## Weird variations on exp(-infinity)...

Can anyone explain the reasoning that went into the programming decisions that led Maple to give these results?

```restart:
is(-infinity, complex); #expected: false
false
is(-infinity-I*infinity, complex); #expected: false
true
exp(-infinity - I) = limit(exp(x-I), x= -infinity); #expected: 0=0
infinity*I = 0
is(exp(x)<>0) assuming x::complex; #expected: true
false
is(exp(x)<>0) assuming x::real; #expected: true
true
coulditbe(exp(x)=0) assuming x::complex; #expected: false
true
```

## Error, (in Maplets:-Display) BoxCell contains an e...

I got my maplet and there error occurs when I try to display it - Error, (in Maplets:-Display) BoxCell contains an element (_Maplets_reference_1235) that cannot be placed in a layout.

How to fix it?

with(Maplets[Elements]);

mpt := Maplet(Window("Точка выше или ниже прямой", [[[ToggleButton[TB1]("Tt", 'group' = 'tb1')], [ToggleButton[TB2]("Tt", 'group' = 'tb1')]], ButtonGroup['tb1']()]));

Display(mpt);

## How to generate symmetric and rotational matrices ...

Hi I want to generate dihedral group of order 8.I have given the commands
with (GroupTheory):

GroupTheory(DihedralGroup);

DihedralGroup(8, s);
D[8]
Elements(DihedralGroup(8, s));
{(), (12345678), (14725836), (16385274), (18765432),

(1357)(2468), (1753)(2864), (13)(48)(57), (15)(24)(68),

(17)(26)(35), (28)(37)(46), (12)(38)(47)(56), (14)(23)(58)(67),

(15)(26)(37)(48), (16)(25)(34)(78), (18)(27)(36)(45)}
but I need symmetric and rotation matrices like

R0=[1,0;0 1],R1=[0,-1;1,0], R2=[-1,0;0,1], R3=[0 1;-1,0],S0=[1 0;0 -1], S1=[0 1 ;1 0], S2=[-1,0;0,1]; S3=[0,-1;-1,0]
Can any one help me how to generate these matrices

## How to test for algebraic equivalence of equations...

I am trying to check to see if two equations are equivalent, subject to rearrangment and scalar multiplication. For example, I would to have a procedure that would determine that each of the following equations are the equivalent:

(a) (1/2)*y*exp(-y)+2*y^3 - x*ln(x) +x^2 = 10
(b) (1/2)*y*exp(-y)+2*y^3 +x^2 = 10 + x*ln(x)

(c) y*exp(-y)+4*y^3 - 2*x*ln(x) +2*x^2 = 20

Is there a systematic way to go about doing this? Thanks!

## vector matrix multiplication...

I have a vector v= [1 ,1,0]
M=[1 2 3; 5 4 3; 7 9 0];

c=v.M

whats wrong with this. error is in the last statement

## Differentiate solution and plot solution ...

Hi

I have a solution obtained using

sol:=pdsolve(PDE,BC);

"sol" is a function depend on variable x,

how can I differentiate this sol ( which a function ) then plot it

many thanks

## How to find element wise modular inverse of a vect...

How to find

a:=[8, 9 ,9 ,7 ,9 ,10 ,5]-1 mod 11

## how to do transformation of vectors...

Hello I want to multiply two vectors like

X=[x,x2,...x10]

G=[g1,g2,...g10]

y=[x1*g1,x2*g2, ........, x10*g10]

How to perform this transformation in maple?

Thanks

## How to check if checkbox is checked or not?...

with(Maplets);
with(Elements);
with(plots);
with(DocumentTools);

I use GetProperty("d", value) = "true"  to check if checkbox is checked but it does not work. How can I check if checkbox is checked?

workk := proc(g)

if GetProperty("d", value) = "true" then

print("true");

else print("False");

end if;

end proc;

mpt := Maplet(Window("aaaa", [[Plotter[f]()],

["Scalar", CheckBox[d]()],

Button("OK", Shutdown())]]));

Display(mpt);

