Good day. Please can someone kindly help to reduce the result of this code. Thank you and kind regards

restart:
s:=(sum(a[j]*x^j,j=0..3)+sum(a[j]*exp(-(j-3)*x),j=4..7)):
F:=diff(s,x):
p1:=simplify(eval(s,x=q))=y[n]:
p2:=simplify(eval(F,x=q))=f[n]:
p3:=simplify(eval(F,x=q+h/3))=f[n+1/3]:
p4:=simplify(eval(F,x=q+h))=f[n+1]:
p5:=simplify(eval(F,x=q+5*h/3))=f[n+5/3]:
p6:=simplify(eval(F,x=q+2*h))=f[n+2]:
p7:=simplify(eval(F,x=q+7*h/3))=f[n+7/3]:
p8:=simplify(eval(F,x=q+3*h))=f[n+3]:


vars:= seq(a[i],i=0..7):
Cc:=eval(<vars>, solve({p||(1..8)}, {vars})):
for i from 1 to 8 do
	a[i-1]:=Cc[i]:
end do:
Cf:=s:
L:=collect(simplify(simplify(expand(eval(Cf,x=q+3*h)),size)), [y[n],f[n],f[n+1/3],f[n+1],f[n+5/3],f[n+2],f[n+7/3],f[n+3]], factor):
length(L);
H := ee -> collect(numer(ee),[exp],h->simplify(simplify(h),size))/collect(denom(ee),[exp],h->simplify(simplify(h),size)):
M:=y[n+3]=(H@expand)(L);
length(M);

CurveFitting.mws

Splines and BSplines etc for curve fitting.

The attached short program uses with(CurveFitting) and BS:=BSpline(2,x);  outputs four expressions, the third being 

2-x, x<2.  I'd like to be able to access this, and plot it. but plots[display](BS[3], x=1..2); comes up with an error message.

Thanks in advance for any help. 

How do you can write equation with Maple 2015

into 

please help me!

hi, i am trying to get a list of equations using the coeff function. I have the following equation:

restart;
Lambda:=-(1/8)*(D[4](a))(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t))*(diff(u(x, y, t), x))-(1/8)*(D[6](a))(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t))*(diff(u(x, y, t), y, x))-(1/8)*(D[7](a))(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t))*(diff(u(x, y, t), x, t))-(1/8)*(D[5](a))(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t))*(diff(u(x, y, t), x, x))-(1/8)*(D[12](a))(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t))*(diff(u(x, y, t), x, t, t))-(1/8)*(D[10](a))(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t))*(diff(u(x, y, t), x, x, t))-(1/8)*(D[11](a))(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t))*(diff(u(x, y, t), y, x, t))-(1/8)*(D[9](a))(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t))*(diff(u(x, y, t), y, x, x))+(1/8*(-3*(D[8](a))(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t))-4))*(diff(u(x, y, t), x, x, x))-(1/8)*(D[1](a))(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t))+(1/4)*(D[8](a))(x, y, t, u(x, y, t), diff(u(x, y, t), x), diff(u(x, y, t), y), diff(u(x, y, t), t), diff(u(x, y, t), x, x), diff(u(x, y, t), y, x), diff(u(x, y, t), x, t), diff(u(x, y, t), y, t), diff(u(x, y, t), t, t))*(diff(u(x, y, t), x, x, x));

Now I am trying to get the coefficients of the derivatives of u(x,y,t). So by hand I have done the calculation of taking the coeffient of diff(u(x,y,t),x,x,x) and setting this equal to zero, and then the coefficient of diff(u(x,y,t),x,x,t) and so on. However when I use the coeff function, it will only allow me to compute the coeff of diff(u(x,y,t),x,x,x) and others of third order. However it will not let me use the deriviateves of u of second and first order.

coeff(Lambda,diff(u(x,y,t),x));

this will not work but 

coeff(Lambda,diff(u(x,y,t),x,x,x));

will work.

Any help would be great thanks.

If I have a fourier series as a function of x and t and summation goes from n=1 to eternity how can I get a new function, say F, with unapply so that F=F(x,t,n)?

