# diffOp(HashTable) -- create a differential operator

## Synopsis

• Function: diffOp
• Usage:
diffOp H
• Inputs:
• H, , or a list of pairs mon => coef
• Outputs:

## 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.