dear sir here i am giving python code exicuting 3d plots but i cant plot animations like

restart;
Nc := .3; M := 1.5; QG := 1.5; Thetaa := .2; n1 := 1; n2 := 0; lambda1 := .1; lambda2 := .1; lambda3 := .1;

p := 2; a := .5; alpha1 := (1/2)*Pi;

p1 := 0.1e-1; p2 := 0.1e-1;
rf := 997.1; kf := .613; cpf := 4179; betaf := 21*10^(-5);

betas1 := .85*10^(-5); rs1 := 3970; ks1 := 40; cps1 := 765;
betas2 := 1.67*10^(-5); rs2 := 8933; ks2 := 401; cps2 := 385;

z1 := 1/((1-p1)^2.5*(1-p2)^2.5);
knf := kf*(ks1+2*kf-2*p1*(kf-ks1))/(ks1+2*kf+p1*(kf-ks1)); khnf := knf*(ks2+2*knf-2*p2*(knf-ks2))/(ks2+2*knf+p2*(knf-ks2));
z2 := 1-p1-p2+p1*rs1/rf+p2*rs2/rf;
z3 := 1-p1-p2+p1*rs1*cps1/(rf*cpf)+p2*rs2*cps2/(rf*cpf);
z4 := khnf/kf;
z5 := 1-p1-p2+p1*rs1*betas1/(rf*betaf)+p2*rs2*betas2/(rf*betaf);
OdeSys := z4*(X*(diff(Theta(X, tau), X, X))+diff(Theta(X, tau), X))/z3-(diff(Theta(X, tau), tau))-Nc*(Theta(X, tau)-Thetaa)^2*z5/z1-M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n1*z2/z3)/(z3*(1-Thetaa)^p)-Nr*(Theta(X, tau)^4-Thetaa^4)/z3+QG*X*(1+lambda1*(Theta(X, tau)-Thetaa)+lambda2*(Theta(X, tau)-Thetaa)^2+lambda3*(Theta(X, tau)-Thetaa)^3)/z3; Cond := {Theta(0, tau) = 1+a*sin(alpha1), Theta(X, 0) = 0, (D[1](Theta))(1, tau) = 0};
OdeSys1 := z4*(X*(diff(Theta(X, tau), X, X))+diff(Theta(X, tau), X))/z3-(diff(Theta(X, tau), tau))-Nc*(Theta(X, tau)-Thetaa)^2*z5/z1-M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n2*z2/z3)/(z3*(1-Thetaa)^p)-Nr*(Theta(X, tau)^4-Thetaa^4)/z3+QG*X*(1+lambda1*(Theta(X, tau)-Thetaa)+lambda2*(Theta(X, tau)-Thetaa)^2+lambda3*(Theta(X, tau)-Thetaa)^3)/z3; Cond1 := {Theta(0, tau) = 1+a*sin(alpha1), Theta(X, 0) = 0, (D[1](Theta))(1, tau) = 0};
OdeSysa := z4*(X*(diff(Theta(X, tau), X, X))+diff(Theta(X, tau), X))/z3-(diff(Theta(X, tau), tau))-Nc*(Theta(X, tau)-Thetaa)^2*z5/z1-M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n1*z2/z3)/(z3*(1-Thetaa)^p)-Nr*(Theta(X, tau)^4-Thetaa^4)/z3+QG*X*(1+lambda1*(Theta(X, tau)-Thetaa)+lambda2*(Theta(X, tau)-Thetaa)^2+lambda3*(Theta(X, tau)-Thetaa)^3)/z3; Conda := {Theta(0, tau) = 1+a*cos(alpha1), Theta(X, 0) = 0, (D[1](Theta))(1, tau) = 0};
OdeSysa1 := z4*(X*(diff(Theta(X, tau), X, X))+diff(Theta(X, tau), X))/z3-(diff(Theta(X, tau), tau))-Nc*(Theta(X, tau)-Thetaa)^2*z5/z1-M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n2*z2/z3)/(z3*(1-Thetaa)^p)-Nr*(Theta(X, tau)^4-Thetaa^4)/z3+QG*X*(1+lambda1*(Theta(X, tau)-Thetaa)+lambda2*(Theta(X, tau)-Thetaa)^2+lambda3*(Theta(X, tau)-Thetaa)^3)/z3; Conda1 := {Theta(0, tau) = 1+a*cos(alpha1), Theta(X, 0) = 0, (D[1](Theta))(1, tau) = 0};

