MaplePrimes Questions

i want to get zero of this function i did all part true but i don't know why my pde not getting zero after substitute each parameter and part 


 

restart

with(PDEtools)

NULL

undeclare(prime)

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

(1)

p := 2*k; n := 1; xi := -p*t+x

2*k

 

1

 

-2*k*t+x

(2)

"U(xi):=(B[1] (RootOf(3 _Z^2-3 _Z-1)+coth(xi)))^(-1/n);u(x,t):=(B[1] (RootOf(3 _Z^2-3 _Z-1)+coth(-p t+x)))^(-1/n) (e)^(ⅈ (k x-t w))"

proc (xi) options operator, arrow, function_assign; (B[1]*(RootOf(3*_Z^2-3*_Z-1)+coth(xi)))^(-1/n) end proc

 

proc (x, t) options operator, arrow, function_assign; (B[1]*(RootOf(3*_Z^2-3*_Z-1)+coth(-p*t+x)))^(-1/n)*exp(I*(k*x-t*w)) end proc

(3)

pde := I*(diff(u(x, t), t))+diff(u(x, t), `$`(x, 2))+eta*u(x, t)+beta*U(xi)^n*u(x, t)+gamma*U(xi)^(2*n)*u(x, t)+delta*U(xi)^(3*n)*u(x, t)+lambda*U(xi)^(4*n)*u(x, t) = 0

I*(2*exp(I*(k*x-t*w))*k*(1-coth(2*k*t-x)^2)/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^2)-I*w*exp(I*(k*x-t*w))/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))))+2*exp(I*(k*x-t*w))*(1-coth(2*k*t-x)^2)^2/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^3)-(2*I)*k*exp(I*(k*x-t*w))*(1-coth(2*k*t-x)^2)/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^2)+2*exp(I*(k*x-t*w))*coth(2*k*t-x)*(-1+coth(2*k*t-x)^2)/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^2)-k^2*exp(I*(k*x-t*w))/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x)))+eta*exp(I*(k*x-t*w))/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x)))+beta*exp(I*(k*x-t*w))/(B[1]^2*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^2)+gamma*exp(I*(k*x-t*w))/(B[1]^3*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^3)+delta*exp(I*(k*x-t*w))/(B[1]^4*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^4)+lambda*exp(I*(k*x-t*w))/(B[1]^5*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^5) = 0

(4)

case1 := [beta = 2*RootOf(3*_Z^2-3*_Z-1)*(n+2)/(B[1]*n^2), delta = 2*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1)*(3*n+2)/(3*n^2), eta = (k^2*n^2*B[1]^2-n^2*w*B[1]^2-1)/(n^2*B[1]^2), gamma = -6*RootOf(3*_Z^2-3*_Z-1)*(n+1)/n^2, lambda = B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7)*(2*n+1)/(9*n^2), A[0] = RootOf(3*_Z^2-3*_Z-1)*B[1], A[1] = 0, B[1] = B[1]]

[beta = 6*RootOf(3*_Z^2-3*_Z-1)/B[1], delta = (10/3)*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1), eta = (k^2*B[1]^2-w*B[1]^2-1)/B[1]^2, gamma = -12*RootOf(3*_Z^2-3*_Z-1), lambda = (1/3)*B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7), A[0] = RootOf(3*_Z^2-3*_Z-1)*B[1], A[1] = 0, B[1] = B[1]]

(5)

pde3 := eval(pde, case1)

``


 

Download test.mw


Could you explain me why the three forms of patmatch behave identically (which seems natural) but the three forms of type do not.
Is there a way to define the type in type such that this latter returns the same thing for a*f(x)+b, f(x)*a+b, b+a*f(x), b+f(x)*a ?
 

Z := f(x)*a+b;
t1 = type(Z, `&+`(algebraic, `&*`(algebraic, function)));
t2 = type(Z, `&+`(`&*`(algebraic, function), algebraic));
t3 = type(Z, `&+`(`&*`(function, algebraic), algebraic));

f(x)*a+b

 

t1 = false

 

t2 = false

 

t3 = true

(1)

p1 = patmatch(Z, A::algebraic*f(X::algebraic) + B::algebraic, 'pat');
pat;
p2 = patmatch(Z, B::algebraic + A::algebraic*f(X::algebraic), 'pat');
pat;
p2 = patmatch(Z, B::algebraic + f(X::algebraic)*A::algebraic, 'pat');
pat;

p1 = true

 

[A = a, B = b, X = x]

 

p2 = true

 

[A = a, B = b, X = x]

 

p2 = true

 

[A = a, B = b, X = x]

(2)

 


 

Download type_vs_patmatch.mw

TIA

 

Recently, Maple has become almost unuseable. Whatever I do, it suddenly becomes non-reponsive, the cursor stops blipping and nothing happens for about a minute, although I can still move the cursor around and the page slider works, suggesting that the kernel has gone mad.

