Miscellaneous

Evaluate (P :: NwtnPgon, x :: FldRatElt)

Evaluate (P :: NwtnPgon, x :: RngIntElt)

-> FldRatElt

Treating P as a piecewise-linear function, evaluates it at x.

LeftEvaluate (P :: NwtnPgon, x :: FldRatElt)

LeftEvaluate (P :: NwtnPgon, x :: RngIntElt)

-> FldRatElt

Evaluates the face of P to the left of x at x.

FactorialValuation (n :: RngIntElt, p :: RngIntElt)

-> RngIntElt

The p-adic valuation of n! (equivalent to Valuation(Factorial(n),p) but more efficient).

BinomialValuation (n :: RngIntElt, k :: RngIntElt, p :: RngIntElt)

-> RngIntElt

The p-adic valuation of n choose k.

UnitFactorial (F :: FldFin, n :: RngIntElt)

-> FldFinElt

The product of the integers up to n which are units in F. By Wilson’s formula, if n=kp+r this is (-1)^k * r!.

ShiftedFactorial (F :: FldFin, n :: RngIntElt)

-> FldFinElt

The product of the integers up to n shifted down to be units of F. This is the product of UnitFactorial(n div p^i) for all i.

ShiftedBinomial (F :: FldFin, n :: RngIntElt, k :: RngIntElt)

-> FldFinElt

The binomial coefficient n choose k shifted down to be a unit of F.