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## Multiplication of two polynomials

The following procedures returns the degree of the product of two polynomial either with real or integer coefficients:

```
int Degree_Product_Polynomial_Interval(int n1,VECTOR &Coeff1,int n2,VECTOR &Coeff2);
int Degree_Product_Polynomial_Interval(int n1,INTEGER_VECTOR &Coeff1,int n2,
INTEGER_VECTOR &Coeff2);
```
Then you may use the following procedure to compute the product of polynomial either with real,integer or interval coefficients:
```
VECTOR Multiply_Polynomial_Interval(int n1,VECTOR &Coeff1,int n2,VECTOR &Coeff2);
INTEGER_VECTOR Multiply_Polynomial_Interval(int n1,INTEGER_VECTOR &Coeff1,
int n2,INTEGER_VECTOR &Coeff2);
INTERVAL_VECTOR Multiply_Polynomial_Interval(int n1,INTERVAL_VECTOR &Coeff1,
int n2,INTERVAL_VECTOR &Coeff2);
```
All these procedures return the coefficients of the product, the leading term being 0 only if one polynomial is equal to 0.

To take into account the rounding errors you may use:

```
INTERVAL_VECTOR Multiply_Polynomial_Safe_Interval(int n1,VECTOR &Coeff1,int n2,VECTOR &Coeff2);
```

Jean-Pierre Merlet 2012-12-20