MaplePrimes Questions

Is there a way to put in intervals and get the output as inequality Notation? Something like this ->

I have a system of 4 nonlinear equations in 4 lambda variables. I cannot obtain a solution using solve():

4_nonlinear_equations.mw

I can sometimes simplify similar systems by rescaling equations to reduce parameters. With only 3 parameters (sigma_v, sigma_d, sigma_d3) in this case, complexity arises from the interactions of the 4 lambdas in the 4 equations. Upon examining the equations (highlighted in yellow), I suspect hidden symmetries. Is it possible to solve the system by rewriting the equations in terms of each other to find an equivalent system? I am exploring if a smarter and simpler reformulation could lead to a solution. Thank you.

I am very frustrated with the geometry package.
I wanted to draw a circle thru 3 points and so I opened the geometry package help pages.
> restart;
> with(geometry);
> with(plots);

Here is the example given there
> circle(c1, [point(A, 0, 0), point(B, 2, 0), point(C, 1, 2)], 'centername' = O1)

As you can see the command uses the point command from the geometry package which is

> point(C, 1, 2)

Maple consistently uses := as the assignment operator. Not with this command. One would expect the syntax to be

>C:=point([-1. 2]);

or some such but no, that is not how it works.Notice that I am not alone in my opinion about this being a violation of standard Maple syntax; the Maple parser AGREES with me

> type(point(C,1,-3),point);
                             false

Perhaps I am just being grouchy but pointplot works fine with
> pointplot([[1, 3],[1.7, 2],[-1, 7]])

But
> pointplot([P1,P2,P3]);
Error, (in plots:-pointplot) number of elements in list must be a multiple of 2

Oh well, let’s see what we get with our circle construction
>display(c1);

Error, (in plots:-display) expecting plot structure but received: c1

Bad guess on my part.

> radius (c1)
yields the correct number and
> center(c1)
yields the name of the circle but
>coordinates(center_c1);
yields what I want. Peculiar but OK , let's go on.
I can write the equation of the circle now that I have the center and radius but hopefully I try

>  equation(c1); and get an error message!!!

The commands center, radius work but equation does not! Here is what works
> Equation(c1)

If one really wants to CONFUSE the user why not eQuaTiOn? Who would guess that? (Sorry to be sarcastic but …) At least with the equation and implicit plot one can finally get a plot of the circle. Is that CLUMSY?

sometimes I need to check if an ode is missing y(x) or not. Since diff(y(x),x) has y(x) in it, then can not just check if the ode has y(x) or not as is, as this will always gives true if diffy(y(x),x) is there of any order.

Currently what I do, is change all y',y'',y''', etc... to Z,Z^2,Z^3,etc... and then after that it is safe to check if y(x) exist or not.

Is there a better way to do this? Below is what I currently do and it works. Just wondering if there could a more elgent way to do this.

restart;

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

ode:=y(x)*diff(y(x),x$2)^2+diff(y(x),x$3)+y(x)*sqrt(diff(y(x),x))+3*x+3=1/(x*y(x)*diff(y(x),x$5));
ode_order := Student:-ODEs:-DifferentialOrder(ode,y(x)):
ode:=convert(ode,D):
for N from 1 to ode_order do
    ode:=eval(ode,[(D@@N)(y)(x)=Z^N]);
od:
ode

y(x)*(diff(diff(y(x), x), x))^2+diff(diff(diff(y(x), x), x), x)+y(x)*(diff(y(x), x))^(1/2)+3*x+3 = 1/(x*y(x)*(diff(diff(diff(diff(diff(y(x), x), x), x), x), x)))

y(x)*Z^4+Z^3+y(x)*Z^(1/2)+3*x+3 = 1/(x*y(x)*Z^5)

has(ode,y(x))

true

 

 

Download find_if_any_ode_has_yx_jan_6_2025.mw

I can do that for a cylinder (in green below) but not for a box geometry.

