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Diff for /OpenXM/src/kan96xx/Kan/dr.sm1 between version 1.1 and 1.27

version 1.1, 1999/10/08 02:12:02 version 1.27, 2004/04/29 11:20:37
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   % $OpenXM: OpenXM/src/kan96xx/Kan/dr.sm1,v 1.26 2003/12/06 02:49:22 takayama Exp $
 %% dr.sm1 (Define Ring) 1994/9/25, 26  %% dr.sm1 (Define Ring) 1994/9/25, 26
 %% This file is error clean.  %% This file is error clean.
   
 @@@.quiet {   }  @@@.quiet {   }
 { (macro package : dr.sm1,   9/26,1995 --- Version 9/8, 1999. ) message } ifelse  { (macro package : dr.sm1,   9/26,1995 --- Version 12/10, 2000. ) message } ifelse
   
 /ctrlC-hook {  /ctrlC-hook {
 %%% define your own routing in case of error.  %%% define your own routing in case of error.
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   /arg1 set    /arg1 set
   [/vars /n /i /xList /dList /param] pushVariables    [/vars /n /i /xList /dList /param] pushVariables
   [    [
        (This is an obsolete macro. Use ring_of_differential_difference_operators)
         error
      (mmLarger) (matrix) switch_function       (mmLarger) (matrix) switch_function
      (mpMult)   (difference) switch_function       (mpMult)   (difference) switch_function
      (red@)     (module1) switch_function       (red@)     (module1) switch_function
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 } def  } def
   
   
   /ring_of_differential_difference_operators {
     /arg1 set
     [/vars /n /i /xList /dList /param /dvar /evar /vars2 ] pushVariables
     [
        /vars arg1 def
        vars tag 6 eq not {
          ( List is expected as the argument for ring_of_differential_difference_operators ) error
        } { } ifelse
        vars 0 get /dvar set
        vars 1 get /evar set
        (mmLarger) (matrix) switch_function
        (mpMult)   (difference) switch_function
        (red@)     (module1) switch_function
        (groebner) (standard) switch_function
        (isSameComponent) (x) switch_function
   
        [dvar to_records pop] /vars set %[x y z]
        vars reverse /xList set         %[z y x]
   
        [evar to_records pop] /vars2 set %[s1 s2]
   
        vars2 reverse  {@@@.Esymbol 2 1 roll 2 cat_n} map
        xList
        join /xList set   %[Es2 Es1 z y x]
   
        vars2 reverse
        vars {@@@.Dsymbol 2 1 roll 2 cat_n} map
        reverse join /dList set              %[s2 s1 Dz Dy Dx]
        [(H)] xList join [@@@.esymbol] join /xList set
        [(h)] dList join [@@@.Esymbol] join /dList set
        [0 1 1 << vars2 length 1 add >>  << xList length >>
           1 1 << vars2 length 1 add >> << xList length 1 sub >> ] /param set
        [ xList dList param ] /arg1 set
     ] pop
     popVariables
     arg1
   } def
   
 /reverse {  /reverse {
   /arg1 set    /arg1 set
   arg1 length 1 lt    arg1 length 1 lt
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   (type?) data_conversion  RationalFunctionP eq    (type?) data_conversion  RationalFunctionP eq
 } def  } def
   
   [(isRing)
    [(obj isRing bool) ]
   ] putUsages
   /isRing {
     (type?) data_conversion  RingP eq
   } def
   
 /toString.tmp {  /toString.tmp {
   /arg1 set    /arg1 set
   [/obj /fname] pushVariables    [/obj /fname] pushVariables
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     /obj arg1 def      /obj arg1 def
     obj isArray      obj isArray
     {      {
        ( [ )         [(LeftBracket)] system_variable %%( [ )
        obj {toString.tmp2} map /r set         obj {toString.tmp2} map /r set
        /n r length 1 sub def         /n r length 1 sub def
        [0 1  n  {         [0 1  n  {
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           ifelse            ifelse
         } for          } for
        ] aload length cat_n         ] aload length cat_n
        ( ] )         [(RightBracket)] system_variable %%( ] )
        3 cat_n         3 cat_n
      }       }
      {       {
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   /arg1 set    /arg1 set
   [/f /k /i /ans] pushVariables    [/f /k /i /ans] pushVariables
   [    [
      /ans (1).. def     /ans (1).. def
      [(QuoteMode)] system_variable {
        /f arg1 def   /k arg2 def
        [(ooPower) f k] extension /ans set
      } {
      /f arg1 def   /k arg2 ..int def       /f arg1 def   /k arg2 ..int def
      k 0 lt {       k 0 lt {
        1 1 << 0 k sub >> {         1 1 << 0 k sub >> {
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          /ans f ans {mul} sendmsg2 def           /ans f ans {mul} sendmsg2 def
        } for         } for
      } ifelse       } ifelse
      /arg1 ans def     } ifelse
      /arg1 ans def
   ] pop    ] pop
   popVariables    popVariables
   arg1    arg1
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Line 2327  newline
   
