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#W  number.gd                    GAP4 package `Utils'             Stefan Kohl
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#Y  Copyright (C) 2015-2025, The GAP Group

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##  this function has been transferred from RCWA
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#F  NextProbablyPrimeInt( <n> ) . . next integer passing `IsProbablyPrimeInt'
##
##  Returns the smallest integer larger than <n> which passes GAP's
##  probabilistic primality test.
##
##  The function `NextProbablyPrimeInt' does the same as `NextPrimeInt',
##  except that for reasons of performance it tests numbers only for
##  `IsProbablyPrimeInt' instead of `IsPrimeInt'.
##  For large <n>, this function is much faster than `NextPrimeInt'.
##
DeclareGlobalName( "NextProbablyPrimeInt" );

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##  this function has been transferred from RCWA
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#F  AllSmoothIntegers( <maxp>, <maxn> )
##
##  Returns the set of all integers in the range [1..<maxn>] which have only
##  prime divisors in the range [2..<maxp>].
##
DeclareGlobalName( "AllSmoothIntegers" );

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##  this function has been transferred from RCWA
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#F  PrimeNumbersIterator(  )
#F  PrimeNumbersIterator( chunksize )
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##  Iterator running through the prime numbers in ascending order.
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DeclareGlobalName( "PrimeNumbersIterator" );

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##  this function has been transferred from RCWA
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#F  RestrictedPartitionsWithoutRepetitions( <n>, <S> )
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##  Given a positive integer n and a set of positive integers S, this func-
##  tion returns a list of all partitions of n into distinct elements of S.
##  The only difference to `RestrictedPartitions' is that no repetitions are
##  allowed.
##
DeclareGlobalName( "RestrictedPartitionsWithoutRepetitions" );

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##  this function has been transferred from RCWA
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#O  AllProducts( <D>, <k> ) . . all products of <k>-tuples of elements of <D>
#M  AllProducts( <l>, <k> ) . . . . . . . . . . . . . . . . . . . . for lists
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DeclareOperation( "AllProducts", [ IsListOrCollection, IsPosInt ] );

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#E  number.gd . . . . . . . . . . . . . . . . . . . . . . . . . . . ends here

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