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How to create a loop in Physics package with one ...

Asked by: Hullzie16 182
loop physics
March 22 2023
2  2

I am trying to create a loop in the Physics package where I am interested in looking at the components of a tensor with one index up and one down. However, when I run the loop it returns the expression with both indices down in my attempts to solve the issue.

I have been fighting with it for an hour now and cant seem to find a fix. Any help will be appreciated, I have attached the file I am working with. 

Thanks in advance. 

LoopQuestion.mw

How to substitute a variable into an expression co...

Asked by: kfplm00 5
substitution subs algsubs
March 22 2023
1  1

The following differential equation occurs during blending of two fluid in a continuous flow stirred tank

I want to replace the quantities in parenthesis on the RHS with the following variables (so-called deviation variables) where the overbar variables are constants and x1, x2 and x are variables.

When I use the subs command or algsubs command, it doesn't perform the substitution.

What is the best way to perform this operation?

Create excel file with sheets of independent varia...

Asked by: vs140580 490
March 22 2023
0  0

Given a excel sheet with data for regression as input column Y will be a dependent variable 

 

Say a maximum of 120 independent variables are their 

 

A function that takes excel as input with headers as in the excel file

 

Do pick all possible subsets of maximum size 5 that is sizes 2,3,4,5 only 

Pick each and eleminate not to store them all together as otherwise storage will be a problem if more data

 

Copy only those subsets of independent variables to seperate seperate sheet

Only those subsets 

where the variables are independent pairwise between them

 

Step 2 function 

Then need to run a multiple linear regression on these subsets like training and test 

And choose the best models I each of cases of number of variable

That is best with 2 variables

Again with 3 variables

Similarly 4 and 5

 

Atleast if possible upto 2 to 3 variables it will be good kind help with your guidance and what is possible 

 

If you are not able give the program of train test regression with charts no issues 

 

Kind help with atleast storing the independent pairwise subsets of size 2 and 3 into seperate sheets in a Excel file atleast

I will do the regression at my end 

How can I handle this error?...

Asked by: OLOWE RUTH 5
syntax differential-equations
March 22 2023
1  4

I'm trying to solve a system of differential equations and encountered this error: Error, (in fsolve) {f1[0], f1[1], f1[2], f1[3], f2[0], f2[1], f2[2], f2[3]} are in the equation, and are not solved for. How can this error be rectified?

Is there a way to make maple simply skip errors an...

Asked by: Jamie128 165
error try-catch
March 21 2023
0  2

For example when I run a worksheet, if there is an error, maple simply prints the error and moves on to the next step. Is there a way to do that with loops.
The try and catch statements are a bit cumbersome and sometimes you have to predict the kind of error statements you may face.

transform PDEs using change of variable...

Asked by: Zeineb 520
pde differential-equations
March 21 2023
0  1

Dear all

I  have a PDE, I would like to substitute the funciton T by another funciton 

How transform the old PDE to a new PDE

transfirm_equation_using_change_variable.mw

thank you

Taking an excel sheet perform operation create new...

Asked by: vs140580 490
excel
March 21 2023
0  5

I will have excel sheet with minium 500 coulmns and 1000 rows say

For sample to explain my question I attach a demo excel

All my columns have headers

I am looking to find all 2 way multiplication and add them as columns to my excel sheet and return it as a new excel sheet say

The column names for the new 2 way column should be like the

header name of column you are multiply * the name of the other columsn

Now in sample file if i multiple column with name A with column with name B I get a new column with header A*B the header name should be inserted and

Below that all the elements of that A column multiplied  with that of B should come

I am looking to form columns for all possible2  way multiplication for the excel I will give.

As you can see the demo file

Excel_to_explain.xlsx

Kind help please

Centered Divided Difference approximations

by: mmcdara 6149 Maple
derivative approximation mtaylor
March 21 2023
3  9


This code enables building Centered Divided Difference (CDD) approximations of derivatives of a univariate function.
Depending on the stencil we choose we can get arbitrary high order approximations.

