class QQt { // implements the ring QQ((t)) of formal Laurent series with // coefficients in QQ (=blackboard bold Q) in one variable/indeterminate constructor(r, N=0n, M=Infinity) { this.a=undefined this.r=undefined this.arr=[] N=BigInt(N) if (M<=N) M=Infinity if (M!=Infinity) M=BigInt(M) this.N=N this.M=M if (r instanceof Function) { this.r=r this.a=(n)=>{ if (n=M) return new QQ(0) else { n=BigInt(n)-this.N while (this.arr.length<=n) this.arr.push(r(this.arr)) return this.arr[n] } } // this.strip() } else if (r instanceof Array) { this.M=this.N+BigInt(r.length) for (let i=0; i{ n=BigInt(n)-N return (n>=0 && n{ n=BigInt(n)-N return (n>=0 && nthis.N+1n) this.M-=1n } } TeX(m=5n, t="t") { t="\\color{blue}" + t +"\\color{black}" m=(m>this.N)?BigInt(m):this.N+5n for (let n=this.arr.length; n0)?"+":"" s+=an.tex s+=(i==0)?"":t s+=(i==0||i==1)?"":"^{"+i+"}" } if (m{ n=BigInt(n) this.a(n).add(f.a(n)) } return sum } mult(f) { if (f.constructor!=QQt) return undefined let M=(this.M==Infinity || f.M==Infinity)?Infinity:this.M+f.M-1n let prod=new QQt(undefined, this.N+f.N, M) prod.a=(n)=>{ n=BigInt(n) if (nn-f.M)?this.N:(n-f.M+1n) for (let i=init; i=f.N; i++) x=x.add(this.a(i).mult(f.a(n-i))) return x } return prod } inverse() { // inverse = inverse wrt multiplication // not to be confused with inversion (inverse wrt substitution) return (new QQt([1])).div(this) } div(f) { return new QQt((arr)=>{ let n=BigInt(arr.length) let x=this.a(this.N+n) for (let i=1n; i<=n && f.N+i{ n=BigInt(n) return (n%k==0) ? this.a(n/k) : new QQ(0) } return foo } inversion() { return this } }