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authordos-reis <gdr@axiomatics.org>2009-06-11 21:51:23 +0000
committerdos-reis <gdr@axiomatics.org>2009-06-11 21:51:23 +0000
commit7bd82b57975bbc1ff5b87fed0739815c620ecdcc (patch)
tree4cf4d2b4af144e87a86cc1ac2f85a5f4148cb8fb /src/algebra/xpoly.spad.pamphlet
parentfb75980589a0611aee3b8e5e25408725a5c5a531 (diff)
downloadopen-axiom-7bd82b57975bbc1ff5b87fed0739815c620ecdcc.tar.gz
* algebra/: Remove quotes from operator namaes in signatures.
Diffstat (limited to 'src/algebra/xpoly.spad.pamphlet')
-rw-r--r--src/algebra/xpoly.spad.pamphlet22
1 files changed, 11 insertions, 11 deletions
diff --git a/src/algebra/xpoly.spad.pamphlet b/src/algebra/xpoly.spad.pamphlet
index ef221d08..f5c9b047 100644
--- a/src/algebra/xpoly.spad.pamphlet
+++ b/src/algebra/xpoly.spad.pamphlet
@@ -43,11 +43,11 @@ OrderedFreeMonoid(S: OrderedSet): OFMcategory == OFMdefinition where
REC ==> Record(gen:S, exp:NNI)
OFMcategory == Join(OrderedMonoid, RetractableTo S) with
- "*": (S, %) -> %
+ *: (S, %) -> %
++ \spad{s * x} returns the product of \spad{x} by \spad{s} on the left.
- "*": (%, S) -> %
+ *: (%, S) -> %
++ \spad{x * s} returns the product of \spad{x} by \spad{s} on the right.
- "**": (S, NNI) -> %
+ **: (S, NNI) -> %
++ \spad{s ** n} returns the product of \spad{s} by itself \spad{n} times.
first: % -> S
++ \spad{first(x)} returns the first letter of \spad{x}.
@@ -80,7 +80,7 @@ OrderedFreeMonoid(S: OrderedSet): OFMcategory == OFMdefinition where
rquo: (%, S) -> Union(%, "failed")
++ \spad{rquo(x, s)} returns the exact right quotient
++ of \spad{x} by \spad{s}.
- "div": (%, %) -> Union(Record(lm: %, rm: %), "failed")
+ div: (%, %) -> Union(Record(lm: %, rm: %), "failed")
++ \spad{x div y} returns the left and right exact quotients of
++ \spad{x} by \spad{y}, that is \spad{[l, r]} such that \spad{x = l * y * r}.
++ "failed" is returned iff \spad{x} is not of the form \spad{l * y * r}.
@@ -205,7 +205,7 @@ FreeModuleCat(R, Basis):Category == Exports where
TERM ==> Record(k: Basis, c: R)
Exports == Join(BiModule(R,R), RetractableTo Basis) with
- "*" : (R, Basis) -> %
+ * : (R, Basis) -> %
++ \spad{r*b} returns the product of \spad{r} by \spad{b}.
coefficient : (%, Basis) -> R
++ \spad{coefficient(x,b)} returns the coefficient
@@ -278,7 +278,7 @@ FreeModule1(R:Ring,S:OrderedSet): FMcat == FMdef where
TERM ==> Record(k:S,c:R)
FMcat == FreeModuleCat(R,S) with
- "*":(S,R) -> %
+ *:(S,R) -> %
++ \spad{s*r} returns the product \spad{r*s}
++ used by \spadtype{XRecursivePolynomial}
FMdef == FreeModule(R,S) add
@@ -419,9 +419,9 @@ XFreeAlgebra(vl:OrderedSet,R:Ring):Category == Catdef where
Catdef == Join(Ring, XAlgebra(R), RetractableTo WORD)
with
- "*": (vl,%) -> %
+ *: (vl,%) -> %
++ \spad{v * x} returns the product of a variable \spad{x} by \spad{x}.
- "*": (%, R) -> %
+ *: (%, R) -> %
++ \spad{x * r} returns the product of \spad{x} by \spad{r}.
++ Usefull if \spad{R} is a non-commutative Ring.
mindeg: % -> WORD
@@ -547,9 +547,9 @@ XPolynomialRing(R:Ring,E:OrderedMonoid): T == C where
T == Join(Ring, XAlgebra(R), FreeModuleCat(R,E),CoercibleFrom E) with
--operations
- "*": (%,R) -> %
+ *: (%,R) -> %
++ \spad{p*r} returns the product of \spad{p} by \spad{r}.
- "#": % -> NonNegativeInteger
+ #: % -> NonNegativeInteger
++ \spad{# p} returns the number of terms in \spad{p}.
maxdeg: % -> E
++ \spad{maxdeg(p)} returns the greatest word occurring in the polynomial \spad{p}
@@ -574,7 +574,7 @@ XPolynomialRing(R:Ring,E:OrderedMonoid): T == C where
++ \spad{quasiRegular(x)} return \spad{x} minus its constant term.
map : (R -> R, %) -> %
++ \spad{map(fn,x)} returns \spad{Sum(fn(r_i) w_i)} if \spad{x} writes \spad{Sum(r_i w_i)}.
- if R has Field then "/" : (%,R) -> %
+ if R has Field then / : (%,R) -> %
++ \spad{p/r} returns \spad{p*(1/r)}.
--assertions