colour := [cyan, black];
colour1 := [red, blue];
NrVals := [2.5, 3.5];
for j to numelems(NrVals) do Ans := pdsolve((eval([OdeSys, Cond], Nr = NrVals[j]))[], numeric, spacestep = 1/200, timestep = 1/100); Plots[j] := Ans:-plot(Theta(X, tau), tau = .8, linestyle = "solid", labels = ["Y", Theta(Y, tau)], color = colour[j], 'axes' = 'boxed'); eta[j] := Ans:-plot((int(z3*z5*Nc*(Theta(X, tau)-Thetaa)^2/(z1*z4)+NrVals[j]*(Theta(X, tau)^4-Thetaa^4)/z4+M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n1*z2/z3)/(z4*(1-Thetaa)^p), X = 0 .. 1))/(z3*z5*Nc*(1-Thetaa)^2/(z1*z4)+NrVals[j]*(-Thetaa^4+1)/z4+M^2*(1-Thetaa)*(1+n1*z2/z3)/z4), tau = 0 .. 2, X = .8, linestyle = "solid", 'axes' = 'boxed', labels = [" τ ", " η "], color = colour[j]); Ans1 := pdsolve((eval([OdeSys1, Cond1], Nr = NrVals[j]))[], numeric, spacestep = 1/200, timestep = 1/100); Plots1[j] := Ans1:-plot(Theta(X, tau), tau = .8, linestyle = "dash", labels = ["Y", Theta(Y, tau)], color = colour[j], 'axes' = 'boxed'); eta1[j] := Ans1:-plot((int(z3*z5*Nc*(Theta(X, tau)-Thetaa)^2/(z1*z4)+NrVals[j]*(Theta(X, tau)^4-Thetaa^4)/z4+M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n2*z2/z3)/(z4*(1-Thetaa)^p), X = 0 .. 1))/(z3*z5*Nc*(1-Thetaa)^2/(z1*z4)+NrVals[j]*(-Thetaa^4+1)/z4+M^2*(1-Thetaa)*(1+n2*z2/z3)/z4), tau = 0 .. 2, X = .8, linestyle = "dash", 'axes' = 'boxed', labels = [" τ ", " η "], color = colour[j]); Ansa := pdsolve((eval([OdeSysa, Conda], Nr = NrVals[j]))[], numeric, spacestep = 1/200, timestep = 1/100); Plotsa[j] := Ansa:-plot(Theta(X, tau), tau = .8, linestyle = "solid", labels = ["Y", Theta(Y, tau)], color = colour1[j], 'axes' = 'boxed'); etaa[j] := Ansa:-plot((int(z3*z5*Nc*(Theta(X, tau)-Thetaa)^2/(z1*z4)+NrVals[j]*(Theta(X, tau)^4-Thetaa^4)/z4+M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n1*z2/z3)/(z4*(1-Thetaa)^p), X = 0 .. 1))/(z3*z5*Nc*(1-Thetaa)^2/(z1*z4)+NrVals[j]*(-Thetaa^4+1)/z4+M^2*(1-Thetaa)*(1+n1*z2/z3)/z4), tau = 0 .. 2, X = .8, linestyle = "solid", 'axes' = 'boxed', labels = [" τ ", " η "], color = colour1[j]); Ansa1 := pdsolve((eval([OdeSysa1, Conda1], Nr = NrVals[j]))[], numeric, spacestep = 1/200, timestep = 1/100); Plotsa1[j] := Ansa1:-plot(Theta(X, tau), tau = .8, linestyle = "dash", labels = ["Y", Theta(Y, tau)], color = colour1[j], 'axes' = 'boxed'); etaa1[j] := Ansa1:-plot((int(z3*z5*Nc*(Theta(X, tau)-Thetaa)^2/(z1*z4)+NrVals[j]*(Theta(X, tau)^4-Thetaa^4)/z4+M^2*(Theta(X, tau)-Thetaa)^(p+1)*(1+n2*z2/z3)/(z4*(1-Thetaa)^p), X = 0 .. 1))/(z3*z5*Nc*(1-Thetaa)^2/(z1*z4)+NrVals[j]*(-Thetaa^4+1)/z4+M^2*(1-Thetaa)*(1+n2*z2/z3)/z4), tau = 0 .. 2, X = .8, linestyle = "dash", 'axes' = 'boxed', labels = [" τ ", " η "], color = colour1[j]) end do;
plotA := plots:-display([seq(Plots[j], j = 1 .. 2)]);
plotB := plots:-display([seq(Plots1[j], j = 1 .. 2)]);
plotAA := plots:-display([seq(Plotsa[j], j = 1 .. 2)]);
plotBB := plots:-display([seq(Plotsa1[j], j = 1 .. 2)]);
plotC := plots:-display([seq(eta[j], j = 1 .. 2)]);
plotD := plots:-display([seq(eta1[j], j = 1 .. 2)]);
plotCC := plots:-display([seq(etaa[j], j = 1 .. 2)]);

