diff options
| -rw-r--r-- | src/algebra/defaults.spad.pamphlet | 8 | ||||
| -rw-r--r-- | src/algebra/naalgc.spad.pamphlet | 2 | ||||
| -rw-r--r-- | src/algebra/polycat.spad.pamphlet | 2 | ||||
| -rw-r--r-- | src/algebra/solvefor.spad.pamphlet | 4 | ||||
| -rw-r--r-- | src/algebra/wtpol.spad.pamphlet | 2 |
5 files changed, 7 insertions, 11 deletions
diff --git a/src/algebra/defaults.spad.pamphlet b/src/algebra/defaults.spad.pamphlet index 490ae98a..5f9ca825 100644 --- a/src/algebra/defaults.spad.pamphlet +++ b/src/algebra/defaults.spad.pamphlet @@ -19,14 +19,12 @@ RepeatedSquaring(S): Exports == Implementation where S: SetCategory with - "*":(%,%)->% + *: (%,%)->% ++ x*y returns the product of x and y Exports == with expt: (S,PositiveInteger) -> S ++ expt(r, i) computes r**i by repeated squaring Implementation == add - x: S - n: PositiveInteger expt(x, n) == one? n => x odd?(n)$Integer=> x * expt(x*x,shift(n,-1) pretend PositiveInteger) @@ -44,14 +42,12 @@ RepeatedSquaring(S): Exports == Implementation where RepeatedDoubling(S):Exports ==Implementation where S: SetCategory with - "+":(%,%)->% + +: (%,%)->% ++ x+y returns the sum of x and y Exports == with double: (PositiveInteger,S) -> S ++ double(i, r) multiplies r by i using repeated doubling. Implementation == add - x: S - n: PositiveInteger double(n,x) == one? n => x odd?(n)$Integer => diff --git a/src/algebra/naalgc.spad.pamphlet b/src/algebra/naalgc.spad.pamphlet index 3f85f7ef..145580f9 100644 --- a/src/algebra/naalgc.spad.pamphlet +++ b/src/algebra/naalgc.spad.pamphlet @@ -93,7 +93,7 @@ MonadWithUnit(): Category == Monad with ++ leftPower(a,n) returns the \spad{n}-th left power of \spad{a}, ++ i.e. \spad{leftPower(a,n) := a * leftPower(a,n-1)} and ++ \spad{leftPower(a,0) := 1}. - "**": (%,NonNegativeInteger) -> % + **: (%,NonNegativeInteger) -> % ++ \spad{a**n} returns the \spad{n}-th power of \spad{a}, ++ defined by repeated squaring. recip: % -> Union(%,"failed") diff --git a/src/algebra/polycat.spad.pamphlet b/src/algebra/polycat.spad.pamphlet index b9780274..4f0d80dd 100644 --- a/src/algebra/polycat.spad.pamphlet +++ b/src/algebra/polycat.spad.pamphlet @@ -50,7 +50,7 @@ AbelianMonoidRing(R:Ring, E:OrderedAbelianMonoid): Category == coefficient: (%,E) -> R ++ coefficient(p,e) extracts the coefficient of the monomial with ++ exponent e from polynomial p, or returns zero if exponent is not present. - if R has Field then "/": (%,R) -> % + if R has Field then /: (%,R) -> % ++ p/c divides p by the coefficient c. if R has CommutativeRing then CommutativeRing diff --git a/src/algebra/solvefor.spad.pamphlet b/src/algebra/solvefor.spad.pamphlet index 6d072ae8..2d335fcb 100644 --- a/src/algebra/solvefor.spad.pamphlet +++ b/src/algebra/solvefor.spad.pamphlet @@ -12,7 +12,7 @@ \section{package SOLVEFOR PolynomialSolveByFormulas} <<package SOLVEFOR PolynomialSolveByFormulas>>= )abbrev package SOLVEFOR PolynomialSolveByFormulas --- Current fields with "**": (%, RationalNumber) -> % are +-- Current fields with **: (%, RationalNumber) -> % are -- ComplexFloat, RadicalExtension(K) and RationalRadical -- SMW June 86, BMT Sept 93 ++ Description: @@ -24,7 +24,7 @@ PolynomialSolveByFormulas(UP, F): PSFcat == PSFdef where UP: UnivariatePolynomialCategory F - F: Field with "**": (%, Fraction Integer) -> % + F: Field with **: (%, Fraction Integer) -> % L ==> List diff --git a/src/algebra/wtpol.spad.pamphlet b/src/algebra/wtpol.spad.pamphlet index 6f3dca56..3893ae48 100644 --- a/src/algebra/wtpol.spad.pamphlet +++ b/src/algebra/wtpol.spad.pamphlet @@ -42,7 +42,7 @@ WeightedPolynomials(R:Ring,VarSet: OrderedSet, E:OrderedAbelianMonoidSup, wtlevel:NonNegativeInteger): Join(Ring, HomotopicTo P) with if R has CommutativeRing then Algebra(R) - if R has Field then "/": ($,$) -> Union($,"failed") + if R has Field then /: ($,$) -> Union($,"failed") ++ x/y division (only works if minimum weight ++ of divisor is zero, and if R is a Field) changeWeightLevel: NonNegativeInteger -> Void |