Art Kalb

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16 years, 207 days

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These are questions asked by Art Kalb

I am trying to simplify the square of a parameterized polynomial mod 2. My parameters are intended to be either 0 or 1. How do I accomplish this?

For example:

 

alias(alpha = RootOf(x^4+x+1))

alpha

(1)

z := alpha^3*a[3]+alpha^2*a[2]+alpha*a[1]+a[0]``

a[3]*alpha^3+a[2]*alpha^2+a[1]*alpha+a[0]

(2)

z2 := collect(`mod`(Expand(z^2), 2), alpha)

a[3]^2*alpha^3+(a[1]^2+a[3]^2)*alpha^2+a[2]^2*alpha+a[0]^2+a[2]^2

(3)

``

``

 

Download Polynomial_Mod_2.mw

 

I would like to simplify the squared parameters modulo 2. a[3]^2=a[3], etc.

Any help would be appreciated. Elegant methods even more so!

Regards.

 

 

 

 

I am trying to get a solution to the heat equation with multiple boundary conditions.

Most of them work but I am having trouble with two things: a Robin boundary condition and initial conditions.

First, here are my equations that work:

returns a solution (actually two including u(x,y,z,t)=0).

 

However, when I try to add:

or

 

I no longer get a solution.

 

Any guidance would be appreciated.

 

Regards.

 

I have uploaded a worksheet with the equations...

Download heat_equation_pde.mw

I have defined my own function to implement inverse erf. I am trying to extend Maple so it recognizes basic identities. For example, I would like to Maple to simplify InverseErf(erf(x)) to x when x is real. I've used the following code in a module, but it doesn't seem to work (the evalf does work). Any suggestions?

ModuleLoad := proc()
global `evalf/InverseErf`;
global `erf/InverseErf`;
global `InverseErf/erf`;
`evalf/InverseErf` := proc(x)
local y,z;

Hi,

 

Is there a way to generate Java or C code to implement a general nth order linear ordinary differential equation?

I am looking to be able to send the coefficients and have it compute the time waveform given initial conditions.

 

Regards.

Hi,

I was wondering if anyone has suggestions how to get answer to this integral?

I know how to do a discrete approximation, but I am looking for the closed form.

 

c>0. n is an integer>0. If someone knows how to do specific values of n, that would be interesting too!

Also, replacing the Chebyshev function by a monomial in x (i.e. x^n) would be equivalent.

Thanks.

 

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