src/rational/elem/cl_RA_mul.cc

   1 // binary operator *
   2
   3 // General includes.
   4 #include "cl_sysdep.h"
   5
   6 // Specification.
   7 #include "cl_rational.h"
   8
   9
  10 // Implementation.
  11
  12 #include "cl_RA.h"
  13 #include "cl_integer.h"
  14 #include "cl_I.h"
  15
  16 const cl_RA operator* (const cl_RA& r, const cl_RA& s)
  17 {
  18 // Methode (vgl. [Buchberger, Collins, Loos: Computer Algebra, S.201])
  19 // r,s beide Integers -> klar.
  20 // r=a/b, s=c ->
  21 //   Bei c=0 Ergebnis 0.
  22 //   g:=ggT(b,c).
  23 //   Falls g=1: Ergebnis (a*c)/b (mit b>1, ggT(a*c,b)=1).
  24 //   Sonst: b':=b/g, c':=c/g, Ergebnis (a*c')/b' (mit ggT(a*c',b')=1).
  25 // r=a, s=c/d analog.
  26 // r=a/b, s=c/d ->
  27 //   g:=ggT(a,d), h:=ggT(b,c).
  28 //   a':=a/g, d':=d/g (nur bei g>1 bedeutet das Rechnung).
  29 //   b':=b/h, c':=c/h (nur bei h>1 bedeutet das Rechnung).
  30 //   Ergebnis ist = (a'*c')/(b'*d').
  31         if (integerp(s)) {
  32                 // s Integer
  33                 DeclareType(cl_I,s);
  34                 if (integerp(r)) {
  35                         // beides Integer
  36                         DeclareType(cl_I,r);
  37                         return r*s;
  38                 } else {
  39                         DeclareType(cl_RT,r);
  40                         var const cl_I& a = numerator(r);
  41                         var const cl_I& b = denominator(r);
  42                         var const cl_I& c = s;
  43                         // r=a/b, s=c, bilde a/b * c.
  44                         if (zerop(c))
  45                                 { return 0; } // c=0 -> Ergebnis 0
  46                         var cl_I g = gcd(b,c);
  47                         if (eq(g,1))
  48                                 // g=1
  49                                 return I_I_to_RT(a*c,b); // (a*c)/b
  50                         else
  51                                 // g>1
  52                                 return I_I_to_RA(a*exquo(c,g),exquopos(b,g)); // (a*(c/g))/(b/g)
  53                 }
  54         } else {
  55                 // s ist Ratio
  56                 DeclareType(cl_RT,s);
  57                 if (integerp(r)) {
  58                         // r Integer
  59                         DeclareType(cl_I,r);
  60                         var const cl_I& a = r;
  61                         var const cl_I& b = numerator(s);
  62                         var const cl_I& c = denominator(s);
  63                         // r=a, s=b/c, bilde a * b/c.
  64                         if (zerop(a))
  65                                 { return 0; } // a=0 -> Ergebnis 0
  66                         var cl_I g = gcd(a,c);
  67                         if (eq(g,1))
  68                                 // g=1
  69                                 return I_I_to_RT(a*b,c); // (a*b)/c
  70                         else
  71                                 // g>1
  72                                 return I_I_to_RA(exquo(a,g)*b,exquopos(c,g)); // ((a/g)*b)/(c/g)
  73                 } else {
  74                         // r,s beide Ratios
  75                         DeclareType(cl_RT,r);
  76                         var const cl_I& a = numerator(r);
  77                         var const cl_I& b = denominator(r);
  78                         var const cl_I& c = numerator(s);
  79                         var const cl_I& d = denominator(s);
  80                         var cl_I ap, dp;
  81                         {
  82                                 var cl_I g = gcd(a,d);
  83                                 if (eq(g,1))
  84                                         { ap = a; dp = d; }
  85                                 else
  86                                         { ap = exquo(a,g); dp = exquopos(d,g); }
  87                         }
  88                         var cl_I cp, bp;
  89                         {
  90                                 var cl_I h = gcd(b,c);
  91                                 if (eq(h,1))
  92                                         { cp = c; bp = b; }
  93                                 else
  94                                         { cp = exquo(c,h); bp = exquopos(b,h); }
  95                         }
  96                         return I_I_to_RA(ap*cp,bp*dp); // (a'*c')/(b'*d')
  97                 }
  98         }
  99 }