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factorWeylAlgebra -- factor a Weyl algebra element

Description

Produces all the factorisations of the element r of a Weyl algebra (unless StopAfter is set to a finite value, in which case the algorithm stops after that many factorisations).

i1 : R = makeWA(QQ[x])

o1 = R

o1 : PolynomialRing, 1 differential variable(s)
i2 : factorWA(x^5*dx^2+7*x^4*dx+8*x^3-x*dx^2+dx)

        3       2                  2             3                2      
o2 = {(x dx + 3x  - x*dx + 1)(dx)(x  + 1), (dx)(x dx - x*dx + 2)(x  + 1),
     ------------------------------------------------------------------------
                                   2         3       2                    
     (x*dx - 1)(dx)(x - 1)(x + 1)(x  + 1), (x dx + 3x  + x*dx - 1)(dx)(x -
     ------------------------------------------------------------------------
                      3
     1)(x + 1), (dx)(x dx + x*dx - 2)(x - 1)(x + 1)}

o2 : List

To reduce their number, two factorisations are considered equivalent if they can be related by (1) switching commuting irreducible factors or (2) switching monomials and degree 0 factors; a normal order is chosen where commuting factors are sorted, and monomials are pushed to the right/left if they're differential/not.

factorWeylAlgebra uses a variety of factorisation strategies, including the one in ``Factoring linear partial differential operators in n variables'', Mark Giesbrecht, Albert Heinle and Viktor Levandovskyy, Journal of Symbolic Computation Volume 75, July–August 2016, Pages 127-148.

Caveat

The ring of r must have variables in the same order as those created by makeWeylAlgebra.

See also

Ways to use factorWeylAlgebra:

  • factorWeylAlgebra(RingElement)

For the programmer

The object factorWeylAlgebra is a method function with options.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/WeylAlgebras/factorWA.m2:499:0.