# RIACA Technical Report No. 2

## An algorithmic approach to conservation laws using
the 3-dimensional Heisenberg algebra

**Jan Sanders** (jansa@can.nl)
and

**Marcel Roelofs** (roelofs@can.nl)

**November 1994**

### Abstract

We describe an algorithmic approach to computing polynomial conservation
laws of systems of polynomial evolution equations in 1 + 1 variables with
time and space dependent coefficients. The approach is based on the extension
of the total derivative operator to an Heisenberg algebra. This allows us
to invert the total derivative on its image. It is shown that the
differential functions in the direct summand of the image of the total
derivative can be identified with the classical covariants of
.
We conclude with various generalizations to systems with more independant
variables and to differential forms

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Last Update: June 24, 1997