Then suddenly it comes back to life, executes where it left off, which in most cases happens while I am typing input. A minute later it's back to sleep. When I look at the CPU usage while it is non-responsive, I can see CPU usage is about 30% (there is nothing else significant running), disk usage is about 1% and there is plenty of memory (everything in total wants about 10GB and I have 32GB).

I have the -nocloud parameter set and finally disconnected the network connection, but that didn't help.

It all seems to have started with the most recent upgrade, although I'm not 100% sure of that.

Is anyone else seeing something like this, or better yet, does anyone have a suggestion to make this behaviour stop?

How does one downgrade to 2024.1?

Thank you.

the second ode is giving me zero also when we back to orginal under the condition by using them must the orginal ode be zero but i don't know where is mistake , when Orginal paper use some thing different but i think they must have same results i don't know i use them wrong i am not sure at here just , when U(xi)=y(z) in my mw

restart

with(PDEtools)

NULL

undeclare(prime)

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

(1)

NULL

G := V(xi) = RootOf(3*_Z^2-3*_Z-1)*B[1]+B[1]*(exp(xi)+exp(-xi))/(exp(xi)-exp(-xi))

V(xi) = RootOf(3*_Z^2-3*_Z-1)*B[1]+B[1]*(exp(xi)+exp(-xi))/(exp(xi)-exp(-xi))

(2)

NULL

p := 2*k

2*k

(3)

ode := I*(-(diff(U(xi), xi))*p*exp(I*(k*x-t*w))-I*U(xi)*w*exp(I*(k*x-t*w)))+(diff(diff(U(xi), xi), xi))*exp(I*(k*x-t*w))+(2*I)*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-U(xi)*k^2*exp(I*(k*x-t*w))+eta*U(xi)*exp(I*(k*x-t*w))+beta*U(xi)^n*U(xi)*exp(I*(k*x-t*w))+gamma*U(xi)^(2*n)*U(xi)*exp(I*(k*x-t*w))+delta*U(xi)^(3*n)*U(xi)*exp(I*(k*x-t*w))+lambda*U(xi)^(4*n)*U(xi)*exp(I*(k*x-t*w)) = 0

I*(-2*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-I*U(xi)*w*exp(I*(k*x-t*w)))+(diff(diff(U(xi), xi), xi))*exp(I*(k*x-t*w))+(2*I)*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-U(xi)*k^2*exp(I*(k*x-t*w))+eta*U(xi)*exp(I*(k*x-t*w))+beta*U(xi)^n*U(xi)*exp(I*(k*x-t*w))+gamma*U(xi)^(2*n)*U(xi)*exp(I*(k*x-t*w))+delta*U(xi)^(3*n)*U(xi)*exp(I*(k*x-t*w))+lambda*U(xi)^(4*n)*U(xi)*exp(I*(k*x-t*w)) = 0

(4)

case1 := [beta = 2*RootOf(3*_Z^2-3*_Z-1)*(n+2)/(B[1]*n^2), delta = 2*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1)*(3*n+2)/(3*n^2), eta = (k^2*n^2*B[1]^2-n^2*w*B[1]^2-1)/(n^2*B[1]^2), gamma = -6*RootOf(3*_Z^2-3*_Z-1)*(n+1)/n^2, lambda = B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7)*(2*n+1)/(9*n^2), A[0] = RootOf(3*_Z^2-3*_Z-1)*B[1], A[1] = 0, B[1] = B[1]]

[beta = 2*RootOf(3*_Z^2-3*_Z-1)*(n+2)/(B[1]*n^2), delta = (2/3)*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1)*(3*n+2)/n^2, eta = (k^2*n^2*B[1]^2-n^2*w*B[1]^2-1)/(n^2*B[1]^2), gamma = -6*RootOf(3*_Z^2-3*_Z-1)*(n+1)/n^2, lambda = (1/9)*B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7)*(2*n+1)/n^2, A[0] = RootOf(3*_Z^2-3*_Z-1)*B[1], A[1] = 0, B[1] = B[1]]

