V = [1,2,3]; f(V,x) = V[x]++; f(V,1) V f(~V,x) = V[x]++; f(~V,1) V L = List([1,2,3]); f(~L,x) = listput(~L,x^2); f(~L,5) L a.inc=a[1]++; V.inc V W=vector(1000,i,i!); f(x)=x[1]; g(~x)=x[1]; x.b = x[1]; default(timer,1); for(i=1,10^5,W[1]) for(i=1,10^5,f(W)) for(i=1,10^5,g(~W)) for(i=1,10^5,W.b) default(timer,0); T = y^2+y+1; p = 2; lift(polrootspadic(x^3-x^2+64*y, [T,p], 5)) qfbsolve(Qfb(1,0,1),65,0) qfbsolve(Qfb(1,0,1),65,1) qfbsolve(Qfb(1,0,1),65,2) qfbsolve(Qfb(1,0,1),65,3) qfbsolve(Qfb(1,0,1),20,0) qfbsolve(Qfb(1,0,1),20,1) qfbsolve(Qfb(1,0,1),20,2) qfbsolve(Qfb(1,0,1),20,3) M = matconcat([factor(12),factor(20)]~) F=matreduce(M) factorback(F) P = x^3+2*x^2+3*x+4; w = rootsof1(4) f = fft(w, P) apply(z->subst(P,x,z),w) fi = fftinv(w, f) Polrev(fi/#fi) w = powers(znprimroot(5),3) f = fft(w, P) apply(z->subst(P,x,z),w) fi = fftinv(w, f) lift(Polrev(fi/#fi)) serlaplace(1/cosh(t+O(t^10))) vector(10,i,eulerfrac(i)) eulervec(5) eulerpol(5) vector(4,i,eulerianpol(i)) f(n) = n! / (n^n * exp(-n) * sqrt(n)); asympnum(f) v = asympnumraw(f, 3) bestappr(v / v[1]) a = ffgen([3,5],'a); b = ffgen([3,10],'b); m = ffembed(a, b); mi= ffinvmap(m); R = ffmaprel(mi,b) minpoly(R) trace(R) norm(R) P = x^8+3*x^4+5; nfsubfields(P) nfsubfieldsmax(P) nfsubfieldscm(P) nfdiscfactors(x^3+3*x+7) nfbasis(x^3+3*x+7,&dK) dK a = 'a; nf = nfinit(a^3-2); idealismaximal(nf,7) idealismaximal(nf,5) id2 = idealprimedec(nf,2)[1]; id3 = idealprimedec(nf,3)[1]; idealdown(nf, idealmul(nf, id2, id3)) bnf=bnfinit(a^2+41); bnf.cyc P=bnrclassfield(bnf,,1) rnfdisc(bnf,P) bnf = bnfinit(x^2-nextprime(2^38), 1); sizebyte(bnf.fu) sizebyte(bnfunits(bnf)) ellheight(ellinit([1,3])) ellheight(ellinit([1,a],nfinit(a^2+1))) lfun(1,-7) lfun(-4,-8) lfun(5,-9) L = lfunshift(1,1); \\ zeta(s-1) lfun(L,1) M = lfunshift(1,1,1); \\ zeta(s)*zeta(s-1) lfun(M,2) G=znstar(7,1); chi=[2]; \\ cubic char of cond 7 V=[rootsof1(3)~,3]; r=sqrtn((-13-sqrt(-27))/14,6); \\ root number an(V)=n->vector(n,i,chareval(G,chi,i,V)); L=lfuncreate([an(V),1,[0],1,7,r]); lfuncheckfeq(L) localbitprec(256); lfuncheckfeq(L) F() = { my(V=[rootsof1(3)~,3]); my(r=sqrtn((-13-sqrt(-27))/14,6)); [an(V),1,[0],1,7,r]; } L = lfuncreate(F); lfuncheckfeq(L) localbitprec(256); lfuncheckfeq(L) G=znstar(17,1); C=[[1],[3],[5],[7]]; lfun([G,C],1) lfunrootres([G,C]) default(timer,1); localprec(1000); lfun([G,C],1); localprec(1000); [lfun([G,c],1)|c<-C]; default(timer,0); bnf = bnfinit(x^2+47); bnr = bnrinit(bnf,1); lfun([bnr,[[1],[2]]],1) find(a,b)= { forell(e,a,b, my(E=ellinit(e[1])); my(F=mffromell(E)[2]); my(Q=mfisetaquo(F)); if(Q,print(e[1],":",Q)),1); } find(1,100) print(strtime(12345678)) derivn((x*(1-x))^4,4) arity((x,y)->x^2+y^2) arity(sin) L=List([1,2,3]);L[1..2] L=List([1,2,3]);L[^1] svg=parplothexport("svg",x=1,10,1/gamma(x));