I am trying to create a procedure that can solve integrals using the Composite Simpson's 3/8 rule. However when I test my procedure against maple's ApproximateInt I am getting the wrong results.

Here is my attempt:

restart;

f:= x -> exp(x)*sin(4*x); # function I am using

simp := proc(a, b, n)
  local h, sum, i, single:
  h := (b-a)/n:
  sum := 0:
  single := (3*h/8) * (f(a) + f(b)): # this is the end points
    for i from a+h by h to b-h do
       sum := sum + (3*h/8) * (3*f(i)):
    end do:
print(evalf(sum + single));
end proc:

simp(0,1,12);
                                                                                0.6224486445
evalf(Student:-Calculus1:-ApproximateInt(f(x), 0..1, method = simpson[3/8], partition=12));

                                                                                0.5323516717

As you can see my answer is not very close to the answer given by Maple. I am not sure why my procedure simp is wrong.

If i use expression with function add() it runs normaly, but if I use expression with Threads:-Add (parallel implementation) it causes error "Error, continuation task already created for the current task" or "Kernel connection has been lost"

Expression:

Array(1 .. N,1 .. 1/2*N-NR-1,(i, m) -> evalf(Add(cosArr2[modp(k*i,N)]/kl[k],k = 1 .. NR+m-1)+Add(cosArr2[modp(k*i,N)]*alpha[k],k = NR+m .. 1/2*N)))

What am I doing wrong? Can I use two Add in one evalf?

How can I create a new object from a stanrd, defined in a given metric? For example I want to define an object by convolution of two indices of the Christoffel symbols? I cannot even to see components of such object.

Many thans for an explanation

Leonid

Composite1:=proc(g,f)
Flist := indets(f): Glist := indets(g): gof:=g:
Subslist1 := [seq( Flist[i]=q, i=1.. nops(Flist))]:
return subs(q=f,subs(Subslist1, gof)): # g(f)
end proc:
#F(g o f) = F(g) o F(f) = F o g o f = (F o g) o (F o f)
Functor := (1/2)*(-y*t2-x*t1-y*t3+sqrt(y^2*t2^2+2*y*t2*x*t1+2*y^2*t2*t3+x^2*t1^2+2*x*t1*y*t3+y^2*t3^2-4*x*t4*y*t9-4*x*t4*y*t8-4*x^2*t4*t7-4*y^2*t5*t9-4*y^2*t5*t8-4*y*t5*x*t7-4*y^2*t6*t9-4*y^2*t6*t8-4*y*t6*x*t7))/(x*t4+y*t5+y*t6);
F1:=x+2;
G1:=3*x+5;
gof:=subs(x=F1, G1);
osys := Composite1(gof, Functor) = Composite1(Composite1(G1, Functor),Composite1(F1, Functor));
sys1 := subs(x=3,subs(y=2, osys));sys2 := subs(x=5,subs(y=1, osys));
sys3 := subs(x=1,subs(y=5, osys));sys4 := subs(x=1,subs(y=2, osys));
sys5 := subs(x=2,subs(y=5, osys));sys6 := subs(x=5,subs(y=2, osys));
sys7 := subs(x=2,subs(y=1, osys));sys8 := subs(x=3,subs(y=5, osys));
sys9 := subs(x=5,subs(y=3, osys));
res:=solve([sys1, sys2, sys3, sys4, sys5, sys6, sys7, sys8, sys9], {t1,t2,t3,t4,t5,t6,t7,t8,t9});
simplify(%);
`~`[lhs](select(evalb, res));