The extension to bivariate functions is based upon what is often named tensorization in numerical analysis: for instance diff(f(x, y), [x, y] is obtained this way (the description here is purely notional)

  1. Let CDD_x the CDD approximation of diff( f(x), x) ) .
    CDD_x is a linear combination of shifted replicates of f(x)
  2. Let s one of this shifted replicates
    Let CDD_y(s) the CDD approximation of diff( s(y), y) ) .
  3. Replace in CDD_x all shifted replicates by their corresponding expression CDD_y(s)


REMARKS:

  • When I write for instance "approximation of diff(f(x), x)", this must be intended as a short for "approximation of diff(f(x), x) at point x=a"
  • I agree that a notation like, for instance, diff(f(a), a) is not rigourous and that something like a Liebnitz notation would be better. Unfortunately I don't know how to get it when I use mtaylor.
     
> 

restart:


CDDF stands for Cendered Divided Difference Formula

> 

CDDF := proc(f, A, H, n, stencil)
  description "f = target function,\nA = point where the derivatives are approximated,\nH = step,\nn = order of the derivative,\nstencil = list of points for the divided differenceCDDF\n";
  local tay, p, T, sol, unknown, Unknown, expr:

  tay := (s, m) -> convert(
                     eval(
                       convert(
                         taylor(op(0, f)(op(1, f)), op(1, f)=A, m),
                         Diff
                       ),
                       op(1, f)=A+s*H),
                     polynom
                   ):

  p   := numelems(stencil):
  T   := add(alpha[i]*tay(i, p+1), i in stencil):
  T   := convert(%, diff):

  if p > n+1 then
    sol := solve([seq(coeff(T, h, i)=0, i in subsop(n+1=NULL, [$0..p]))], [seq(alpha[i], i in stencil)])[];
  else
    sol := solve([seq(coeff(T, H, i)=0, i in subsop(n+1=NULL, [$0..n]))], [seq(alpha[i], i in stencil)])[];
  end if:

  if `and`(is~(rhs~(sol)=~0)[]) then
    WARNING("no solution found"):
    return
  else
    unknown := `union`(indets~(rhs~(sol))[])[];
    Unknown := simplify(solve(eval(T, sol) = Diff(op(0, f)(A), A$n), unknown));
    sol     := lhs~(sol) =~ eval(rhs~(sol), unknown=Unknown);
    expr    := normal(eval(add(alpha[i]*op(0, f)(A+i*H), i in stencil), sol));
  end if:

  return expr
end proc:
> 

Describe(CDDF)


# f = target function,
# A = point where the derivatives are approximated,
# H =
# step,
# n = order of the derivative,
# stencil = list of points for the divided
# differenceCDDF
#
CDDF( f, A, H, n, stencil )
 

  
> 

# 2-point approximation of diff(f(x), x) | x=a

CDDF(f(x), a, h, 1, [-1, 1]);
convert(simplify(mtaylor(%, h=0, 4)), Diff);

-(1/2)*(f(a-h)-f(a+h))/h

  

Diff(f(a), a)+(1/6)*(Diff(Diff(Diff(f(a), a), a), a))*h^2

 (1)
> 

# 3-point approximation of diff(f(x), x$2) | x=a

CDDF(f(x), a, h, 2, [-1, 0, 1]);
convert(simplify(mtaylor(%, h=0)), Diff);

-(-f(a-h)+2*f(a)-f(a+h))/h^2

  

Diff(Diff(f(a), a), a)+(1/12)*(Diff(Diff(Diff(Diff(f(a), a), a), a), a))*h^2

 (2)
> 

# 5-point pproximation of diff(f(x), x$2) | x=a

CDDF(f(x), a, h, 2, [$-2..2]);
convert(simplify(mtaylor(%, h=0, 8)), Diff);

-(1/12)*(f(a-2*h)-16*f(a-h)+30*f(a)-16*f(a+h)+f(a+2*h))/h^2

  

Diff(Diff(f(a), a), a)-(1/90)*(Diff(Diff(Diff(Diff(Diff(Diff(f(a), a), a), a), a), a), a))*h^4

 (3)
> 

# 7-point approximation of diff(f(x), x$2) | x=a

CDDF(f(x), a, h, 2, [$-3..3]);
# simplify(taylor(%, h=0, 10));
convert(simplify(mtaylor(%, h=0, 10)), Diff);

-(1/180)*(-2*f(a-3*h)+27*f(a-2*h)-270*f(a-h)+490*f(a)-270*f(a+h)+27*f(a+2*h)-2*f(a+3*h))/h^2

  

