# Figurate Numbers v1.6.0 - Sonic Pi Web
# Source: https://github.com/edelveart/figurate_numbers
# Author: Edgar Delgado Vega
# Bundle: arith_transform

module FigurateNumbers;module ModNUtils;extend self;def n_power(n,power)n.pow(power);end;def mod_reduc(n,mod)n%mod;end;def q_residues(n,power,mod)mod_reduc(n_power(n,power),mod);end;def inversion(n,mod)inv=n*-1;mod_reduc(inv,mod);end;end;end;module FigurateNumbers;module PAdicUtils;extend self;def prime?(n)return false if n<2;return true if n==2;return false if n.even?;divisor=3;while divisor*divisor<=n;return false if(n%divisor).zero?;divisor+=2;end;true;end;def first_n_primes(n)return [] if n<=0;return [2] if n==1;primes=[2];candidate=3;while primes.length<n;primes<<candidate if prime?(candidate);candidate+=2;end;primes;end;def padic_valuation(base_ten_number,p)raise"#{p} is not a prime number" unless prime?(p);index=0;return index if base_ten_number<1;while base_ten_number%(p**index)==0
index+=1;end;index-1;end;def padic_norm(base_ten_number,p)return 0 if base_ten_number==0
power=padic_valuation(base_ten_number,p);1.0/p**power;end;def padic_expansion(base_ten_number,p,precision=11,reverse_trim=false)
inverse_limit_arr=[];(1...precision).each do |index|power=p**index;inverse_limits=((base_ten_number%power)+power)%power;inverse_limit_arr<<inverse_limits;end;p_adic_expansion_array=[inverse_limit_arr[0]];(0...(precision-2)).each do |index|a1=inverse_limit_arr[index+1];a0=inverse_limit_arr[index];power=p**(index+1);digits=(a1-a0)/power;p_adic_expansion_array<<digits;end;if reverse_trim;reversed=p_adic_expansion_array.reverse;first_nonzero_index=reversed.index{|digit|digit!=0}||0;reversed[first_nonzero_index..-1];else p_adic_expansion_array;end;end;end;end;module FigurateNumbers;module ArithTransform;extend self;def n_residue(n,pow,mod)ModNUtils.q_residues(n,pow,mod);end;def pc_inversion(n,mod)ModNUtils.inversion(n,mod);end;def padic_val(n,p)PAdicUtils.padic_valuation(n,p);end;def ring_padic_val(seq,p)seq.map do |delta|PAdicUtils.padic_valuation(delta,p);end;end;def padic_norm(n,p)PAdicUtils.padic_norm(n,p);end;def ring_padic_norm(seq,p)seq.map do |delta|PAdicUtils.padic_norm(delta,p);end;end;def padic_expansion(n,p,precision=11,reverse:false)PAdicUtils.padic_expansion(n,p,precision,reverse);end;def ring_padic_expansion(seq,p,precision=11,reverse:false)seq.map do |delta|PAdicUtils.padic_expansion(delta,p,precision,reverse);end;end;def figuratenomial(n,k,seq)Utils.figurate_binomial(n,k,seq);end;end;end;module FigurateNumbers;extend ArithTransform;end;ArithTransform=FigurateNumbers::ArithTransform