diff options
Diffstat (limited to 'src/algebra/catdef.spad.pamphlet')
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 11 |
1 files changed, 0 insertions, 11 deletions
diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index b2d2c42e..56860d9f 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -408,8 +408,6 @@ DivisionRing(): Category == Join(EntireRing, Algebra Fraction Integer) with "**": (%,Integer) -> % ++ x**n returns x raised to the integer power n. - "^" : (%,Integer) -> % - ++ x^n returns x raised to the integer power n. inv : % -> % ++ inv x returns the multiplicative inverse of x. ++ Error: if x is 0. @@ -419,7 +417,6 @@ DivisionRing(): Category == add n: Integer x: % - _^(x:%, n:Integer):% == x ** n import RepeatedSquaring(%) x ** n: Integer == zero? n => 1 @@ -824,7 +821,6 @@ Group(): Category == Monoid with inv: % -> % ++ inv(x) returns the inverse of x. "/": (%,%) -> % ++ x/y is the same as x times the inverse of y. "**": (%,Integer) -> % ++ x**n returns x raised to the integer power n. - "^": (%,Integer) -> % ++ x^n returns x raised to the integer power n. unitsKnown ++ unitsKnown asserts that recip only returns ++ "failed" for non-units. conjugate: (%,%) -> % @@ -836,7 +832,6 @@ Group(): Category == Monoid with import RepeatedSquaring(%) x:% / y:% == x*inv(y) recip(x:%) == inv(x) - _^(x:%, n:Integer):% == x ** n x:% ** n:Integer == zero? n => 1 n<0 => expt(inv(x),(-n) pretend PositiveInteger) @@ -1014,14 +1009,11 @@ Monoid(): Category == SemiGroup with one?: % -> Boolean ++ one?(x) tests if x is equal to 1. "**": (%,NonNegativeInteger) -> % ++ x**n returns the repeated product ++ of x n times, i.e. exponentiation. - "^" : (%,NonNegativeInteger) -> % ++ x^n returns the repeated product - ++ of x n times, i.e. exponentiation. recip: % -> Union(%,"failed") ++ recip(x) tries to compute the multiplicative inverse for x ++ or "failed" if it cannot find the inverse (see unitsKnown). add import RepeatedSquaring(%) - _^(x:%, n:NonNegativeInteger):% == x ** n one? x == x = 1 sample() == 1 recip x == @@ -1614,12 +1606,9 @@ SemiGroup(): Category == SetCategory with "*": (%,%) -> % ++ x*y returns the product of x and y. "**": (%,PositiveInteger) -> % ++ x**n returns the repeated product ++ of x n times, i.e. exponentiation. - "^": (%,PositiveInteger) -> % ++ x^n returns the repeated product - ++ of x n times, i.e. exponentiation. add import RepeatedSquaring(%) x:% ** n:PositiveInteger == expt(x,n) - _^(x:%, n:PositiveInteger):% == x ** n @ \section{category SETCAT SetCategory} |