i have been having a hard trouble working on excercise 4a since i cannot understand how to differentiate a trig function that has x in degrees. How is it done?

.

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## How do i differentiate a cosx function when x is in degrees?

## Integer linear programming can’t find global minimum

## Is this really prime number?

## HoldFirst being overridden by Activate

## Using list of rules from imported .mat file

## center of mass, total momentum

## How to solve a system of two equations and two variables in function of others terms

## How to set up patterns when using SequenceSplit

## Evaluating part(s) of a function which outputs another function [duplicate]

## Transform a field with derivatives

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i have been having a hard trouble working on excercise 4a since i cannot understand how to differentiate a trig function that has x in degrees. How is it done?

.

I was working with Project Euler Problem 418 using Mathematica and got in trouble.

I wrote a function to find the unique factorization triple which minimizes c / a for integer n.

`FactorizationTriple[n_] := Block[{factor, base, exponent, l, e, varmat, vars, cons1, cons2, cons3, solve, a, b, c}, factor = FactorInteger[n]; base = factor[[All, 1]]; exponent = factor[[All, 2]]; l = Length[factor]; varmat = Table[e[i, j], {i, 1, 3}, {j, 1, l}]; vars = Flatten[varmat]; cons1 = Thread[0 <= vars]; cons2 = Thread[exponent == Total[varmat, {1}]]; cons3 = {varmat[[1]].N[Log[base]] <= varmat[[2]].N[Log[base]] <= varmat[[3]].N[Log[base]]}; solve = FindMinimum[{varmat[[3]].N[Log[base]] - varmat[[1]].N[Log[base]], Join[cons1, cons2, cons3], Element[vars, Integers]}, vars]; a = Times @@ (Power @@@ ({base, Table[e[1, j], {j, 1, l}] /. solve[[2]]}\[Transpose])); b = Times @@ (Power @@@ ({base, Table[e[2, j], {j, 1, l}] /. solve[[2]]}\[Transpose])); c = Times @@ (Power @@@ ({base, Table[e[3, j], {j, 1, l}] /. solve[[2]]}\[Transpose])); {a, b, c}] `

Since both *f* and *cons* in `FindMinum`

are linear, I thought it uses `Method->"LinearProgramming"`

and I expected it to return a global minimum.

`FactorizationTriple`

does work when n = 165 or 100100 or 20!, but it can’t give me the correct answer when n = 43!:

`AbsoluteTiming[FactorizationTriple[43!]] {1044.17, {392385912744443904, 392388272221065120, 392389380337500000}} `

The correct answer is `{a, b, c} = {392386762388275200, 392388272221065120, 392388530688000000}`

.

**Questions:**

- Should I use
`NMinimize`

or`LinearProgramming`

instead? (I had some try but failed.) - How to set the options in
`FindMinum`

? - How to improve the efficiency of
`FactorizationTriple`

? (It’s too slow now.)

Using the primality test on this site (www.javascripter.net/math/calculators/100digitbigintcalculator.htm) I found that the concatenation of the digit reversal of the first 548 odd primes in the reverse order is a prime(!). It is a 1998-digit prime, but it took more than an hour for this ‘calculator’ to stated that it is a prime, it was a ‘super-slowly’ calculation. Could you confirm that this result is correct?. that prime is 7693749334931393…91713111753. Thanx.

So here’s the problem `a=1;a=2`

works because of the `HoldFirst`

attribute of `Set`

, so that it does not become `1=2`

But `a=1;Activate[Inactivate[a=2]]`

does not because the attributes of `Set`

is lost during `Inactivate`

. So how do I avoid this problem?

I’m attempting to learn Mathematica to replace MATLAB. However, I have some data in .mat files which contains named variables.

Whenever I import the .mat file, I get a list of rules. What’s the best way to go about using these? Let’s say I wanted to plot some of the LabeledData, say “n2_den”. Would I do something like `ListLinePlot[data]/.n2_den`

? Or would I be better off just converting the list of rules to a list like one of the recommendations shows when I import?

