1 files changed, 179 insertions, 0 deletions
diff --git a/src/hyper/pages/XPBWPOLY.ht b/src/hyper/pages/XPBWPOLY.ht
new file mode 100644
index 00000000..3352a675
--- /dev/null
+++ b/src/hyper/pages/XPBWPOLY.ht
@@ -0,0 +1,179 @@
+% Copyright The Numerical Algorithms Group Limited 1992-94. All rights reserved.
+% !! DO NOT MODIFY THIS FILE BY HAND !! Created by ht.awk.
+\newcommand{\XPBWPolynomialXmpTitle}{XPBWPolynomial}
+\newcommand{\XPBWPolynomialXmpNumber}{9.88}
+%
+% =====================================================================
+\begin{page}{XPBWPolynomialXmpPage}{9.88 XPBWPolynomial}
+% =====================================================================
+\beginscroll
+Initialisations
+\xtc{
+}{
+\spadpaste{a:Symbol := 'a \bound{a}}
+}
+\xtc{
+}{
+\spadpaste{b:Symbol := 'b \bound{b}}
+}
+\xtc{
+}{
+\spadpaste{RN    := Fraction(Integer) \bound{RN}}
+}
+\xtc{
+}{
+\spadpaste{word   := OrderedFreeMonoid Symbol \bound{word}}
+}
+\xtc{
+}{
+\spadpaste{lword := LyndonWord(Symbol) \bound{lword}}
+}
+\xtc{
+}{
+\spadpaste{base  := PoincareBirkhoffWittLyndonBasis Symbol \bound{base}}
+}
+\xtc{
+}{
+\spadpaste{dpoly := XDistributedPolynomial(Symbol, RN) \bound{dpoly} \free{RN}}
+}
+\xtc{
+}{
+\spadpaste{rpoly := XRecursivePolynomial(Symbol, RN) \bound{rpoly} \free{RN}}
+}
+\xtc{
+}{
+\spadpaste{lpoly := LiePolynomial(Symbol, RN) \bound{lpoly} \free{RN}}
+}
+\xtc{
+}{
+\spadpaste{poly  := XPBWPolynomial(Symbol, RN) \bound{poly} \free{RN}}
+}
+\xtc{
+}{
+\spadpaste{liste : List lword := LyndonWordsList([a,b], 6) \bound{liste} \free{lword a b }}
+}
+
+Let's make some polynomials
+\xtc{
+}{
+\spadpaste{0$poly \free{poly}}
+}
+\xtc{
+}{
+\spadpaste{1$poly \free{poly}}
+}
+\xtc{
+}{
+\spadpaste{p : poly := a \free{a poly} \bound{p}}
+}
+\xtc{
+}{
+\spadpaste{q : poly := b \free{b poly} \bound{q}}
+}
+\xtc{
+}{
+\spadpaste{pq: poly := p*q \free{p q poly} \bound{pq}}
+}
+\xtc{
+Coerce to distributed polynomial
+}{
+\spadpaste{pq :: dpoly \free{pq dpoly}}
+}
+
+Check some polynomial operations
+\xtc{
+}{
+\spadpaste{mirror pq \free{pq}}
+}
+\xtc{
+}{
+\spadpaste{ListOfTerms pq \free{pq}}
+}
+\xtc{
+}{
+\spadpaste{reductum pq \free{pq}}
+}
+\xtc{
+}{
+\spadpaste{leadingMonomial pq \free{pq}}
+}
+\xtc{
+}{
+\spadpaste{coefficients pq \free{pq}}
+}
+\xtc{
+}{
+\spadpaste{leadingTerm pq \free{pq}}
+}
+\xtc{
+}{
+\spadpaste{degree pq \free{pq}}
+}
+\xtc{
+}{
+\spadpaste{pq4:=exp(pq,4) \bound{pq4} \free{pq}}
+}
+\xtc{
+}{
+\spadpaste{log(pq4,4) - pq \free{pq4 pq} }
+}
+
+Calculations with verification in \axiomType{XDistributedPolynomial}.
+\xtc{
+}{
+\spadpaste{lp1 :lpoly := LiePoly liste.10 \free{liste lpoly} \bound{lp1}}
+}
+\xtc{
+}{
+\spadpaste{lp2 :lpoly := LiePoly liste.11 \free{liste lpoly} \bound{lp2}}
+}
+\xtc{
+}{
+\spadpaste{lp  :lpoly := [lp1, lp2] \free{lp1 lp2 lpoly} \bound{lp}}
+}
+\xtc{
+}{
+\spadpaste{lpd1: dpoly := lp1 \free{lp1 dpoly} \bound{lpd1}}
+}
+\xtc{
+}{
+\spadpaste{lpd2: dpoly := lp2 \free{lp2 dpoly} \bound{lpd2}}
+}
+\xtc{
+}{
+\spadpaste{lpd : dpoly := lpd1 * lpd2 - lpd2 * lpd1 \free{dpoly lpd1 lpd2} \bound{lpd}}
+}
+\xtc{
+}{
+\spadpaste{lp :: dpoly - lpd \free{lpd dpoly lp}}
+}
+
+Calculations with verification in \axiomType{XRecursivePolynomial}.
+\xtc{
+}{
+\spadpaste{p := 3 * lp \free{lp} \bound{pp}}
+}
+\xtc{
+}{
+\spadpaste{q := lp1 \free{lp1} \bound{qq}}
+}
+\xtc{
+}{
+\spadpaste{pq:= p * q \free{pp qq} \bound{pqpq}}
+}
+\xtc{
+}{
+\spadpaste{pr:rpoly := p :: rpoly \free{rpoly pp} \bound{pr}}
+}
+\xtc{
+}{
+\spadpaste{qr:rpoly := q :: rpoly \free{rpoly qq} \bound{qr}}
+}
+\xtc{
+}{
+\spadpaste{pq :: rpoly - pr*qr \free{pr qr rpoly pqpq} }
+}
+\endscroll
+\autobuttons
+\end{page}
+%