(5)

n := 1

1

(6)

G := U(xi) = (B[1]*(RootOf(3*_Z^2-3*_Z-1)+coth(xi)))^(-1/n)

U(xi) = 1/(B[1]*(RootOf(3*_Z^2-3*_Z-1)+coth(xi)))

(7)

pde3 := eval(ode, case1)

I*(-2*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-I*U(xi)*w*exp(I*(k*x-t*w)))+(diff(diff(U(xi), xi), xi))*exp(I*(k*x-t*w))+(2*I)*(diff(U(xi), xi))*k*exp(I*(k*x-t*w))-U(xi)*k^2*exp(I*(k*x-t*w))+(k^2*B[1]^2-w*B[1]^2-1)*U(xi)*exp(I*(k*x-t*w))/B[1]^2+6*RootOf(3*_Z^2-3*_Z-1)*U(xi)^2*exp(I*(k*x-t*w))/B[1]-12*RootOf(3*_Z^2-3*_Z-1)*U(xi)^3*exp(I*(k*x-t*w))+(10/3)*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1)*U(xi)^4*exp(I*(k*x-t*w))+(1/3)*B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7)*U(xi)^5*exp(I*(k*x-t*w)) = 0

(8)

odetest(eval(G, case1), pde3)

79584*exp(I*k*x-I*t*w+12*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-127440*exp(I*k*x-I*t*w+10*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+8352*exp(I*k*x-I*t*w+6*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-27792*exp(I*k*x-I*t*w+8*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-24*exp(2*xi-I*t*w+I*k*x)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+4752*exp(I*k*x-I*t*w+4*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-479376*exp(I*k*x-I*t*w+12*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+138240*exp(I*k*x-I*t*w+10*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+70560*exp(18*xi+I*k*x-I*t*w)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-492912*exp(I*k*x-I*t*w+16*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+777888*exp(I*k*x-I*t*w+14*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+16608*exp(I*k*x-I*t*w+8*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-1056*exp(I*k*x-I*t*w+6*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*exp(I*k*x-I*t*w+4*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-39000*exp(18*xi+I*k*x-I*t*w)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-50400*exp(I*k*x-I*t*w+16*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+121440*exp(I*k*x-I*t*w+14*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+27000*RootOf(3*_Z^2-3*_Z-1)*exp(18*xi+I*k*x-I*t*w)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-55080*RootOf(3*_Z^2-3*_Z-1)*exp(18*xi+I*k*x-I*t*w)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+7200*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+16*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+394416*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+16*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-205920*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+14*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-609984*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+14*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-244512*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+12*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+366768*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+12*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-42480*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+10*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-144720*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+10*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-48672*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+8*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+8208*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+8*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+9504*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+6*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+20736*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+6*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+4*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+18576*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+4*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-72*RootOf(3*_Z^2-3*_Z-1)*exp(2*xi-I*t*w+I*k*x)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+1080*RootOf(3*_Z^2-3*_Z-1)*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))

(9)

simplify(-492912*exp(I*k*x-I*t*w+16*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+777888*exp(I*k*x-I*t*w+14*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+16608*exp(I*k*x-I*t*w+8*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-1056*exp(I*k*x-I*t*w+6*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*exp(I*k*x-I*t*w+4*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-39000*exp(18*xi+I*k*x-I*t*w)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-50400*exp(I*k*x-I*t*w+16*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+121440*exp(I*k*x-I*t*w+14*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+79584*exp(I*k*x-I*t*w+12*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-127440*exp(I*k*x-I*t*w+10*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+8352*exp(I*k*x-I*t*w+6*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-27792*exp(I*k*x-I*t*w+8*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-24*exp(2*xi-I*t*w+I*k*x)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+4752*exp(I*k*x-I*t*w+4*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-479376*exp(I*k*x-I*t*w+12*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+138240*exp(I*k*x-I*t*w+10*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+70560*exp(18*xi+I*k*x-I*t*w)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-55080*RootOf(3*_Z^2-3*_Z-1)*exp(18*xi+I*k*x-I*t*w)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+7200*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+16*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+394416*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+16*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-205920*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+14*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-609984*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+14*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-244512*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+12*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+366768*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+12*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-42480*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+10*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-144720*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+10*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-48672*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+8*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+8208*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+8*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+9504*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+6*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+20736*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+6*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+288*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+4*xi)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+18576*RootOf(3*_Z^2-3*_Z-1)*exp(I*k*x-I*t*w+4*xi)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))-72*RootOf(3*_Z^2-3*_Z-1)*exp(2*xi-I*t*w+I*k*x)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+1080*RootOf(3*_Z^2-3*_Z-1)*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1))+27000*RootOf(3*_Z^2-3*_Z-1)*exp(18*xi+I*k*x-I*t*w)/(B[1]*(3125*exp(20*xi)+25000*exp(18*xi)+76875*exp(16*xi)+108000*exp(14*xi)+55650*exp(12*xi)-12432*exp(10*xi)-11130*exp(8*xi)+4320*exp(6*xi)-615*exp(4*xi)+40*exp(2*xi)-1)))