 /tolower.aux {  /tolower.aux {
   /arg1 set    /arg1 set
   arg1 64 gt  arg1 96 lt and    arg1 64 gt  arg1 91 lt and
   { arg1 32 add }    { arg1 32 add }
   { arg1 } ifelse    { arg1 } ifelse
 } def  } def
Line 2459  newline
Line 2511  newline
 [(ord_w)  [(ord_w)
  [(ff [v1 w1 v2 w2 ... vm wm] ord_w d)   [(ff [v1 w1 v2 w2 ... vm wm] ord_w d)
   (poly ff; string v1; integer w1; ...)    (poly ff; string v1; integer w1; ...)
   (order of ff by the weight vector [w1 w2 ...])    (order of the initial of ff by the weight vector [w1 w2 ...])
   (Example: [(x,y) ring_of_polynomials 0] define_ring )    (Example: [(x,y) ring_of_polynomials 0] define_ring )
   (          (x^2 y^3-x). [(x) 2 (y) 1] ord_w ::)    (          (x^2 y^3-x). [(x) 2 (y) 1] ord_w ::)
  ]   ]
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   arg1    arg1
 } def  } def
   
   [(ord_w_all)
    [(ff [v1 w1 v2 w2 ... vm wm] ord_w d)
     (poly ff; string v1; integer w1; ...)
     (order of ff by the weight vector [w1 w2 ...])
     (Example: [(x,y,t) ring_of_polynomials 0] define_ring )
     (          (x^2 y^3-x-t). [(t) 1 ] ord_w_all ::)
    ]
   ] putUsages
   /ord_w_all {
     /arg2 set /arg1 set
     [/ord_w_all-in /fff /fff-in /www /rrr /iii /ddd /zzz /ddd-tmp] pushVariables
     [
       /fff arg1 def
       /www arg2 def
       fff (0). eq { /ddd -intInfinity def /ord_w_all.LLL goto} { } ifelse
       /ddd -intInfinity def
       fff (ring) dc /rrr set
       /zzz (0) rrr ,, def
       fff init /fff-in set
       fff fff-in sub /fff set
       {
        /ddd-tmp 0 def
        0 2 www length 1 sub {
          /iii set
          fff-in << www iii get rrr ,, >> degree
          << www iii 1 add get >> mul
          ddd-tmp add /ddd-tmp set
        } for
        ddd-tmp ddd gt { /ddd ddd-tmp def }  {  } ifelse
        fff zzz eq { exit } {  } ifelse
        fff init /fff-in set
        fff fff-in sub /fff set
       } loop
       /ord_w_all.LLL
       /arg1 ddd def
     ] pop
     popVariables
     arg1
   } def
   
 [(laplace0)  [(laplace0)
  [   [
  (f [v1 ... vn] laplace0 g)   (f [v1 ... vn] laplace0 g)
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    arg1     arg1
 } def  } def
   
   /distraction2* {
     /arg1 set
     [/in-distraction2* /aa /f /vlist /xlist /dlist /slist ] pushVariables
     [(CurrentRingp)] pushEnv
     [
        /aa arg1 def
        /f aa 0 get def
        /vlist aa 1 get def
        /xlist aa 2 get def
        /dlist aa 3 get def
        /slist aa 4 get def
        vlist isArray
        {
           vlist { toString } map   /vlist set
        }
        {
           vlist toString to_records  /vlist set
         } ifelse
        xlist isArray
        {
           xlist { toString } map   /xlist set
        }
        {
           xlist toString to_records  /xlist set
         } ifelse
        slist isArray
        {
           slist { toString } map   /slist set
        }
        {
           slist toString to_records  /slist set
         } ifelse
        [vlist from_records ring_of_differential_operators 0] define_ring pop
        f toString .
        xlist { . } map
        dlist { toString . } map
        slist { toString . } map
        distraction2 /arg1 set
     ] pop
     popEnv
     popVariables
     arg1
   } def
   
