here is my code. for alpha and beta the value is always the same.i just change the value of rho.is it possible all these set value of rho is displayed in one graph? the purpose of this is i want to see the difference of the graph for different values of rho.
Tmp = 0.1316;
a[T_, M_, P_, ρ_] := D[P^3 + P (-1 + T) + 2 M^2 P ρ, P];
b[T_, M_, P_, ρ_] := D[P^3 + P (-1 + T) + 2 M^2 P ρ, M];
c[T_, M_, P_, α_, β_, ρ_] :=
D[M (T - Tmp) Tmp α^2 β +
M^3 Tmp^2 α^2 β + 2 M P^2 ρ, P];
d[T_, M_, P_, α_, β_, ρ_] :=
D[M (T - Tmp) Tmp α^2 β +
M^3 Tmp^2 α^2 β + 2 M P^2 ρ, M];
D1[T_, M_, P_, α_, β_, ρ_] :=
a[T, M, P, ρ]*d[T, M, P, α, β, ρ] -
b[T, M, P, ρ]*c[T, M, P, α, β, ρ];
D1[T, M, P, α, β, ρ]
P[T_, α_, β_, ρ_] :=
Sqrt[( α^2 β - 1.` T α^2 β +
T α^2 β ρ -
1.` Tmp α^2 β ρ)/( α^2 β -
1.` ρ^2)];
M[T_, α_, β_, ρ_] :=
Sqrt[(-1.` T α^2 β + Tmp α^2 β - (
1.` ρ ( α^2 β - 1.` T α^2 β +
T α^2 β ρ -
1.` Tmp α^2 β ρ))/( α^2 β -
1.` ρ^2))/( α^2 β)];
TM[ α_, β_, ρ_] :=
Table[{T, M[T, α, β, ρ]}, {T, 0, 2, 0.0001}];
TP[ α_, β_, ρ_] :=
Table[{T, P[T, α, β, ρ]}, {T, 0, 2, 0.0001}];
LTP[ α_, β_, ρ_] :=
ListPlot[TP[ α, β, ρ],
PlotStyle -> {Purple, PointSize[0.005]}];
LTM[ α_, β_, ρ_] :=
ListPlot[TM[ α, β, ρ],
PlotStyle -> {Magenta, PointSize[0.005]}];
Manipulate[
Show[LTP[ α, β, ρ], LTM[ α, β, ρ],
AxesLabel -> {"T", "M/P"},
PlotRange -> {{0, x}, {0, y}},
PlotLabel -> "M/P againts temperature", ImageSize -> Large]
, { α, {0.5, 1, 1.5, 2}}, { β, {0.5, 1, 1.5,
2}}, { ρ, {0.0, -0.01, -0.05, -0.1, -0.5}}, {x, 0.01, 2,
0.01}, {y, 0.01, 2, 0.01}]
a
,b
,c
,d
,D1
are not used in yourManipulate
expression so you may safely omit them from your posted code. That will simplify your question and reduce the effort required to help you. $\endgroup$