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Diff for /OpenXM/src/kan96xx/Kan/usage.sm1 between version 1.1.1.1 and 1.10

version 1.1.1.1, 1999/10/08 02:12:02 version 1.10, 2004/09/16 23:53:44
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   %% $OpenXM: OpenXM/src/kan96xx/Kan/usage.sm1,v 1.9 2004/09/11 01:00:42 takayama Exp $
 %% usage.sm1  %% usage.sm1
 %%  [(key word)  %%  [(key word)
 %%    [(   )  %%    [(   )
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    (The user cannot use the variable names h, e, H and E.)     (The user cannot use the variable names h, e, H and E.)
    (cf. show_ring, system_variable --- CurrentRing)     (cf. show_ring, system_variable --- CurrentRing)
    (    print_switch_status, switch_function)     (    print_switch_status, switch_function)
      (Example: [(x,y) ring_of_differential_operators [[(Dx) 1 (Dy) 1]])
      (           weight_vector 0] define_ring)
      (   Define the ring of differential operators Q<x,y,Dx,Dy> with the order)
      (   obtained by refining the partial order defined by the weight vector)
      (   [x,y,Dx,Dy] = [0,0,1,1] )
      (Example: [(x,y) ring_of_differential_operators 0 [(weightedHomogenization) 1]])
      (          define_ring )
      (Example: [(x,y) ring_of_differential_operators [[(x) -1 (Dx) 1]] weight_vector)
      (          0 [(degreeShift) [[1 0 1]]] ])
      (          define_ring )
    (Example: [(x,y,z) ring_of_differential_operators (Dx,Dy) elimination_order 0] define_ring)     (Example: [(x,y,z) ring_of_differential_operators (Dx,Dy) elimination_order 0] define_ring)
    (         Dx,Dy, and Dz are corresponding differential operators to the )     (         Dx,Dy, and Dz are corresponding differential operators to the )
    (         space variables x, y and z.)     (         space variables x, y and z.)
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 [(ring_of_difference_operators)  [(ring_of_difference_operators)
  [ (string ring_of_difference_operators)   [ (string ring_of_difference_operators)
      (!!! OBSOLETE !!!)
    (  )     (  )
    (This command has not been maintained since 1996. So, there may be)     (This command has not been maintained since 1996. So, there may be)
    (troubles if it is used with new features of kan/sm1.)     (troubles if it is used with new features of kan/sm1.)
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  ]   ]
 ] putUsages  ] putUsages
   
   [(ring_of_differential_difference_operators)
    [ ([string1 string2]  ring_of_differential_difference operators)
      (This command is used to define a ring of differential-difference operators )
      (with the macros define_ring, weight_vector and elimination_order.)
      (string1 is a set of variables for differential operators.)
      (string2 is a set of variables for difference operators.)
      (The user cannot use the variable names h, e, H and E.)
      (cf. show_ring, system_variable --- CurrentRing)
      (    print_switch_status, switch_function)
      (Example: [[(x,y) (s)] ring_of_differential_difference_operators )
      (          [[(Es) 1] [(s) 1]] weight_vector 0] define_ring)
      (         Dx and Dy are corresponding differential operators to the )
      (         space variables x and y.  Try show_ring to see the commutation)
      (         relations.)
    ]
   ] putUsages
   
 [(define_ring)  [(define_ring)
   [( [varlist ring_of_??? order characteristic options] define_ring)    [( [varlist ring_of_??? order characteristic options] define_ring)
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    (    <<ring_of_???>> ring_of_polynomials, ring_of_differential_operators, )     (    <<ring_of_???>> ring_of_polynomials, ring_of_differential_operators, )
    (    ring_of_difference_operators)     (    ring_of_difference_operators)
    (    <<order>> elimination_order, weight_vector)     (    <<order>> elimination_order, weight_vector)
    (    ring_def,ring , << ,, >>)     (    ring_def,ring , << __ >>)
   ]    ]
 ] putUsages  ] putUsages
   
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  [(string . polynomial)   [(string . polynomial)
   (Parse the string as a polynomial in the current ring and put it on the stack)    (Parse the string as a polynomial in the current ring and put it on the stack)
   (Example ( (x+2)^3 ) .)    (Example ( (x+2)^3 ) .)
     ({ commands }.  executes the commands.  << . >> is equivalent to exec.)
  ]   ]
 ] putUsages  ] putUsages
   
Line 245  def
Line 274  def
 [(join)  [(join)
  [(list1 list2 join list3)   [(list1 list2 join list3)
   (Ex.  [1 2] [3 [4 (ab)]] join  [1 2 3 [4 (ab)]])    (Ex.  [1 2] [3 [4 (ab)]] join  [1 2 3 [4 (ab)]])
     (Note: Join should use for arrays. It works for list too,)
     (      but it does not copy cells. cf. cons)
     (      So, it might generate looped lists or destroy other lists.)
  ]   ]
 ] putUsages  ] putUsages
   
Line 277  def
Line 309  def
  [(obj toVectors vec)   [(obj toVectors vec)
   (Convert the internal expression of vector into the array <<vec>>.)    (Convert the internal expression of vector into the array <<vec>>.)
   (obj can be  [n [g1 ... gm]] where n is the length of the vector.)    (obj can be  [n [g1 ... gm]] where n is the length of the vector.)
     $cf. [(toe_) array_of_poly] gbext $
   $Example 1: [(x) ring_of_polynomials 0] define_ring  $    $Example 1: [(x) ring_of_polynomials 0] define_ring  $
   $           (e_ + 2).  toVectors :: $    $           (e_ + 2).  toVectors :: $
   (        --->  [2  , 1] )    (        --->  [2  , 1] )
Legend:
Removed from v.1.1.1.1  
changed lines
  Added in v.1.10
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