## 669 Reputation

19 years, 282 days

## solving quartic equation...

k^4-k^2*(4*u*m+2*q^2)+k*(8*m*E*q)+4*m^2*(D^2-e^2+(q^2/2*m-u)^2)=0;
solve(%,k);

The result is about 10,000 characters long, so probably not of much use to you...

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G A Edgar

## Let G(x) denote the no. of ways of repre...

Perhaps there is some connection between x and n ?

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G A Edgar

## really?...

Another remark: Do you really need the determinant?  Or would some other calculation suffice?

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G A Edgar

## Assignment in Maple is := Maybe you wan...

Assignment in Maple is :=

Maybe you want to do something like this...

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G A Edgar

## Probably you should also say what OS you...

Probably you should also say what OS you are going to use to run it.  On my Mac, Maple versions prior to 9 won't run in MacOS 10.8, for example.

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G A Edgar

## guess...

I'm guessing it is this...

Int(Int(u*v/sqrt(2*Pi)*(1/2+1/2*erf(1/2*sqrt(2)*u))*(1/2-1/2*erf(1/2*sqrt(2)*v))*exp(-(u^2+v^2)/2),u=-infinity..v),v=-infinity..infinity);

General advice: for evaluation of multiple integral, try Student[MultivariateCalculus][MultiInt]

I get  (1/24)*2^(1/2)*(-3+2*3^(1/2))/Pi^(1/2)  for this ...

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G A Edgar

## possibility...

A possibility.

Sum of the geometric series sum(x^b,b=0..a-1) comes out as (x^a-1)/(x-1) according to Maple .  Which is almost right: it is right except when x=1 .  Now your sum

sum(cos((2*Pi*b*12)/(a)),b=0..a-1)

is real part of geometric series

sum(exp((I*2*Pi*b*x)/(a)),b=0..a-1)

so Maple computes it as zero.  That is correct unless exp(2*Pi*x/a) is 1.  So assigning 0 for this symbolic sum is the best Maple knows how to do.

With "add" we tell Maple not to try a symbolic sum, just add the items (but to do that we cannot have symbolic upper limit a-1 unevaluated).

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G A Edgar

## round-off...

shouldn't evalf(a) and evalf(b) give exact same result?

Yes, they are the same (up to round-off error).  Try Digits:=50 first, then do these evalf's, and see what you get.

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G A Edgar

## 1D...

Here it is in 1D Maple input format:

```u:=int(-4*(16*c+3)*exp(-1/(2)*sqrt(-16*c-3*Zeta))
/(64*exp(-sqrt(-16*c-3*Zeta))+256*c*exp(-sqrt(-16*c-3*Zeta))
+8*exp(-1/(2)*sqrt(-16*c-3*Zeta)) +1),
Zeta);```
`But "don't use 2D input" is not a very good reply to the OP... Someone`
`who uses 2D input should help him out (I don't).`
` `

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G A Edgar

## special case...

First do the simplest special case, c=1, n=1 ...

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G A Edgar

## common sense...

Yes,  the line through the two points  A(1, 1) and B(1, -2*m + 2) is a vertical line, so it does not have an equation of the form y=k*x+q ... What do you want in that case?

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G A Edgar

## according to maple...

according to Maple...

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G A Edgar

## Use `...` or "..." for strings inside th...

Use `...` or "..." for strings inside the cat.  Also, you may need to substitute k into lf[k] before you make it into a string ?

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G A Edgar

## You can also use "surd" for real-valued ...

You can also use "surd" for real-valued odd roots.  See ?surd

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G A Edgar

## Is there some relation between f and F ?...

Is there some relation between f and F ?  In F"(n)(s) is that the second derivative with respect to s ?

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G A Edgar

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