partfrac
Decomposes a rational expression into partial fractions with respect to a variable.
Nerdamer handles rational expressions with distinct or repeated linear factors, supported irreducible quadratic factors, and improper fractions that first require polynomial division.
When no useful decomposition is available, the original expression is returned unchanged.
Examples
These examples use Nerdamer Notation.
Decompose a rational function with two distinct linear factors.
partfrac((4*k-1)/(k*(k+2)),k) // → (-1/2)*k^-1+(9/2)*(2+k)^-1
Reduce an improper rational expression when the remainder is zero.
partfrac((x^2-1)/(x-1),x) // → 1+x
Decompose a denominator containing a repeated linear factor.
partfrac(1/(x^2*(x-1)),x)Interfaces
The same operation is available through the interfaces below.
Nerdamer Notation
Use this form inside input passed to nerdamer(...).
partfrac(arg1, [arg2])nerdamer.partfrac
Call the operation through the default nerdamer import.
nerdamer.partfrac(x: ExpressionInput, variable?: ExpressionInput): ExpressionParameters
| Name | Type | Description |
|---|---|---|
x | ExpressionInput | Rational expression to decompose. |
variable | ExpressionInput | Main variable; defaults to the first variable reported by the expression. |
Returns
Expression — A new decomposition when one is found, otherwise the original parsed expression.
Direct JavaScript / TypeScript API
Import the operation directly from its package entry point.
import { partfrac } from 'nerdamer/algebra';partfrac(x: ExpressionInput, variable?: ExpressionInput): ExpressionParameters
| Name | Type | Description |
|---|---|---|
x | ExpressionInput | Rational expression to decompose. |
variable | ExpressionInput | Main variable; defaults to the first variable reported by the expression. |
Returns
Expression — A new decomposition when one is found, otherwise the original parsed expression.