plotDD := plots:-display([seq(etaa1[j], j = 1 .. 2)]);
plots:-display([plotA, plotB, plotAA, plotBB], size = [700, 700]);

plots:-display([plotC, plotD, plotCC, plotDD], size = [700, 700]);

how to take animation of the plots

i have seen some plots in maple also for that reason i have posted this question here

paper2_new_efficiency_plots_2025.mw

Hi,
I want to solve equations (1) and (2) to obtain the values of certain quantities, for example x and f. In fact, both equations must be satisfied simultaneously for \tau and f. Since there are other parameters in these equations (for example \tau, M, etc.), and I do not know the optimal values of these parameters, I would like to solve equations (1) and (2) over given ranges for tau, M, and so on. I know that I should use loop commands, but I keep encountering errors. Please guide me.
fsolve.mw

Hi 
How can I plot f3=0 for different values of Tch and qc?

1.mw

How to get amultiple line plots in one graph for differnt values of E1 := .1,0.2,0.3,and 0.4 with differnt color line red,blue,black and green and how to get numerical values for the all E1 value in one matrix form 

at E1=0.1 value of diff(g(x), x, x), diff(f(x), x, x),diff(f(x), x) and diff(g(x),  x).

AGM_method_single_line_plot.mw

How to solve two boundary problems in one graph not getting graphs shown in pdf
symetry_paper_work.mw
symmetry_graphs_pdf.pdf

How to get table values 

why this error is getting. but in the published paper for the same parameter it is converging. what is the mistake in this worksheet please rectify it in sachin_base_paper.mw

Someone should please help me compute the left and right eigenvectors of the system below. The purpose is to compute values for 'a' and 'b' in the bifurcation formula.

Thank you

Download CBD2.mw

It is not difficult to manually check the validity of the identity  sqrt(x+2*sqrt(x-1)) = sqrt(x-1)+1 , which is true at least for all  x>=1 . I don't know of any Maple command that directly makes this simplification:

expr:=sqrt(x+2*sqrt(x-1));
simplify(expr);
simplify(expr) assuming x>=1;

It was possible to simplify it only by making a variable substitution  x=y+1 (and then a reverse substitution  y=x-1 ) :

expr1:=subs(x=y+1,expr);
simplify(expr1);
subs(y=x-1, %);

By the way,  the CAS Mathematica also cannot cope with simplifying the expression  expr .

Good day.

I am constructing a 4-set Venn Diagram and I would like to know if it is possible to fix the number of decimal places in the solution.