alpha:= (1/2)*(-y*t2-x*t1-y*t3+sqrt(y^2*t2^2+2*y*t2*x*t1+2*y^2*t2*t3+x^2*t1^2+2*x*t1*y*t3+y^2*t3^2-4*x*t4*y*t9-4*x*t4*y*t8-4*x^2*t4*t7-4*y^2*t5*t9-4*y^2*t5*t8-4*y*t5*x*t7-4*y^2*t6*t9-4*y^2*t6*t8-4*y*t6*x*t7))/(x*t4+y*t5+y*t6);
g := -y/x;
f := (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x);
subs(p=f,subs(q=f,subs(x=p,subs(y=q,g))));
g := (1/2)*(-x+sqrt(x^2-4*y*x-4*y^2))/(x+y);
f := x*y;
gof := subs(p=f,subs(q=f,subs(x=p,subs(y=q,g))));
lhsgofoalpha := subs(q= alpha,subs(p=alpha, subs(x=p,subs(y=q,gof))));
foalpha := subs(p= alpha,subs(q=alpha,subs(x=p,subs(y=q,f))));
rhsgofoalpha := subs(x= foalpha,subs(y= foalpha, g));
osys := lhsgofoalpha = rhsgofoalpha;
sys1 := subs(x=3,subs(y=2, osys));
sys2 := subs(x=5,subs(y=1, osys));
sys3 := subs(x=1,subs(y=5, osys));
sys4 := subs(x=1,subs(y=2, osys));
sys5 := subs(x=2,subs(y=5, osys));
sys6 := subs(x=5,subs(y=2, osys));
sys7 := subs(x=2,subs(y=1, osys));
sys8 := subs(x=3,subs(y=5, osys));
sys9 := subs(x=5,subs(y=3, osys));
res:=solve([Re(sys1)=0, Re(sys2) =0, Re(sys3) =0, Re(sys4) =0, Re(sys5) =0, Re(sys6) =0, Re(sys7) =0, Re(sys8) =0, Re(sys9) =0], {t1,t2,t3,t4,t5,t6,t7,t8,t9});

i assign 

seta := [x+1, x^2]

setb := [x^3, 2*x+5]

does morphism mean that

i use card_prod

to get

(x+1, x^3)

(x+1, 2*x+5)

(x^2, x^3)

(x^2, 2*x+5)

such that i composite each of 4 sets still satisfy F(f o g) = f o g

example

subs(x=x^3, x+1)

(A o C) o Colimit = (B o C) o Colimit

if known A, B, C and framework of Colimit

can it be said colimit?

Bonus, what are A,B,C? <- this can be not answered

Hi all,

I tried to create the*.exe file by C and call the kernel of maple for calculation.

To understand the OpenMaple, I ran the OpenMaple C code sample, “simple.c” in “<Maple>\ samples\OpenMaple\simple” through Microsoft Visual C++ 2008 but got the incorrect result:

It’s seems that the error is happen due to the wrong maple directory. But according to the description of "kernelopts" in help, the value of mapledir cannot be set.

Refer to the description of  "OpenMaple,Examples" in help , both header file path and library file path had been set:

O/S: Windows (32-bit)

Header file Directories: "C:\Program Files\Maple 17\extern\include"

Library Directories: "C:\Program Files\Maple 17\bin.win"

Environment Variable: "C:\program files\Maple 17\bin.win"

I'd appreciate any help on this topic. Thank a lot.

Has anyone used Maple for Empirical Mode Decomposition ? Any tips, Maple docs ? I can't seem to find anything when searching Maple sites.

I have recently written a maple program to deconvolute gamma-ray spectra using the Richardson-Lucy algrithm. Although this method works well I would prefer to use a method based on the Maximum Entropy algorithm, and would like to know if anyone has tried to write a Maple program to deconvolute 1 dimensional data?

In ode solve command i generated a large array data. The output shows a large order matrix of this form

[110001x6 Matrix

Datatype:Anything

Storage:rectangular

order:Fortran_order].

I want to export this matrix into a notepad. Which can then be used for plotting in TecPlot. 

Looking for good response

I'm trying to display some flow lines for a vector field. The vector field I have is:

What I put into Maple is:

I've tried this with a number of points, but I always get an error message along the lines of:

"Error, (in Student:-VectorCalculus:-FlowLine) cannot determine if this expression is true or false: (2.*(1)(0)-4.)^2+(-2.+4.*(1)(0))^2 < 0.9e-9"

Could someone please shed some light as to what's going wrong for me? I would be very grateful for any help.

