mylist = {0, 2, 4, 2d, 2d^2, 2d(1+d), -(2(1+d)+((4d^3)/(1-d)))(d-1)} ;
For pairs of consecutive elements you can use BlockMap
:
BlockMap[Reduce[#[[1]] >= #[[2]], d] &, mylist, 2, 1]
{False, False, d <= 2, 0 <= d <= 1, d <= 0,
d <= -(1/Sqrt[2]) || 1/Sqrt[2] <= d <= 1}
Alternatively, you can use MapThread
:
MapThread[Reduce[# >= #2, d] &, {Most@mylist, Rest@mylist}]
same result
For all possible pairs, use Tuples
:
Reduce[#[[1]] >= #[[2]], d]& /@ Tuples[mylist, {2}]
{True, False, False, d <= 0, d == 0, -1 <= d <= 0,
d <= Root[1 - #^2 + 2 #^3& , 1, 0], True, True, False,
d <= 1, -1 <= d <= 1, 1/2 (-1 - Sqrt[5]) <= d <= 1/2 (-1 + Sqrt[5]),
d <= 1/2, True, True, True,
d <= 2, -Sqrt[2] <= d <= Sqrt[2], -2 <= d <= 1, d <= 1, d >= 0,
d >= 1, d >= 2, d ∈ Reals, 0 <= d <= 1, d == 0,
d <= Root[1 - # - #^2 + 2 #^3& , 1, 0], d ∈ Reals,
d <= -1 || d >= 1, d <= -Sqrt[2] || d >= Sqrt[2], d <= 0 || d >= 1,
d ∈ Reals, d <= 0, d <= Root[1 - 2 #^2 + 2 #^3& , 1, 0],
d <= -1 || d >= 0,
d <= 1/2 (-1 - Sqrt[5]) || d >= 1/2 (-1 + Sqrt[5]),
d <= -2 || d >= 1, d ∈ Reals, d >= 0, d ∈ Reals,
d <= -(1/Sqrt[2]) || 1/Sqrt[2] <= d <= 1,
d >= Root[1 - #^2 + 2 #^3& , 1, 0], d == 0 || d >= 1/2, d >= 1,
d >= Root[1 - # - #^2 + 2 #^3& , 1, 0],
d >= Root[
1 - 2 #^2 + 2 #^3& , 1, 0], -(1/Sqrt[2]) <= d <= 1/Sqrt[2] ||
d >= 1, d ∈ Reals}
Update: Form your example in the comments, it seems that you need Subsets
:
Reduce[#[[1]] >= #[[2]], d]& /@ Subsets[mylist, {2}]
{False, False, d <= 0, d == 0, -1 <= d <= 0,
d <= Root[1 - #^2 + 2 #^3& , 1, 0], False, d <= 1, -1 <= d <= 1,
1/2 (-1 - Sqrt[5]) <= d <= 1/2 (-1 + Sqrt[5]), d <= 1/2,
d <= 2, -Sqrt[2] <= d <= Sqrt[2], -2 <= d <= 1, d <= 1, 0 <= d <= 1,
d == 0, d <= Root[1 - # - #^2 + 2 #^3& , 1, 0], d <= 0,
d <= Root[1 - 2 #^2 + 2 #^3& , 1, 0],
d <= -(1/Sqrt[2]) || 1/Sqrt[2] <= d <= 1}
If needed, use ToRadicals
to get transform Root
expressions:
ToRadicals @ %
{False, False, d <= 0, d == 0, -1 <= d <= 0,
d <= 1/6 (1 - 1/(53 - 6 Sqrt[78])^(1/3) - (53 - 6 Sqrt[78])^(
1/3)), False, d <= 1, -1 <= d <= 1,
1/2 (-1 - Sqrt[5]) <= d <= 1/2 (-1 + Sqrt[5]), d <= 1/2,
d <= 2, -Sqrt[2] <= d <= Sqrt[2], -2 <= d <= 1, d <= 1, 0 <= d <= 1,
d == 0, d <=
1/6 (1 - 7/(44 - 3 Sqrt[177])^(1/3) - (44 - 3 Sqrt[177])^(1/3)),
d <= 0, d <=
1/3 (1 - 2^(2/3)/(23 - 3 Sqrt[57])^(1/3) - (23 - 3 Sqrt[57])^(1/3)/
2^(2/3)), d <= -(1/Sqrt[2]) || 1/Sqrt[2] <= d <= 1}
BlockMap[Reduce[#,d]&@@#&, mylist,2,1]
? $\endgroup$ – kglr Jun 13 '19 at 18:04mylist={0,2,4,2d,2d^2,2d(1+d),-(2(1+d)+((4d^3)/(1-d)))(d-1)}
$\endgroup$ – Jay Schyler Raadt Jun 13 '19 at 18:10