Mathematica 2.0 for SPARC
Copyright 1988-91 Wolfram Research, Inc.
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In[1]:= <<Euclid.m
Package Euclid` loaded
0.166667 Second

In[2]:= <<Numbers.m

Quotient::shdw: Warning: Symbol Quotient appears in multiple contexts 
    {Numbers`, System`}; definitions in context Numbers`
     may shadow or be shadowed by other definitions.
Package Numbers` loaded
0.483333 Second

In[3]:= Euclid`ETrace[s__]:=Print[s]
0. Second

In[4]:= ContFractGeneric[a1_, a2_,quorem_, normunit_] returns the Euclidean 
   representation of a and b with respect to the function quorem[x_, y_],  that
   returns a list {q, r} such that x = q y + r, and the function  unitnorm[x_]
   that returns a list {y, u} such that x = u y with y the  unit-normalized x.
   The list returned is
  		 {q[[3]], u[[3]],..., q[[t+1]], u[[t+1]], a[[t]]}
  such that
  		 a[[i]] = q[[i+2]] a[[i+1]] + u[[i+2]] a[[i+2]],
  a[[i+2]] unit-normalized, for all 1 <= i <= t-1, a[[t+1]]==0.

In[4]:=                                     nu[x_]:=List[Abs[x], Sign[x] ]
0. Second

In[5]:= ContFractGeneric[314159, 100000, Numbers`QuotientRemainder, nu]
Quotient=3, Remainder=14159, Unit=1
Quotient=7, Remainder=887, Unit=1
Quotient=16, Remainder=33, Unit=-1
Quotient=27, Remainder=4, Unit=-1
Quotient=8, Remainder=1, Unit=1
Quotient=4, Remainder=0, Unit=0
0.0666667 Second

Out[5]= {3, 1, 7, 1, 16, -1, 27, -1, 8, 1, 4, 0, 1}

In[6]:= <<Polynom.m

Global`Modulus::shdw: 
   Warning: Symbol Modulus appears in multiple contexts {Global`, System`}
    ; definitions in context Global`
     may shadow or be shadowed by other definitions.
Package Polynom` loaded
0.333333 Second

In[7]:= f=RandomPoly[10, 1, x]
0.0333333 Second

              2    3    4    5    7    8    9
Out[7]= -1 - x  - x  - x  - x  - x  + x  + x

In[8]:= g=RandomPoly[9, 1, x]
0.0166667 Second

              2    3    5    6    8    9
Out[8]= -1 - x  + x  + x  + x  - x  - x

In[9]:= qr2[a_, b_]:=Map[Expand, {PolynomialQuotient[a, b, x], PolynomialRemainder[a, b, x]} ]
0.0166667 Second

In[10]:= ContFractGeneric[f, g, qr2, Function[List[#, 1] ] ]
                               2    4    6    7
Quotient=-1, Remainder=-2 - 2 x  - x  + x  - x , Unit=1
                    2                         2      3      4      5
Quotient=2 + 2 x + x , Remainder=3 + 4 x + 5 x  + 5 x  + 4 x  + 3 x , Unit=1
                        2                              2      3       4
           13    7 x   x               5    11 x   46 x    4 x    35 x
Quotient=-(--) + --- - --, Remainder=-(-) - ---- - ----- - ---- - -----, Unit=1
           27     9    3               9     27     27      27     27
                                                       2        3
           3456    81 x            351   1917 x   918 x    783 x
Quotient=-(----) - ----, Remainder=--- + ------ - ------ + ------, Unit=1
           1225     35             245    1225     1225     1225
                                                                  2
           1599850    42875 x            72275   149450 x   1225 x
Quotient=-(-------) - -------, Remainder=----- + -------- - -------, Unit=1
           613089      21141             22707    22707      2523
           24463008    1975509 x            195953   415454 x
Quotient=-(--------) - ---------, Remainder=------ + --------, Unit=1
           1500625      1500625              3675      3675
          93586478125    1500625 x               6030675
Quotient=------------- - ---------, Remainder=-(---------), Unit=1
         1553418235044   349396814              205234276
           40216272085028    85265400901304 x
Quotient=-(--------------) - ----------------, Remainder=0, Unit=1
            22162730625        22162730625
0.266667 Second

                                                 2
                            2       13    7 x   x        3456    81 x
Out[10]= {-1, 1, 2 + 2 x + x , 1, -(--) + --- - --, 1, -(----) - ----, 1, 
                                    27     9    3        1225     35
 
       1599850    42875 x       24463008    1975509 x
>    -(-------) - -------, 1, -(--------) - ---------, 1, 
       613089      21141        1500625      1500625
 
      93586478125    1500625 x       40216272085028    85265400901304 x
>    ------------- - ---------, 1, -(--------------) - ----------------, 1, 
     1553418235044   349396814        22162730625        22162730625
 
        6030675
>    -(---------)}
       205234276

In[11]:= nu2[a_]:=MonicLC[a, x]
0. Second

In[12]:= ContFractGeneric[f, g, qr2, nu2]
                              2    4    6    7
Quotient=-1, Remainder=2 + 2 x  + x  - x  + x , Unit=-1
                                               2      3      4
                     2                4 x   5 x    5 x    4 x     5
Quotient=-2 - 2 x - x , Remainder=1 + --- + ---- + ---- + ---- + x , Unit=3
                                       3     3      3      3
                                                 2      3
         13   7 x    2            3   11 x   46 x    4 x     4       35
Quotient=-- - --- + x , Remainder=- + ---- + ----- + ---- + x , Unit=--
         9     3                  7    35     35      35             27
                                            2
         128                65   71 x   34 x     3       261
Quotient=--- + x, Remainder=-- + ---- - ----- + x , Unit=----
         105                29    29     29              1225
         1306                  59    122 x    2       315
Quotient=---- + x, Remainder=-(--) - ----- + x , Unit=---
         1015                  9       9              841
         3232                233           14326
Quotient=---- + x, Remainder=--- + x, Unit=-----
         261                 494            81
           62365                         14769
Quotient=-(-----) + x, Remainder=1, Unit=------
           4446                          244036
         233
Quotient=--- + x, Remainder=0, Unit=1
         494
0.266667 Second

                              2     13   7 x    2  35  128      261   1306
Out[12]= {-1, -1, -2 - 2 x - x , 3, -- - --- + x , --, --- + x, ----, ---- + x, 
                                    9     3        27  105      1225  1015
 
     315  3232      14326    62365       14769   233
>    ---, ---- + x, -----, -(-----) + x, ------, --- + x, 1, 1}
     841  261        81      4446        244036  494

In[13]:=