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