## How i can calculate invlaplace?...

How i can calculate invlaplace?

iman1.mw

 > > > >  (1)
 > > > ## how I can reach the result in dsolve...

Hi,

How can I find the same result reported in the figure for dsolve the differential equation?

nima.mw ## How can I subtitute without geting the result corr...

When I input
restart;
a := 2;
b := 3;
p := x^2 - a*x - b*x +a*b ;

I get p := x^2 - 5*x + 6
How can I get x^2 - 2 x - 3x + 6.
General question. I have (a,b) in a list [[2,3],[-3,7],[9,10]]. How to subtitute them to get the result
[[x^2 - 2x - 3x + 6, x^2 + 3x - 7x -21, x^2 - 9x - 10x + 90]?

## Why does my Fourier series summation have so many ...

I am trying to learn Maple and Fourier transform by calculating the coefficients and the resuting summation as follows:

```restart;

assume(n>0);

assume(N>0);

target_f := x -> piecewise(-Pi < x and x < 0, 0, 0 < x and x < Pi, x, Pi < x and x < 2*Pi, 0, 2*Pi < x and x < 3*Pi, x - 2*Pi)

a0 := simplify(int(target_f(x), x = -Pi .. Pi)/(2*Pi))

a_n := int(target_f(x)*cos(n . x), x = -Pi .. Pi)/Pi

b_n := int((target_f(x)) . (sin(n*x)), x = -Pi .. Pi)/Pi

fourier_f := N -> a0 + sum(a_n*cos(n*x) + b_n*sin(n . x), n = 1 .. N)```

I am making fourier_f as a function of N becasue I want to see the effect of increasing partial sums. The resulting output of the summation "fourier_f" has a lot of terms. The output looks like this:

```               /        /  N
|        |-----
|        | \
1         1    |   2    |  )   /
- Pi + ------- |4 N  Pi | /    |-
4            2 |        |----- |
4 Pi N  \        \n = 1 \

\
|
|
sin(n x) (cos(n Pi) n Pi - sin(n Pi))\|   /   2
-------------------------------------|| + \I N  Pi LerchPhi(
2                   ||
n  Pi                //

2
-exp(-I x), 1, N) - 2 N  LerchPhi(-exp(-I x), 2, N) - I N Pi

\
+ 2/ exp(I N (Pi - x))

- I N Pi (LerchPhi(-exp(I x), 1, N) N - 1) exp(I N (-Pi + x))

2
- I N  Pi LerchPhi(-exp(-I x), 1, N) exp(-I N (Pi + x))

/   2
+ I Pi N exp(-I N (Pi + x)) + \I N  Pi LerchPhi(-exp(I x), 1, N

2                                       \
) - 2 N  LerchPhi(-exp(I x), 2, N) - I N Pi + 2/ exp(I N (Pi

2
+ x)) + 2 exp(-I x N) N  LerchPhi(exp(-I x), 2, N)

2
+ 2 exp(I x N) N  LerchPhi(exp(I x), 2, N)

2                            2
- 2 N  polylog(2, exp(-I x)) - 2 N  polylog(2, exp(I x))

2                             2
+ 2 N  polylog(2, -exp(-I x)) + 2 N  polylog(2, -exp(I x))

\
|
|
|
- 2 exp(-I x N) - 2 exp(I x N)|
|
/
```

The target function is not that complicated. I am using the target function shown in this YouTube video: https://www.youtube.com/watch?v=praNtRezlkw&list=PLPBSZvbAshbxULtiBcygm1qh7BtsDv3DW&index=12

It gave me similar output when the target function was x2.  I am not sure what's going on because for a simple square wave, I was able to make this work correctly.

I am deliberately not using existing packages because I want to learn Maple syntax.

Can someone please tell me what's my mistake ?

## How to accelerate a nested numeric procedure if it...

Wolfram's marketing literature states that a compiled function may generate the dates for the years 1 through 5.7 million in a couple of seconds rather than in minutes (comparing to the "uncompiled implementation").
The given function in this link can be translated into Maple language as follows:

```(*
Note that this is only a mathematical program that outputs some data,
hence 'Easter(-2, 1)' will never return real Gregorian Easter dates!
*)
Easter:=proc(BEGIN::integer,END::integer,\$)::Array(BEGIN..END,[integer[1..12],integer[1..31]]);# the parent function
description "https://www.wolfram.com/language/12/code-compilation/compute-the-date-of-easter.html";
local computus::procedure[[integer[1 .. 12], integer[1 .. 31]]](integer):=proc(Year::integer,` \$`)::[integer[1..12],integer[1..31]];# the child function
local a::nonnegint,b::integer,c::nonnegint,d::integer,e::nonnegint,f::integer,g::nonnegint,h::nonnegint,i::nonnegint,j::nonnegint,k::nonnegint,Month::integer[1..12],Day::integer[1..31];
(* For compatibility, when `Year` is nonpositive, the command `iquo` must be replaced with slower `floor`. *)
if Year<=0 then
a,b,c:=Year mod 19,floor(Year/100),Year mod 100;
d,e,f:=floor(b/4),b mod 4,floor((8*b+13)/25);
g,h,i:=19*a+b-d-f+15 mod 30,floor(c/4),c mod 4;
j:=floor((a+11*g)/319);k:=2*e+2*h-i-g+j+32 mod 7;
Month:=floor((g-j+k+90)/25);Day:=g-j+k+Month+19 mod 32
else
a,b,c:=irem(Year,19),iquo(Year,100),irem(Year,100):
d,e,f:=iquo(b,4),irem(b,4),iquo(8*b+13,25);
g,h,i:=irem(19*a+b-d-f+15,30),iquo(c,4),irem(c,4);
j:=iquo(a+11*g,319);k:=irem(2*e+2*h-i-g+j+32,7);
Month:=iquo(g-j+k+90,25);Day:=irem(g-j+k+Month+19,32)
fi;
[Month,Day]
end;
Array(BEGIN..END,computus)
end:```

However, as "no nested procedures can be translated" to optimized native machine code (cf. ), executing `Easter(1, 5700000)` has to take at least two minutes Is there some workaround that can provide improved performance for such a numerical procedure that contains a nested procedure? In other words, is it possible to produce the `result` (without modifying the algorithm) in two seconds in modern Maple as that Wolfram marketing literature claims?