Box_geometry_and_pendulum.msim

 

intersections := proc(P, Q, T)
local R, W, w, t, a, b, sol, buff, v;
sol := []; if T = Y then W := X; else W := Y; end if;
R := resultant(P, Q, T);
print(`Résultant :`);
print(R);
w := fsolve(R, W); t := [];
for v in [w] do t := [op(t), fsolve(subs(W = v, P), T)]; end do;
for a in [w] do for b in [t] do if T = Y then buff := abs(subs(X = a, Y = b, P)) + abs(subs(X = a, Y = b, Q));
printf(`X=%a,   Y=%a   --->  %a\\n`, a, b, buff); if buff < 1/100000000 then sol := [op(sol), [a, b]]; end if;
else buff := abs(subs(X = b, Y = a, P)) + abs(subs(X = b, Y = a, Q));
printf(`X=%a,   Y=%a   --->  %a\\n`, b, a, buff); if buff < 1/100000000 then sol := [op(sol), [b, a]];
end if; end if; end do; end do;
printf(`Nombre de solutions :  %a\\n`, nops(sol)); print(sol); end proc;
Try with :
intersections(X^2 + Y^2 - 1, X - Y, X); Would you like to develop this procedure which does not give the number of solutions ?Thank you.

i want to factoring the (m+G'/G) in my long equation but i use some trick but still i can't get the exactly system and still G will remain in my system what should i factoring for remove this G(xi) from my system is all about factoring , my system of equation are wrong contain G(xi) How i can remove it by taking a factoring or any other technique,

not parameter is arbitrary except V and sigma''

restart

with(PDEtools)

with(LinearAlgebra)

with(Physics)

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

 

declare(Omega(x, t)); declare(U(xi)); declare(u(x, y, z, t)); declare(Q(xi)); declare(V(xi))

Omega(x, t)*`will now be displayed as`*Omega

 

U(xi)*`will now be displayed as`*U

 

u(x, y, z, t)*`will now be displayed as`*u

 

Q(xi)*`will now be displayed as`*Q

 

V(xi)*`will now be displayed as`*V

(2)

NULL

ode := (-V*a[2]+a[1])*(diff(diff(U(xi), xi), xi))+U(xi)*(((-gamma+sigma)*k+b)*U(xi)^2-a[1]*k^2+(w*a[2]-alpha)*k-w) = 0

(-V*a[2]+a[1])*(diff(diff(U(xi), xi), xi))+U(xi)*(((-gamma+sigma)*k+b)*U(xi)^2-a[1]*k^2+(w*a[2]-alpha)*k-w) = 0

(3)

F := sum(e[i]*(m+(diff(G(xi), xi))/G(xi))^i, i = -1 .. 1)

e[-1]/(m+(diff(G(xi), xi))/G(xi))+e[0]+e[1]*(m+(diff(G(xi), xi))/G(xi))

(4)

D1 := diff(F, xi)

-e[-1]*((diff(diff(G(xi), xi), xi))/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*((diff(diff(G(xi), xi), xi))/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)

(5)

NULL

S := diff(G(xi), `$`(xi, 2)) = -(2*m*mu+lambda)*(diff(G(xi), xi))-mu

diff(diff(G(xi), xi), xi) = -(2*m*mu+lambda)*(diff(G(xi), xi))-mu

(6)

E1 := subs(S, D1)

-e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)

(7)

D2 := diff(E1, xi)

2*e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)*((diff(diff(G(xi), xi), xi))/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)/(m+(diff(G(xi), xi))/G(xi))^3-e[-1]*(-(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))/G(xi)-(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2-2*(diff(G(xi), xi))*(diff(diff(G(xi), xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*(-(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))/G(xi)-(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2-2*(diff(G(xi), xi))*(diff(diff(G(xi), xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)

(8)

E2 := subs(S, D2)

2*e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)^2/(m+(diff(G(xi), xi))/G(xi))^3-e[-1]*(-(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*(-(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)

