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