## find arbitrary coieficent with condition ...

i am looking for special solution i want give the maple equation and give what answer i want with condition for example i just want thus solution which is A_0,A_1,B_1 not equal to zero and other parameter like (w,lambda,k) are free just this three not equal to zero.

restart
with(SolveTools);
with(LinearAlgebra);
eq12 := -alpha*k^2*A[0] - alpha*k^2*A[1] - alpha*k^2*B[1] + A[0]^3*beta[4] + (3*A[0]^2)*A[1]*beta[4] + (3*A[0]^2)*B[1]*beta[4] + (3*A[0])*A[1]^2*beta[4] + (6*A[0])*A[1]*B[1]*beta[4] + (3*A[0])*B[1]^2*beta[4] + A[1]^3*beta[4] + (3*A[1]^2)*B[1]*beta[4] + (3*A[1])*B[1]^2*beta[4] + B[1]^3*beta[4] + A[0]^2*beta[3] + (2*A[0])*A[1]*beta[3] + (2*A[0])*B[1]*beta[3] + A[1]^2*beta[3] + (2*A[1])*B[1]*beta[3] + B[1]^2*beta[3] - w*A[0] - w*A[1] - w*B[1] = 0

eq10 := (2*alpha)*k^2*A[1] - (2*alpha)*k^2*B[1] - (8*alpha)*lambda^2*A[1] + (8*alpha)*lambda^2*B[1] - (8*gamma)*lambda^2*A[1] + (8*gamma)*lambda^2*B[1] - (6*A[0]^2)*A[1]*beta[4] + (6*A[0]^2)*B[1]*beta[4] - (12*A[0])*A[1]^2*beta[4] + (12*A[0])*B[1]^2*beta[4] - (6*A[1]^3)*beta[4] - (6*A[1]^2)*B[1]*beta[4] + (6*A[1])*B[1]^2*beta[4] + (6*B[1]^3)*beta[4] - (4*A[0])*A[1]*beta[3] + (4*A[0])*B[1]*beta[3] - (4*A[1]^2)*beta[3] + (4*B[1]^2)*beta[3] + (2*w)*A[1] - (2*w)*B[1] = 0

eq8 := -(3*A[1]^2)*B[1]*beta[4] - (3*A[1])*B[1]^2*beta[4] - (2*A[0])*A[1]*beta[3] - (2*A[0])*B[1]*beta[3] + w*A[1] + w*B[1] - (3*A[0]^2)*B[1]*beta[4] + alpha*k^2*A[1] + alpha*k^2*B[1] - (3*A[0]^2)*A[1]*beta[4] + (3*alpha)*k^2*A[0] + (32*alpha)*lambda^2*A[1] + (32*alpha)*lambda^2*B[1] + (32*gamma)*lambda^2*A[1] + (32*gamma)*lambda^2*B[1] - (3*A[0]^3)*beta[4] + (15*A[0])*A[1]^2*beta[4] - (18*A[0])*A[1]*B[1]*beta[4] + (15*A[0])*B[1]^2*beta[4] + (15*A[1]^3)*beta[4] + (15*B[1]^3)*beta[4] - (3*A[0]^2)*beta[3] + (5*A[1]^2)*beta[3] - (6*A[1])*B[1]*beta[3] + (5*B[1]^2)*beta[3] + (3*w)*A[0] = 0

eq6 := -(4*alpha)*k^2*A[1] + (4*alpha)*k^2*B[1] - (48*alpha)*lambda^2*A[1] + (48*alpha)*lambda^2*B[1] - (48*gamma)*lambda^2*A[1] + (48*gamma)*lambda^2*B[1] + (12*A[0]^2)*A[1]*beta[4] - (12*A[0]^2)*B[1]*beta[4] - (20*A[1]^3)*beta[4] + (12*A[1]^2)*B[1]*beta[4] - (12*A[1])*B[1]^2*beta[4] + (20*B[1]^3)*beta[4] + (8*A[0])*A[1]*beta[3] - (8*A[0])*B[1]*beta[3] - (4*w)*A[1] + (4*w)*B[1] = 0

