next up previous contents
Next: The Polynomial Package Up: CGBLisp User Guide and Previous: The Geometric Theorem Prover

Subsections

The Monomial Order Package

lex >

$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$ [FUNCTION]

Return T if P > Q with respect to lexicographic order, otherwise NIL. The second returned value is T if P=Q, otherwise it is NIL.

total - degree

$\textstyle\parbox{\pboxargslen}{\em m {\sf \&optional} (start 0) (end (length m)) \/}$ [FUNCTION]

Return the todal degree of a monomoal M.

grlex >

$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$ [FUNCTION]

Return T if P > Q with respect to graded lexicographic order, otherwise NIL. The second returned value is T if P=Q, otherwise it is NIL.

grevlex >

$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$ [FUNCTION]

Return T if P > Q with respect to graded reverse lexicographic order, NIL otherwise. The second returned value is T if P=Q, otherwise it is NIL.

revlex >

$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$ [FUNCTION]

Return T if P > Q with respect to reverse lexicographic order, NIL otherwise. The second returned value is T if P=Q, otherwise it is NIL. This is not and admissible monomial order because some sets do not have a minimal element. This order is useful in constructing other orders.

invlex >

$\textstyle\parbox{\pboxargslen}{\em p q {\sf \&optional} (start 0) (end (length p)) \/}$ [FUNCTION]

Return T if P > Q with respect to inverse lexicographic order, NIL otherwise The second returned value is T if P=Q, otherwise it is NIL.

elimination - order

$\textstyle\parbox{\pboxargslen}{\em k {\sf \&key} (primary$-$order
 \char93 'lex$\gt$) (secondary$-$order
 \char93 'lex$\gt$) \/}$ [FUNCTION]

Return a predicate which compares monomials according to the K - th elimination order. Two optional arguments are PRIMARY - ORDER and SECONDARY - ORDER and they should be term orders which are used on the first K and the remaining variables.

elimination - order - 1

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

A special case of the ELIMINATION - ORDER when there is only one primary variable.

next up previous contents
Next: The Polynomial Package Up: CGBLisp User Guide and Previous: The Geometric Theorem Prover
Marek Rychlik
3/21/1998