What is SHASTA?

Mount Shasta is a 4317-meter somewhat active volcano in Northern California. Its snow-capped multiple-crater summit, which appears on the cover of this guide¹is a well-known california landmark as well as a ski resort. This guide describes however SHASTA, an interactive interface to the $\Sigma{}^{{\rm it}}$ library that provides some efficient computations revolving around difference operators and systems in ${\mathbb{Q}}[n,E]$ or ${\mathbb{Q}}(n)[E]$. In fact, the main goal of SHASTA is to provide access to selected functionalities of the $\Sigma{}^{{\rm it}}$ library to other computer algebra systems, or to users who do not own an Aldor compiler, or who feel more confortable with interactive access to a library. The functionalities currently provided by SHASTA are the ones that tend to be missing from several commercial computer algebra systems, namely:

• Basic arithmetic in ${\mathbb{Q}}[n,E]$, including adjoints and left and right gcd's and lcm's.
• Exterior powers.
• Rational kernels, i.e.  $\mbox{Ker}(L) \cap {\mathbb{Q}}(n)$ for $L \in {\mathbb{Q}}[n,E]$, and rational solutions of inhomogeneous equations of the form $L y = g$.
• Rational kernels of systems of the form $Y(x+1) = A(x) Y(x)$.
• Hypergeometric solutions, i.e. the solutions $y$ of $L y = 0$ such that $y(n+1)/y(n) \in {\mathbb{Q}}(n)$.
• Factorisation and decomposition of second and third-order operators.

If you do not need any of the above computations, then you probably will not have much use for SHASTA. Otherwise, since SHASTA provides implementations of several recent algorithms for those computations, it is worth trying it and reading further.