(9)

D3 := diff(E2, xi)

-6*e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)^2*((diff(diff(G(xi), xi), xi))/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)/(m+(diff(G(xi), xi))/G(xi))^4+4*e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)*(-(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))/G(xi)-(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2-2*(diff(G(xi), xi))*(diff(diff(G(xi), xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)/(m+(diff(G(xi), xi))/G(xi))^3+2*e[-1]*(-(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)*((diff(diff(G(xi), xi), xi))/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)/(m+(diff(G(xi), xi))/G(xi))^3-e[-1]*((2*m*mu+lambda)^2*(diff(diff(G(xi), xi), xi))/G(xi)+(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+3*(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))*(diff(G(xi), xi))/G(xi)^2+6*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))^2/G(xi)^3-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(diff(G(xi), xi), xi))/G(xi)^2+6*(diff(G(xi), xi))^2*(diff(diff(G(xi), xi), xi))/G(xi)^3-6*(diff(G(xi), xi))^4/G(xi)^4)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*((2*m*mu+lambda)^2*(diff(diff(G(xi), xi), xi))/G(xi)+(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+3*(2*m*mu+lambda)*(diff(diff(G(xi), xi), xi))*(diff(G(xi), xi))/G(xi)^2+6*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))^2/G(xi)^3-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(diff(G(xi), xi), xi))/G(xi)^2+6*(diff(G(xi), xi))^2*(diff(diff(G(xi), xi), xi))/G(xi)^3-6*(diff(G(xi), xi))^4/G(xi)^4)

(10)

E3 := subs(S, D3)

-6*e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)^3/(m+(diff(G(xi), xi))/G(xi))^4+6*e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)*(-(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)/(m+(diff(G(xi), xi))/G(xi))^3-e[-1]*((2*m*mu+lambda)^2*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)+4*(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+12*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))^2/G(xi)^3-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2/G(xi)^2-6*(diff(G(xi), xi))^4/G(xi)^4)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*((2*m*mu+lambda)^2*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)+4*(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+12*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))^2/G(xi)^3-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)^2/G(xi)^2-6*(diff(G(xi), xi))^4/G(xi)^4)

(11)

NULL

NULL

K := U(xi) = F

K1 := diff(U(xi), xi) = E1

K2 := diff(U(xi), `$`(xi, 2)) = E2

K3 := diff(U(xi), `$`(xi, 3)) = E3

NULL

L := eval(ode, {K, K1, K2, K3})

(-V*a[2]+a[1])*(2*e[-1]*((-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-(diff(G(xi), xi))^2/G(xi)^2)^2/(m+(diff(G(xi), xi))/G(xi))^3-e[-1]*(-(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3)/(m+(diff(G(xi), xi))/G(xi))^2+e[1]*(-(2*m*mu+lambda)*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)/G(xi)-3*(-(2*m*mu+lambda)*(diff(G(xi), xi))-mu)*(diff(G(xi), xi))/G(xi)^2+2*(diff(G(xi), xi))^3/G(xi)^3))+(e[-1]/(m+(diff(G(xi), xi))/G(xi))+e[0]+e[1]*(m+(diff(G(xi), xi))/G(xi)))*(((-gamma+sigma)*k+b)*(e[-1]/(m+(diff(G(xi), xi))/G(xi))+e[0]+e[1]*(m+(diff(G(xi), xi))/G(xi)))^2-a[1]*k^2+(w*a[2]-alpha)*k-w) = 0

(12)

NULL

# rewritting rule

RR := isolate(m+diff(G(xi), xi)/(G(xi))=Phi, diff(G(xi), xi)/G(xi));

(diff(G(xi), xi))/G(xi) = Phi-m

(13)

# Apply RR and collect wrt Phi

subs(RR, L):
normal(%):
PhiN := collect(numer(lhs(%)), phi):
PhiD := denom(lhs(%%));

Phi^3*G(xi)^4

(14)



with(LargeExpressions):

