Art Kalb

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13 years, 318 days

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These are questions asked by Art Kalb

Hi,

I was wondering if anyone has a clever way to code the Cayley Omega process?
For those who are wondering, the Omega process is a differential operator. Given an n-dimensional space (x[1],x[2],x[3],...,x[n]), and n forms Q[1](x[1][1],x[1][2],x[1][3],etc) Q[2](x[2][1],x[2][2],x[2][3],etc) ... Q[n](x[n][1],x[n][1],x[n][1],etc), the operator is the determinant of the matrix who entries are the partial differential operators del/delx[i][j].

Thoughts? Suggestions?

 

Thanks.

I am trying to figure out how to simplify expressions like:

2^(6p+q) mod 3 (where p,q are variables representing integers)

Anybody know how to do this?

Even better would be something that solves 2^n=2 (mod 3) -> n=1 (mod 6)

 

Suggestions?

 

 

 

Hi,

 

I am having trouble getting a pattern match to the Heaviside function.

patmatch(Heaviside(x), Heaviside(a::algebraic))

returns "false" whereas I would expect it to return true.

On the other hand:

patmatch(Heaviside(x), Heaviside(x::algebraic))

returns true.

 

What am I missing?

 

Regards.

 

Is there a way to force the branch choice with the LambertW?

If I turn on all _EnvAllSolutions:=true:

I get a placeholder for the branch. Unfortunately the name of this placeholder changes every time I re-evaluate.

Is there a way to force this to take a certain value?

 

Regards.

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.

 

 

 

 

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