## 1355 Reputation

15 years, 172 days
University of Twente (retired)
Enschede, Netherlands

My "website" consists of a Maple Manual in Dutch

## textplot...

`?textplot`

## What do you want?...

It is not quite clear what your maplet is expected to do. After typing: "1,2" in the Input Box, clicking the button "addition" results in the value 3.
If you want entering digits by pressing the number buttons, you must use at least different mames of variables to store the values. Etcetera. I'm affraid that a radical redesign of the program set-up is needed.

## Notation?...

Perhaps you mean output in uξ-notation?

```restart; with(PDEtools):
declare( );
du := diff(u(xi),xi,xi);```

gives the desired output; and

```OFF;
du```

prints the second derivative of u in the normal layout.

## Exact or approximate...

I think from rounding errors, because you use floating point numbers in your input.

```C := convert~(A,rational):
LinearAlgebra:-Determinant(C);```

has only even powers of x in the output, as expected.

## You forgot a multiplication symbol...

```f := (-x^2+eta^2+2*x*xi+2*x*eta-xi^2-2*xi*eta-2*x*y-2*y*eta+2*xi*y+y^2) *
(-x^2-2*x*eta+eta^2+2*x*xi+2*xi*eta-xi^2+2*x*y-2*xi*y-2*y*eta+y^2) -
(x-xi)^4+6*((x-xi)^2)*(-y+eta)^2-(-y+eta)^4;
expand(f)```

gives zero.

## No ploblem in Maple 14...

```X := <seq(i,i=1..19)>:
Y := Vector( 19,
RandomTools:-Generate( float(range=1..2)*10^integer(range=-13..-6), makeproc=true ) ):
plots:-logplot(X,Y, style=point);```

## partial derivatives...

Defining the function:

`f := (x,y) -> x+(y-1)*arcsin(sqrt(x/y));`

Second derivative wrt x:

`D[1,1](f);`

and with y=1 substituted:

`D[1,1](f)(x,1);`

## Typing errors?...

You write for example

`deltat*x^3`

where problably is meant:

`deltat(x)^3`

or

`deltat(x^3)`

There are a lot more of this kind of errors/ambiguities.

## Eigenfrequency...

What do you mean by "the wrong eigenfrequency"? What is the desired unit? degrees per second? What unit has the "2" in sin(2*t)? degrres per second indeed?

## complexplot...

```z := 3*exp(t*I):
plots:-complexplot( 6/z, t=-Pi..Pi );
```

or directly:

`plot( [Re(6/z),Im(6/z), t=-Pi..Pi] );`

No,

`Nabla.Nabla(F)`

is not the Hessian, but the Laplacian. You have to use parentheses to get the gradient.
To have full control over your input, you can better work in worksheet mode, and choose "Maple Notation"} for Input Display.

I suppose that you want the greatest of the two y-values in your list.
That is not always the first solution that is produced by the solve command.
So you may try

```B := NULL:
for t from 10 by 2 to 100 do
h := [solve({x*y*z = 6*t^3, x-y-z = 0, x+y+z = 6*t}, {x, y, z})]:
B := B,max(subs~(h,y)):
end do:
A := [B];
```

## What do you mean?...

Do you mean a numerical approximation for the derivatives?
Are the θ[i] values equidistant, i.e. is θ[i+1] − θ[i] = h for all i?
Then you can use the central differentiation formula's

If you really want to use Maple for this conversion:

```> eq := A*sin(theta) + B*cos(theta) = C*cos(theta+delta);
> s := solve( identity(eq, theta), {A,B} );
```

Now you have A,B as functions of C and δ.

```> solve( s, {C,delta} ): allvalues(%);
```

Your second question: you get a list of possibble equivalent trigonometric expressions by

```> trigsubs(cos(theta+phi)*cos(theta+omega*t));
```

## Where is the documentation?...

`?copy`

If A is a rtable, the assignment

`B := A;`

results in two names referring to the same structure.

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