Random Primitive

[Jan Medina]

Hi everybody.

There is a procedure or library in SAGE that allows finding a random primitive element on a finite field?

[leif]

http://sagemath.org/doc/reference/finite_rings/sage/rings/finite_rings/finite_field_base.html?highlight=primitive_element#sage.rings.finite_rings.finite_field_base.FiniteField.multiplicative_generator


-leif

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[Jan Medina]

i know that but this function only give you one generator, always the same but i want a random generator of a multiplicate group of a finite field.

[Jan Medina]

I did this algorithm to find a primitive element of a multiplicative group on a finite field. This is a basic algorithm
def random_primitive(p,h):
    F.<x>=GF(p^h)
    s=p^h-1
    r=F.random_element()
    j=0
    if r!=0:
        for t in prime_factors(s):
            if r^(s/t)==1:
                j=j+1
        if j==0:
            return r           
        else:
            return random_primitive(p,h)
    else:
        return random_primitive(p,h)

[John Cremona]

Any reason not to just test r.multiplicative_order() ?

John Cremona

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[Jan Medina]

I think this is a fast algorithm. Im not sure what fast can be just testing the multiplicative order