8. ÎÁÙÀß ÂÛÑØÀß ÌÀÒÅÌÀÒÈÊÀ (%i17) (%o17) (%i18) (%o18) remainder((x+1)*(x-1)2/(x3+1),x); 1 x2 − x + 1 quotient((x+1)*(x-1)2/(x3+1),x); x−2 x2 − x + 1 (%i19) (%o19) fa torout(a*u2*x2+2*a*u*x2+a*x2-a*u2-2*a*u-a,x); (%i20) (%o20) g fa tor(10); (%i21) (%o21) gfa tor(x4-1); (%i22) (%o22) lopow((x+y)2 + (x+y)a, x+y); 2 a u (x − 1) (x + 1) + 2 a u (x − 1) (x + 1) + a (x − 1) (x + 1) 2 (1 + %i) (1 + 2 %i) (2 + %i) (x − 1) (x + 1) (x − %i) (x + %i) min(2, a) Ïðè ïðèìåíåíèè óíêöèè polynomialp(p,L) ïðåäèêàò oeffp äîëæåí ïðèíèìàòü çíà÷åíèå true äëÿ êàæäîãî êîýèöèåíòà, à ïðåäèêàò exponp äëÿ âñåõ ïîêàçàòåëåé ñòåïåíè ïåðåìåííûõ â L. (%i23) (%o23) polynomialp((x-1)*(x+y), [x,y℄); (%i24) (%o24) polynomialp((x-1)*(x+y)a, [x,y℄); true false Äîïîëíèòåëüíûå âîçìîæíîñòè ðàáîòû ñ ïîëèíîìàìè îïðåäåëåíû â ðàìêàõ áàçèñîâ ðåáíåðà, óíêöèè äëÿ ðàáîòû ñ êîòîðûìè âêëþ÷åíû â ïàêåò grobner. (%i25) (%o25) denom(sin(x)/10* os(x)/y); (%i26) (%o26) partfra ((x5-3*x4+2*x3-x2+5*x-1)/(x5*(x3-1)),x); 10 y x+1 2 1 1 5 1 1 − − + − + + x2 + x + 1 x x2 x3 x4 x5 x−1 226