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rat

x:3;

rat((x-x^n)/(1-x)-n*x...

Calculate

rat

a_n: a_1+d*(n-1);

s_n: (a_1+a_n)/2*n;

rat(s_n/a_n^2);

Calculate

rat

i: 3;

n: 2^i;

rat((x-x^n)/(1-x)-n*x...

Calculate

rat

eq:(1+(k[2]+k[3])/d)*...

eq:rat(eq);

Calculate

rat-resultant

f: a*x^2+b*x+c;

g: y-(n1*x+n0)/(d1*x+...

r: rat(resultant(f,g,...

Calculate

rat

eq1: (x-x1)^2+(y-y1)^...

eq2: (x-x2)^2+(y-y2)^...

eq3: rat(eq1-eq2);

Calculate

rat

Ta: - (k1*Pa) * (Tb +...

Tb: - (k2*Pb) * (Ta +...

Tab: - (k4r*Pab) * (T...

Calculate

rat

n: 100000000;

k: 3;

rat((k+1)*n^k-n^(k+1)...

Calculate

rat

A:((x - 2*y)^4/(x^2 -...

rat (A, y, a);

Calculate

rat-remainder-resultant

A:u^4+p*u^2+q*u+r;

B:v^2+b-u*(c*v^2+e);

C:v^4+k*v+m;

Calculate

rat

Run Example
(%i1)n:4;
(%o1)                                  4
(%i2) m:m;
(%o2)                                  m
(%i3) subst([w=0],rat(diff((1+a*w+b*w^2)^m,w,n)));
       4  4        2        4   3        2       2         4   2
(%o3) a  m  + (12 a  b - 6 a ) m  + (12 b  - 36 a  b + 11 a ) m
                                                          2       2        4
                                                 + (- 12 b  + 24 a  b - 6 a ) m
(%i4) 
Run Example
n:2;
(%o1)                                  2
(%i2) m:m;
(%o2)                                  m
(%i3) subst([w=0],rat(diff(exp(a*w^2)^m,w,n)));
(%o3)                                2 a m
(%i4) 
Run Example
declare(m,integer);
(%o1)                                done
(%i2) factorial_expand:true;
(%o2)                                true
(%i3) epsilon(n,k):=(binomial(n,k)*gamma(3/2)/gamma(3/2-n+k)-(-1)^n*binomial(n-1,k-1)*n!/k!);
                                            3
                       binomial(n, k) gamma(-)
                                            2
(%o3) epsilon(n, k) := -----------------------
                                3
                          gamma(- - n + k)
                                2
                                                    n
                                               (- 1)  binomial(n - 1, k - 1) n!
                                             - --------------------------------
                                                              k!
(%i4) G(m):=-m*(4*m-3)/2;
                                    (- m) (4 m - 3)
(%o4)                       G(m) := ---------------
                                           2
(%i5) rat(epsilon(2*m,2*m-4)-G(m)*epsilon(2*m-1,2*m-4));
                8         7          6          5          4          3
(%o5)/R/ (1024 m  - 8704 m  + 30976 m  - 59680 m  + 67036 m  - 43756 m
                                                                 2
                                                        + 15309 m  - 2205 m)/96
(%i6) epsilon(4,1)-G(2)*epsilon(3,1);
                                      15
(%o6)                                 --
                                      4
(%i7) epsilon(2,1);
(%o7)                                 - 1
(%i8) epsilon(2,0);
                                        1
(%o8)                                 - -
                                        4
(%i9) 
[algebraic,carg,ev,expand,float,linsolve,numer,pi,polarform,rat,rhs,simp,true] [algebraic,carg,ev,expand,float,linsolve,numer,pi,rat,rhs,simp,true] [at,block,denom,float,mod,numer,rat,ratprint] [at,factor,rat] [at,rat,sqrt] [at,rat] [atan,beta,diff,ev,gamma,rat] [bftorat,block,delete,float,if,integerp,mod,rat,ratdenom,ratepsilon,ratprint] [binomial,ceiling,coeff,expand,rat,sum] [binomial,declare,expand,factorial_expand,gamma,rat,true] [binomial,floor,rat,sum] [coeff,expand,factor,rat,remainder,resultant,subst] [coeff,expand,factor,rat,remainder,resultant] [coeff,expand,factor,rat,resultant,solve,subst] [coeff,expand,factor,rat,resultant,solve] [coeff,expand,factor,rat,resultant] [coeff,expand,print,rat,sum] [coeff,expand,rat,remainder,resultant] [coeff,expand,rat,resultant,subst] [coeff,expand,rat,resultant] [coeff,factor,rat,remainder,resultant,subst] [coeff,factor,rat,remainder,resultant] [coeff,factor,rat,resultant,subst] [coeff,factor,rat,resultant] [coeff,rat,remainder,resultant] [coeff,rat,resultant] [coeff,rat] [determinant,expand,makelist,matrix,rat,solve] [diff,do,expand,gcd,print,rat] [diff,exp,gamma,plot2d,rat,rootscontract] [diff,expand,plot2d,rat,subst] [diff,rat,subst] [diff,rat] [display2d,false,rat] [disprule,false,grind,map,partfrac,properties,radexpand,rat,simp,tellsimp] [exp,rat] [expand,rat,round,sum] [expand,rat,subst,sum] [expand,rat,subst] [expand,rat,sum] [expand,rat] [fpprec,rat] [imagpart,rat,realpart] [inf,kill,limit,print,rat] [num,rat,rhs,solve,subst] [rat,remainder,resultant] [rat,resultant] [rat,solve] [rat,subst] [rat]

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