-- Copyright 1993-1999,2004 by Daniel R. Grayson needs "fold.m2" needs "methods.m2" InfiniteNumber = new Type of Number InfiniteNumber.synonym = "infinite number" infinity = new InfiniteNumber from {1} neginfinity = new InfiniteNumber from {-1} - InfiniteNumber := x -> if x === infinity then neginfinity else infinity setAttribute(infinity,ReverseDictionary,symbol infinity) setAttribute( infinity,PrintNames, "infinity") setAttribute(-infinity,PrintNames, "-infinity") toString InfiniteNumber := net InfiniteNumber := toExternalString InfiniteNumber := x -> getAttribute(x,PrintNames) IndeterminateNumber = new Type of Number IndeterminateNumber.synonym = "indeterminate number" indeterminate = new IndeterminateNumber from {} setAttribute(indeterminate,ReverseDictionary,symbol indeterminate) toString IndeterminateNumber := net IndeterminateNumber := toExternalString IndeterminateNumber := x -> "indeterminate" texMath IndeterminateNumber := x -> texMath toString x numeric(ZZ, IndeterminateNumber) := (prec, x) -> ( numeric(prec, 0) * numeric(prec, infinity)) numeric IndeterminateNumber := x -> numeric(defaultPrecision, x) InfiniteNumber ? InfiniteNumber := (x,y) -> x#0 ? y#0 InfiniteNumber + InfiniteNumber := (x,y) -> if x === y then x else indeterminate InfiniteNumber - InfiniteNumber := (x,y) -> if x =!= y then x else indeterminate InfiniteNumber * InfiniteNumber := (x,y) -> if x === y then infinity else neginfinity InfiniteNumber / InfiniteNumber := InfiniteNumber // InfiniteNumber := (x,y) -> indeterminate InfiniteNumber ^ InfiniteNumber := (x,y) -> ( if y < 0 then 0 else if x > 0 then infinity else indeterminate ) InfiniteNumber ..< InfiniteNumber := InfiniteNumber .. InfiniteNumber := (i,j) -> if i < j then error "infinite range specified" else () InfiniteNumber == InfiniteNumber := (x,y) -> x === y isFinite = method() isFinite Number := isFinite0 isFinite InfiniteNumber := x -> false InfiniteNumber + Number := (i,j) -> ( if isFinite j then i else if isANumber j then if ((i > 0 and j > 0) or (i < 0 and j < 0)) then i else indeterminate else indeterminate ) Number + InfiniteNumber := (i,j) -> j + i InfiniteNumber - Number := (i,j) -> i + (-j) Number - InfiniteNumber := (i,j) -> i + (-j) InfiniteNumber + CC := InfiniteNumber - CC := (i,j) -> if isANumber j then promote(1/0.,CC) else indeterminate CC + InfiniteNumber := CC - InfiniteNumber := (i,j) -> j+i InfiniteNumber * QQ := InfiniteNumber * ZZ := (i,j) -> ( if isANumber j then -- if j > 0 then i else if j < 0 then -i else if j == 0 then j else indeterminate if j > 0 then i else if j < 0 then -i else indeterminate else indeterminate ) InfiniteNumber * RR := (i,j) -> ( if (isANumber j and j > 0) then i else if (isANumber j and j < 0) then -i else if j == 0 then 0_RR else 1/0.-1/0. ) InfiniteNumber * CC := (i,j) -> ( if (isANumber j and j != 0) then promote(1/0.,CC) else if j == 0 then 0_CC else (1/0.-1/0.+ii) ) Number * InfiniteNumber := (i,j) -> j * i Number // InfiniteNumber := Number / InfiniteNumber := (i,j) -> if isFinite i then 0 else indeterminate InfiniteNumber // Number := InfiniteNumber / Number := (i,j) -> ( if (isFinite j and j > 0) then i else if (isFinite j and j < 0) then -i else indeterminate) InfiniteNumber // RR := InfiniteNumber / RR := (i,j) -> ( if (isFinite j and j > 0.) then i else if (isFinite j and j < 0.) then -i else if j === 0. then i else if j === -0. then -i else 1/0.-1/0. ) InfiniteNumber // CC := InfiniteNumber / CC := (i,j) -> ( if isFinite j then promote(1/0.,CC) else 1/0.-1/0.+ii ) InfiniteNumber ^ ZZ := (x,n) -> ( if (n > 0 and even n) then infinity else if (n > 0 and odd n) then x else if n < 0 then 0 else indeterminate ) InfiniteNumber ^ QQ := (x,q) -> if (odd denominator q or x > 0) then x ^ (numerator q) else indeterminate InfiniteNumber ^ RR := (x,r) -> ( if (x > 0 and r > 0.) then x else if (x > 0 and r < 0.) then 0. else indeterminate ) ZZ ^ InfiniteNumber := (n,x) -> ( if n==1 then 1 else if n==0 and x > 0 then 0 else if n==0 and x < 0 then indeterminate else if n > 1 and x > 0 then infinity else if n > 1 and x < 0 then 0 else indeterminate ) RR ^ InfiniteNumber := (r,x) -> ( if (0. < r and r < 1. and x > 0) then 0. else if (r > 1. and x > 0) then infinity else if (0. < r and r < 1. and x < 0) then infinity else if (r > 1. and x < 0) then 0. else if r == 1. then 1. else indeterminate ) QQ ^ InfiniteNumber := (r,x) -> ( if (0 < r and r < 1 and x > 0) then 0 else if (r > 1 and x > 0) then infinity else if (0 < r and r < 1 and x < 0) then infinity else if (r > 1 and x < 0) then 0 else if r == 1 then 1 else indeterminate ) InfiniteNumber == Number := Number == InfiniteNumber := (x,y) -> false Thing ? InfiniteNumber := (x,y) -> if y === infinity then symbol < else symbol > InfiniteNumber ? Thing := (x,y) -> if x === infinity then symbol > else symbol < RR == InfiniteNumber := (x,y) -> isInfinite x and ( x < 0 and y < 0 or x > 0 and y > 0 ) InfiniteNumber == RR := (x,y) -> y == x RR ? InfiniteNumber := (x,y) -> ( if ( not isANumber(x) ) then symbol incomparable else if isInfinite(x) then ( if (x > 0. and y > 0) then symbol == else if (x < 0. and y < 0) then symbol == else if (x > 0. and y < 0) then symbol > else symbol < ) else if y > 0 then symbol < else symbol > ) InfiniteNumber ? RR := (x,y) -> ( if ( not isANumber(y) ) then ( symbol incomparable ) else if isInfinite(y) then ( if (x > 0 and y > 0.) then symbol == else if (x < 0 and y < 0.) then symbol == else if (x > 0 and y < 0.) then symbol > else symbol < ) else if x > 0 then symbol > else symbol < ) CC ? InfiniteNumber := (x,y) -> if (isANumber(x) and not isFinite(x)) then symbol == else symbol incomparable InfiniteNumber ? CC := (x,y) -> if (isANumber(y) and not isFinite(y)) then symbol == else symbol incomparable texMath InfiniteNumber := i -> if i === infinity then "\\infty" else "{-\\infty}" max VisibleList := x -> if #x === 0 then -infinity else fold((i,j) -> if i > j then i else j, x) min VisibleList := x -> if #x === 0 then infinity else fold((i,j) -> if i < j then i else j, x) -- Local Variables: -- compile-command: "make -C $M2BUILDDIR/Macaulay2/m2 " -- End:

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