diff options
Diffstat (limited to 'src/algebra/xpoly.spad.pamphlet')
| -rw-r--r-- | src/algebra/xpoly.spad.pamphlet | 22 |
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 |