The attached worksheet is given as an example; the default number of decimal places seems to be 2. I would like this to be either 0 or 1 (for both absolute and relative values). 

Does anyone know how to do this? 

Thanks for reading!

MaplePrimes_Venn_Diagram.mw

How to solve these pde equations in maple to get the similar type graphs.

Ode equations we can solve directly but these equations are pde .

in the article they have solved the governing equations by series solution? 

can we solve these equations in maple also by series solution or any other method is there to solve these equations

Someone please help me with the computation of the right and left eigenvectors. my system of equation is attached below

Download Cotton_DFE_and_Jacobian.mw

Please, I am encountering error trying to run these codes for sensitivity analysis using the formula for sensitivity analysis

Download Computed_Sensitivity_Analys_for_CBD.mw

In the book by W.G. Chinn, N.E. Steenrod "First Concepts of Topology" the another remarkable theorem was proved: any two flat bounded regions can be cut by a single straight line so that each of these regions is divided into two regions of equal area (the second  pancake problem). This is an existence theorem which does not provide any way to find this cut. In this post I made an attempt to find such cut for any 2 convex regions on the plane bounded by a piecewise smooth self-non-intersecting curves.
The Each_Into_2_Equal_Areas procedure returns a list of coordinates of 4 endpoints of the cutting segments. This procedure significantly uses my old procedures  Area  and  Picture , which can be found in detail at the link  https://mapleprimes.com/posts/145922-Perimeter-Area-And-Visualization-Of-A-Plane-Figure-  . The formal arguments of the Each_Into_2_Equal_Areas procedure are the lists  L1  and  L2 specifying the boundaries of the regions to be cut. When specifying  L1  and  L2 , the boundary can be passed clockwise or counterclockwise, but it is necessary that the parameter t (when specifying each link) should go in ascending order. This can always be achieved by replacing  t  with  -t  if necessary. The Pic procedure draws a picture of the source regions and cutting segments. For ease of use, the code for the  Area  and  Picture   procedure is also provided. It is also worth noting that the procedure also works for "not too" non-convex regions (see examples below).

restart;
Area := proc(L) 
local i, var, e, e1, e2, P; 
for i to nops(L) do 
if type(L[i], listlist(algebraic)) then 
P[i] := (1/2)*add(L[i, j, 1]*L[i, j+1, 2]-L[i, j, 2]*L[i, j+1, 1], j = 1 .. nops(L[i])-1) else 
var := lhs(L[i, 2]); 
if type(L[i, 1], algebraic) then e := L[i, 1]; 
if nops(L[i]) = 3 then P[i] := (1/2)*(int(e^2, L[i, 2])) else 
if var = y then P[i] := (1/2)*simplify(int(e-var*(diff(e, var)), L[i, 2])) else 
P[i] := (1/2)*simplify(int(var*(diff(e, var))-e, L[i, 2])) end if end if else e1 := L[i, 1, 1]; e2 := L[i, 1, 2]; 
P[i] := (1/2)*simplify(int(e1*(diff(e2, var))-e2*(diff(e1, var)), L[i, 2])) end if end if end do; 
abs(add(P[i], i = 1 .. nops(L))); 
end proc:

Picture := proc(L, C, N::posint := 100, Boundary::list := [linestyle = 1]) 
local i, var, var1, var2, e, e1, e2, P, Q, h; 
global Border;
uses plottools; 
for i to nops(L) do 
if type(L[i], listlist(algebraic)) then P[i] := op(L[i]) else 
var := lhs(L[i, 2]); var1 := lhs(rhs(L[i, 2])); var2 := rhs(rhs(L[i, 2])); h := (var2-var1)/N; 
if type(L[i, 1], algebraic) then e := L[i, 1]; 
if nops(L[i]) = 3 then P[i] := seq(subs(var = var1+h*i, [e*cos(var), e*sin(var)]), i = 0 .. N) else 
P[i] := seq([var1+h*i, subs(var = var1+h*i, e)], i = 0 .. N) fi else e1 := L[i, 1, 1]; e2 := L[i, 1, 2]; P[i] := seq(subs(var = var1+h*i, [e1, e2]), i = 0 .. N) fi; fi; od; 
Q := [seq(P[i], i = 1 .. nops(L))]; Border := curve([op(Q), Q[1]], op(Boundary)); [polygon(Q, C), Border] 
end proc:

