## 35 Reputation

8 years, 267 days

## Vector Calculus - How to expand Vector I...

Maple

Hello,

Is it possible to expand vector calculus identities directly in Maple without taking them to basis form (i.e. their component partial derivatives).

For example:

restart

with(Physics[Vectors]):

Given the Left Hand Side, can Maple come up with the RHS on its own?

Many Thanks.

## Truncating Small Errors ...

Maple

Hello,

This is a problem encountered in most engineering equations. An equation is given with some variables very small that they can be ignored. Basically the mathematical equivalent of an engineering approximation.

Below is a very simple example:

Both R and r are between 10E3 and 50E3.
gm is between 1 and 10.

So regardless of actual values the answer to 4significant figures can always be approximated by:

eqn1~ R*gm*r

Is there any way to tell MAPLE to approximate an equation such that it is only accurate to certain decimal places? I have tried using "fnormal()" with "assuming"  statements but it always requires some of the variables be assigned actual numeric values.

I was wondering if there was a way to get this approximation without having to assign values to any of the variables but only by specifying the range of values for each variable.

Thanks.

## Splitting an equation by its addition te...

Maple

Hi, I wondered if anyone knows a way to separate out addition (or subtraction) terms in an equation.

For example given eqn1:

eqn1:= (1/2)*p+1+(-4*p^2-p-1)/(3*p^3+7*p^2+2*p+2)

I would like to get the first rational term before the first plus (or minus) sign. In this case it would be (p/2).

This is a trivial example shown above but the real value in this is that I want to customize my own factorizations using the pratial fraction function of Maple. In this case I would not know eqn1 before hand but it would be the solution to some previous factorization and I need just the first term (before the first plus sign).

If anyone knows any tips or tricks that will set me on the right path to doing this it is most appreciated.

Maple

Hi,

Would anyone know how to customize the CompleteSquare function. Reason is I am trying to extend it to complex numbers. Examples below. (Unfortunately the text editor is playing up but if you could copy and paste the text below in your Maple you should be able to see it more clearly).

eqn1 := x__1^2+4*x__1*x__2+2*x__2^2;

with(Student[Precalculus]):

CompleteSquare(eqn1, [x__1, x__2]);

This gives the answer below which is correct.

2*(x__2+x__1)^2-x__1^2

However consider the complex function below:

x__1*conjugate(x__1)-conjugate(x__1)*x__2+3*conjugate(x__1)*x__3-conjugate(x__2)*x__1+2*x__2*conjugate(x__2)+3*conjugate(x__3)*x__1+14*x__3*conjugate(x__3)

I am trying to factorize this into the following:

(x__1-x__2+3*x__3)*(conjugate(x__1)-conjugate(x__2)+3*conjugate(x__3))+(x__2+3*x__3)*(conjugate(x__2)+3*conjugate(x__3))-4*x__3*conjugate(x__3)

The technique I am trying is to first try to come up with a generalized form of the CompleteSquare function and then try to extend it to complex factorization but so far haven't been successful.

## Recognize specific algebraic forms...

Maple

Hi,

Wondered if anyone could help with the query below.

Consider f(x,y) defined as:
f := proc (x, y) options operator, arrow; x*y/(x+y) end proc

Then f(A, B); becomes:
(A * B )/(A + B)

now consider the polynomial:(poly2)

poly2:=(A*B+A*X+B*X)*(Y+X)/((A+B)*X*(2*Y+X))

This polynomial is just the expansion of the polynomial below (lets call it poly1) which MAPLE does not recognize.

(A*B/(A+B)+X)/(X+Y*X/(Y+X))

Here you can see that A,B on top and X,Y on the bottom are clearly of the form f(x,y).

Is there a way you can get MAPLE to recognize certain algebraic forms such that the polynomial poly2 could be written either as poly1 (already shown above) or as poly3 below:

poly3:=(f(A, B)+X)/(X+f(Y, X))

I have tried using simplify in the following form but not much luck. It doesn't seem to recognize anything other than the obvious.

simplify(poly2, {A*B/(A+B) = F1}, tdeg(A, B))

(I am still a bit new to the MAPLE syntax and procedures so apologies if I have missed something obvious function that can do this.)

Thanks.

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