#Please do not post homework #James Betti, 2 Feb 2025, Assignment 1 AM := proc(G) local n,E,adj,i,e: n := G[1]; E := G[2]; adj := [[0$n]$n]; for e in E do adj[e[1]][e[2]] := 1; adj[e[2]][e[1]] := 1; od; adj; end: AM([2,{{1,2}}]); Image := proc(pi, G) local n,E,e: n := G[1]; E := G[2]; E := {seq({pi[e[1]],pi[e[2]]},e in E)}; [n, E]; end: # Below is some ``Maple V Primer'' scrap work. 105/25; 105/25-1/5; %+1/5; seq(sqrt(i),i=1..10); evalf(%); convert(%[2],rational); # changing to a float is irreversible 3*4^(1/2)+5; simplify(%); (x^2)^(1/2); simplify(%); assume(x>0); simplify(%%); x := 'x'; # remove assumption about x y := x^3+3*x^2+3*x+1; simplify(y^(1/3)); radsimp(y^(1/3)); assume(x>-1); # sometimes `simplify` needs some help simplify(y^(1/3)); assume(x<-1); simplify(y^(1/3)); x := 'x'; p := (x+y+1)*(x-y+1)*(x-y-1); q := expand(p); coeff(q,x,2); coeff(p,x,2); # not what we want, so be careful degree(q,x); x := 1: y := 2: p; x := 'x': y := 'y': p; # restoring variables also changes `p` eqn := x^2-x=1; R := solve(eqn,x); simplify(R[1]*R[2]); ifactor(5003266235067621177579); ithprime(1000000); eqn1 := x^3+a*x=14: eqn2 := a^2-x=7: isolve({eqn1,eqn2}); assign(%); # handy shortcut to put variables in scope a := 'a': b := 'b':