30 April 2017 (UTC)
Does a curve of constant width necessarily enclose a convex region? Our article describes it as convex in the first sentence, implying that this is either a necessary property or a definitional feature, but is it really necessary? (Certainly the width is defined for non-convex shapes, as shown in the diagram in the lead of Mean width.) Thanks. Loraof ( talk) 19:59, 30 April 2017 (UTC)