[1] | 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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