Diff(Diff(f(a), a), a)+(1/560)*(Diff(Diff(Diff(Diff(Diff(Diff(Diff(Diff(f(a), a), a), a), a), a), a), a), a))*h^6

 (4)
> 

# 4-point staggered approximation of diff(f(x), x$3) | x=a

CDDF(f(x), a, h, 3, [seq(-3/2..3/2, 1)]);
convert(simplify(mtaylor(%, h=0, 6)), Diff);

-(f(a-(3/2)*h)-3*f(a-(1/2)*h)+3*f(a+(1/2)*h)-f(a+(3/2)*h))/h^3

  

Diff(Diff(Diff(f(a), a), a), a)+(1/8)*(Diff(Diff(Diff(Diff(Diff(f(a), a), a), a), a), a))*h^2

 (5)
> 

# 6-point staggered approximation of diff(f(x), x$3) | x=a

CDDF(f(x), a, h, 3, [seq(-5/2..5/2, 1)]);
# simplify(taylor(%, h=0, 8));
convert(simplify(mtaylor(%, h=0, 8)), Diff);

(1/8)*(f(a-(5/2)*h)-13*f(a-(3/2)*h)+34*f(a-(1/2)*h)-34*f(a+(1/2)*h)+13*f(a+(3/2)*h)-f(a+(5/2)*h))/h^3

  

Diff(Diff(Diff(f(a), a), a), a)-(37/1920)*(Diff(Diff(Diff(Diff(Diff(Diff(Diff(f(a), a), a), a), a), a), a), a))*h^4

 (6)
> 

# 5-point approximation of diff(f(x), x$4) | x=a

CDDF(f(x), a, h, 4, [$-2..2]);
convert(simplify(mtaylor(%, h=0, 8)), Diff);

(f(a-2*h)-4*f(a-h)+6*f(a)-4*f(a+h)+f(a+2*h))/h^4

  

Diff(Diff(Diff(Diff(f(a), a), a), a), a)+(1/6)*(Diff(Diff(Diff(Diff(Diff(Diff(f(a), a), a), a), a), a), a))*h^2

 (7)
> 

# 7-point approximation of diff(f(x), x$4) | x=a

CDDF(f(x), a, h, 4, [$-3..3]);
convert(simplify(mtaylor(%, h=0, 10)), Diff);

(1/6)*(-f(a-3*h)+12*f(a-2*h)-39*f(a-h)+56*f(a)-39*f(a+h)+12*f(a+2*h)-f(a+3*h))/h^4

  

Diff(Diff(Diff(Diff(f(a), a), a), a), a)-(7/240)*(Diff(Diff(Diff(Diff(Diff(Diff(Diff(Diff(f(a), a), a), a), a), a), a), a), a))*h^4

 (8)


A FEW 2D EXTENSIONS

> 

# diff(f(x, y), [x, y]) approximation over a (2 by 2)-point stencil

stencil := [-1, 1]:

# step 1: approximate diff(f(x, y), x) over stencil < stencil >

fx  := CDDF(f(x), a, h, 1, stencil):
fx  := eval(% , f=(u -> f[u](y))):
ix  := [indets(fx, function)[]]:

# step 2: approximate diff(g(y), y) over stencil < stencil > where
#         g represents any function in fx.

fxy := add(map(u -> CDDF(u, b, k, 1, stencil)*coeff(fx, u), ix)):

# step 3: rewrite fxy in a more convenient form

[seq(u=op([0, 0], u)(op([0, 1], u), op(1, u)), u in indets(fxy, function))]:
fxy := simplify( eval(fxy, %) );

convert(mtaylor(fxy, [h=0, k=0]), Diff)

(1/4)*(f(a-h, b-k)-f(a-h, b+k)-f(a+h, b-k)+f(a+h, b+k))/(k*h)

  

Diff(Diff(f(a, b), a), b)+(1/6)*(Diff(Diff(Diff(Diff(f(a, b), a), a), a), b))*h^2+(1/6)*(Diff(Diff(Diff(Diff(f(a, b), a), b), b), b))*k^2

 (9)
> 

# Approximation of diff(f(x, y), [x, x, y, y] a (3 by 3)-point stencil


stencil := [-1, 0, 1]:

# step 1: approximate diff(f(x, y), x) over stencil < stencil >

fx  := CDDF(f(x), a, h, 2, stencil):
fx  := eval(% , f=(u -> f[u](y))):
ix  := [indets(fx, function)[]]:

# step 2: approximate diff(g(y), y) over stencil < stencil > where
#         g represents any function in fx.

fxy := add(map(u -> CDDF(u, b, k, 2, stencil)*coeff(fx, u), ix)):

# step 3: rewrite fxy in a more convenient form

[seq(u=op([0, 0], u)(op([0, 1], u), op(1, u)), u in indets(fxy, function))]:
fxy := simplify( eval(fxy, %) );

convert(mtaylor(fxy, [h=0, k=0], 8), Diff)

-(2*f(a, b-k)-4*f(a, b)+2*f(a, b+k)-f(a-h, b-k)+2*f(a-h, b)-f(a-h, b+k)-f(a+h, b-k)+2*f(a+h, b)-f(a+h, b+k))/(h^2*k^2)

  

Diff(Diff(Diff(Diff(f(a, b), a), a), b), b)+(1/12)*(Diff(Diff(Diff(Diff(Diff(Diff(f(a, b), a), a), a), a), b), b))*h^2+(1/12)*(Diff(Diff(Diff(Diff(Diff(Diff(f(a, b), a), a), b), b), b), b))*k^2

 (10)
> 

# Approximation of diff(f(x, y), [x, x, y] a (3 by 2)-point stencil

stencil_x := [-1, 0, 1]:
stencil_y := [-1, 1]:

# step 1: approximate diff(f(x, y), x) over stencil < stencil >

fx  := CDDF(f(x), a, h, 2, stencil_x):
fx  := eval(% , f=(u -> f[u](y))):
ix  := [indets(fx, function)[]]:

# step 2: approximate diff(g(y), y) over stencil < stencil > where
#         g represents any function in fx.

fxy := add(map(u -> CDDF(u, b, k, 1, stencil_y)*coeff(fx, u), ix)):

# step 3: rewrite fxy in a more convenient form

[seq(u=op([0, 0], u)(op([0, 1], u), op(1, u)), u in indets(fxy, function))]:
fxy := simplify( eval(fxy, %) );

convert(mtaylor(fxy, [h=0, k=0], 6), Diff)

(1/2)*(2*f(a, b-k)-2*f(a, b+k)-f(a-h, b-k)+f(a-h, b+k)-f(a+h, b-k)+f(a+h, b+k))/(h^2*k)

  

Diff(Diff(Diff(f(a, b), a), a), b)+(1/12)*(Diff(Diff(Diff(Diff(Diff(f(a, b), a), a), a), a), b))*h^2+(1/6)*(Diff(Diff(Diff(Diff(Diff(f(a, b), a), a), b), b), b))*k^2

 (11)
> 

# Approximation of the laplacian of f(x, y)

stencil := [-1, 0, 1]:

# step 1: approximate diff(f(x, y), x) over stencil < stencil >

fx  := CDDF(f(x), a, h, 2, stencil):
fy  := CDDF(f(y), b, k, 2, stencil):

fxy := simplify( eval(fx, f=(u -> f(u, b))) + eval(fy, f=(u -> f(a, u))) );

convert(mtaylor(fxy, [h=0, k=0], 6), Diff)

(f(a-h, b)-2*f(a, b)+f(a+h, b))/h^2+(f(a, b-k)-2*f(a, b)+f(a, b+k))/k^2

  

Diff(Diff(f(a, b), a), a)+Diff(Diff(f(a, b), b), b)+(1/12)*(Diff(Diff(Diff(Diff(f(a, b), a), a), a), a))*h^2+(1/12)*(Diff(Diff(Diff(Diff(f(a, b), b), b), b), b))*k^2

 (12)
> 

 


 

Download CDD.mw

Global setting of character size in maple 2022...

Asked by: kjell 40
font gui size
March 21 2023
1  1

Hello!

I have changed the the global character size from 12 to 14 but it is not stable. Suddenly size 12 is coming up when a try to copy a row to a another row in the same worksheet.

It is very annoying!!

Any tips????