(((244512*B[1]^2-366768)*exp(10*xi)+(205920*B[1]^2+609984)*exp(12*xi)+(-7200*B[1]^2-394416)*exp(14*xi)+42480*exp(8*xi)*B[1]^2-27000*exp(16*xi)*B[1]^2-288*exp(2*xi)*B[1]^2-9504*exp(4*xi)*B[1]^2+48672*exp(6*xi)*B[1]^2+72*B[1]^2+144720*exp(8*xi)+55080*exp(16*xi)-18576*exp(2*xi)-20736*exp(4*xi)-8208*exp(6*xi)-1080)*RootOf(3*_Z^2-3*_Z-1)+(-79584*B[1]^2+479376)*exp(10*xi)+(-121440*B[1]^2-777888)*exp(12*xi)+(50400*B[1]^2+492912)*exp(14*xi)+127440*exp(8*xi)*B[1]^2+39000*exp(16*xi)*B[1]^2-288*exp(2*xi)*B[1]^2+1056*exp(4*xi)*B[1]^2-16608*exp(6*xi)*B[1]^2+24*B[1]^2-138240*exp(8*xi)-70560*exp(16*xi)-4752*exp(2*xi)-8352*exp(4*xi)+27792*exp(6*xi)-288)*exp(2*xi-I*t*w+I*k*x)/(B[1]^3*(-3125*exp(20*xi)-25000*exp(18*xi)-76875*exp(16*xi)-108000*exp(14*xi)-55650*exp(12*xi)+12432*exp(10*xi)+11130*exp(8*xi)-4320*exp(6*xi)+615*exp(4*xi)-40*exp(2*xi)+1))

(10)

Download ode.mw

this is my first time something like that   coming up my equation after taking integral exponential coming up why?

g1.mw

the series is so complicated but have a strange pattern if you watch the index of parameter  they are not repeated 

Hi,

I am looking for a simpler way to find the equation of a parabola passing through 3 points. I see that using the Geometry package requires defining the parabola with 5 distinct points. Thank you for your guidance.QuestionParabole.mw

Do you think the result of String(0.016)  should be "0.016"  instead of ".16e-1" ?

Any reason why it gives the second form and not the first?  Now have to keep using sprintf to force formating as decimal point. Is this documented somewhere? quick search did not find anything do far.

Maple 2024.2 on windows.

s:="0.016";

"0.016"

z:= :-parse(s);

0.16e-1

String(z);

".16e-1"

sprintf("%0.3f",z);

"0.016"

 

 

Download string_of_decimal_number.mw

I'd like to know the details of the method Statistics:-Mean uses to numerically estimate the expectation of a random variable.

showstat seems of no use and neither seems to be LibraryTools[Browse]();

Here are two examples: the first one (1D) suggests  Statistics:-Mean could use some evalf/Int method, but the conclusion to draw from the second example (R2 --> R) is less clear.

How_does_Mean_proceed.mw

Thanks in advance

PS: I already asked a similar question months ago but didn't get any reply.
       Even answers such as “We don't know” or “We don't care” would suit me better than their absence.

