 |
 |
Hello Johann, hello everybody, My solution is slower but simpler: maxterm1(u,n,x,c_,v_):=PROG( v_:=TERMS(EXPAND(u^n),x),c_:=SUBST(v_,x,1),v_ SUB POSITION(MAX(c_),c_) ) However, the result of maxterm1(4*x^3 + 3*x^2 + 2*x + 1,100) namely 39824366720341062302484823668460396313761926035630933326602206546298515593960~ 4195463780443664821745*x^200 is obtained in < 2 seconds. Best regards, Valeriu On 2/6/2007, "Johann Wiesenbauer" <[log in to unmask]> wrote: >Hi folks, > >Now that Josef Boehm is about to reissue the DNL #13, I had a look at R. >Schorn's problem on page 3, namely to compute the maximal coefficient of >the polynomial > >(4x^3+3x^2+2x+1)^20 > >Well, that was almost 13 years ago and it took Derive 387.2s then to find >the answer 8842311087597693745, which turns out to be the coefficient of x^40. > >Just to take into account the advances of both Derive and computers since >then, I would like to increase the exponent to say 100, and pose this as a >new challenge. (As there are vacations at the universities right now, I >thought, you might feel like a challenge!) In other words, what is the >maximal coefficient in the expansion of > >(4x^3+3x^2+2x+1)^100 > >and in which monomial does it occur? > >I for my part also got my teeth into this nice problem and just in case you >want to compare with my solution (in Derive 6.10), you will find it in the >attachment. > >Cheers, >Johann)