Regards

Kjell

Shortest walks using LinearAlgebra:-Generic

by: dharr 5712 Maple
linearalgebra graphtheory walk
March 21 2023
3  4

Recently Mapleprimes user @vs140580  asked here about finding the shortest returning walk in a graph (explained more below). I provided an answer using the labelled adjacency matrix. @Carl Love pointed out that the storage requirements are significant. They can be reduced by storing only the vertices in the walks and not the walks themselves. This can be done surprisingly easily by redefining how matrix multiplication is done using Maple's LinearAlgebra:-Generic package.

(The result is independent of the chosen vertex.)

> 

restart
> 

with(GraphTheory)

Consider the following graph. We want to find, for a given vertex v, the shortest walk that visits all vertices and returns to v. A walk traverses the graph along the edges, and repeating an edge is allowed (as distinct from a path, in which an edge can be used only once).

> 

G := AddVertex(PathGraph(5), [6, 7]); AddEdge(G, {{3, 7}, {4, 6}, {6, 7}}); DrawGraph(G, layout = circle, size = [250, 250])

GRAPHLN(undirected, unweighted, [1, 2, 3, 4, 5, 6, 7], Array(1..7, {(1) = {2}, (2) = {1, 3}, (3) = {2, 4}, (4) = {3, 5}, (5) = {4}, (6) = {}, (7) = {}}), `GRAPHLN/table/2`, 0)

> 

n := NumberOfVertices(G)

7

> 

A := AdjacencyMatrix(G)

As is well known, the (i, j) entry of A^k gives the number of walks of length k between vertices i and j. The labelled adjacency matrix shows the actual walks.

> 

Alab := `~`[`*`](A, Matrix(n, n, symbol = omega))

Matrix(%id = 36893490455680637396)

For example, the (3,3) entry of Alab^2 has 3 terms, one for each walk of length 2 that starts and ends at vertex 3. The `&omega;__i,j` factors in a term give the edges visited.

So the algorithm to find the shortest walk is to raise Alab to successively higher powers until one of the terms in the diagonal entry for the vertex of interest has indices for all the vertices.

> 

Alab^2

Matrix(%id = 36893490455709504684)

The expressions for higher powers get very large quickly, so an algorithm that only retains the sets of vertices in each term as a set of sets will use less storage space. So we can consider the following modified labelled adjacency matrix.

> 

B := Matrix(n, n, proc (i, j) options operator, arrow; if A[i, j] = 1 then {{i, j}} else {} end if end proc)

Matrix(%id = 36893490455703852204)

Now we need to modify how we do matrix multiplication, but Maple has the LinearAlgebra:-Generic package to do this. We can redefine addition and multiplication to operate correctly on the sets of sets.

Consider two sets of sets of vertices for walks.

> 

a := {{7}, {1, 3}, {2, 6, 7}}; b := {{1, 2}, {2, 3, 8}}

{{7}, {1, 3}, {2, 6, 7}}

{{1, 2}, {2, 3, 8}}

Addition is just combining the possibilities, and set union will do this. And addition of "zero" should add no possibilities, so we take {} as zero.

> 

`union`(a, b); `union`(a, {})

{{7}, {1, 2}, {1, 3}, {2, 3, 8}, {2, 6, 7}}

{{7}, {1, 3}, {2, 6, 7}}

Multiplication is just combining all pairs by union. Notice here that {7} union {1,3,5} and {1,5} union {3,7} give the same result, but that we do not get duplicates in the set.

> 

{seq(seq(`union`(i, j), `in`(i, a)), `in`(j, b))}

{{1, 2, 3}, {1, 2, 7}, {1, 2, 3, 8}, {1, 2, 6, 7}, {2, 3, 7, 8}, {2, 3, 6, 7, 8}}

The unit for multiplication should leave the set of sets unchanged, so {{}} can be used

> 

{seq(seq(`union`(i, j), `in`(i, a)), `in`(j, {{}}))}

{{7}, {1, 3}, {2, 6, 7}}

And we should check that zero multiplied by a is zero

> 

{seq(seq(`union`(i, j), `in`(i, a)), `in`(j, {}))}

{}

Define these operations for the LinearAlgebraGeneric package:

> 

F[`=`] := `=`; F[`/`] := `/`; F[`0`] := {}; F[`1`] := {{}}; F[`+`] := `union`; F[`*`] := proc (x, y) options operator, arrow; {seq(seq(`union`(i, j), `in`(i, x)), `in`(j, y))} end proc

Warning, (in F[*]) `j` is implicitly declared local

Warning, (in F[*]) `i` is implicitly declared local

Compare B^2 with Alab^2. We have lost information about the details of the walks except for the vertices visited.