restart;
with(plots);
with(geometry);
_EnvHorizontalName := 'x';
_EnvVerticalName := 'y';
HC := HorizontalCoord;
VC := VerticalCoord;
a := 11;
b := 7;
t := (3*Pi)/8;
c := sqrt(a^2 - b^2);
ellipse(e1, x^2/a^2 + y^2/b^2 = 1);
point(Oo, 0, 0);
point(A, a*cos(t), b*sin(t));
point(B, a*cos(t + 2/3*Pi), b*sin(t + 2/3*Pi));
point(C, a*cos(t + 4/3*Pi), b*sin(t + 4/3*Pi));
point(G, (A[1] + B[1] + C[1])/3, (A[2] + B[2] + C[2])/3);
eval(coordinates(G));
line(NorA, y - A[2] = a^2*A[2]*(x - A[1])/b^2, [x, y]);
line(NorB, y - B[2] = a^2*B[2]*(x - B[1])/b^2, [x, y]);
line(NorC, y - C[2] = a^2*C[2]*(x - C[1])/b^2, [x, y]);
lieu := a^2*x^2 + b^2*y^2 - c^4/4 = 0;
Lieu := implicitplot(lieu, x = -a .. a, y = -b .. b, color = green);
tx := textplot([[coordinates(A)[], "A"], [coordinates(B)[], "B"], [coordinates(C)[], "C"], [coordinates(Oo)[], "O"]], font = [times, bold, 16], align = [above, left]);
dr := draw([e1(color = blue), NorA(color = red), NorB(color = red), NorC(color = red), A(color = red, symbol = solidcircle, symbolsize = 12), B(color = red, symbol = solidcircle, symbolsize = 12), C(color = red, symbol = solidcircle, symbolsize = 12), Oo(color = red, symbol = solidcircle, symbolsize = 12)]);
display([dr, tx, Lieu], scaling = constrained, axes = normal, title = "Ellipse et normales ", titlefont = [HELVETICA, 14]);
      [1        1        1       1        1        1     ]
      [- A[1] + - B[1] + - C[1], - A[2] + - B[2] + - C[2]]
      [3        3        3       3        3        3     ]

                              NorA

                              NorB

                              NorC

Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix

I have a simple nested for loop in a worksheet:

[> for x in [ -1, 1 ] do for y in [ -1, 1 ] do x*y end do end do

When I press Enter, nothing happens. What am I (as a novice) missing?

Scott

I am calling a proc inside a module, where this module had local module variable initialized to false;

This works fine when calling the proc normally.

When calling it from Grid:-Run() it says it is not seeing the module local variable at all.

Why does this happen and is there a workaround this? Here a simple worksheet showing this.

I hope there is a way to make the proc inside the module see the local module variables when using it from Grid node. Otherwise, this whole thing will not work for me, as I have few variables initialized at modules level in number of places.

restart;

A := module()
  local DEBUG_MSG::truefalse:=false;
  export work_proc:=proc(n::integer)
     print("My flag is ",DEBUG_MSG);
  end proc;
end module;

 

_m1690230418240

#THis works as expected
A:-work_proc(0)

"My flag is ", false

#this does not work. THe call works OK, but inside A:-workproc() it does not see module local variables.

Grid:-Set(A:-work_proc):
Grid:-Run(0,A:-work_proc,[ 0 ]);
Grid:-Wait();

"My flag is ", DEBUG_MSG

 

 

Download grid_with_module_local_variable_feb_7_2025.mw


Update 2/7/2025

I tried to change the access to the module local variables from the module local procs, by adding explicit A:- to each variable name where A here is the module name.

This works for normal calls, but not when using Grid to call the proc.

This workaround fail, it gives error that module does not export `%1`

May be I have to redo all my code not to use local module variables. But in some places I have to do this, in order to detect if something has happened before or not. I use module local variables to store state the presist after call is completed.

It looks like Grid is not meant to be used for calling proc() that uses/lives inside modules. But this makes Grid not very useful then for large application.

restart;

A := module()
  local DEBUG_MSG::truefalse:=false;
  export work_proc:=proc(n::integer)
     print("My flag is ",A:-DEBUG_MSG);
  end proc;
end module;

 

_m1690230418240

#THis works as expected
A:-work_proc(0)

"My flag is ", false

#this does not work. THe call works OK, but inside A:-workproc() it does not see module local variables.

Grid:-Set(A:-work_proc):
Grid:-Run(0,A:-work_proc,[ 0 ]);
Grid:-Wait();

Error, (in work_proc) module does not export `%1`

 

 

Download grid_with_module_local_variable_feb_7_2025_V2.mw

I also tried to make the module variable as export instead of local, and that also did not work. I am starting to run out of ideas what else to try...

restart;

A := module()
  export DEBUG_MSG::truefalse:=false;
  export work_proc:=proc(n::integer)
     print("My flag is ",A:-DEBUG_MSG);
  end proc;
end module;

 

_m1690230418208

#THis works as expected
A:-work_proc(0)

"My flag is ", false

#this does not work. THe call works OK, but inside A:-workproc() it does not see module local variables.