Has someone an idea how to solve the 1. question for ANY number of mass points and a clue to the 2. question?

center of mass system, momentum

I want to Find **C1** and **C2** in terms of ** a** and

`60 + 31 a + 4 a^2 + 4 C1 C2 (4 + a) (873 + 444 a + 56 a^2) e + 128 C1^2 C2^2 (3 + a) (4 + a) (9 + 2 a) (33 + 8 a) e^2 - 3072 C1^3 C2^3 (4 + a)^2 (9 + 2 a)^3 e^3 == 0 60 + 31 a + 4 a^2 + C1 C2 (4 + a) (3267 + 8 a (207 + 26 a)) e + 16 C1^2 C2^2 (4 + a) (9 + 2 a) (837 + 468 a + 64 a^2) e^2 - 4 C1^3 C2^3 (4 + a) (9 + 2 a)^2 (18333 + 8472 a + 976 a^2) e^3 == 0 `

When I used “Solve”,

`Solve[{60 + 31 a + 4 a^2 + 4 C1 C2 (4 + a) (873 + 444 a + 56 a^2) e + 128 C1^2 C2^2 (3 + a) (4 + a) (9 + 2 a) (33 + 8 a) e^2 - 3072 C1^3 C2^3 (4 + a)^2 (9 + 2 a)^3 e^3 == 0, 60 + 31 a + 4 a^2 + C1 C2 (4 + a) (3267 + 8 a (207 + 26 a)) e + 16 C1^2 C2^2 (4 + a) (9 + 2 a) (837 + 468 a + 64 a^2) e^2 - 4 C1^3 C2^3 (4 + a) (9 + 2 a)^2 (18333 + 8472 a + 976 a^2) e^3 == 0}, {C1, C2}] `

I got: {}

Thanks for helping!!!

Given a list

`lst={0,0,0,0,0,"A1",0,0,0,"B2",0,0,"C3","D4","E5",0,0,0,"F6"} `

How to split it as

`{{0,0,0,0,0},{"A1",0,0,0},{"B2",0,0},{"C3"},{"D4"},{"E5",0,0,0},{"F6"}} `

I want to use `SequenceSplit`

but didn’t know how to set up the right `pattern`

.

`SequenceSplit[lst, {_String} -> {}] `

Thanks!

This question already has an answer here:

- Evaluation in lambda function 2 answers

I would like to define a function `f(n)`

which outputs another function as follows:

`f[n_] := PolynomialRemainder[#,ChebyshevT[n,x],x]& `

However, I would like the `ChebyshevT[n,x]`

*part* of the function to be *evaluated* when `f`

is called, so that for instance when `f(2)`

is evaluated I get `PolynomialRemainder[#,-1+2x^2,x]&`

instead of `PolynomialRemainder[#,ChebyshevT[2,x],x]&`

.

How do I do that? If I wrap the function body in an `Evaluate`

as follows:

`f[n_] := Evaluate[PolynomialRemainder[#,ChebyshevT[n,x],x]]& `

then the whole definition gets evaluated, and the input `#`

is assumed to be free of `x`

, resulting in `f[2] = #&`

.

Given a function of Cartesian coordinates $ (x, y)$ in $ g(x, y) = \frac{d}{dx}f(x, y)-y\frac{d}{dy}f(x, y)$ , I want to transform this expression to polar coordinates $ (r,\phi)$ . I saw a solution using built-in chain rule here: Change variables in differential expressions and a possible solution using replacement here: Transformation of Derivatives under change of coordinates. I also came across FransformedField , which seems very succinct but it would only tranform $ (x, y)$ in the expression but not the derivatives, i.e. it gives me the following:

`TransformedField["Cartesian" -> "Polar", D[f[x, y], x] - x*D[f[x, y], y], {x, y} -> {r, \[Phi]} ] `

output

$ $ f^{(1,0)}(r \cos (\phi ),r \sin (\phi ))-r \cos (\phi ) f^{(0,1)}(r \cos (\phi ),r \sin (\phi ))$ $ .

I wonder why this is the case? Or if there is any trick to make it work with `TransformedField`

?

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