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NoetherianOperators :: diffOp(HashTable)

diffOp(HashTable) -- create a differential operator

Synopsis

Description

The HashTable H should contain monomials as keys and polynomials as values, all of which should lie in the same ring. The keys represent monomials of each term (in $dx$ variables), and the value represent the coefficient.

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing
i2 : H = new HashTable from {x^2 => x+y+3, y^2*x^5 => 2*x}

                2
o2 = HashTable{x  => x + y + 3}
                5 2
               x y  => 2x

o2 : HashTable
i3 : D1 = diffOp H

          5  2                2
o3 = 2x*dx dy  + (x + y + 3)dx

o3 : DiffOp

Alternatively, diffOp can also create differential operators from lists of key => value pairs

i4 : D2 = diffOp {x^2 => x+y+3, y^2*x^5 => 2*x}

          5  2                2
o4 = 2x*dx dy  + (x + y + 3)dx

o4 : DiffOp
i5 : D1 == D2

o5 = true

For a simpler way of creating differential operators, see diffOp(RingElement).

Caveat

The constructors new DiffOp from HashTable and new DiffOp from List are for internal use only. Use diffOp(HashTable) and diffOp(List) instead.

See also