# jumpingNumbers(...,Interval=>...) -- interval for jumping numbers

## Description

Specify the interval in which to search for jumping numbers. IntervalType may be "Closed" (default), "Open", "ClosedOpen", or "OpenClosed".

 i1 : R = QQ[x,y]; i2 : I = monomialIdeal(y^2,x^3); o2 : MonomialIdeal of R i3 : jumpingNumbers(I) -- default: interval [5/6, 2] 5 7 4 3 5 11 2 o3 = {{-, -, -, -, -, --, 2}, {monomialIdeal (x, y), monomialIdeal (x , y), 6 6 3 2 3 6 ------------------------------------------------------------------------ 2 2 3 2 monomialIdeal (x , x*y, y ), monomialIdeal (x , x*y, y ), monomialIdeal ------------------------------------------------------------------------ 3 2 2 4 2 2 3 4 (x , x y, y ), monomialIdeal (x , x y, x*y , y ), monomialIdeal (x , ------------------------------------------------------------------------ 3 2 3 x y, x*y , y )}} o3 : List i4 : jumpingNumbers(I,Interval=>{1,3/2}) -- [1,3/2] 7 4 3 2 2 2 o4 = {{-, -, -}, {monomialIdeal (x , y), monomialIdeal (x , x*y, y ), 6 3 2 ------------------------------------------------------------------------ 3 2 monomialIdeal (x , x*y, y )}} o4 : List i5 : jumpingNumbers(I,IntervalType=>"Open") -- (5/6,2) 7 4 3 5 11 2 2 2 o5 = {{-, -, -, -, --}, {monomialIdeal (x , y), monomialIdeal (x , x*y, y ), 6 3 2 3 6 ------------------------------------------------------------------------ 3 2 3 2 2 monomialIdeal (x , x*y, y ), monomialIdeal (x , x y, y ), monomialIdeal ------------------------------------------------------------------------ 4 2 2 3 (x , x y, x*y , y )}} o5 : List i6 : jumpingNumbers(I,Interval=>{1,3/2},IntervalType=>"ClosedOpen") -- [1,3/2) 7 4 2 2 2 o6 = {{-, -}, {monomialIdeal (x , y), monomialIdeal (x , x*y, y )}} 6 3 o6 : List

## Further information

• Default value: {0, infinity}
• Function: jumpingNumbers -- jumping numbers
• Option key: Interval -- name for an optional argument