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Can I disable maple's use of the ' funct...

nmacsai 280 Maple 2022
derivative prime
September 22 2022
3 4

restartNULL

NULL``

Can I disable maple's use of the ' function? (aka prime/derivative function)

 

For example, if

 

f := x^2+1

x^2+1

 (1)

it's derivative is obtained as

 

Diff(f(x), x) = diff(f(x), x)

Diff(x^2+1, x) = 2*x

 (2)

.

We used the prime operator on the f to obtain f' on the right-hand-side.

 

The problem is, I use prime notation as a naming convention like in defining an integral equation such as:

"psi(t)=∫G(t,t')*psi(t') ⅆt' ."

NULL

This is common practice in many texts.

 

Is there a way that I can disable the operator function of ' so I can use it as a naming scheme? I have tried using the Alias( ) command which works on one evaluation but if an equation is passed to another function the Alias( ) command is extinguished by the previous evaluation and it takes the derivative again which is undesired.

how_do_i_disable_prime_operation.mw

With(Phyiscs[Vectors]) can I create vect...

nmacsai 280 Maple
coordinates vector physics
July 11 2022
0 0

Unit_vectors_from_different_coordinate_systems.mw
 

restart

NULLNULL

with(Physics)``

with(Vectors)

NULL

It's common in mathematical physics to use cartesian unit vectors to describe the position of a point in space.

 

r_(t) = x(t)*_i+y(t)*_j

r_(t) = x(t)*_i+y(t)*_j

 (1)

Sometimes it neccessary to convert a position vector like `#mover(mi("r"),mo("→"))`(t) to another cartensian coordinate system with different unit vectors, I call the primed system. In the primed system the position vector looks like:

"(r')(t)=x'(t) (i')+y'(t) (j')"

When using Physics[Vectors] and the unit vector hat notations to define vectors in cartesian space, can I define more than one cartesian space such as:

`#mover(mi("r"),mo("→"))`(t) = x(t)*`#mover(mi("i"),mo("∧"))`+y(t)*`#mover(mi("j"),mo("∧"))`

NULL

and

  "(r')(t)=x'(t) (i')+y'(t) (j')"?

Another way to ask the same thing: Can I define the position vector in different coordinates, each system having a distinct pair of orthogonal unit vectors?

 

The short answer I think is no. Given the current implementation it's not clear how one would go about defining the relationships between unit vectors from different coordinate systems. See below.

 

In 2D the transformation corresponds to a rotation of a vector the plane. The tranformation is characterized by the rotation angle α.

 

 

 

The unit vectors from different systems are related through scalar products.

 

"(i)*i' =(|i|)*|i'|*cos(alpha)=cos(alpha)"``NULL

NULL

"(j)*(j)' =(|j|)*|(j)'|*cos(alpha)=cos(alpha)"NULLNULL

``

"(j)*(i)' =(|j|)*|(i)'|*cos(3 alpha)=cos(3 alpha)"``NULL

 

Is there a way to implement scalar products of vectors from different coordinate systems using the Physics Tensors package? Here I create three different coordinate systems. I don't know whether the unit vectors systems X and Y have the same (i, j, k) unit vectors or does each system have its own triplet?

NULL

Setup(coordinates = cartesian, metric = Euclidean, dimension = 3, spacetimeindices = lowercaselatin, geometricdifferentiation = true)

[coordinatesystems = {X}, dimension = 3, geometricdifferentiation = true, metric = {(1, 1) = 1, (2, 2) = 1, (3, 3) = 1}, spacetimeindices = lowercaselatin]
````

 (2)

Coordinates(Y, Z, Z = cylindrical)

{X, Y, Z}

 (3)

NULL

NULL


 

Download Unit_vectors_from_different_coordinate_systems.mw

 

How do I format express an exponent in s...

nmacsai 280 Maple 2022
typesetting plotting exponent
July 07 2022
1 1

Formatting_exponents_in_typesetting_situations.mw
How do I format express an exponent in standard notation when typesetting a caption?  10^2 displays as 100 when I want it to display as 10^2 but without the caret.

restart

with(plots)

logplot(10^x, x = 0 .. 8, size = [300, 300], legend = [y(x) = 10^x], legendstyle = [location = top], caption = typeset("How do I type,", 10^8, ", and have it show up as 10^8 in the caption?"))

  

NULL

Download Formatting_exponents_in_typesetting_situations.mw

How do I access numerical formatting fro...

nmacsai 280 Maple
July 06 2022
1 0

How do I access numerical formatting from command line?

The help page shows you how to use the point and click menus to change the numerical formatting. It works fine but I want a command to convert from say decimal to scientific notation. Am I missing something?

Here the gui menu on the right hand side of a typical worksheet.

This is the help page for "Numerical Formatting" but there is not much about commands, just the point and click menus. If anyone knows where to search for these commands, please respond. Thanks.

https://maplesoft.com/support/help/maple/view.aspx?path=worksheet/expressions/numericformatting

Is there a better way to impletment a t...

nmacsai 280 Maple
June 13 2022
1 4

transparent_background_in_plots.mw

Is there a better way to impletment a transparent background when genereating plots?

Here I generate a plot with a yellow background.

plot(sin(x), x = 0 .. 4*Pi, background = yellow);


I want the background to be completely transparent instead of yellow.

plot(sin(x), x = 0 .. 4*Pi, background = none);

Error, (in plot) Unable to find image file, none

none is not an accepted color, so an error is returned. Is there such a color as "clear" that is fully transparent? Is there a better way to impletment a transparent background when genereating plots?

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