# Formal Manipulation of Polynomials

### Christoph Karl Walter Grein

####
Original Version 8 July 2004

Last update 1 September 2004

This package allows formal manipulation of polynomials of several variables.
Polynomials can be added, multiplied, integrated and differentiated.
Variables may be substituted by other polynomials.
A polynomial may be evaluated by replacing (some of) the variables with
values.

`P (x, y, z) := xy + 4z`^{3} + x

P_{x}(x, y, z) = y + 1

P_{z}(x, y, z) = 12z^{2}

`P (x, 1, z) = 2x + 4z`^{3}

P (1, 2, 3) = 111

`Q (x, y) := x + 4y`^{4} + 1

`P (Q (x, w), x, z) = (x + 4w`^{4} + 1) x + 4z^{3} + (x + 4w^{4} + 1) =

1 + 2x + x^{2} + 4z^{3} + 4w^{4} + 4xw^{4}
View here the Ada specification.

The package is released under the GMGPL.
Download from here.

**Updates** |
**Reason** |

**1 Sep 2004** |
Renamed to Polynomials (used the silly name Multinomials before, don't know why). |

**23 July 2004** |
A distorting misprint in Test_Value corrected. |

**21 July 2004** |
Multiple differentiation and integration. |

**15 July 2004** |
Function Value (the inverse of Image) added. |

**8 July 2004** |
First release. |