LLE := collect(PhiN, Phi, Veil[phi] ):
LLE / PhiD = 0;

(Phi^6*phi[1]+3*Phi^5*phi[2]-Phi^4*phi[3]-Phi^3*phi[4]-Phi^2*phi[5]+Phi*phi[6]-phi[7])/(Phi^3*G(xi)^4) = 0

(15)

# phi[i] coefficients


phis := [ seq( phi[i] = simplify(Unveil[phi](phi[i]), size), i=1..LastUsed[phi] ) ]:

print~( phis ):

phi[1] = G(xi)^4*e[1]^3*((-gamma+sigma)*k+b)

 

phi[2] = e[1]^2*G(xi)^4*e[0]*((-gamma+sigma)*k+b)

 

phi[3] = -3*e[1]*G(xi)^4*(-(1/3)*a[1]*k^2+(-e[-1]*(gamma-sigma)*e[1]+(-gamma+sigma)*e[0]^2+(1/3)*w*a[2]-(1/3)*alpha)*k+b*e[-1]*e[1]+b*e[0]^2-(1/3)*w)

 

phi[4] = (2*e[1]*(V*a[2]-a[1])*(diff(G(xi), xi))^3+3*e[1]*G(xi)*(2*m*mu+lambda)*(V*a[2]-a[1])*(diff(G(xi), xi))^2+e[1]*(V*a[2]-a[1])*G(xi)*((2*m*mu+lambda)^2*G(xi)+3*mu)*(diff(G(xi), xi))+G(xi)^2*(-(6*e[-1]*((-gamma+sigma)*k+b)*e[1]-a[1]*k^2+k*w*a[2]+((-gamma+sigma)*k+b)*e[0]^2-k*alpha-w)*e[0]*G(xi)+e[1]*mu*(2*m*mu+lambda)*(V*a[2]-a[1])))*G(xi)

 

phi[5] = -3*e[-1]*G(xi)^4*(-(1/3)*a[1]*k^2+(-e[-1]*(gamma-sigma)*e[1]+(-gamma+sigma)*e[0]^2+(1/3)*w*a[2]-(1/3)*alpha)*k+b*e[-1]*e[1]+b*e[0]^2-(1/3)*w)

 

phi[6] = 4*((1/2)*(V*a[2]-a[1])*(diff(G(xi), xi))^3+(3/2)*(V*a[2]-a[1])*(m*mu+(1/2)*lambda)*G(xi)*(diff(G(xi), xi))^2+(V*a[2]-a[1])*((m*mu+(1/2)*lambda)^2*G(xi)+(3/4)*mu)*G(xi)*(diff(G(xi), xi))+(1/2)*((3/2)*e[0]*((-gamma+sigma)*k+b)*e[-1]*G(xi)+(V*a[2]-a[1])*(m*mu+(1/2)*lambda)*mu)*G(xi)^2)*e[-1]*G(xi)

 

phi[7] = 8*e[-1]*((1/4)*(V*a[2]-a[1])*(diff(G(xi), xi))^4+(V*a[2]-a[1])*(m*mu+(1/2)*lambda)*G(xi)*(diff(G(xi), xi))^3+(V*a[2]-a[1])*((m*mu+(1/2)*lambda)^2*G(xi)+(1/2)*mu)*G(xi)*(diff(G(xi), xi))^2+(V*a[2]-a[1])*(m*mu+(1/2)*lambda)*mu*G(xi)^2*(diff(G(xi), xi))+(1/4)*(-(1/2)*((-gamma+sigma)*k+b)*e[-1]^2*G(xi)^2+mu^2*(V*a[2]-a[1]))*G(xi)^2)

(16)

# WATCHOUT: you have 9 coefficients and so its desirable to have the same number of unknowns

unknowns := indets(rhs~(phis), {e[-1],e[0],e[1],'identical'(mu),'identical'(lambda),'identical'(a[1]),'identical'(alpha)});

