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Jul
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revised In a finite field, is there ever a homomorphism from the additive group to the multiplicative group?
clarify, I hope.
Jul
8
comment In a finite field, is there ever a homomorphism from the additive group to the multiplicative group?
@MorganRodgers: You are right that the additive group of integers modulo 4 has a completely different addition operator than GF(4), the finite field of four elements {0, 1, a, 1+a}. I don't know what I was thinking. You are probably right that I am "simply" mapping GF(5) to itself using additive notation in A and multiplicative notation in M -- but isn't that almost exactly what the original question asked for?
Jul
8
revised In a finite field, is there ever a homomorphism from the additive group to the multiplicative group?
fix oops pointed out in comments
Jul
7
comment In a finite field, is there ever a homomorphism from the additive group to the multiplicative group?
@MorganRodgers: In the first example, the finite field A is the additive group of integers modulo 4 -- or in other words, A is the set of four integers {0, 1, 2, 3}. In the second more general example, A is the additive group of of integers modulo N-1, where N is a Fermat prime. (The first example is a special case of the second example). How could I edit this answer to make that more clear?
Jun
18
comment insphere/circumsphere ratio of a polyhedron the same as its dual polyhedron?
You may want to look at David Moews answer, which already covers all those shapes. Do you have anything to add that isn't already covered by that answer?
Jun
18
comment insphere/circumsphere ratio of a polyhedron the same as its dual polyhedron?
The original question already pointed out that the ratios seemed to be equal for the duals of the 5 Platonic solids. This answer shows that the ratios actually are exactly equal, which is nice to know. What about other dual solids, such as the triangular prism and its dual the triangular bipyramid, the cuboctahedron and its dual the rhombic dodecahedron, the Archimedean solids and their duals the Catalan solids, etc.?
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answered If $f(t)$ is periodic, is there any $t$ that would equal to DC components?
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answered In a finite field, is there ever a homomorphism from the additive group to the multiplicative group?
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Aug
19
answered Simulate repeated rolls of a 7-sided die with a 6-sided die
Aug
18
comment Simulate repeated rolls of a 7-sided die with a 6-sided die
@Daenyth: Huh? I see 35 non-X possibilities, 5 of them result in a 7, which gives the correct desired probability of 5/35 = 1/7 chance of resulting in a 7.
Aug
18
revised Simulate repeated rolls of a 7-sided die with a 6-sided die
clarified (I hope)