GaloisGroupUtilities R¶

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R: Ring

GaloisGroupUtilities provides several useful functions.

fillPascalTriangle: () -> Void: fillPascalTriangle() fills the stored table.

pascalTriangle: (NonNegativeInteger, Integer) -> R: pascalTriangle(n, r) returns the binomial coefficient C(n, r)=n!/(r! (n-r)!) and stores it in a table to prevent recomputation.

rangePascalTriangle: () -> NonNegativeInteger: rangePascalTriangle() returns the maximal number of lines stored.

rangePascalTriangle: NonNegativeInteger -> NonNegativeInteger: rangePascalTriangle(n) sets the maximal number of lines which are stored and returns the previous value.

safeCeiling: R -> Integer if R has FloatingPointSystem: safeCeiling(x) returns the integer which is greater than any integer with the same floating point number representation.

safeFloor: R -> Integer if R has FloatingPointSystem: safeFloor(x) returns the integer which is lower or equal to the largest integer which has the same floating point number representation.

safetyMargin: () -> NonNegativeInteger if R has FloatingPointSystem: safetyMargin() returns the number of low weight digits we do not trust in the floating point representation (used by safeCeiling).

safetyMargin: NonNegativeInteger -> NonNegativeInteger if R has FloatingPointSystem: safetyMargin(n) sets to n the number of low weight digits we do not trust in the floating point representation and returns the previous value (for use by safeCeiling).

sizePascalTriangle: () -> NonNegativeInteger: sizePascalTriangle() returns the number of entries currently stored in the table.