CuspΒΆ
qetacusp.spad line 110 [edit on github]
Cusp implements representatives of cusps of a subgroup of $SL2Z$
- <=: (%, %) -> Boolean
- from PartialOrder 
- <: (%, %) -> Boolean
- from PartialOrder 
- >=: (%, %) -> Boolean
- from PartialOrder 
- >: (%, %) -> Boolean
- from PartialOrder 
- coerce: % -> OutputForm
- from CoercibleTo OutputForm 
- cusp: Matrix Integer -> %
- cusp(mat)returns the cusp represented by the transformation matrix- mat. It returns cusp(- mat(1,1),- mat(2,1)). cusp is a left-inverse of cuspToMatrix, i.e. cusp(cuspToMatrix(- c))- =c.
- cuspToMatrix: % -> Matrix Integer
- cuspToMatrix(x)returns a matrix gamma=[[a,- b],[- c,- d]] corresponding to the cusp (a:c).
- denom: % -> Integer
- For - x=(a:c) denom(- x) returns- c. We assure that denom(- x)- >=0.
- hash: % -> SingleInteger
- from Hashable 
- hashUpdate!: (HashState, %) -> HashState
- from Hashable 
- infinity?: % -> Boolean
- infinity?(x)returns- trueif and only if- xis the cusp (1:0).
- infinity: () -> %
- infinity()returns the cusp (1:0).
- latex: % -> String
- from SetCategory 
- max: (%, %) -> %
- from OrderedSet 
- min: (%, %) -> %
- from OrderedSet 
- moebiusTransform: (Integer, Integer, Integer, Integer, %) -> %
- moebiusTransform(a,b,c,d,tau)computes the Moebius transform of- tau, i.e. (a*tau+b)/(c*tau+d). Input condition: a*d-- b*cis nonzero.
- moebiusTransform: (Matrix Integer, %) -> %
- moebiusTransform(m, tau)computes the Moebius transform of tau. Input condition: not zero? determinant- m,
- numer: % -> Integer
- For - x=(a:c) numer(- x) returns a.
- rational: % -> Fraction Integer
- If not infinity?( - x) then rational(- x) returns the rational number numer(- x)/denom(- x).
- smaller?: (%, %) -> Boolean
- from Comparable