COEFFS := solve(rhs~(phis), unknowns)

{alpha, lambda, mu, a[1], e[-1], e[0], e[1]}

 

{alpha = alpha, lambda = lambda, mu = mu, a[1] = a[1], e[-1] = 0, e[0] = 0, e[1] = 0}, {alpha = alpha, lambda = lambda, mu = mu, a[1] = -(gamma*k*e[0]^2-k*sigma*e[0]^2-b*e[0]^2-k*w*a[2]+alpha*k+w)/k^2, e[-1] = 0, e[0] = e[0], e[1] = 0}, {alpha = (1/2)*(-G(xi)^4*gamma*k^3*e[-1]^2+G(xi)^4*k^3*sigma*e[-1]^2-4*G(xi)^2*(diff(G(xi), xi))*V*k^2*m*mu^2*a[2]+4*G(xi)*(diff(G(xi), xi))^3*V*k^2*m*mu*a[2]+G(xi)^4*b*k^2*e[-1]^2+4*G(xi)^2*(diff(G(xi), xi))*k*m*mu^2*w*a[2]-4*G(xi)*(diff(G(xi), xi))^3*k*m*mu*w*a[2]-2*G(xi)^2*V*k^2*mu^2*a[2]+2*G(xi)*(diff(G(xi), xi))^2*V*k^2*mu*a[2]-2*G(xi)*(diff(G(xi), xi))*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*V*k^2*mu*a[2]+2*(diff(G(xi), xi))^4*V*k^2*a[2]+2*(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*V*k^2*a[2]-4*G(xi)^2*(diff(G(xi), xi))*m*mu^2*w+2*G(xi)^2*k*mu^2*w*a[2]+4*G(xi)*(diff(G(xi), xi))^3*m*mu*w-2*G(xi)*(diff(G(xi), xi))^2*k*mu*w*a[2]+2*G(xi)*(diff(G(xi), xi))*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*k*mu*w*a[2]-2*(diff(G(xi), xi))^4*k*w*a[2]-2*(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*k*w*a[2]-2*G(xi)^2*mu^2*w+2*G(xi)*(diff(G(xi), xi))^2*mu*w-2*G(xi)*(diff(G(xi), xi))*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*mu*w+2*(diff(G(xi), xi))^4*w+2*(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*w)/((2*m*mu^2*(diff(G(xi), xi))*G(xi)^2-2*m*mu*(diff(G(xi), xi))^3*G(xi)+mu*(diff(G(xi), xi))*G(xi)*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)-(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)+mu^2*G(xi)^2-mu*(diff(G(xi), xi))^2*G(xi)-(diff(G(xi), xi))^4)*k), lambda = RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)/G(xi), mu = mu, a[1] = -(1/2)*(-G(xi)^4*gamma*k*e[-1]^2+G(xi)^4*k*sigma*e[-1]^2-4*G(xi)^2*(diff(G(xi), xi))*V*m*mu^2*a[2]+4*G(xi)*(diff(G(xi), xi))^3*V*m*mu*a[2]+G(xi)^4*b*e[-1]^2-2*G(xi)^2*V*mu^2*a[2]+2*G(xi)*(diff(G(xi), xi))^2*V*mu*a[2]-2*mu*G(xi)*(diff(G(xi), xi))*V*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*a[2]+2*(diff(G(xi), xi))^4*V*a[2]+2*(diff(G(xi), xi))^3*V*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)*a[2])/(2*m*mu^2*(diff(G(xi), xi))*G(xi)^2-2*m*mu*(diff(G(xi), xi))^3*G(xi)+mu*(diff(G(xi), xi))*G(xi)*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)-(diff(G(xi), xi))^3*RootOf(4*m^2*mu^2*(diff(G(xi), xi))*G(xi)^2+2*m*mu^2*G(xi)^2+6*m*mu*(diff(G(xi), xi))^2*G(xi)+3*mu*(diff(G(xi), xi))*G(xi)+2*(diff(G(xi), xi))^3+(4*m*mu*(diff(G(xi), xi))*G(xi)+mu*G(xi)+3*(diff(G(xi), xi))^2)*_Z+(diff(G(xi), xi))*_Z^2)+mu^2*G(xi)^2-mu*(diff(G(xi), xi))^2*G(xi)-(diff(G(xi), xi))^4), e[-1] = e[-1], e[0] = 0, e[1] = 0}

