# poly2sym

Create symbolic polynomial from vector of coefficients

## Syntax

``p = poly2sym(c)``
``p = poly2sym(c,var)``

## Description

example

````p = poly2sym(c)` creates the symbolic polynomial expression `p` from the vector of coefficients `c`. The polynomial variable is `x`. If `c = [c1,c2,...,cn]`, then ```p = poly2sym(c)``` returns ${c}_{1}{x}^{n-1}+{c}_{2}{x}^{n-2}+...+{c}_{n}$.This syntax does not create the symbolic variable `x` in the MATLAB® Workspace.```

example

````p = poly2sym(c,var)` uses `var` as a polynomial variable when creating the symbolic polynomial expression `p` from the vector of coefficients `c`.```

## Examples

### Create Polynomial Expression

Create a polynomial expression from a symbolic vector of coefficients. If you do not specify a polynomial variable, `poly2sym` uses `x`.

```syms a b c d p = poly2sym([a, b, c, d])```
```p = a*x^3 + b*x^2 + c*x + d```

Create a polynomial expression from a symbolic vector of rational coefficients.

`p = poly2sym(sym([1/2, -1/3, 1/4]))`
```p = x^2/2 - x/3 + 1/4```

Create a polynomial expression from a numeric vector of floating-point coefficients. The toolbox converts floating-point coefficients to rational numbers before creating a polynomial expression.

`p = poly2sym([0.75, -0.5, 0.25])`
```p = (3*x^2)/4 - x/2 + 1/4```

### Specify Polynomial Variable

Create a polynomial expression from a symbolic vector of coefficients. Use `t` as a polynomial variable.

```syms a b c d t p = poly2sym([a, b, c, d], t)```
```p = a*t^3 + b*t^2 + c*t + d```

To use a symbolic expression, such as `t^2 + 1` or `exp(t)`, instead of a polynomial variable, substitute the variable using `subs`.

```p1 = subs(p, t, t^2 + 1) p2 = subs(p, t, exp(t))```
```p1 = d + a*(t^2 + 1)^3 + b*(t^2 + 1)^2 + c*(t^2 + 1) p2 = d + c*exp(t) + a*exp(3*t) + b*exp(2*t)```

## Input Arguments

collapse all

Polynomial coefficients, specified as a numeric or symbolic vector. Argument `c` can be a column or row vector.

Polynomial variable, specified as a symbolic variable.

## Output Arguments

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Polynomial, returned as a symbolic expression.

## Tips

• When you call `poly2sym` for a numeric vector `c`, the toolbox converts the numeric vector to a vector of symbolic numbers using the default (rational) conversion mode of `sym`.

## Version History

Introduced before R2006a