Grid:-Set(A:-work_proc):
Grid:-Run(0,A:-work_proc,[ 0 ]);
Grid:-Wait();

Error, (in work_proc) `%1` does not evaluate to a module

 

 

Download grid_with_module_local_variable_feb_7_2025_V3.mw

Update

I think now that using module level local variables will not work with parallel processing anyway. It is like using global variable in parallel processing. Does not work without synchorization of access to this shared variable. 

So this means I have to change my code and not use any module local variables, and pass any information between functions via arguments only.

Using module local variable is more convenient, but I now realize this design is not good for parallel processing.  This means some code changes I have to do. 

On the positive side, I find using Grid can really speed things up. On some tests, up to 10 times faster. The larger the number of problems to process, the more speed up is gained.

So I think it is worth to rewrite my code and remove any use of local level module variables.

How i can get FN from N-soliton to FN for M-lump by applying long wave method and using limit How we can get the series of lump , there is some example for nowing how lump work like f[2] for 1 lump and f[4] for two lump and f[6] for 3 lump i, and also in last of work i showed the series of for n soliton which we can change it to m-lump  but i don't know how work and a[12] will change to b[12] by applying long wave method

m-lump.mw

After my maple (2023) had a crash (froze) and i forc closed it all my files are opened and then changed. All equation fields are changed into "Maple Input" type equations. This completely ruins all my "document" type files where the appearance of the equations was important. More than that most of the changed equations give rise to errors. So the file is basically destroyed. The odd thing is that the file looks fine the first few seconds, but then it is changed completely.
I have uninstalled 2023, and installed Maple 2024 without success. 

Plz help!

Hello

I encountered a few problems. One is that in the first section, I wanted to use the definition above instead of f (s ) and g (s ), which means that when the variable changes under the integral sign, it should detect and replace it.

And the next is that in the Equality section, I should sort by p and set the coefficients to zero. And then, for example, solve for the zero power of p and get the value of f0 and use it in subsequent solutions. Can you help me?

restart;
EQUATIONS

equ1:=diff(f(t),t)-1-t-t^2-g(t)-int(f(s)+g(s),s=0..t)=0;

equ2:=diff(g(t),t)+1+t-f(t)+int(f(s)-g(s),s=0..t)=0;
 

diff(f(t), t)-1-t-t^2-g(t)-(int(f(s)+g(s), s = 0 .. t)) = 0

 

diff(g(t), t)+1+t-f(t)+int(f(s)-g(s), s = 0 .. t) = 0

(1)

f(t):=sum(f[i](t)*p^i,i=0..1);

f[0](t)+f[1](t)*p

(2)

g(t):=sum(g[i](t)*p^i,i=0..1);

g[0](t)+g[1](t)*p

(3)


HPMs

hpm1:=(1-p)*(diff(f(t),t)-1-t-t^2)+p*(-diff(f(t),t)+1+t+t^2-g(t)-int(f(s)+g(s),s=0..t))=0;

hpm2:=(1-p)*(diff(g(t),t)+1+t)+p*(diff(g(t),t)-1-t+f(t)-int(f(s)-g(s),s=0..t))=0;

(1-p)*(diff(f[0](t), t)+(diff(f[1](t), t))*p-1-t-t^2)+p*(-(diff(f[0](t), t))-(diff(f[1](t), t))*p+1+t+t^2-g[0](t)-g[1](t)*p-(int(f(s)+g(s), s = 0 .. t))) = 0

 

(1-p)*(diff(g[0](t), t)+(diff(g[1](t), t))*p+1+t)+p*(diff(g[0](t), t)+(diff(g[1](t), t))*p-1-t+f[0](t)+f[1](t)*p-(int(f(s)-g(s), s = 0 .. t))) = 0

(4)

``

Collect

A:=collect(hpm1,p);

(-2*(diff(f[1](t), t))-g[1](t))*p^2+(2*t^2-2*(diff(f[0](t), t))+diff(f[1](t), t)-g[0](t)-(int(f(s)+g(s), s = 0 .. t))+2*t+2)*p-t^2+diff(f[0](t), t)-t-1 = 0

(5)

EqualityNULL

for i from 0 to degree(A,p) do EQ[i]:=simplify(coeff(A,p,i)); end do;

Error, final value in for loop must be numeric or character

 
   

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