(17)

case1 := COEFFS[2]

{alpha = alpha, lambda = lambda, mu = mu, a[1] = -(gamma*k*e[0]^2-k*sigma*e[0]^2-b*e[0]^2-k*w*a[2]+alpha*k+w)/k^2, e[-1] = 0, e[0] = e[0], e[1] = 0}

(18)

NULL

F1 := subs(case1, F)

e[0]

(19)

F2 := subs(case1, ode)

(-a[2]*V-(gamma*k*e[0]^2-k*sigma*e[0]^2-b*e[0]^2-k*w*a[2]+alpha*k+w)/k^2)*(diff(diff(U(xi), xi), xi))+U(xi)*(((-gamma+sigma)*k+b)*U(xi)^2+k*e[0]^2*gamma-k*e[0]^2*sigma-b*e[0]^2-k*w*a[2]+k*alpha+(w*a[2]-alpha)*k) = 0

(20)

W := U(xi) = F1

U(xi) = e[0]

(21)

NULL

E := diff(G(xi), xi) = -(-2*m*mu-lambda)*exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu/(2*m*mu+lambda)

diff(G(xi), xi) = -(-2*m*mu-lambda)*exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu/(2*m*mu+lambda)

(22)

W1 := subs(E, W)

U(xi) = e[0]

(23)

W2 := subs(case1, W1)

U(xi) = e[0]

(24)

W3 := rhs(U(xi) = e[0])

e[0]

(25)

W4 := convert(W3, trig)

e[0]

(26)

W5 := W4

e[0]

(27)

odetest(W2, F2)

0

(28)

Download G-factoring.mw

I see this question
https://mathematica.stackexchange.com/questions/309952/how-to-choose-6-numbers-from-the-following-set-so-that-they-represent-the-length
and tried

primes := [seq(ithprime(i), i = 1 .. 20)];
with(combinat);
all_combinations := choose(primes, 6);

I can not make next part.

I’m trying to solve a stiff system 1-D PDEs numerically in Maple but I’m getting the following error:

“Error, (in pdsolve/numeric/match_PDEs_BCs) cannot handle systems with multiple PDE describing the time dependence of the same dependent variable, or having no time dependence”

I included a picture of the PDEs and their BCs in the attached maple file. For easy reading, the attached file includes highlighted sections for parameters and variables. You can skip those to PDEs, BCs and ICs sections at the end of the document to reach the error I’m facing.

For reference, I used another software to solve the system and I was able to get the results in few seconds, so I think it is solvable. However, personally I prefer to use Maple so any inputs, insights, workarounds that I could use to handle the system in Maple would be of great help to me. Thank you.

question.mw

Dear Maple users

I am using the LinearInterpolation command from the Interpolation package. When I however want to integrate the result from one number to another, I only receive an abstract result. It is probably an easy question, but somehow I can't figure it out. I tried using MakeFunction and evalf command in order to receive a number for the integral. I hope someone can help.

Erik

Download Using_interpolation.mw

Hi,

Is there any other way to interrupt a MapleFlow (2024.2) evaluation, other then the red circled ! icon?

Sometimes MF gets stuck in an "Evaluating" state and the red circled ! icon doesn´t work.

Thanks very much in advance for any help.

How do I explain this:

isolve({a*b=4,a>=1,b>=1});

I noticed a strange (for me) appearence of a dollar:

I know $ as an end of parameters marker, but here its role seems strange.
Is it a typsetting issue?

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