[Maxima-commits] CVS: maxima/doc/info solve_rec.texi,1.11,1.12

[Alexey B. <bes...@us...>]

Update of /cvsroot/maxima/maxima/doc/info
In directory 23jxhf1.ch3.sourceforge.com:/tmp/cvs-serv5554

Modified Files:
	solve_rec.texi 
Log Message:
@group stuff


Index: solve_rec.texi
===================================================================
RCS file: /cvsroot/maxima/maxima/doc/info/solve_rec.texi,v
retrieving revision 1.11
retrieving revision 1.12
diff -u -d -r1.11 -r1.12
--- solve_rec.texi	25 Feb 2008 10:12:23 -0000	1.11
+++ solve_rec.texi	31 Dec 2008 18:05:51 -0000	1.12
@@ -15,12 +15,14 @@
 
 @example
 (%i1) load("solve_rec")$
+@group
 (%i2) solve_rec((n+4)*s[n+2] + s[n+1] - (n+1)*s[n], s[n]);
                                     n
                  %k  (2 n + 3) (- 1)          %k
                    1                            2
 (%o2)       s  = -------------------- + ---------------
              n     (n + 1) (n + 2)      (n + 1) (n + 2)
+@end group
 @end example
 
 @opencatbox
@@ -38,15 +40,20 @@
 Example:
 
 @example
+@group
 (%i3) rec: x[n+2] = x[n+1] + x[n]/n;
                                       x
                                        n
 (%o3)               x      = x      + --
                      n + 2    n + 1   n
+@end group
+@group
 (%i4) solve_rec(rec, x[n]);
 WARNING: found some hypergeometrical solutions! 
 (%o4)                    x  = %k  n
                           n     1
+@end group
+@group
 (%i5) reduce_order(rec, n, x[n]);
 (%t5)                    x  = n %z
                           n       n
@@ -61,6 +68,8 @@
 
 (%o6)             (- n - 2) %u     - %u
                               n + 1     n
+@end group
+@group
 (%i6) solve_rec((n+2)*%u[n+1] + %u[n], %u[n]);
                                      n
                             %k  (- 1)
@@ -77,6 +86,7 @@
          2   /     (j + 1)!     1
              ====
              j = 0
+@end group
 @end example
 
 @opencatbox
@@ -110,6 +120,7 @@
 
 @example
 (%i1) load("simplify_sum")$
+@group
 (%i2) sum(binom(n+k,k)/2^k, k, 0, n)
                              + sum(binom(2*n, 2*k), k, 0, n);
          n                            n
@@ -119,11 +130,14 @@
         /               k            /
         ====           2             ====
         k = 0                        k = 0
+@end group
+@group
 (%i3) simplify_sum(%);
                                n
                               4     n
 (%o3)                         -- + 2
                               2
+@end group
 @end example
 
 @opencatbox
@@ -152,6 +166,7 @@
 Example of linear recurrence with constant coefficients:
 
 @example
+@group
 (%i2) solve_rec(a[n]=a[n-1]+a[n-2]+n/2^n, a[n]);
                         n          n
            (sqrt(5) - 1)  %k  (- 1)
@@ -165,37 +180,46 @@
                                  + ------------------ - ----
                                             n              n
                                            2            5 2
+@end group
 @end example
 
 Example of linear recurrence with polynomial coefficients:
 
 @example
+@group
 (%i7) 2*x*(x+1)*y[x] - (x^2+3*x-2)*y[x+1] + (x-1)*y[x+2];
                          2
 (%o7) (x - 1) y      - (x  + 3 x - 2) y      + 2 x (x + 1) y
                x + 2                   x + 1                x
+@end group
+@group
 (%i8) solve_rec(%, y[x], y[1]=1, y[3]=3);
                               x
                            3 2    x!
 (%o9)                 y  = ---- - --
                        x    4     2
+@end group
 @end example
 
 Example of Ricatti type recurrence:
 
 @example
+@group
 (%i2) x*y[x+1]*y[x] - y[x+1]/(x+2) + y[x]/(x-1) = 0;
                             y         y
                              x + 1     x
 (%o2)         x y  y      - ------ + ----- = 0
                  x  x + 1   x + 2    x - 1
+@end group
 (%i3) solve_rec(%, y[x], y[3]=5)$
+@group
 (%i4) ratsimp(minfactorial(factcomb(%)));
                                    3
                                30 x  - 30 x
 (%o4) y  = - -------------------------------------------------
        x        6      5       4       3       2
              5 x  - 3 x  - 25 x  + 15 x  + 20 x  - 12 x - 1584
+@end group
 @end example
 
 
@@ -218,16 +242,20 @@
 Example:
 
 @example
+@group
 (%i1) (x+4)*a[x+3] + (x+3)*a[x+2] - x*a[x+1] + (x^2-1)*a[x];
 (%o1)  (x + 4) a      + (x + 3) a      - x a
                 x + 3            x + 2      x + 1
                                                    2
                                                + (x  - 1) a
                                                             x
+@end group
+@group
 (%i2) solve_rec_rat(% = (x+2)/(x+1), a[x]);
                        1
 (%o2)      a  = ---------------
             x   (x - 1) (x + 1)
+@end group
 @end example
 
 
@@ -259,6 +287,7 @@
 Returns the recurrence sattisfied by the sum
 
 @example
+@group
      hi
     ====
     \
@@ -266,6 +295,7 @@
     /
     ====
   k = lo
+@end group
 @end example
 
 where summand is hypergeometrical in @var{k} and @var{n}. If @var{lo} and @var{hi}
@@ -278,18 +308,26 @@
 
 @example
 (%i1) load("simplify_sum")$
+@group
 (%i2) summand: binom(n,k);
 (%o2)                           binomial(n, k)
+@end group
+@group
 (%i3) summand_to_rec(summand,k,n);
 (%o3)                      2 sm  - sm      = 0
                                n     n + 1
+@end group
+@group
 (%i7) summand: binom(n, k)/(k+1);
                                 binomial(n, k)
 (%o7)                           --------------
                                     k + 1
+@end group
+@group
 (%i8) summand_to_rec(summand, [k, 0, n], n);
 (%o8)               2 (n + 1) sm  - (n + 2) sm      = - 1
                                 n             n + 1
+@end group
 @end example
 
 @opencatbox