Introduction to Polynomials Polynomials
(C1) ISLINEAR(EXP,VAR):=BLOCK([C], C:BOTHCOEF(RAT(EXP,VAR),VAR), IS(FREEOF(VAR,C) AND C[1]#0))$ (C2) ISLINEAR((R**2-(X-R)**2)/X,X); (D2) TRUE
(C1) COEFF(2*A*TAN(X)+TAN(X)+B=5*TAN(X)+3,TAN(X)); (D1) 2 A + 1 = 5 (C2) COEFF(Y+X*%E**X+1,X,0); (D2) Y + 1
(C1) CONTENT(2*X*Y+4*X**2*Y**2,Y); (D1) [2*X, 2*X*Y**2+Y].
(C1) DIVIDE(X+Y,X-Y,X); (D1) [1, 2 Y] (C2) DIVIDE(X+Y,X-Y); (D2) [ - 1, 2 X]
(Note that Y is the main variable in C2)
(C1) EXP1:2*X^2+Y*X+Z; 2 (D1) Z + X Y + 2 X (C2) EXP2:3*X+5*Y-Z-1; (D2) - Z + 5 Y + 3 X - 1 (C3) EXP3:Z^2+X-Y^2+5; 2 2 (D3) Z - Y + X + 5 (C4) ELIMINATE([EXP3,EXP2,EXP1],[Y,Z]); 8 7 6 5 4 (D3) [7425 X - 1170 X + 1299 X + 12076 X + 22887 X 3 2 - 5154 X - 1291 X + 7688 X + 15376]
(C1) (N+1)^B*N!^B; B B (D1) (N + 1) N! (C2) FACTCOMB(%);
(C1) (X+1)*((U+V)^2+A*(W+Z)^2),EXPAND; 2 2 2 2 (D1) A X Z + A Z + 2 A W X Z + 2 A W Z + A W X + V X 2 2 2 2 + 2 U V X + U X + A W + V + 2 U V + U (C2) FACTORSUM(%); 2 2 (D2) (X + 1) (A (Z + W) + (V + U) )
(C1) GFACTOR(X**4-1); (D1) (X - 1) (X + 1) (X + %I) (X - %I)
(C1) ((X-2*Y)**4/(X**2-4*Y**2)**2+1)*(Y+A)*(2*Y+X) /(4*Y**2+X**2); 4 (X - 2 Y) (Y + A) (2 Y + X) (------------ + 1) 2 2 2 (X - 4 Y ) (D1) ------------------------------------ 2 2 4 Y + X (C2) RAT(%,Y,A,X); 2 A + 2 Y (D2)/R/ --------- X + 2 Y
(C1) S:A*X+B*X+5$ (C2) RATCOEF(S,A+B); (D2) X
(C1) (4*X**3+10*X-11)/(X**5+5); 3 4 X + 10 X - 11 (D1) ---------------- 5 X (C2) MODULUS:3$ (C3) MOD(D1); 2 X + X - 1 (D3) -------------------- 4 3 2 X + X + X + X + 1 (C4) RATDIFF(D1,X); 5 4 3 X - X - X + X - 1 (D4) ------------------------------ 8 7 5 4 3 X - X + X - X + X - X + 1
(C1) RATEXPAND((2*X-3*Y)**3); 3 2 2 3 (D1) - 27 Y + 54 X Y - 36 X Y + 8 X (C2) (X-1)/(X+1)**2+1/(X-1); X - 1 1 (D2) -------- + ----- 2 X - 1 (X + 1) (C3) EXPAND(D2); X 1 1 (D3) ------------ - ------------ + ----- 2 2 X - 1 X + 2 X + 1 X + 2 X + 1 (C4) RATEXPAND(D2); 2 2 X 2 (D4) --------------- + --------------- 3 2 3 2 X + X - X - 1 X + X - X - 1
(C1) SIN(X/(X^2+X))=%E^((LOG(X)+1)**2-LOG(X)**2); 2 2 X (LOG(X) + 1) - LOG (X) (D1) SIN(------) = %E 2 X + X (C2) RATSIMP(%); 1 2 (D2) SIN(-----) = %E X X + 1 (C3) ((X-1)**(3/2)-(X+1)*SQRT(X-1))/SQRT((X-1)*(X+1)); 3/2 (X - 1) - SQRT(X - 1) (X + 1) (D3) -------------------------------- SQRT(X - 1) SQRT(X + 1) (C4) RATSIMP(%); 2 (D4) - ----------- SQRT(X + 1) (C5) X**(A+1/A),RATSIMPEXPONS:TRUE; 2 A + 1 ------ A (D5) X
(C5) RATWEIGHT(A,1,B,1); (D5) [[B, 1], [A, 1]] (C6) EXP1:RAT(A+B+1)$ (C7) %**2; 2 2 (D7)/R/ B + (2 A + 2) B + A + 2 A + 1 (C8) RATWTLVL:1$ (C9) EXP1**2; (D9)/R/ 2 B + 2 A + 1
Note: The RATFAC and RATWEIGHT schemes are incompatible and may not both be used at the same time.
KILL(...,RATWEIGHTS)
and
SAVE(...,RATWEIGHTS);
both work.
(C1) SQFR(4*X**4+4*X**3-3*X**2-4*X-1); 2 2 (D1) (X - 1) (2 X + 1)