eq4 := -(3*A[1]^2)*B[1]*beta[4] - (3*A[1])*B[1]^2*beta[4] - (2*A[0])*A[1]*beta[3] - (2*A[0])*B[1]*beta[3] + w*A[1] + w*B[1] - (3*A[0]^2)*B[1]*beta[4] + alpha*k^2*A[1] + alpha*k^2*B[1] - (3*A[0]^2)*A[1]*beta[4] - (3*alpha)*k^2*A[0] + (32*alpha)*lambda^2*A[1] + (32*alpha)*lambda^2*B[1] + (32*gamma)*lambda^2*A[1] + (32*gamma)*lambda^2*B[1] + (3*A[0]^3)*beta[4] - (15*A[0])*A[1]^2*beta[4] + (18*A[0])*A[1]*B[1]*beta[4] - (15*A[0])*B[1]^2*beta[4] + (15*A[1]^3)*beta[4] + (15*B[1]^3)*beta[4] + (3*A[0]^2)*beta[3] - (5*A[1]^2)*beta[3] + (6*A[1])*B[1]*beta[3] - (5*B[1]^2)*beta[3] - (3*w)*A[0] = 0

eq2 := (2*alpha)*k^2*A[1] - (2*alpha)*k^2*B[1] - (8*alpha)*lambda^2*A[1] + (8*alpha)*lambda^2*B[1] - (8*gamma)*lambda^2*A[1] + (8*gamma)*lambda^2*B[1] - (6*A[0]^2)*A[1]*beta[4] + (6*A[0]^2)*B[1]*beta[4] + (12*A[0])*A[1]^2*beta[4] - (12*A[0])*B[1]^2*beta[4] - (6*A[1]^3)*beta[4] - (6*A[1]^2)*B[1]*beta[4] + (6*A[1])*B[1]^2*beta[4] + (6*B[1]^3)*beta[4] - (4*A[0])*A[1]*beta[3] + (4*A[0])*B[1]*beta[3] + (4*A[1]^2)*beta[3] - (4*B[1]^2)*beta[3] + (2*w)*A[1] - (2*w)*B[1] = 0

eq0 := alpha*k^2*A[0] - alpha*k^2*A[1] - alpha*k^2*B[1] - A[0]^3*beta[4] + (3*A[0]^2)*A[1]*beta[4] + (3*A[0]^2)*B[1]*beta[4] - (3*A[0])*A[1]^2*beta[4] - (6*A[0])*A[1]*B[1]*beta[4] - (3*A[0])*B[1]^2*beta[4] + A[1]^3*beta[4] + (3*A[1]^2)*B[1]*beta[4] + (3*A[1])*B[1]^2*beta[4] + B[1]^3*beta[4] - A[0]^2*beta[3] + (2*A[0])*A[1]*beta[3] + (2*A[0])*B[1]*beta[3] - A[1]^2*beta[3] - (2*A[1])*B[1]*beta[3] - B[1]^2*beta[3] + w*A[0] - w*A[1] - w*B[1] = 0

COEFFS := solve({eq0, eq10, eq12, eq2, eq4, eq6, eq8}, {k, lambda, w, A[0], A[1], B[1]})


## How to correct the code for Delay Differential Equ...

Good day, all.

Please I want to solve the following delay differential equation:

