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- (*start*)
- (*Associated Mathematica program*)
- Clear[h, x, k, s, s1, nn, m];
- $MaxRootDegree = 1000;
- m = 10;(*m must be an even integer and greater than 4*)
- h = 400;
- gcd = GCD @@ Table[Round[Log[n]*h]/h, {n, 1, m}]
- Table[Round[Log[n]*h]/h, {n, 1, m}]/gcd
- r = 100;
- integer = 0;
- s = 1/gcd*(2*Pi*I*integer -
- Log[Root[
- Sum[(-1)^(n + 1) #1^(Round[Log[n]*h]/h/gcd), {n, 1, m}] &, r]])
- N[s, 80]
- N[Sum[(-1)^(n + 1)/(E^(Round[Log[n]*h]/h))^s, {n, 1, m}]]
- s1 = 1/gcd*(2*Pi*I*integer -
- Log[Root[
- polynomial =
- Sum[Sum[#1^k, {k, Round[Log[m - (2*q - 1)]*h]/h/gcd,
- Round[Log[m - (2*q - 2)]*h]/h/gcd - 1}], {q, 1, m/2}] &,
- r - 1]])
- N[s1, 80]
- N[Sum[(-1)^(n + 1)/(E^(Round[Log[n]*h]/h))^s1, {n, 1, m}]]
- (*end*)
- (*start*)
- sort = Sort[
- Flatten[Table[
- Table[k, {k, Round[Log[m - (2*q - 1)]*h]/h/gcd,
- Round[Log[m - (2*q - 2)]*h]/h/gcd - 1}], {q, 1, m/2}]]]
- "Plot of exponents of polynomial"
- ListLinePlot[sort]
- "Plot of coefficients of polynomial"
- ListPlot[Sum[
- Table[If[sort[[n]] == k, 1, 0], {k, 1, Max[sort]}], {n, 1,
- Length[sort]}], Filling -> 0]
- (*end*)
- (*start*)
- (*m must be an even integer and greater than 4*)
- m = 20;
- h = 200; sort =
- Sort[Flatten[
- Table[Table[
- k, {k, Round[Log[m - (2*q - 1)]*h]/h/gcd,
- Round[Log[m - (2*q - 2)]*h]/h/gcd - 1}], {q, 1, m/2}]]]
- "Plot of exponents of polynomial"
- ListLinePlot[sort]
- "Plot of coefficients of polynomial"
- ListPlot[Sum[
- Table[If[sort[[n]] == k, 1, 0], {k, 1, Max[sort]}], {n, 1,
- Length[sort]}], Filling -> 0]
- (*end*)
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