## Stop computations when complex number detected...

I think this is a simple thing but I cannot find the solution. I have lots of complicated computations in Maple 2015 (with different functions of different packages), but I need the final result to be real numbers/functions. Is there a way to prevent maple following along with computations if it detects a potential complex number? For example, if in some internal step is taking sqrt(x) it should stop and tell something like: "you must assume x is positive".

## Maple implicitplot with two conditions...

Dear Maple experts

I am using the following two implicitplot commands successfully for variables diffr1 and diffr2:

implicitplot(diffr1, 0. .. 1, 0. .. 1.0, filledregions = true, coloring = [cyan, yellow]);

implicitplot(diffr2, 0. .. 1, 0. .. 1.0, filledregions = true, coloring = [cyan, yellow]);

Now I want to have a plot that mixes them. For example, if diffr1>0 and diffr2>0 I get a color. if diffr1>0 and diffr2<0 I get another color, etc. Is there any way to do that?

## ​​​​​​​In search for references...

Could someone provide me with the references used when implementing the Statistics:-PredictiveLeastSquares function?

TIA

## How can I remove this error? "Error, missing opera...

Hi,
Apparently I have a problem but I can't find it. Please advise what is the source of the error?
1.mw

## How do I delete the output from a procedure?...

I have a great deal of output from a procedure that I wrote clumsily.  How can I delete that output without highlighting and pressing the delete button.  Maple help is often of no help whatsoever.

## Simplest way to direct output to a PDF...

What is the simplest way to direct all Maple output, and only Maple output, into a PDF?

My preference would be to include a command at the beginning of a worksheet so that causes all output returned by Maple, print and graphics, to be directed to a named PDF.  Does such a command or set of commands exist, and if so, what is the process to get it to work?

An alternative is to have a command at the end of a worksheet that causes Maple to print the worksheet to a PDF.  Does that exist, and if so, what is it?

## Finding possible bases for a given periodlenght of...

For example: n=78 (is squarefree because 2 x 3 x 13)

Possible periodlenghts in different bases for 1/78  are  {2,3,4,6,12} this is calculated with Multiplicative-Order (Maple).

Now we pick a period from above, for example 6.

The question is:

Which possible bases exist for 1/78 with  periodlenght of 6 ?

The result is: possible bases calculated with Multiplicative-Order
are {17,23,29,35,43,49}.

Question:
Is there a formular to calculate the bases directly or with less calculations than the Maple-Command ?

Thanks for helping :)

## newtons method ...

hi i am trying to create a procedure for newton rhapson method, which finds roots of a function. the first procedure i made work but now i want it to show an error message for when the function diverges at x0 and when the derivative at x0 = 0. can someone pls advise me how to fix it? thank you:)

NM1 := proc(f, xold)
local x1, x0, precision;
x0 := xold;
x1 := evalf(x0 - f(x0)/D(f)(x0));
precision := 10^(-3);
if limit(f,(x0)) = 0 then
error("Newton's Method cannot do the calculation");
end if;
if D(f)(x0) = 0 then
error("Newton's Method cannot do the calculation");
else
while abs(x1-x0) > precision do
x0 := x1;
print(x0);
x1 := evalf(x0 - f(x0)/D(f)(x0));
end do;
end if;

return x1;
end proc:

## Select some terms from an expression...

Dear users!

I hope everyone is fine here. I have the following expression:

r*y[0, 1]+y[0, 0]+(1/6)*r*(r-1)*(1+r)*y[-1, 3]+(1/2)*r*(r-1)*y[-1, 2]+(1/120)*r*(r-1)*(r-2)*(1+r)*(2+r)*y[-2, 5]+(1/24)*r*(r-1)*(r-2)*(1+r)*y[-2, 4]+(1/720)*r*(r-1)*(r-2)*(r-3)*(r-4)*(1+r)*y[-3, 8]+(1/360)*r*(r-1)^2*(r-2)*(r-3)*(1+r)*y[-3, 7]+(1/720)*r*(r-1)*(r-2)*(r-3)*(1+r)*(2+r)*y[-3, 6]:

What is the procedure to select some terms in the above expression for example for N=2 I just want the following terms:

y[0, 0]+r*y[0, 1]+(1/2)*r*(r-1)*y[-1, 2];

and for N=3 I just want the following terms:

y[0, 0]+r*y[0, 1]+(1/2)*r*(r-1)*y[-1, 2]+(1/6)*r*(r-1)*(1+r)*y[-1, 3];

and for N=4 I want:

(1/24)*r*(r-1)*(r-2)*(1+r)*y[-2, 4]+y[0, 0]+r*y[0, 1]+(1/2)*r*(r-1)*y[-1, 2]+(1/6)*r*(r-1)*(1+r)*y[-1, 3];

and so on,

in the descending order in first suffices and ascending order in second suffices (like term having y[0,0],  y[0,1], y[-1,2], y[-1,3], y[-2,4]). I am waiting for your response. Thanks.