sum
Evaluates a finite symbolic sum over an integer index.
With concrete integer bounds, Nerdamer substitutes the index through the inclusive range and adds the resulting symbolic terms. If a bound is still symbolic, the sum remains unevaluated.
Examples
These examples use Nerdamer Notation.
Sum a simple finite integer range.
sum(k,k,1,5)
// → 15Combine symbolic indexing, a Vector, size(...), and a finite sum.
V:[x,x^2-1,2]; sum(3*V[k],k,0,size(V)[0]-1)
// → 3+3*x+3*x^2Substitute a finite integer range through an expression with symbolic parameters.
sum((a*k+b)^2,k,1,5)
// → (b+a)^2+(b+2*a)^2+(b+3*a)^2+(b+4*a)^2+(b+5*a)^2Interfaces
The same operation is available through the interfaces below.
Nerdamer Notation
Use this form inside input passed to nerdamer(...).
sum(arg1, arg2, arg3, arg4)nerdamer.sum
Call the operation through the default nerdamer import.
nerdamer.sum(expr: Expression, index: Expression, lower: Expression, upper: Expression): ExpressionParameters
| Name | Type | Description |
|---|---|---|
expr | Expression | The expression to be summed. |
index | Expression | The index variable (must be a plain symbol). |
lower | Expression | The lower bound (integer required for evaluation). |
upper | Expression | The upper bound (integer required for evaluation). |
Returns
Expression — The summation result or a symbolic sum node.
Direct JavaScript / TypeScript API
Import the operation directly from its package entry point.
import { sum } from 'nerdamer/calculus';sum(expr: Expression, index: Expression, lower: Expression, upper: Expression): ExpressionParameters
| Name | Type | Description |
|---|---|---|
expr | Expression | The expression to be summed. |
index | Expression | The index variable (must be a plain symbol). |
lower | Expression | The lower bound (integer required for evaluation). |
upper | Expression | The upper bound (integer required for evaluation). |
Returns
Expression — The summation result or a symbolic sum node.