## modp has bugs and it's disgusting...

All of his should work very readily

 >
 >
 >
 >
 >
 >
 >

## simplifying an expression...

Hey,

Is anyone of you capable of simplifying this expression

f1:=(-3*sin(8*x) + 3*sin(8*x + 2*y) - 3*sin(8*x + 6*y) + 3*sin(8*y + 8*x) + 3*sin(8*y + 6*x) + 3*sin(8*y) - 18*sin(8*y + 4*x) + 3*sin(8*y + 2*x) - 45*sin(6*y + 6*x) + 87*sin(4*y + 6*x) - 3*sin(6*x - 2*y) - 87*sin(6*x + 2*y) + 18*sin(4*x - 4*y) - 93*sin(4*x + 4*y) + 93*sin(4*x + 6*y) - 51*sin(2*x - 4*y) - 342*sin(2*x + 4*y) - 3*sin(-6*y + 2*x) + 51*sin(6*y + 2*x) - 93*sin(-2*y + 4*x) + 342*sin(-2*y + 2*x) + 639*sin(2*x + 2*y) - 639*sin(2*x) + 45*sin(6*x) + 93*sin(4*x) + 231*sin(4*y) - 225*sin(2*y) - 63*sin(6*y) - 57*sqrt(3)*cos(2*x) - 375*sqrt(3)*cos(2*y) + sqrt(3)*cos(8*y + 8*x) - 5*sqrt(3)*cos(8*x + 6*y) - 7*sqrt(3)*cos(8*y + 6*x) + sqrt(3)*cos(8*x) + 192*sqrt(3)*cos(2*y + 4*x) + 43*sqrt(3)*cos(-2*y + 4*x) - 7*sqrt(3)*cos(6*x + 2*y) + 7*sqrt(3)*cos(-6*y + 2*x) - 5*sqrt(3)*cos(6*y) - 149*sqrt(3)*cos(4*x + 4*y) - 149*sqrt(3)*cos(4*x) - 65*sqrt(3)*cos(6*y + 2*x) + 126*sqrt(3)*cos(2*x + 4*y) - 65*sqrt(3)*cos(2*x - 4*y) - 5*sqrt(3)*cos(8*x + 2*y) - sqrt(3)*cos(8*y) + 7*sqrt(3)*cos(8*y + 2*x) + 6*sqrt(3)*cos(8*x + 4*y) - 57*sqrt(3)*cos(2*x + 2*y) + 125*sqrt(3)*cos(4*y) + 126*sqrt(3)*cos(-2*y + 2*x) - 7*sqrt(3)*cos(6*x - 2*y) + 19*sqrt(3)*cos(6*x) + 43*sqrt(3)*cos(4*x + 6*y) + 19*sqrt(3)*cos(6*y + 6*x) - 7*sqrt(3)*cos(4*y + 6*x) + 246*sqrt(3))/(2*(-261*sin(4*x + y) - 297*sin(2*x + 3*y) - 48*sin(5*y + 6*x) + 126*sin(5*y + 2*x) + 9*sin(5*y + 8*x) + 12*sin(7*y + 6*x) - 9*sin(7*y + 4*x) - 36*sin(5*y + 4*x) + 261*sin(3*y + 4*x) + 9*sin(-3*y + 4*x) + 297*sin(-y + 2*x) - 135*sin(3*y) - 21*sin(5*y) - 147*cos(y)*sqrt(3) - 9*sqrt(3)*cos(7*y + 4*x) - 3*sqrt(3)*cos(5*y + 8*x) - 3*sqrt(3)*cos(3*y + 8*x) + 54*sqrt(3)*cos(6*x + 3*y) + 5*sqrt(3)*cos(-5*y + 2*x) + 5*sqrt(3)*cos(7*y + 2*x) - 2*sqrt(3)*cos(6*x - y) - 20*sqrt(3)*cos(6*x + y) - 69*sqrt(3)*cos(4*x + y) + 68*sqrt(3)*cos(4*x - y) + 2*sqrt(3)*cos(8*x + y) + 2*sqrt(3)*cos(7*y + 8*x) - 20*sqrt(3)*cos(5*y + 6*x) - 2*sqrt(3)*cos(7*y + 6*x) + 68*sqrt(3)*cos(5*y + 4*x) - 9*sqrt(3)*cos(-3*y + 4*x) - 69*sqrt(3)*cos(3*y + 4*x) - 171*sqrt(3)*cos(2*x + 3*y) - 35*sqrt(3)*cos(5*y) + 171*sqrt(3)*cos(3*y) - 171*sqrt(3)*cos(-y + 2*x) + 354*sqrt(3)*cos(2*x + y) + sqrt(3)*cos(7*y) + 639*sin(y) - 9*sin(3*y + 8*x) - 12*sin(6*x - y) + 3*sin(7*y) - 9*sin(7*y + 2*x) + 9*sin(-5*y + 2*x) + 48*sin(6*x + y) + 36*sin(4*x - y) - 126*sin(2*x - 3*y)))

into

cos(y-Pi/3).