Each_Into_2_Equal_Areas:=proc(L1::list, L2::list)
local D, n, m, L10, L20, S1,S2, f, L11, L21, i, j, k, s, A, B, C , sol;

f:=(X,Y)->expand((y-X[2])*(Y[1]-X[1])-(x-X[1])*(Y[2]-X[2]));
L10:=map(p->`if`(type(p,listlist),[[p[1,1]+t*(p[2]-p[1])[1],p[1,2]+t*(p[2]-p[1])[2]],t=0..1],p), L1);
L20:=map(p->`if`(type(p,listlist),[[p[1,1]+t*(p[2]-p[1])[1],p[1,2]+t*(p[2]-p[1])[2]],t=0..1],p), L2);
S1:=Area(L1); S2:=Area(L2);  
n:=nops(L1); m:=nops(L2);

for i from 1 to n do
for j from i to n do

for k from 1 to m do
for s from k to m do

if not ((nops({i,j})=1 and type(L1[i],listlist)) or (nops({k,s})=1 and type(L2[k],listlist))) then

A:=eval(L10[i,1],t=t1): 
B:=eval(L10[j,1],t=t2):
C:=eval(L20[k,1],t=t3): 
D:=eval(L20[s,1],t=t4):

L11:=`if`(j=i,[subsop([2,2]=t1..t2,L10[i]),[B,A]],`if`(j=i+1,[subsop([2,2]=t1..op([2,2,2],L10[i]),L10[i]),subsop([2,2]=op([2,2,1],L10[j])..t2,L10[j]),[B,A]], [subsop([2,2]=t1..op([2,2,2],L10[i]),L10[i]),op(L10[i+1..j-1]),subsop([2,2]=op([2,2,1],L10[j])..t2,L10[j]),[B,A]])):

L21:=`if`(s=k,[subsop([2,2]=t3..t4,L20[k]),[D,C]],`if`(s=k+1,[subsop([2,2]=t3..op([2,2,2],L20[k]),L20[k]),subsop([2,2]=op([2,2,1],L20[s])..t4,L20[s]),[D,C]], [subsop([2,2]=t3..op([2,2,2],L20[k]),L20[k]),op(L20[k+1..s-1]),subsop([2,2]=op([2,2,1],L20[s])..t4,L20[s]),[D,C]])):

sol:=fsolve(simplify({Area(L11)-S1/2,Area(L21)-S2/2,eval(f(A,B),[x=C[1],y=C[2]]),eval(f(A,B),[x=D[1],y=D[2]])}),{t1=op([2,2,1],L10[i])..op([2,2,2],L10[i]),t2=op([2,2,1],L10[j])..op([2,2,2],L10[j]),t3=op([2,2,1],L20[k])..op([2,2,2],L20[k]),t4=op([2,2,1],L20[s])..op([2,2,2],L20[s])});

if type(sol,set(`=`)) then  return eval([A,B,C,D],sol) fi;

fi;
od: od: od: od:
end proc:

Pic := proc(L1,L2,col1,col2,Size:=[800,400])
local P1, P2, P3, T, P;
uses plots, plottools;
P1, P2 := Picture(L1, color=col1), Picture(L2, color=col2):
P3 := line(Sol[1..2][],color=red,thickness=3), line(Sol[3..4][],color=red,thickness=3), line(Sol[1],Sol[4],linestyle=2,thickness=3,color=red):
T:=textplot([[Sol[1][],"A"],[Sol[2][],"B"],[Sol[3][],"C"],[Sol[4][],"D"]], font=[times,18], align=[left,above]);
P:=pointplot(Sol, symbol=solidcircle, color=red, symbolsize=10);
display(P1,P2,P3,T,P, scaling=constrained, size=Size, axes=none);
end proc: 

