1 | \begin{lisp:documentation}{scalar$-$times$-$poly}{FUNCTION}{c p {\sf \&optional} (ring *coefficient$-$ring*) }
|
---|
2 | Return product of a scalar C by a polynomial P with coefficient ring
|
---|
3 | RING.
|
---|
4 | \end{lisp:documentation}
|
---|
5 |
|
---|
6 | \begin{lisp:documentation}{term$-$times$-$poly}{FUNCTION}{term f {\sf \&optional} (ring *coefficient$-$ring*) }
|
---|
7 | Return product of a term TERM by a polynomial F with coefficient ring
|
---|
8 | RING.
|
---|
9 | \end{lisp:documentation}
|
---|
10 |
|
---|
11 | \begin{lisp:documentation}{monom$-$times$-$poly}{FUNCTION}{m f }
|
---|
12 | Return product of a monomial M by a polynomial F with coefficient
|
---|
13 | ring RING.
|
---|
14 | \end{lisp:documentation}
|
---|
15 |
|
---|
16 | \begin{lisp:documentation}{minus$-$poly}{FUNCTION}{f {\sf \&optional} (ring *coefficient$-$ring*) }
|
---|
17 | Changes the sign of a polynomial F with coefficients in coefficient
|
---|
18 | ring RING, and returns the result.
|
---|
19 | \end{lisp:documentation}
|
---|
20 |
|
---|
21 | \begin{lisp:documentation}{sort$-$poly}{FUNCTION}{poly {\sf \&optional} (pred \#'lex$>$) (start 0) (end (unless (null poly) (length (caar poly)))) }
|
---|
22 | Destructively Sorts a polynomial POLY by predicate PRED; the
|
---|
23 | predicate is assumed to take arguments START and END in addition to
|
---|
24 | the pair of monomials, as the functions in the ORDER package do.
|
---|
25 | \end{lisp:documentation}
|
---|
26 |
|
---|
27 | \begin{lisp:documentation}{poly+}{FUNCTION}{p q {\sf \&optional} (pred \#'lex$>$) (ring *coefficient$-$ring*) }
|
---|
28 | Returns the sum of two polynomials P and Q with coefficients in
|
---|
29 | ring RING, with terms ordered according to monomial order PRED.
|
---|
30 | \end{lisp:documentation}
|
---|
31 |
|
---|
32 | \begin{lisp:documentation}{poly$-$}{FUNCTION}{p q {\sf \&optional} (pred \#'lex$>$) (ring *coefficient$-$ring*) }
|
---|
33 | Returns the difference of two polynomials P and Q with coefficients
|
---|
34 | in ring RING, with terms ordered according to monomial order PRED.
|
---|
35 | \end{lisp:documentation}
|
---|
36 |
|
---|
37 | \begin{lisp:documentation}{poly*}{FUNCTION}{p q {\sf \&optional} (pred \#'lex$>$) (ring *coefficient$-$ring*) }
|
---|
38 | Returns the product of two polynomials P and Q with coefficients in
|
---|
39 | ring RING, with terms ordered according to monomial order PRED.
|
---|
40 | \end{lisp:documentation}
|
---|
41 |
|
---|
42 | \begin{lisp:documentation}{poly$-$op}{FUNCTION}{f m g pred ring }
|
---|
43 | Returns F$-$M*G, where F and G are polynomials with coefficients in
|
---|
44 | ring RING, ordered according to monomial order PRED and M is a
|
---|
45 | monomial.
|
---|
46 | \end{lisp:documentation}
|
---|
47 |
|
---|
48 | \begin{lisp:documentation}{poly$-$expt}{FUNCTION}{poly n {\sf \&optional} (pred \#'lex$>$) (ring *coefficient$-$ring*) }
|
---|
49 | Exponentiate a polynomial POLY to power N. The terms of the
|
---|
50 | polynomial are assumed to be ordered by monomial order PRED and with
|
---|
51 | coefficients in ring RING. Use the Chinese algorithm; assume N$>$=0
|
---|
52 | and POLY is non$-$zero (not NIL).
|
---|
53 | \end{lisp:documentation}
|
---|
54 |
|
---|
55 | \begin{lisp:documentation}{poly$-$mexpt}{FUNCTION}{plist monom {\sf \&optional} (pred \#'lex$>$) (ring *coefficient$-$ring*) }
|
---|
56 | Raise a polynomial vector represented ad a list of polynomials
|
---|
57 | PLIST to power MULTIINDEX. Every polynomial has its terms ordered by
|
---|
58 | predicate PRED and coefficients in the ring RING.
|
---|
59 | \end{lisp:documentation}
|
---|
60 |
|
---|
61 | \begin{lisp:documentation}{poly$-$constant$-$p}{FUNCTION}{p }
|
---|
62 | Returns T if P is a constant polynomial.
|
---|
63 | \end{lisp:documentation}
|
---|
64 |
|
---|
65 | \begin{lisp:documentation}{poly$-$extend}{FUNCTION}{p {\sf \&optional} (m (list 0)) }
|
---|
66 | Given a polynomial P in k[x[r+1],...,xn], it returns the same
|
---|
67 | polynomial as an element of k[x1,...,xn], optionally multiplying it
|
---|
68 | by a monomial x1\symbol{94}m1*x2\symbol{94}m2*...*xr\symbol{94}mr,
|
---|
69 | where m=(m1,m2,...,mr) is a multiindex.
|
---|
70 | \end{lisp:documentation}
|
---|
71 |
|
---|
72 | \begin{lisp:documentation}{poly$-$extend$-$end}{FUNCTION}{p {\sf \&optional} (m (list 0)) }
|
---|
73 | Similar to POLY$-$EXTEND, but it adds new variables at the end.
|
---|
74 | \end{lisp:documentation}
|
---|
75 |
|
---|
76 | \begin{lisp:documentation}{poly$-$zerop}{FUNCTION}{p }
|
---|
77 | Returns T if P is a zero polynomial.
|
---|
78 | \end{lisp:documentation}
|
---|
79 |
|
---|
80 | \begin{lisp:documentation}{lt}{FUNCTION}{p }
|
---|
81 | Returns the leading term of a polynomial P.
|
---|
82 | \end{lisp:documentation}
|
---|
83 |
|
---|
84 | \begin{lisp:documentation}{lm}{FUNCTION}{p }
|
---|
85 | Returns the leading monomial of a polynomial P.
|
---|
86 | \end{lisp:documentation}
|
---|
87 |
|
---|
88 | \begin{lisp:documentation}{lc}{FUNCTION}{p }
|
---|
89 | Returns the leading coefficient of a polynomial P.
|
---|
90 | \end{lisp:documentation}
|
---|
91 |
|
---|