---
title: "FromCoefficientRules"
language: "en"
type: "Symbol"
summary: "FromCoefficientRules[list, {x1, x2, ...}] constructs a polynomial from a list of rules for exponent vectors and coefficients."
keywords: 
- polynomial coefficients
- from coefficient rules
- polynomial from rules
- polynomial from coefficients
canonical_url: "https://reference.wolfram.com/language/ref/FromCoefficientRules.html"
source: "Wolfram Language Documentation"
related_functions: 
  - 
    title: "CoefficientRules"
    link: "https://reference.wolfram.com/language/ref/CoefficientRules.en.md"
  - 
    title: "FromDigits"
    link: "https://reference.wolfram.com/language/ref/FromDigits.en.md"
related_tutorials: 
  - 
    title: "Polynomial Orderings"
    link: "https://reference.wolfram.com/language/tutorial/AlgebraicManipulation.en.md#450638201"
---
# FromCoefficientRules

FromCoefficientRules[list, {x1, x2, …}] constructs a polynomial from a list of rules for exponent vectors and coefficients.

## Details

* ``FromCoefficientRules`` acts as the inverse of ``CoefficientRules``.

* ``FromCoefficientRules`` takes a list in the form ``{{e11, e12, …} -> c1, {e21, …} -> c2, …}`` returned by ``CoefficientRules``.

## Examples (1)

### Basic Examples (1)

```wl
In[1]:= CoefficientRules[(x + y) ^ 3, {x, y}]

Out[1]= {{3, 0} -> 1, {2, 1} -> 3, {1, 2} -> 3, {0, 3} -> 1}

In[2]:= FromCoefficientRules[%, {x, y}]

Out[2]= x^3 + 3 x^2 y + 3 x y^2 + y^3

In[3]:= % == (x + y) ^ 3//Simplify

Out[3]= True
```

## See Also

* [`CoefficientRules`](https://reference.wolfram.com/language/ref/CoefficientRules.en.md)
* [`FromDigits`](https://reference.wolfram.com/language/ref/FromDigits.en.md)

## Tech Notes

* [Polynomial Orderings](https://reference.wolfram.com/language/tutorial/AlgebraicManipulation.en.md#450638201)

## History

* [Introduced in 2008 (7.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn70.en.md)