## Thomas Richard

Mr. Thomas Richard

## 3496 Reputation

14 years, 134 days
Maplesoft Europe GmbH
Technical professional in industry or government
Aachen, North Rhine-Westphalia, Germany

## Very simple...

The two linear equations you feed to solve are contradictory for f2. Check this in a separate step:

```lineq1 := -2*A*xc - B*yc = D; lineq2 := -B*xc - 2*C*yc = E;
4*lineq1 + 3*lineq2;```

For f1, they have a solution.

## Simple reason...

The use ... end use construct is newer than those control structures affected by interface(longdelim). One could think about introducing end as a short form for end use, but that would be counterproductive, as the recommendation is to use the long form for better readability.

## subs versus algsubs...

I do not fully understand your question. You really should upload your worksheet to make it easier for others to help.

Anyway, here's my attempt. The algsubs command won't work because of the presence of sqrt. Fortunately, we can use subs here (simpler syntactic substitution), and by providing an assumption on c, we can simplify the result.

 > # https://www.mapleprimes.com/questions/238930-How-To-Do-The-Algebraic-Extension-In
 > restart:
 > U := -2*a[0]*((x^3*a[1] + 42)*diff(y(x), x, x) - 6*y(x)*x*a[1])*sqrt(-a[0]*(a[1]^2 + 3)) - 3*x^2*((1/3*a[1]^3 + a[0] + a[1])*x + (8*a[1]^2 + 24)*a[0])*diff(y(x), x, x);
 (1)
 > V := diff(U,x);
 (2)
 > # resultants:
 > R0 := resultant(U,V,a[0]);
 > R1 := resultant(U,V,a[1]);
 > #
 > S := simplify(subs((-a[0]*(a[1]^2+3))=c^2,U)) assuming c>=0;
 (3)
 > #
 >
 >

## Yes!...

Just supply the output=DataFrame option to the ExcelTools:-Import command. The default type is Matrix.

## Variables beginning with underscore are ...

Please see the ?_ (or ?underscore) help page.

## Wrong command...

The command for grouping multiple terms into a common fraction is normal:

`normal(e);`

## Looks better in newer versions...

The defaults for scaletorange haven been improved in Maple 2023.

Independently of that, I suggest assigning A:=abs(j) (much shorter) and inserting another plot option: scaling=constrained (otherwise the circle looks too elliptic).

 > restart:
 > with(plots):
 > a := 1/2:
 > j := BesselJ(0,sqrt(2*I)*sqrt(x^2+y^2)*a)/BesselJ(0,sqrt(2*I)*a);
 (1)
 > A := abs(j); # shorter than A := sqrt(Re(j)^2 + Im(j)^2);
 (2)
 > densityplot(A, x = -1 .. 1, y = -sqrt(-x^2 + 1) .. sqrt(-x^2 + 1), grid = [68, 68], style = patchnogrid, scaling=constrained, scaletorange = 0 .. 1);
 >

## Known limitation...

Color functions are available for 3D plots only.

## Straightforward...

This is fairly simple if we use the Matrix constructor along with your mapping (shown here in 1D Math aka Maple notation):

``&Delta;PV1` := Matrix(12, 8, (i, j) -> 100*(100*H0[i] - 100*H1[i,j])/((100 - H0[i])*H1[i,j]))`

See the modified worksheet. I deleted some stuff at the end - perhaps you still need that, sorry. Also, I had to remove the absolute path from the Import call to make it work on my machine.

QuestionPrimes_TR.mw

## Simplification to 0 is possible...

Since your worksheet contains no dsolve call, it is unclear where your solution is coming from, and what assumptions on parameters are needed. However, the odetest result can be simplified as follows:

```ot2 := odetest(G1, pde2);
simplify(ot2,'symbolic');```

Note that the 'symbolic' option must be handled with care, as it may not be valid for all parameter values in the complex domain.

## Assumption required...

If we assume(x0>1) then it works in Maple 2024.1 as well. Perhaps the solution process gets stuck without this information.

## MatrixDecomposition with option method=L...

According to the documentation, the Crout algorithm is for tridiagonal matrices only. Perhaps you have some other definition (or naming convention)? Anyway, the result can be obtained by the MatrixDecomposition command of the Student:-NumericalAnalysis package, using method=LDU option. Worksheet attached:

## combine plus simplify...

You can verify the IVP solution as follows (using Maple 2024.1 here, currently with no Physics updates):

`simplify(combine(residual)) assuming positive;`

It will return [0,0].

## Suggestion...

I don't think proper fading is supported, but if I interpret your question correctly, it is sufficient to let both endpoints depend on the animation parameter:

`plots[animate]( plot, [sin(t), t=x..x+Pi], x=0..4*Pi );`

That should apply to space curves as well, but I did not actually try (today is very busy for me, sorry).

## All correct and straightforward...

This is the expected behaviour of expand and combine for trig expressions. Since you started with the latter command, take a look at the ?combine help page, notably the 2nd bullet item of the Description section. The subpage ?combine,trig has more details.

In your example, expand returns a polynomial in cos(x). [You may omit the trig option, by the way.] In this particular sense, it is the inverse operation of combine which yields a cos of a multiple of x as your input expression. For ordinary polynomials, the inverse of expand is factor.

A different question is which representation is simpler - that's debatable, of course.

I cannot say much about the Context Panel, as I'm rarely ever using it.

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