 /message-quiet  {  /message-quiet  {
   @@@.quiet { pop } { message } ifelse    @@@.quiet { pop } { message } ifelse
 } def  } def
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 ]] putUsages  ]] putUsages
   
 /cancelCoeff {  /cancelCoeff {
     /arg1 set
     [(reduceContent) arg1] gbext 0 get
   } def
   /cancelCoeff_org {
  /arg1 set   /arg1 set
  [/in-cancelCoeff /ff /gg /dd /dd2] pushVariables   [/in-cancelCoeff /ff /gg /dd /dd2] pushVariables
  [  /ff arg1 def   [  /ff arg1 def
Line 3487  $ [ff ff] fromVectors :: $ 
Line 3627  $ [ff ff] fromVectors :: $ 
 [(nl)  [(nl)
 [(nl is the newline character.)  [(nl is the newline character.)
  $Example: [(You can break line) nl (here.)] cat message$   $Example: [(You can break line) nl (here.)] cat message$
   ]] putUsages
   
   /to_int {
     /arg1 set
     [/to-int /ob /ans] pushVariables
     [
       /ob arg1 def
       /ans ob def
       ob isArray {
         ob {to_int} map /ans set
         /LLL.to_int goto
       } {  } ifelse
       ob isInteger {
         ob (universalNumber) dc /ans set
         /LLL.to_int goto
       } {  } ifelse
       /LLL.to_int
       /arg1 ans def
     ] pop
     popVariables
     arg1
   } def
   [(to_int)
   [(obj to_int obj2)
    (All integers in obj are changed to universalNumber.)
    (Example: /ff [1 2 [(hello) (0).]] def  ff { tag } map ::)
    (         ff to_int { tag } map :: )
   ]] putUsages
   
   /define_ring_variables {
     [/in-define_ring_variables /drv._v /drv._p /drv._v0] pushVariables
   %% You cannot use these names for names for polynomials.
     [
        /drv._v getVariableNames def
        /drv._v0 drv._v def
        drv._v { dup /drv._p set (/) 2 1 roll ( $) drv._p ($. def ) } map cat
        /drv._v set
   %     drv._v message
        [(parse) drv._v] extension
     ] pop
     popVariables
   } def
   [(define_ring_variables)
   [(It binds  a variable <<a>> in the current ring to the sm1 variable <<a>>.)
    (For example, if x is a variable in the current ring, it defines the sm1)
    (variable x by /x (x) def)
   ]] putUsages
   
   /boundp {
     /arg1 set
     [/a /ans] pushVariables
     [
       /a arg1 def
       [(parse) [(/) a ( load tag 0 eq { /ans 0 def } )
                       (               { /ans 1 def } ifelse )] cat ] extension
       /arg1 ans def
     ] pop
     popVariables
     arg1
   } def
   [(boundp)
    [( a boundp b)
     (string a, b is 0 or 1.)
     (If the variable named << a >> is bounded to a value,)
     (it returns 1 else it returns 0.)
     $Example: (hoge) boundp ::$
   ]] putUsages
   [(isSubstr)
    [
     (s1 s2 isSubstr pos)
     (If s1 is a substring of s2, isSubstr returns the position in s2 from which)
     (s1 is contained in s2.)
     (If s1 is not a substring of s2, then isSubstr returns -1.)
    ]
   ] putUsages
   /isSubstr {
     /arg2 set /arg1 set
     [/in-isSubstr /s1 /s2 /i1 /i2 /n1 /n2
      /ans /flg
     ]  pushVariables
     [
       /s1 arg1 def
       /s2 arg2 def
       s1 (array) dc /s1 set
       s2 (array) dc /s2 set
       /n1 s1 length def
       /n2 s2 length def
       /ans -1 def
       0 1 n2 n1 sub {
         /i2 set
         /flg 1 def
         0 1 n1 1 sub {
           /i1 set
           s1 i1 get s2 i2 i1 add get eq {
           } {
             /flg 0 def exit
           } ifelse
         } for
         flg {
           /ans i2 def
           /isSubstr.L2 goto
         } { /ans -1 def } ifelse
       } for
       /isSubstr.L2
       /arg1 ans def
     ] pop
     popVariables
     arg1
   } def
   
   [(execve)
    [
      (command execve)
      ([arg0 arg1 arg2 ...] execve )
      (It executes the command by the system call execve.)
      (cf. system, forkExec)
    ]
   ] putUsages
   