ODE := diff(y(t), t$2) = (2*(1-y(t-1)^2))*(diff(y(t), t))-y(t) ics := y(0) = 1, (D(y))(0) = 0 using the following codes but there is an error. Please kindly help to modify the codes. restart; Digits:=30: f:=proc(n) 2*(1-(y[n-1])^2)*delta[n]+y[n]: end proc: g:=proc(n) -4*y[n-1]*delta[n-1]+2*(1-(y[n-1])^2)*f(n)-delta[n]: end proc: e1:=y[n+2] = -y[n]+2*y[n+1]+(1/120)*h^2*(-3*h*g(n+2)+3*g(n)*h+16*f(n+2)+16*f(n)+88*f(n+1)): e2:=h*delta[n] = -y[n]+y[n+1]-(1/1680)*h^2*(-128*h*g(n+1)-11*h*g(n+2)+59*g(n)*h+40*f(n+2)+520*f(n)+280*f(n+1)): e3:=h*delta[n+1] = -y[n]+y[n+1]+(1/1680)*h^2*(-152*h*g(n+1)-10*h*g(n+2)+32*g(n)*h+37*f(n+2)+187*f(n)+616*f(n+1)): e4:=h*delta[n+2] = -y[n]+y[n+1]+(1/1680)*h^2*(128*h*g(n+1)-101*h*g(n+2)+53*g(n)*h+744*f(n+2)+264*f(n)+1512*f(n+1)): inx:=0: ind:=0: iny:=1: h:=1/2: n:=1: omega:=10: u:=omega*h: N:=solve(h*p = 10, p): err := Vector(round(N)): exy_lst := Vector(round(N)): numerical_y1:=Vector(round(N)): c:=1: for j from 0 to 2 do t[j]:=inx+j*h: end do: vars:=y[n+1],y[n+2],delta[n+1],delta[n+2]: step := [seq](eval(x, x=c*h), c=1..N): printf("%6s%45s%45s\n", "h","Num.y","Num.z"); #eval(<vars>, solve({e||(1..4)},{vars})); st := time(): for k from 1 to N/2 do par1:=x[0]=t[0],x[1]=t[1],x[2]=t[2]: par2:=y[n]=iny,delta[n]=ind: res:=eval(<vars>, fsolve(eval({e||(1..4)},[par1,par2]), {vars})); for i from 1 to 2 do printf("%6.5f%45.30f%45.30f\n", h*c,res[i],res[i+2]): numerical_y1[c] := res[i]: c:=c+1: end do: iny:=res[2]: ind:=res[4]: inx:=t[2]: for j from 0 to 2 do t[j]:=inx + j*h: end do: end do: v:=time() - st; v/4; printf("Maximum error is %.13g\n", max(err)); NFE=evalf((N/4*3)+1); #get array of numerical and exact solutions for y1 numerical_array_y1 := [seq(numerical_y1[i], i = 1 .. N)]: #exact_array_y1 := [seq(exy[i], i = 1 .. N)]: #get array of time steps time_t := [seq](step[i], i = 1 .. N): #display graphs for y1 with(plots): numerical_plot_y1 := plot(time_t, numerical_array_y1, style = [point], symbol = [asterisk], color = [blue,blue],symbolsize = 20, legend = ["TFIBF"]); Thank you, and best regards. ## Issues in using isolating variables from constrain... Asked by: I can't isolate a variable from the constraint and move it to one side of the inequality. For example, it's like having theta <= all other terms. I've tried using the isolate and eval functions, but they aren't producing any results or simplifying the expression. What am I doing wrong? Attaching sheet below (issue marked yellow in background): N_1.mw ## Explore a surface... Asked by: Dear all, I'd like to explore graphically a polynomial surface depending on two parameters a and b. The problem is that, as soon as I start playing with the sliders, Maple freezes and I have to 'force quit'. Can you please tell me if you have the same problem with this example? Thanks.  > restart:  > with(plots):  > K := 1 - y*x - (1 - x)*(b*x^3 + a*x^2 + x + 1)*(1 - y)*(b*y^3 + a*y^2 + y + 1)  (1)  > Explore(plot3d(K, x=0..1, y=0..1, font= [Times, bold, 20], labels= ['x', 'y','z'], labelfont= [Times, bold, 40], title = "K(x,y)"), b = 0..1., a=0..1.); Download Explore.mw ## Regarding fsolve and assign in a for loop in Maple... Asked by: Hello Dear Professional users, I have a question regarding the "fsolve" command and also the "assign" command in Maple. In my previous codes, I just used one time from "fsolve" and then "assign" command. Today, I want to use "fsolve" and "assign" in a for loop. But, I can not get the results correctly. For example, previously I reach a system of algebraic equations and the solve my problem easily: N:=8: y:=sum(a[n]*t^n,n=0..N): y:=unapply(y,t): *****some calculations with a[n] coefficients ***** A:={a set of nonlinear algebraic equations in terms of a[n]}%The number of equations is N+1 (same as the number of a[n] for n=0..N) sol:=fsolve(A): assign(sol) plot(y(t),t=0..1) **************************************************************************************************** **************************************************************************************************** **************************************************************************************************** Today, my problem is: N:=8: M:=4: for i from 1 to M do y[i]:=sum(a[i,n]*t^n,n=0..N): y[i]:=unapply(y[i],t): end do for i from 1 to M do *****some calculations with a[n] coefficients ***** @A[i]:={a set of nonlinear algebraic equations in terms of a[i,n]}%The number of equations is N+1 (same as the number of a[n] for n=0..N) @sol[i]:=fsolve(A[i]): @assign(sol[i]) @plot(y[i](t),t=0..1) end do **************************************************************************************************** **************************************************************************************************** **************************************************************************************************** What I should write instead of "A[i]", "sol[i]", and "assign(sol[i])" the lines started with @A[i],.... @sol[i],... @assign(sol[i]),.... Thanks for your attention in advance With kind