> 

LinearAlgebra:-Generic:-MatrixMatrixMultiply[F](B, B)

Matrix(%id = 36893490455680647164)

So here is a procedure for finding the length of the shortest walk starting and ending at vertex v.

> 

WalkLength:=proc(G::Graph,v)
  uses GraphTheory;
  local x,y,i,j,vv,A,B,F,n,vertset;
  if IsDirected(G) then error "graph must be undirected" end if;
  if not member(v,Vertices(G),'vv') then error "vertex not in graph" end if;
  if not IsConnected(G) then return infinity end if;
  F[`=`]:=`=`:F[`/`]:=`/`: # not required but have to be specified
  F[`0`]:={}:
  F[`1`]:={{}}:
  F[`+`]:=`union`;
  F[`*`]:=(x,y)->{seq(seq(i union j, i in x), j in y)};
  n:=NumberOfVertices(G);
  vertset:={$(1..n)};
  A:=Matrix(n,n, (i, j)-> if AdjacencyMatrix(G)[i, j] = 1 then {{i, j}} else {} end if);
  B:=copy(A);
  for i from 2 do
    B:=LinearAlgebra:-Generic:-MatrixMatrixMultiply[F](B,A);
  until vertset in B[vv,vv];
  i;
end proc:
> 

WalkLength(G, 1)

10

> 

NULL

Download WalksGenericSetOfSets.mw

Why does the procedure maximize still return a wro...

Asked by: sursumCorda 922
minimize maximize
March 21 2023
2  18

Here is an apparent instance: 

> 

interface(version);
> 

maximize((1+20230321)*x*y-(x^2+y^2)*(1/2))``

`Standard Worksheet Interface, Maple 2023.0, Windows 10, March 6 2023 Build ID 1689885`

  

0

 (1)
> 

NULL

Download incorrectAgain.mw

Why???
Quite evidently, its supremum cannot be 0. (There are, of course, other approaches to compute it symbolically, yet I just wonder about the cause of this bug.)

limit at infinity ...

Asked by: Zeineb 520
derivative infinity limit
March 21 2023
0  5

Dear all

I have an equation obtained from partial derivable of some functions, I would like to compute the limit when my variable named Pe goes to infinity. 

I hope to get a more appreciate presentation of my code to obtain the limit (  Pe -> + infty)

limit_infinity.mw

All derivative are well compute, but How can I add the limit as Pe goes to infinity

Thank you 

Ask Question about simplify cos and tan...

Asked by: HiCJ 5
simplify simplification trig
March 20 2023
1  2

Why doesn't Maple simplify sin(x) / cos (y) as tan

how can i plot of uu10000...

Asked by: permanoon123 165
complex complexplot plotting
March 20 2023
0  6
> 

restart
> 

with(plottools)
> 

with(plots)
> 

with(CurveFitting)
> 

Digits := 10
> 

with(GaussInt)
> 

w := GInearest(0+I)

I

 (1)
> 

NULL
> 

"f(t):=7.0*(e)^((-(t-13180)^(2))/(2000000))+4.7*(e)^((-(t-16000)^(2))/(3200000)):"
> 

p1 := plot(f(t), t = 0 .. 20000, color = green); plots[display]({p1})

 
> 

NULL
> 

D1 := 15
> 

epsilon := 200000
> 

L := 6500
> 

v := .7

.7

 (2)
> 

t := 10000

10000

 (3)
> 

i = sqrt(-1)

i = I

 (4)
> 

"k(n) := evalf((2 *Pi*n)/(L))"

proc (n) options operator, arrow, function_assign; evalf(2*Pi*n/L) end proc

 (5)
> 

f(n) = (int(f(t)*exp(-w*k(n)*x), x = 0 .. L))/L
> 

NULL
> 

"C(x, t) := (&sum;) exp(-v* t*k(n)- D1 *t*(k(n)^())^(2)- epsilon *t*(k(n))^(4)) *f(n)* exp(w*k(n)* x)"

proc (x, t) options operator, arrow, function_assign; sum(exp(-v*t*k(n)-D1*t*k(n)^2-varepsilon*t*k(n)^4)*f(n)*exp(w*k(n)*x), n = 1 .. 10) end proc

