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Subsections

The Polynomial Package

scalar $-$ times $-$ poly

$\textstyle\parbox{\pboxargslen}{\em c p {\sf \&optional} (ring *coefficient$-$ring*) \/}$ [FUNCTION]

Return product of a scalar C by a polynomial P with coefficient ring RING.

term $-$ times $-$ poly

$\textstyle\parbox{\pboxargslen}{\em term f {\sf \&optional} (ring *coefficient$-$ring*) \/}$ [FUNCTION]

Return product of a term TERM by a polynomial F with coefficient ring RING.

monom $-$ times $-$ poly

$\textstyle\parbox{\pboxargslen}{\em m f \/}$ [FUNCTION]

Return product of a monomial M by a polynomial F with coefficient ring RING.

minus $-$ poly

$\textstyle\parbox{\pboxargslen}{\em f {\sf \&optional} (ring *coefficient$-$ring*) \/}$ [FUNCTION]

Changes the sign of a polynomial F with coefficients in coefficient ring RING, and returns the result.

sort $-$ poly

$\textstyle\parbox{\pboxargslen}{\em poly {\sf \&optional} (pred \char93 'lex$\gt$) (start 0) (end (unless (null poly) (length (caar poly)))) \/}$ [FUNCTION]

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.

poly+

$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (pred \char93 'lex$\gt$) (ring *coefficient$-$ring*) \/}$ [FUNCTION]

Returns the sum of two polynomials P and Q with coefficients in ring RING, with terms ordered according to monomial order PRED.

poly $-$

$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (pred \char93 'lex$\gt$) (ring *coefficient$-$ring*) \/}$ [FUNCTION]

Returns the difference of two polynomials P and Q with coefficients in ring RING, with terms ordered according to monomial order PRED.

poly*

$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (pred \char93 'lex$\gt$) (ring *coefficient$-$ring*) \/}$ [FUNCTION]

Returns the product of two polynomials P and Q with coefficients in ring RING, with terms ordered according to monomial order PRED.

poly $-$ op

$\textstyle\parbox{\pboxargslen}{\em f m g pred ring \/}$ [FUNCTION]

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.

poly $-$ expt

$\textstyle\parbox{\pboxargslen}{\em poly n {\sf \&optional} (pred \char93 'lex$\gt$) (ring *coefficient$-$ring*) \/}$ [FUNCTION]

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).

poly $-$ mexpt

$\textstyle\parbox{\pboxargslen}{\em plist monom {\sf \&optional} (pred \char93 'lex$\gt$) (ring *coefficient$-$ring*) \/}$ [FUNCTION]

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.

poly $-$ constant $-$ p

$\textstyle\parbox{\pboxargslen}{\em p \/}$ [FUNCTION]

Returns T if P is a constant polynomial.

poly $-$ extend

$\textstyle\parbox{\pboxargslen}{\em p {\sf \&optional} (m (list 0)) \/}$ [FUNCTION]

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^m1*x2^m2*...*xr^mr, where m=(m1,m2,...,mr) is a multiindex.