regards, Emran ## Given that the solution of a PDE is known, how can... Asked by: Hello I am trying to understand how to use Maple to solve a PDE. Below it is a problem (Henon-Heilles system) where the answer is known. with(PDEtools); infolevel[pdsolve]:=3: declare(Hamil(x,y,u,v)); PDEHamil := u*diff(Hamil(x, y, u, v), x) + v*diff(Hamil(x, y, u, v), y) + (-2*x*y - x)*diff(Hamil(x, y, u, v), u) + (-x^2 + y^2 - y)*diff(Hamil(x, y, u, v), v) = 0; pdsolve(PDEHamil)  Maple returns no solution, but one solution is: sH:=1/2*(u^2+v^2)+1/2*(x^2+y^2-2/3*y^3)+x^2*y; simplify(eval(subs(Hamil(x,y,u,v)=sH,PDEHamil))); 0=0  What am I missing? Many thanks. ## trouble installing Syrup... Asked by: I am trying to install Syrup in my home computer (I have it installed in my work computer). I followed the instructions in the Readme file: From Standard Maple: Open the file Syrup-Installer.mla. To do so, use File -> Open, choose file type "Maple Library Archive (.mla)", select the file, and click "Open". Everything seemed to work and the help page opened up: But, it is not the syrup help page. furthermore, when I type ?Syrup, it doesn't open it either. When I try to run a worksheet that uses Syrup (that works on my work computer), I get these errors: I"m going to reboot now and try again. Jorge ## How to change datatype of multiple columns in data... Asked by: I was working with a Dataframe when I wanted to change the datatype of multiple columns at the same time as this is quite a large dataframe. I found in the helpfile that I can change datatype by the following command: SubsDatatype(Data, plts, float) which then change the datatype of "plts" into float. I had hoped that using multiple columns in the command would work in this way: SubsDatatype(Data, [plts, act], float) but apparently not. Is there a way to do this or do I have to do it column by column? Additionally I have another question about dataframes. I would like to replace "0" in the dataframe by a "blank" as you can do in excel. How do you do this in a dataframe? Thanks in advance for any help given! ## How find list of solution for ordinary differentia... Asked by: restart; with(DEtools); ode := diff(y(x), x) = epsilon - y(x)^2; d 2 ode := --- y(x) = epsilon - y(x) dx sol := dsolve(ode); / (1/2) (1/2)\ (1/2) sol := y(x) = tanh\_C1 epsilon + x epsilon / epsilon P := particularsol(ode); (1/2) (1/2) P := y(x) = epsilon , y(x) = -epsilon , / y(x) \ (1/2) arctanh|------------| - x epsilon + _C1 = 0 | (1/2)| \epsilon /  i am looking for finding all solution of this equation like this picture below ## Covariant Derivative of Einstein Tensor for specif... Asked by: Dear all, I would like to find how I can calculate covariant derivative of Einstein tensor for an arbitrary metric ds_2=-A(r)*dt^2+B(r)*dr^2+dtheta^2+sin(theta)^2*dphi^2 with best ## Error with minimize/maximize... Asked by: Dear all, I have this polynomial function G(x, y) := (-0.14*y^3 + 1.20000000000000*y^2 - 1.26000000000000*y + 0.200000000000000)*x^3 + (1.20*y^3 - 10.0800000000000*y^2 + 10.0800000000000*y - 1.20000000000000)*x^2 + (-8.82*y + 10.08*y^2 - 1.26*y^3)*x + 1. - 1.2*y^2 + 0.2*y^3 I don't understand why the command minimize(G(x,y),x=0..1,y=0..1); produces the error Error, (in RootOf/RootOf:-algnum_in_range) invalid input: RootOf/RootOf:-rootof_in_range expects its 1st argument, rt, to be of type ('RootOf')(polynom(rational,_Z),identical(index) = posint), but received RootOf(7*_Z^3-93*_Z^2+327*_Z-187) Thanks for your advices, Nicola ## Adding H-type error bars to a plot of 2d points... Asked by: Using ScatterPlot (or ErrorPlot), one can add error bars to a 2d point plot of data. However, the bars are single lines. I wish to create a plot with H-type error bars in both the horizontal and vertical directions. Below is an example showing how the bars should appear. (This image is taken from a previous question about adding error bars.) I do not need to reproduce this figure exactly. The location of the data points and the size of the error bars are irrelevant. The closest I have seen is using BoxPlot. Has this question been asked and answered? If so, I cannot find it. ## define conformable fractional derivative for calcu... Asked by: there is any way for define conformable fractional derivative in partial differential equation restart; with(PDEtools); pde := a*diff(psi(x, t), x$ 2) + (b*abs(psi(x, t))^(-2*n) + c*abs(psi(x, t))^(-n) + d*abs(psi(x, t))^n + f*abs(psi(x, t))^(2*n))*psi(x, t) = 0;
pde + i*diff(u(x, t), [t \$ beta]) = 0;


how define a  fractional derivative in sense of conformable derivative

## where does the csgn(L) come from in the solution, ...

I don't understand where the the csgn(L) comes from in the solution below:

all the variables are defined as real:

coupled_network_vbat.mw

Thanks in advance for any help.

Jorge

## gcd for large degree polynomials...

I notice that the command gcd(a,b), if a and b are large degree polynomials, takes too much time and often crashes Windows (not only Maple).