PS: Actually I managed by expanding the thing out and converting to exp then expanding again and using radnormal. In essence I leave the question, because maybe somebody can explain to me why radnormal seems to be superior (sometimes) to simplify which I thought of as the USEALL choice. Thanks

 >
 (1)
 >

## GlobalOptimization benchmarks...

Does Maplesoft provide success percentage of this toolbox on benchmark functions?. I cannot see much options in the global solve command (from maple help page) other than population size etc.

## Sieving failures...

I recieved the following error:

But when I review the procedure ifactor, it doesnt tell me anything about A Quadratic Sieve algorithm, and it's really long and looks dodgey and suspicious, like line 24 for example, why is it computing the greatest integer divisor of a local variable and a random enormous square free number? and then another with an additional factor a few lines later?

## How to solve or reduce a set of nonlinear equation...

Hello

I need to solve or reduce (similar to the command Reduce in Mathematica) sets of nonlinear equations.  One such example is shown below:

`eqns := {-1+theta[3, 6] = 0, 1-theta[3, 6] = 0, alpha+rho-theta[2, 2]+theta[3, 3] = 0, -theta[3, 6]^2+1 = 0, theta[2, 2]*theta[3, 6]-alpha = 0, theta[2, 2]*theta[3, 6]^2-alpha = 0, -2*theta[3, 3]*theta[3, 6]-2*rho = 0, theta[1, 2]*theta[2, 1]*theta[3, 6]^2+1 = 0, -alpha^2+rho^2+theta[2, 2]^2-theta[3, 3]^2 = 0, -theta[2, 2]^2*theta[3, 6]+2*theta[2, 2]*theta[3, 3]*theta[3, 6]+alpha^2+2*alpha*rho = 0, -theta[1, 3]*theta[2, 2]^2*theta[3, 0]+theta[1, 3]*theta[2, 2]*theta[3, 0]*theta[3, 3]-alpha^2*beta-alpha*beta*rho = 0, -theta[1, 2]*theta[2, 1]*theta[2, 2]*theta[3, 6]+2*theta[1, 2]*theta[2, 1]*theta[3, 3]*theta[3, 6]-alpha-2*rho = 0, -theta[1, 2]*theta[2, 1]*theta[2, 2]*theta[3, 3]+theta[1, 2]*theta[2, 1]*theta[3, 3]^2+theta[1, 3]*theta[2, 2]*theta[3, 0]*theta[3, 6]+alpha*beta+alpha*rho+rho^2 = 0, -alpha^2*rho-alpha*rho^2+theta[1, 2]*theta[2, 1]*theta[2, 2]-theta[1, 2]*theta[2, 1]*theta[3, 3]+theta[1, 3]*theta[3, 0]*theta[3, 6]-theta[2, 2]^2*theta[3, 3]+theta[2, 2]*theta[3, 3]^2+alpha+beta+rho = 0}`

and the indeterminates are:

`fc := {theta[1, 2], theta[1, 3], theta[2, 1], theta[2, 2], theta[3, 0], theta[3, 3], theta[3, 6]}`

Since I do know the solution, I issued the following command to check for typos.

```seq(subs(theta[1,2]=-1,theta[1,3]=-1,theta[2,1]=1,theta[2,2]=alpha,theta[3,0]=beta,theta[3,3]=-rho,theta[3,6]=1,eqns[i]),i=1..nops(eqns))
```

and the outcome is zero for all equations.

When I try the command solve as follows:

`solve(eqns,fc);`

the result is

`{theta[1, 2] = theta[1, 2], theta[1, 3] = theta[1, 3], theta[2, 1] = -1/theta[1, 2], theta[2, 2] = alpha, theta[3, 0] = -beta/theta[1, 3], theta[3, 3] = -rho, theta[3, 6] = 1}`

that should be right but it is not what I am expecting.

How can maple return the solution needed?

Some sets of solutions do not have a solution as the one above.  Some indeterminates cannot be found, is there a way maple returns the solution of the ones that can be solved and reduced the set of equations into two parts, solved ones e non solved ones?  I can provide an example if needed.

Many thanks.

Ed

 First 373 374 375 376 377 378 379 Last Page 375 of 2173
﻿