/usr/share/axiom-20170501/src/algebra/FLALG.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 | )abbrev category FLALG FreeLieAlgebra
++ Author: Michel Petitot (petitot@lifl.fr)
++ Date Created: 91
++ Date Last Updated: 7 Juillet 92
++ Fix History: compilation v 2.1 le 13 dec 98
++ Description:
++ The category of free Lie algebras.
++ It is used by domains of non-commutative algebra:
++ \spadtype{LiePolynomial} and
++ \spadtype{XPBWPolynomial}.
FreeLieAlgebra(VarSet,R) : Category == SIG where
VarSet : OrderedSet
R : CommutativeRing
XRPOLY ==> XRecursivePolynomial(VarSet,R)
XDPOLY ==> XDistributedPolynomial(VarSet,R)
RN ==> Fraction Integer
LWORD ==> LyndonWord(VarSet)
SIG ==> Join(LieAlgebra(R)) with
coef : (XRPOLY , $) -> R
++ \axiom{coef(x,y)} returns the scalar product of \axiom{x} by
++ \axiom{y}, the set of words being regarded as an orthogonal basis.
coerce : VarSet -> $
++ \axiom{coerce(x)} returns \axiom{x} as a Lie polynomial.
coerce : $ -> XDPOLY
++ \axiom{coerce(x)} returns \axiom{x} as distributed polynomial.
coerce : $ -> XRPOLY
++ \axiom{coerce(x)} returns \axiom{x} as a recursive polynomial.
degree : $ -> NonNegativeInteger
++ \axiom{degree(x)} returns the greatest length of a word in the
++ support of \axiom{x}.
--if R has Module(RN) then
-- Hausdorff : ($,$,PositiveInteger) -> $
lquo : (XRPOLY , $) -> XRPOLY
++ \axiom{lquo(x,y)} returns the left simplification of \axiom{x}
++ by \axiom{y}.
rquo : (XRPOLY , $) -> XRPOLY
++ \axiom{rquo(x,y)} returns the right simplification of \axiom{x}
++ by \axiom{y}.
LiePoly : LWORD -> $
++ \axiom{LiePoly(l)} returns the bracketed form of \axiom{l} as
++ a Lie polynomial.
mirror : $ -> $
++ \axiom{mirror(x)} returns \axiom{Sum(r_i mirror(w_i))}
++ if \axiom{x} is \axiom{Sum(r_i w_i)}.
trunc : ($, NonNegativeInteger) -> $
++ \axiom{trunc(p,n)} returns the polynomial \axiom{p}
++ truncated at order \axiom{n}.
varList : $ -> List VarSet
++ \axiom{varList(x)} returns the list of distinct entries
++ of \axiom{x}.
eval : ($, VarSet, $) -> $
++ \axiom{eval(p, x, v)} replaces \axiom{x} by \axiom{v}
++ in \axiom{p}.
eval : ($, List VarSet, List $) -> $
++ \axiom{eval(p, [x1,...,xn], [v1,...,vn])} replaces \axiom{xi}
++ by \axiom{vi} in \axiom{p}.
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