So instead of plotting F from n=1 to eternity I want to plot e.g from n=1 to n=10

if known solution [a,b,c,d]

solve([eq2, eq3, eq4, ....], [a,b,c,d])

but not equal to known solution a,b,c,d even if number of equations more than number of variables.

then guess that there are some necessary and sufficient conditions unknown.

how to find the necessary and sufficient conditions from solutions?

is there options to set for this?

or can eliminate function help to find necessary and sufficient conditions and how to do?

I'm perplexed by the fact that this bug is not fixed in Maple 2018:

seq(alias(a[i] = RootOf(_Z1^6-3*_Z1^2-2*_Z1+11, index = i)), i = 1 .. 6);
ee := a[1]*a[5]+a[2]*a[6]+a[3]*a[4];
evala(ee); # wrong
     -320/449*a[1]-(16/449*(a[2]^2))*a[1]^4*a[3]-(16/449*(a[2]^3))*a[3]*a[1]^2-
     (56/449*(a[2]^2))*a[1]^3*a[3]-(16/449*(a[2]^2))*a[1]^5*a[3]+(32/449*a[2])*
     a[3]*a[1]^5-(60/449*(a[2]^2))*a[1]^2*a[3]-(256/449*a[2])*a[1]*a[3]+(64/449*
     a[2])*a[3]*a[1]^2+(128/449*(a[2]^2))*a[3]*a[1]-(32/449*(a[2]^3))*a[3]*a[1]^3-
     (16/449*(a[2]^3))*a[3]*a[1]^4-(24/449*a[2])*a[3]*a[1]^4+(256/449*a[1])*a[2]+
     (88/449*(a[1]^4))*a[2]-220/449*a[3]-680/449*a[2]-128/449*(a[1]^4)-(48/449*
     (a[2]^2))*a[1]^4-(32/449*(a[1]^5))*a[2]-(48/449*(a[2]^2))*a[1]^3+(128/449*
     a[2])*a[1]^3-(48/449*(a[2]^3))*a[1]^3+(256/449*(a[2]^3))*a[1]-(32/449*
     (a[2]^3))*a[1]^5-(88/449*(a[2]^3))*a[1]^2-(232/449*a[3])*a[2]+(66/449*
     (a[2]^2))*a[3]+(130/449*(a[1]^2))*a[3]+(24/449*(a[1]^5))*a[3]+(64/449*
     (a[1]^4))*a[3]+(228/449*(a[2]^3))*a[3]+(164/449*a[3])*a[1]^3-(192/449*
     a[3])*a[1]-(256/449*(a[2]^2))*a[1]-196/449*(a[1]^3)+40/449*(a[1]^5)+110/449*
     (a[2]^2)-324/449*(a[2]^3)-18/449*(a[1]^2)+1780/449+(40/449*(a[2]^2))*a[1]^2+
     (32/449*(a[2]^2))*a[1]^5

(along with quite a few bugs that are less critical but seem trivial to fix, like INTERVAL(1..2, 3..4) being displayed as INTERVAL(1..2)).

Are the issues reported on MaplePrimes not being looked into by anyone?

EDIT: And now the original post (the first link above) is gone, for which I don't have any reasonable explanation. Here is the post: i.imgur.com/9kIhPz5.jpg. Here is what I'm seeing now: i.imgur.com/yC4cqE3.jpg.

I am trying to solve the equation

exp(2*sin(t))-1=0, over the interval 0 <= t <=  16

I tried entering this into Maple:

solve({exp(2*sin(t))-1=0, 0 <= t,t <= 16}, AllSolutions, Explicit)

When I enter it, Maple just says "Evaluating"... and then returns nothing.

I tried "solve" without AllSolutions/Explicit, and even fsolve.

Then Maple only gives me the trivial result t = 0.

Is there a way to approximate the roots, like a root solver.

Ideally I would like to get the exact roots over the interval [0,16].