   /execve {
     /execve.arg set
     [(forkExec) execve.arg [ ] 1] extension
   } def
   
   [(beginEcart)
    [
      (beginEcart)
      (Set the environments for the ecart division algorithm.)
    ]
   ] putUsages
   
   /ecart.debug_reduction1 0 def
   /beginEcart {
     (red@) (ecart) switch_function
     [(Ecart) 1] system_variable
     [(CheckHomogenization) 0] system_variable
     [(ReduceLowerTerms) 0] system_variable
     [(AutoReduce) 0] system_variable
     [(EcartAutomaticHomogenization) 0] system_variable
     ecart.debug_reduction1 {
       (red@) (debug) switch_function
     } {  } ifelse
   } def
   
   [(endEcart)
    [
      (endEcart)
      (End of using the ecart division algorithm.)
    ]
   ] putUsages
   
   /endEcart {
     (red@) (standard) switch_function
     [(Ecart) 0] system_variable
     [(degreeShift) (reset)] homogenize pop
   } def
   
   /ord_ws_all {
     /arg2 set /arg1 set
     [(ord_ws_all) arg1 arg2] gbext
   } def
   [(ord_ws_all)
    [
      (fv wv ord_ws_all degree)
      (  ord_ws_all returns the ord with respect to the weight vector wv.)
      $Example: [(x,y) ring_of_differential_operators 0] define_ring  $
      $        (Dx^2+x*Dx*Dy+2). [(Dx) 1 (Dy) 1] weightv ord_ws_all ::  $
      (  )
      (fv [wv shiftv] ord_ws_all degree)
      (  ord_ws_all returns the ord with respect to the weight vector wv and)
      (  the shift vector shiftv.)
      $Example: [(x,y) ring_of_differential_operators 0] define_ring  $
      $        [(Dx^2+x*Dx*Dy+2). (Dx).] [[(Dx) 1 (Dy) 1] weightv [0 2]] ord_ws_all ::$
      (  )
      (cf: init, gbext.   Obsolete: ord_w, ord_w_all)
    ]
   ] putUsages
   
   [(newVector)
    [( n newVector vec)
   ]] putUsages
   /newVector {
     /arg1 set
     [/in-newVector /n] pushVariables
     [
       /n arg1 def
       [(newVector) n] extension /arg1 set
     ] pop
     popVariables
     arg1
   } def
   
   [(newMatrix)
    [( [m n] newMatrix mat)
   ]] putUsages
   /newMatrix {
     /arg1 set
     [/in-newMatrix /n] pushVariables
     [
       /n arg1 def
       [(newMatrix) n 0 get n 1 get] extension /arg1 set
     ] pop
     popVariables
     arg1
   } def
   
   /addStdoutStderr {
     [(>) (stringOut://@@@stdout) (2>) (stringOut://@@@stderr)] join
   } def
   
   [(,,,)
   [(reparse a polynomial or polynomials)]
   ] putUsages
   /,,, {
     /arg1 set
     [/in-reparse /ff] pushVariables
     [
       /ff arg1 def
       ff tag 6 eq {
         ff { ,,, } map /arg1 set
       } {
         ff toString . /arg1 set
       } ifelse
     ] pop
     popVariables
     arg1
   } def
   
   /usages {
     /arg1 set
     [/name /flag /n /k /slist /m /i /sss] pushVariables
     [
       /name arg1 def
       /flag true def
   
    %BUG: should use regular expression in a future.
    name tag 1 eq {
      @.usages { 0 get } map shell { (, ) nl } map /sss set
    } {
   
       /sss [ ] def
      @.usages length /n set
      0 1 << n 1 sub >>
      {
         /k set
         name << @.usages k get 0 get >> eq
         {
           /slist @.usages k get 1 get def
           /m slist length def
           0 1 << m 1 sub >> {
             /i set
             sss slist i get append nl append /sss set
           } for
           /flag false def
         }
         { }
         ifelse
      } for
   
      %BUG:  cannot get usages of primitives.
      flag
      {name Usage  /sss [(Usage of ) name ( could not obtained.) nl ] def}
      { }
      ifelse
    } ifelse
      /arg1 sss cat def
      ] pop
      popVariables
      arg1
   } def
   [(usages)
    [(key usages usages-as-a-string)
     (num usages list-of-key-words)
 ]] putUsages  ]] putUsages
   
 ;  ;
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  Added in v.1.27
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