 (6)
> 

uu10000 := [seq(evalf(C(L-j, t)), j = 0 .. 6500, 100)]

[0.8582270020e-37+0.7071768085e-46*I, 0.8542115620e-37-0.8289193755e-38*I, 0.8422030662e-37-0.1650065052e-37*I, 0.8223146210e-37-0.2455737186e-37*I, 0.7947335229e-37-0.3238382907e-37*I, 0.7597194496e-37-0.3990668010e-37*I, 0.7176019535e-37-0.4705546418e-37*I, 0.6687772885e-37-0.5376326775e-37*I, 0.6137045955e-37-0.5996735584e-37*I, 0.5529014934e-37-0.6560976155e-37*I, 0.4869391210e-37-0.7063782859e-37*I, 0.4164366719e-37-0.7500470239e-37*I, 0.3420554942e-37-0.7866976371e-37*I, 0.2644927960e-37-0.8159900244e-37*I, 0.1844750367e-37-0.8376532722e-37*I, 0.1027510610e-37-0.8514880864e-37*I, 0.2008503850e-38-0.8573685436e-37*I, -0.6275071112e-38-0.8552431450e-37*I, -0.1449829443e-37-0.8451351706e-37*I, -0.2258447115e-37-0.8271423331e-37*I, -0.3045824843e-37-0.8014357420e-37*I, -0.3804631338e-37-0.7682581907e-37*I, -0.4527807059e-37-0.7279217843e-37*I, -0.5208629116e-37-0.6808049422e-37*I, -0.5840773014e-37-0.6273487939e-37*I, -0.6418370476e-37-0.5680530177e-37*I, -0.6936062957e-37-0.5034711554e-37*I, -0.7389050434e-37-0.4342054446e-37*I, -0.7773134955e-37-0.3609012248e-37*I, -0.8084758661e-37-0.2842409660e-37*I, -0.8321035975e-37-0.2049379645e-37*I, -0.8479779638e-37-0.1237297776e-37*I, -0.8559520434e-37-0.4137144557e-38*I, -0.8559520435e-37+0.4137144402e-38*I, -0.8479779639e-37+0.1237297769e-37*I, -0.8321035979e-37+0.2049379630e-37*I, -0.8084758664e-37+0.2842409653e-37*I, -0.7773134957e-37+0.3609012242e-37*I, -0.7389050442e-37+0.4342054433e-37*I, -0.6936062961e-37+0.5034711548e-37*I, -0.6418370481e-37+0.5680530171e-37*I, -0.5840773026e-37+0.6273487928e-37*I, -0.5208629121e-37+0.6808049418e-37*I, -0.4527807065e-37+0.7279217840e-37*I, -0.3804631352e-37+0.7682581900e-37*I, -0.3045824850e-37+0.8014357418e-37*I, -0.2258447130e-37+0.8271423327e-37*I, -0.1449829450e-37+0.8451351705e-37*I, -0.6275071183e-38+0.8552431450e-37*I, 0.2008503694e-38+0.8573685437e-37*I, 0.1027510603e-37+0.8514880865e-37*I, 0.1844750360e-37+0.8376532724e-37*I, 0.2644927944e-37+0.8159900249e-37*I, 0.3420554936e-37+0.7866976374e-37*I, 0.4164366713e-37+0.7500470242e-37*I, 0.4869391201e-37+0.7063782866e-37*I, 0.5529014927e-37+0.6560976160e-37*I, 0.6137045944e-37+0.5996735595e-37*I, 0.6687772877e-37+0.5376326784e-37*I, 0.7176019529e-37+0.4705546426e-37*I, 0.7597194490e-37+0.3990668022e-37*I, 0.7947335225e-37+0.3238382916e-37*I, 0.8223146207e-37+0.2455737195e-37*I, 0.8422030659e-37+0.1650065065e-37*I, 0.8542115619e-37+0.8289193856e-38*I, 0.8582270020e-37]

 (7)
 

``

Download 0_one.mw

Maple on-line help...

Asked by: MichalKvasnicka 167
documentation on-line
March 20 2023
4  16

Could someone explain to me why the Maple online help pages (see here) are still apparently matching the Maple 2021 release for the past few years? Does this mean that all the information on the Maple online help pages is out of date, or just this one specific page is terribly out of date?

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