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Online Algebra Calculator
Many of users do not use powerful Maxima computer algebra system for systematic work, but for ad hoc algebraic calculations – equations, functions, matrixes, etc. only. To do this job, it is not useful to download the whole application from a web site.
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ratsubst
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(%i1)Z0: (p1 - p2)/SE; p1 - p2 (%o1) ------- SE (%i2) Z1 : ratsubst(sqrt(p*(1-p)*((1/n1)+(1/n2))),SE,Z0); p2 - p1 (%o2) - ------------------------- 1 1 sqrt((-- + --) (1 - p) p) n2 n1 (%i3) Z2 : ratsubst((p1*n1+p2*n2)/(n1+n2),p,Z1); p2 - p1 (%o3) - -------------------------------------------------------------------- 2 2 2 2 n2 (p2 - p2) + n1 n2 ((2 p1 - 1) p2 - p1) + n1 (p1 - p1) sqrt(- ------------------------------------------------------------) 2 2 n1 n2 + n1 n2 (%i4) Z3 : ratsubst(x*p2,p1,Z2); (%o4) p2 x - p2 ----------------------------------------------------------------------------- 2 2 2 2 2 2 p2 (n1 x + 2 n1 n2 x + n2 ) + p2 (- n1 x + n1 n2 (- x - 1) - n2 ) sqrt(- ---------------------------------------------------------------------) 2 2 n1 n2 + n1 n2 (%i5) solve(Z3,x); (%o5) [x = 1] (%i6)
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eq: ratsubst(sin(a)^2,1-cos(a)^2,trigexpand(cos(9*a))); 8 6 4 (%o1) 256 cos(a) sin (a) - 448 cos(a) sin (a) + 240 cos(a) sin (a) 2 - 40 cos(a) sin (a) + cos(a) (%i2)
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k:0; (%o1) 0 (%i2) deg:8; (%o2) 8 (%i3) f(s,k,deg):=block([eq],eq:expand(sum(a[2*ii]*(s-s0)^(2*ii),ii,0,deg)),if k> 0 then ( eq: diff(eq,s,k) ),return(eq)); (%o3) f(s, k, deg) := block([eq], eq : 2 ii expand(sum(a (s - s0) , ii, 0, deg)), 2 ii if k > 0 then eq : diff(eq, s, k), return(eq)) (%i4) g(s,k,deg):=block([eq],eq:expand(sum((-s)^ii*sum(a[2*jj]*binomial(2*jj,ii)*s0^(2*jj-ii),jj,ceiling(ii/2),deg),ii,0,deg)),if k> 0 then ( eq: diff(eq,s,k) ),return(eq)); (%o4) g(s, k, deg) := block([eq], eq : ii 2 jj - ii ii expand(sum((- s) sum(a binomial(2 jj, ii) s0 , jj, ceiling(--), 2 jj 2 deg), ii, 0, deg)), if k > 0 then eq : diff(eq, s, k), return(eq)) (%i5) ff:ratsubst(0,s^(deg/2),f(s,k,deg)); 16 15 2 14 (%o5) a s0 - 16 a s s0 + (120 a s + a ) s0 16 16 16 14 3 13 2 12 + (- 560 a s - 14 a s) s0 + (91 a s + a ) s0 16 14 14 12 3 11 2 10 + (- 364 a s - 12 a s) s0 + (66 a s + a ) s0 14 12 12 10 3 9 2 8 + (- 220 a s - 10 a s) s0 + (45 a s + a ) s0 12 10 10 8 3 7 2 6 + (- 120 a s - 8 a s) s0 + (28 a s + a ) s0 10 8 8 6 3 5 2 4 3 3 + (- 56 a s - 6 a s) s0 + (15 a s + a ) s0 + (- 20 a s - 4 a s) s0 8 6 6 4 6 4 2 2 3 2 + (6 a s + a ) s0 + (- 4 a s - 2 a s) s0 + a s + a 4 2 4 2 2 0 (%i6) gg:ratsubst(0,s^(deg/2),g(s,k,deg)); 16 15 2 14 (%o6) a s0 - 16 a s s0 + (120 a s + a ) s0 16 16 16 14 3 13 2 12 + (- 560 a s - 14 a s) s0 + (91 a s + a ) s0 16 14 14 12 3 11 2 10 + (- 364 a s - 12 a s) s0 + (66 a s + a ) s0 14 12 12 10 3 9 2 8 + (- 220 a s - 10 a s) s0 + (45 a s + a ) s0 12 10 10 8 3 7 2 6 + (- 120 a s - 8 a s) s0 + (28 a s + a ) s0 10 8 8 6 3 5 2 4 3 3 + (- 56 a s - 6 a s) s0 + (15 a s + a ) s0 + (- 20 a s - 4 a s) s0 8 6 6 4 6 4 2 2 3 2 + (6 a s + a ) s0 + (- 4 a s - 2 a s) s0 + a s + a 4 2 4 2 2 0 (%i7) rat(ff-gg); (%o7)/R/ 0 (%i8)
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