Examples of use.

local D:
L1:=[[[8,0],[6,7]],[[6,7],[2,5]],[[2,5],[0,2]],[[0,2],[0,0]],[[0,0],[8,0]]]:
L2:=[[[5*cos(t)+16,5*sin(t)],t=Pi/2..Pi],[[5*cos(t)+16,5*sin(t)/2],t=Pi..2*Pi],[[21,0],[16,5]]]:
Sol:=Each_Into_2_Equal_Areas(L1,L2): Points:=[A,B,C,D]:
seq(Points[i]=Sol[i], i=1..4);
Pic(L1,L2,"Yellow","LightBlue",[900,400]);

The specified regions may overlap:

L1:=[[[8,0],[6,7]],[[6,7],[2,5]],[[2,5],[0,2]],[[0,2],[0,0]],[[0,0],[8,0]]]:
L2:=[[[5*cos(t)+9,5*sin(t)],t=Pi/2..Pi],[[5*cos(t)+9,5*sin(t)/2],t=Pi..2*Pi],[[14,0],[9,5]]]:
Sol:=Each_Into_2_Equal_Areas(L1,L2):  Points:=[A,B,C,D]:
seq(Points[i]=Sol[i], i=1..4);
Pic(L1,L2,"Yellow","LightBlue");

If there is a solution for which the cutting segments intersect the boundary of each of the regions at 2 points, then the procedure also works for such non-convex regions:

L1:=[[[cos(t),sin(t)],t=Pi/3..2*Pi-Pi/3],[[cos(-t)+1,sin(-t)],t=-Pi-Pi/3..-Pi+Pi/3]]:
L2:=[[[cos(t)+2,sin(t)],t=-Pi/6..Pi+Pi/6],[[cos(-t)+2,sin(-t)-1],t=-5*Pi/6..-Pi/6]]:
Sol:=Each_Into_2_Equal_Areas(L1,L2): Points:=[A,B,C,D]:
seq(Points[i]=Sol[i], i=1..4);
Pic(L1,L2,"Yellow","LightBlue");

A number of other interesting examples can be found in the attached file.

Each_Into_2_Equal_Areas1.mw

Hi,

I want to solve a first order ODE and (i) plot phi vs. x and then (ii) export data of the plotted curve as an T-shape ASCII file. I try to do this by Maple, but there are some errors and I couldn’t get the mentioned curve and ASCII file. Please, help me to remove errors:
(dphi/dx)**2+2*V(phi)=0,

where V(phi)= (1-alpha)*M^2 - (1-alpha)*M*sqrt(M^2 - 2*phi) + mu*(mu + beta*nu)*(1 - exp(phi/(mu + beta*nu))) + 
            (nu/beta)*(mu + beta*nu)*(1 - exp(beta*phi/(mu + beta*nu))) + (alpha/gamma1)*(1 - exp(-gamma1*phi)),

where we assume mu := 0.01, nu := 1 - mu, beta := 0.05, alpha := 0.3, M := sqrt(0.704), gamma1 := 0.001.
As it is seen from the attached figure, V(phi) and dV(phi)/dx =0 for phi=0 and phi=phi_m (two extreme points of V(phi)) and d^V(phi)/dphi^2<0 at phi=0 and phi=phi_m (phi and x are real). 

From the attached figure, it seems that phi=phi_m at x=0 and phi->0 as x-> infinity. (Hint: I expect the plot of V(phi) vs. phi and phi vs. x be similar to the curve "A" in the attached file).

Thanks.
rk4.mw

is(cos(x)=sqrt(1-sin(x)^2) or cos(x)=-sqrt(1-sin(x)^2)) assuming real;

                                          false  

In a simpler situation the result is correct

is(x=0 or x<>0) assuming real;

                                           true