Wolfram has no problem solving this exactly.https://www.wolframalpha.com/input/?i=solve(%5Bexp(2*sin(t))-1%3D0,+0+%3C%3D+t,t+%3C%3D+16%5D,+AllSolutions,+Explicit)

I posted the worksheet

solveroots.mw

Could some Maple expert help me understand why pdsolve gives me this error message from trying to solve this Schrödinger pde and if there is a work around?

restart;
pde:=I*diff(f(x,t),t)=-diff(f(x,t),x$2)+2*x^2*f(x,t);
bc:=f(-infinity,t)=0,f(infinity,t)=0;
sol:=pdsolve([pde,bc],f(x,t));

I must be doing something wrong, but do not see it.

Mathematica solves the above as follows

pde=I D[f[x,t],t]==-D[f[x,t],{x,2}] + 2 x^2 f[x,t];
bc={f[-Infinity,t]==0,f[Infinity,t]==0};
sol=DSolve[{pde,bc},f[x,t],{x,t}]

thank you

Have been using Maple on and off the last couple years, and am stuck on trying to get the output of a symbolic polynomial solution into MATLAB code.  

The original equation I am trying to solve (for lambda):

And the way I am attempting to solve it in Maple: 

I won't put the entire output of that last expression here :P.

However upon attempting to convert to MATLAB code, I get an error:

> Matlab(res);
Error, (in Translate) options [-(1/4)*(-3*K+3*K*nu^2)/(3*t^2*nu^2-3*t^2)+(1/12)*3^(1/2)*((-3*K^2*(pi^2*(9*K^2+((-1024*pi^2*t^6-81*K^4+81*K^4*nu^2)/(-1+nu^2))^(1/2))*(-1+nu^2)^2)^(1/3)+3*K^2*(pi^2*(9*K^2+((-1024*pi^2*t^6-81*K^4+81*K^4*nu^2)/(-1+nu^2))^(1/2))*(-1+nu^2)^2)^(1/3)*nu^2+4*2^(1/3)*(pi^2*(9*K^2+((-1024*pi^2*t^6-81*K^4+81*K^4*nu^2)/(-1+nu^2))^(1/2))*(-1+nu^2)^2)^(2/3)*t^2-32*pi^2*2^(2/3)*t^4+32*pi^2*2^(2/3)*t^4*nu^2)/((pi^2*(9*K^2+((-1024*pi^2*t^6-81*K^4+81*K^4*nu^2)/(-1+nu^2))^(1/2))*(-1+nu^2)^2)^(1/3)*(-1+nu^2)))^(1/2)/t^2-(1/12)*(-(18*K^2*(pi^2*(9*K^2+((-1024*pi^2*t^6-81*K^4+81*K^4*nu^2)/(-1+nu^2))^(1/2))*(-1+nu^2)^2)^(1/3)*((-3*K...
 

I'm guessing it's something to do with the fact that the allvalues() funciton spits out four answers (and I want to examine them one at a time in MATLAB to know which one is right for me).

Any thoughts?

B

> S:=-1/2*((-30*sqrt(3)+81*I)^(2/3)+21+2*sqrt(3)*(-30*sqrt(3)+81*I)^(1/3)-6*(-30*sqrt(3)+81*I)^(1/3)+I*sqrt(3)*(-30*sqrt(3)+81*I)^(2/3)-21*I*sqrt(3))/(-30*sqrt(3)+81*I)^(1/3);

When I enter

simplify(S);

a not much simpler expression involving arctan is output
but when I enter

factor(S);

the expected simplification to the number

3

is output.

This is not a but report, just a report of curious behavior.

I am using Maple 2016 on a Windows 10 PC.

I just installed Maple 2018.   There are long delays when typing imput into a worksheet.  Never had this problem with Maple 2017. I assume that there is some new debugging going on during my input.  But, whatever it is, is there a way to turn it off?

Hello. I have the system of inequalities -x / 2> 0, -x> 0, (-x-y) / 2> 0, (-x-z) / 2> 0, -y> 0, -z> 0. Tell me, please, how to build a graph on it?

Error, (in is/internal) too many levels of recursion

I get the error above when attempting to solve for the roots of partial derivative.  My results are below:

Download 2_many_levels_of_recursion.mw

How I can pdsolve this partial fractional  equation?

1.mw
 

Download 1.mw