\begin{lisp:documentation}{scalar$-$times$-$poly}{FUNCTION}{c p {\sf \&optional} (ring *coefficient$-$ring*) }
Return product of a scalar C by a polynomial P with coefficient ring
RING. 
\end{lisp:documentation}

\begin{lisp:documentation}{term$-$times$-$poly}{FUNCTION}{term f {\sf \&optional} (ring *coefficient$-$ring*) }
Return product of a term TERM by a polynomial F with coefficient ring
RING. 
\end{lisp:documentation}

\begin{lisp:documentation}{monom$-$times$-$poly}{FUNCTION}{m f }
Return product of a monomial M by a polynomial F with coefficient
ring RING. 
\end{lisp:documentation}

\begin{lisp:documentation}{minus$-$poly}{FUNCTION}{f {\sf \&optional} (ring *coefficient$-$ring*) }
Changes the sign of a polynomial F with coefficients in coefficient
ring RING, and returns the result.
\end{lisp:documentation}

\begin{lisp:documentation}{sort$-$poly}{FUNCTION}{poly {\sf \&optional} (pred \#'lex$>$) (start 0) (end (unless (null poly) (length (caar poly)))) }
Destructively Sorts a polynomial POLY by predicate PRED; the
predicate is assumed to take arguments START and END in addition to
the pair of monomials, as the functions in the ORDER package do.
\end{lisp:documentation}

\begin{lisp:documentation}{poly+}{FUNCTION}{p q {\sf \&optional} (pred \#'lex$>$) (ring *coefficient$-$ring*) }
Returns the sum of two polynomials P and Q with coefficients in
ring RING, with terms ordered according to monomial order PRED.
\end{lisp:documentation}

\begin{lisp:documentation}{poly$-$}{FUNCTION}{p q {\sf \&optional} (pred \#'lex$>$) (ring *coefficient$-$ring*) }
Returns the difference of two polynomials P and Q with coefficients
in ring RING, with terms ordered according to monomial order PRED.
\end{lisp:documentation}

\begin{lisp:documentation}{poly*}{FUNCTION}{p q {\sf \&optional} (pred \#'lex$>$) (ring *coefficient$-$ring*) }
Returns the product of two polynomials P and Q with coefficients in
ring RING, with terms ordered according to monomial order PRED.
\end{lisp:documentation}

\begin{lisp:documentation}{poly$-$op}{FUNCTION}{f m g pred ring }
Returns F$-$M*G, where F and G are polynomials with coefficients in
ring RING, ordered according to monomial order PRED and M is a
monomial.
\end{lisp:documentation}

\begin{lisp:documentation}{poly$-$expt}{FUNCTION}{poly n {\sf \&optional} (pred \#'lex$>$) (ring *coefficient$-$ring*) }
Exponentiate a polynomial POLY to power N. The terms of the
polynomial are assumed to be ordered by monomial order PRED and with
coefficients in ring RING.  Use the Chinese algorithm; assume N$>$=0
and POLY is non$-$zero (not NIL).
\end{lisp:documentation}

\begin{lisp:documentation}{poly$-$mexpt}{FUNCTION}{plist monom {\sf \&optional} (pred \#'lex$>$) (ring *coefficient$-$ring*) }
Raise a polynomial vector represented ad a list of polynomials
PLIST to power MULTIINDEX.  Every polynomial has its terms ordered by
predicate PRED and coefficients in the ring RING.
\end{lisp:documentation}

\begin{lisp:documentation}{poly$-$constant$-$p}{FUNCTION}{p }
Returns T if P is a constant polynomial.
\end{lisp:documentation}

\begin{lisp:documentation}{poly$-$extend}{FUNCTION}{p {\sf \&optional} (m (list 0)) }
Given a polynomial P in k[x[r+1],...,xn], it returns the same
polynomial as an element of k[x1,...,xn], optionally multiplying it
by a monomial x1\symbol{94}m1*x2\symbol{94}m2*...*xr\symbol{94}mr,
where m=(m1,m2,...,mr) is a multiindex.
\end{lisp:documentation}

\begin{lisp:documentation}{poly$-$extend$-$end}{FUNCTION}{p {\sf \&optional} (m (list 0)) }
Similar to POLY$-$EXTEND, but it adds new variables at the end.
\end{lisp:documentation}

\begin{lisp:documentation}{poly$-$zerop}{FUNCTION}{p }
Returns T if P is a zero polynomial.
\end{lisp:documentation}

\begin{lisp:documentation}{lt}{FUNCTION}{p }
Returns the leading term of a polynomial P.
\end{lisp:documentation}

\begin{lisp:documentation}{lm}{FUNCTION}{p }
Returns the leading monomial of a polynomial P.
\end{lisp:documentation}

\begin{lisp:documentation}{lc}{FUNCTION}{p }
Returns the leading coefficient of a polynomial P.
\end{lisp:documentation}

