I have this function and I use RegionPlot to see in which part of the domain, the function is negative:
f := 1/4 x^2 Sinh[(2 \[Pi] x)/
3]^2 Sinh[\[Pi] x]^2 (-512 Sinh[(\[Pi] x)/3] +
128 x^2 Sinh[(\[Pi] x)/3] + 64 Sinh[\[Pi] x] +
32 x^2 Sinh[\[Pi] x] + 4 x^4 Sinh[\[Pi] x] -
128 Sinh[(5 \[Pi] x)/3] - 64 x^2 Sinh[(5 \[Pi] x)/3] -
8 x^4 Sinh[(5 \[Pi] x)/3] + 576 Sinh[(7 \[Pi] x)/3] -
96 x^2 Sinh[(7 \[Pi] x)/3] + 4 x^4 Sinh[(7 \[Pi] x)/3])^2 -
4 (256 Cosh[(2 \[Pi] x)/3]^2 - 128 x^2 Cosh[(2 \[Pi] x)/3]^2 +
16 x^4 Cosh[(2 \[Pi] x)/3]^2 +
256 x^2 Sinh[(2 \[Pi] x)/
3]^2) Sinh[\[Pi] x]^2 (64 Sinh[(\[Pi] x)/3]^2 -
32 x^2 Sinh[(\[Pi] x)/3]^2 + 4 x^4 Sinh[(\[Pi] x)/3]^2 -
16 Sinh[(\[Pi] x)/3] Sinh[\[Pi] x] -
4 x^2 Sinh[(\[Pi] x)/3] Sinh[\[Pi] x] +
x^4 Sinh[(\[Pi] x)/3] Sinh[\[Pi] x] +
1/4 x^6 Sinh[(\[Pi] x)/3] Sinh[\[Pi] x] + Sinh[\[Pi] x]^2 +
x^2 Sinh[\[Pi] x]^2 + 3/8 x^4 Sinh[\[Pi] x]^2 +
1/16 x^6 Sinh[\[Pi] x]^2 + 1/256 x^8 Sinh[\[Pi] x]^2 -
256 Cosh[(2 \[Pi] x)/3]^2 Sinh[\[Pi] x]^2 +
128 x^2 Cosh[(2 \[Pi] x)/3]^2 Sinh[\[Pi] x]^2 -
16 x^4 Cosh[(2 \[Pi] x)/3]^2 Sinh[\[Pi] x]^2 +
32 Sinh[(\[Pi] x)/3] Sinh[(5 \[Pi] x)/3] +
8 x^2 Sinh[(\[Pi] x)/3] Sinh[(5 \[Pi] x)/3] -
2 x^4 Sinh[(\[Pi] x)/3] Sinh[(5 \[Pi] x)/3] -
1/2 x^6 Sinh[(\[Pi] x)/3] Sinh[(5 \[Pi] x)/3] -
4 Sinh[\[Pi] x] Sinh[(5 \[Pi] x)/3] -
4 x^2 Sinh[\[Pi] x] Sinh[(5 \[Pi] x)/3] -
3/2 x^4 Sinh[\[Pi] x] Sinh[(5 \[Pi] x)/3] -
1/4 x^6 Sinh[\[Pi] x] Sinh[(5 \[Pi] x)/3] -
1/64 x^8 Sinh[\[Pi] x] Sinh[(5 \[Pi] x)/3] +
4 Sinh[(5 \[Pi] x)/3]^2 + 4 x^2 Sinh[(5 \[Pi] x)/3]^2 +
3/2 x^4 Sinh[(5 \[Pi] x)/3]^2 + 1/4 x^6 Sinh[(5 \[Pi] x)/3]^2 +
1/64 x^8 Sinh[(5 \[Pi] x)/3]^2 -
144 Sinh[(\[Pi] x)/3] Sinh[(7 \[Pi] x)/3] +
60 x^2 Sinh[(\[Pi] x)/3] Sinh[(7 \[Pi] x)/3] -
7 x^4 Sinh[(\[Pi] x)/3] Sinh[(7 \[Pi] x)/3] +
1/4 x^6 Sinh[(\[Pi] x)/3] Sinh[(7 \[Pi] x)/3] +
18 Sinh[\[Pi] x] Sinh[(7 \[Pi] x)/3] +
6 x^2 Sinh[\[Pi] x] Sinh[(7 \[Pi] x)/3] -
1/4 x^4 Sinh[\[Pi] x] Sinh[(7 \[Pi] x)/3] -
1/8 x^6 Sinh[\[Pi] x] Sinh[(7 \[Pi] x)/3] +
1/128 x^8 Sinh[\[Pi] x] Sinh[(7 \[Pi] x)/3] -
36 Sinh[(5 \[Pi] x)/3] Sinh[(7 \[Pi] x)/3] -
12 x^2 Sinh[(5 \[Pi] x)/3] Sinh[(7 \[Pi] x)/3] +
1/2 x^4 Sinh[(5 \[Pi] x)/3] Sinh[(7 \[Pi] x)/3] +
1/4 x^6 Sinh[(5 \[Pi] x)/3] Sinh[(7 \[Pi] x)/3] -
1/64 x^8 Sinh[(5 \[Pi] x)/3] Sinh[(7 \[Pi] x)/3] +
81 Sinh[(7 \[Pi] x)/3]^2 - 27 x^2 Sinh[(7 \[Pi] x)/3]^2 +
27/8 x^4 Sinh[(7 \[Pi] x)/3]^2 -
3/16 x^6 Sinh[(7 \[Pi] x)/3]^2 +
1/256 x^8 Sinh[(7 \[Pi] x)/3]^2);
RegionPlot[a f < 0, {x, 3.46572, 3.46574}, {a, 0, 1},
PlotPoints -> 60]
This is the result:
I am sure that the blue part should be a continuous domain. How can I get a better result? Is there an alternative way instead of increasing the number of plotpoints? Since it is not easy for my system and it takes much time.
ContourPlot
in the title and text but it isRegionPlot
in the code. $\endgroup$