Thanks.

a := matrix(...);
b := Convert to hermit matrix from a;
Norm(MatrixMatrixMultiply(b, a), 2) = Norm(a,2)^2

i have tried, but not exactly equal
Norm(MatrixMatrixMultiply(b, a), 2) = 0.01
Norm(a,2)^2 = 0.1

Guess what matrix a is?

run a command string in C# by calling maple

it can run in maple if copy into maple

however return input string was not in correct format

String commandstring = "restart;with(LinearAlgebra):with(ExcelTools): filename := "0257.HK";open3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "B2:B100");high3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "C2:C100");low3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "D2:D100");close3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "E2:E100");n := 30;Round := proc(x,n::integer:=1) parse~(sprintf~(cat("%.",n,"f"),x)); end proc: t:=1; gg :=Matrix(n+1,1); ggg :=Matrix(n+1,1); for k from 0 to n do InputMatrix3 := Matrix([[close3[t+1+k] , close3[t+k], close3[t+2+k]],[close3[t+k], close3[t+2+k],0],[close3[t+2+k],0 , 0]]): InputMatrix3b := Matrix([[close3[t+2+k], close3[t+1+k] , close3[t+3+k]],[close3[t+1+k] , close3[t+3+k],0],[close3[t+3+k],0 , 0]]): InputMatrix3c := Matrix([[close3[t+3+k] , close3[t+2+k], close3[t+4+k]],[close3[t+2+k], close3[t+4+k],0],[close3[t+4+k],0 , 0]]): Old_Asso_eigenvector := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3)): Old_Asso_eigenvector2 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3b), InputMatrix3b)): Old_Asso_eigenvector3 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3c), InputMatrix3c)): gg[k+1,1] :=Old_Asso_eigenvector[2][1,1]; od;Round(Re(gg[1,1][1,1]));";

(g o f ) o alpha =g o (f o alpha)
restart;alpha := (1/2)*(-x-x*t1-y*t2-y*t3+sqrt(x^2+2*x^2*t1+2*x*y*t2+2*x*y*t3+x^2*t1^2+2*x*t1*y*t2+2*x*t1*y*t3+y^2*t2^2+2*y^2*t2*t3+y^2*t3^2-4*x*t4*y*t9-4*x^2*t4*t7-4*x*t4*y*t8-4*y^2*t9-4*y*x*t7-4*y^2*t8-4*y^2*t5*t9-4*y*t5*x*t7-4*y^2*t5*t8-4*y^2*t6*t9-4*y*t6*x*t7-4*y^2*t6*t8))/(x*t4+y+y*t5+y*t6);
g := -y/x;
f := (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x);
subs(p=f,subs(q=f,subs(x=p,subs(y=q,g)))); # -1
g := (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x);
f := x*y;
gof := subs(p=f,subs(q=f,subs(x=p,subs(y=q,g)))); # -(1/3)*(y/x+sqrt(-2*y^2/x^2))*x/y
lhsgofoalpha := subs(q= alpha,subs(p=alpha, subs(x=p,subs(y=q,gof))));
foalpha := subs(p= alpha,subs(q=alpha,subs(x=p,subs(y=q,f))));
rhsgofoalpha := subs(x= foalpha,subs(y= foalpha, g));
osys := lhsgofoalpha = rhsgofoalpha;
sys1 := subs(x=0, osys);
sys2 := subs(y=0, osys);
sys3 := subs(x=1, osys);
sys4 := subs(y=1, osys);
sys5 := subs(x=2, osys);
sys6 := subs(y=2, osys);
sys7 := subs(x=3, osys);
sys8 := subs(y=3, osys);
sys9 := subs(x=4, osys);
sys1 := subs(x=3,subs(y=2, osys));
sys2 := subs(x=5,subs(y=1, osys));
sys3 := subs(x=1,subs(y=5, osys));
sys4 := subs(x=1,subs(y=2, osys));
sys5 := subs(x=2,subs(y=5, osys));
sys6 := subs(x=5,subs(y=2, osys));
sys7 := subs(x=2,subs(y=1, osys));
sys8 := subs(x=3,subs(y=5, osys));
sys9 := subs(x=5,subs(y=3, osys));
res:=solve([sys1, sys2, sys3, sys4, sys5, sys6, sys7, sys8, sys9], {t1,t2,t3,t4,t5,t6,t7,t8,t9});
eval(osys,res);
simplify(%);
`~`[lhs](select(evalb, res));