randomLinearMF -- Generates a linear d-fold factorization of a random degree d polynomial

Usage:

randomLinearMF(ZZ, Ring)
Inputs:
- ZZ, an integer, An integer representing the degree
- Ring, a ring, The ring object
- RingElement, a ring element, An element in the ring
- Symbol, a symbol, A symbol representing the indeterminate
Outputs:
- a ZZ/d graded factorization,

Description

Generates a linear d-fold factorization of a random degree $d$ polynomial using the linearMF command. If the ring has too many variables the output may be a factorization that is too large to be useful.

i1 : Q = QQ[x,y,z];

i2 : d = 3;

i3 : K = randomLinearMF(d, Q, t) --way too many terms!

     /   Q[t]   \19683     /   Q[t]   \19683     /   Q[t]   \19683     /   Q[t]   \19683
o3 = |----------|      <-- |----------|      <-- |----------|      <-- |----------|
     | 2        |          | 2        |          | 2        |          | 2        |
     \t  + t + 1/          \t  + t + 1/          \t  + t + 1/          \t  + t + 1/
                                                                        
     0                     1                     2                     0

o3 : ZZdFactorization

i4 : S = QQ[x,y]

o4 = S

o4 : PolynomialRing

i5 : K' = randomLinearMF(d, S, t)

     /   S[t]   \27     /   S[t]   \27     /   S[t]   \27     /   S[t]   \27
o5 = |----------|   <-- |----------|   <-- |----------|   <-- |----------|
     | 2        |       | 2        |       | 2        |       | 2        |
     \t  + t + 1/       \t  + t + 1/       \t  + t + 1/       \t  + t + 1/
                                                               
     0                  1                  2                  0

o5 : ZZdFactorization

i6 : isdFactorization K'

            6 3     2    5   2   2 3
o6 = (true, -x  + 6x y + -x*y  + -y )
            7            4       9

o6 : Sequence

Ways to use randomLinearMF:

randomLinearMF(ZZ,Ring)
randomLinearMF(ZZ,Ring,RingElement)
randomLinearMF(ZZ,Ring,Symbol)

For the programmer

The object randomLinearMF is a method function.

The source of this document is in MatrixFactorizations/MatrixFactorizationsDOC.m2:5529:0.