share/simplification/ineq.mac

   1 /* coded by LPH prior to MAY 12, 1983 */
   2 /* re-coded for DOE MACSYMA */
   3
   4 /* I made some changes so that ineq loads without       */
   5 /* asking for the sign of d. Mario Rodriguez, 30-4-2006 */
   6
   7 /*
   8 eval_when([translate,batch,demo,load,loadfile],
   9 matchdeclare([a,b],true,c,negp,d,posp),
  10 matchdeclare([e,f,g,h],freeof("<=",">=","<",">","=")));
  11 */
  12
  13
  14 matchdeclare([a,b],true,c,negp,d,posp)$
  15 matchdeclare([e,f,g,h],freeof("<=",">=","<",">","="))$
  16
  17 negp(u):=
  18    (mode_declare(u,any,function(negp),boolean),
  19     if asksign(u)='neg then true);
  20 posp(u):=
  21    (mode_declare(u,any,function(posp),boolean),
  22     if asksign(u)='pos then true);
  23 define_variable(?matchreverse,true,boolean);
  24
  25
  26 /*
  27 eval_when(translate,simp:false);
  28 */
  29
  30 simp:false$
  31 tellsimpafter((a<b)*c,a*c>b*c);
  32 tellsimpafter((a>b)*c,a*c<b*c);
  33 tellsimpafter(("<="(a,b))*c,">="(a*c,b*c));
  34 tellsimpafter((">="(a,b))*c,"<="(a*c,b*c));
  35 tellsimpafter((a<b)*d,a*d<b*d);
  36 tellsimpafter((a>b)*d,a*d>b*d);
  37 tellsimpafter(("<="(a,b))*d,"<="(a*d,b*d));
  38 tellsimpafter((">="(a,b))*d,">="(a*d,b*d));
  39
  40 tellsimpafter((a<b)+e,a+e<b+e);
  41 tellsimpafter(("<="(a,b))+e,"<="(a+e,b+e));
  42 tellsimpafter((a>b)+e,a+e>b+e);
  43 tellsimpafter((">="(a,b))+e,">="(a+e,b+e));
  44
  45 tellsimpafter((e<f)+(g<h),e+g<f+h);
  46 tellsimpafter((e<f)+("<="(g,h)),e+g<f+h);
  47 tellsimpafter(("<="(e,f))+("<="(g,h)),"<="(e+g,f+h));
  48 tellsimp((g<h)+(e=f),g+e<h+f);
  49 tellsimp(("<="(g,h))+(e=f),"<="(g+e,h+f));
  50 tellsimp((e=f)+(g<h),g+e<h+f);
  51 tellsimp((e=f)+("<="(g,h)),"<="(g+e,h+f));
  52 tellsimp((e=f)+(g>h),g+e>h+f);
  53 tellsimp((e=f)+(">="(g,h)),">="(g+e,h+f));
  54 tellsimp((g>h)+(e=f),g+e>h+f);
  55 tellsimp((">="(g,h))+(e=f),">="(g+e,h+f));
  56 tellsimpafter((e>f)+(g>h),e+g>f+h);
  57 tellsimpafter((e>f)+(">="(g,h)),e+g>f+h);
  58 tellsimpafter((">="(e,f))+(">="(g,h)),">="(e+g,f+h));
  59 simp:true$
  60
  61 /*
  62 eval_when(translate,simp:true);
  63 */