===================================================================
RCS file: /home/cvs/OpenXM/src/kan96xx/Kan/dr.sm1,v
retrieving revision 1.1.1.1
retrieving revision 1.36
diff -u -p -r1.1.1.1 -r1.36
--- OpenXM/src/kan96xx/Kan/dr.sm1 1999/10/08 02:12:02 1.1.1.1
+++ OpenXM/src/kan96xx/Kan/dr.sm1 2004/09/09 11:42:22 1.36
@@ -1,8 +1,9 @@
+% $OpenXM: OpenXM/src/kan96xx/Kan/dr.sm1,v 1.35 2004/09/09 03:14:46 takayama Exp $
%% dr.sm1 (Define Ring) 1994/9/25, 26
%% This file is error clean.
@@@.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 {
%%% define your own routing in case of error.
@@ -49,7 +50,7 @@
} for
] /dList set
- [(H)] xList join [@@@.esymbol] join /xList set
+ [@@@.Hsymbol] xList join [@@@.esymbol] join /xList set
[(h)] dList join [@@@.Esymbol] join /dList set
[0 %% dummy characteristic
<< xList length >> << xList length >> << xList length >>
@@ -166,7 +167,7 @@
vars reverse /xList set %[z y x]
vars {@@@.Dsymbol 2 1 roll 2 cat_n} map
reverse /dList set %[Dz Dy Dx]
- [(H)] xList join [@@@.esymbol] join /xList set
+ [@@@.Hsymbol] xList join [@@@.esymbol] join /xList set
[(h)] dList join [@@@.Esymbol] join /dList set
[0 1 1 1 << xList length >>
1 1 1 << xList length 1 sub >> ] /param set
@@ -256,6 +257,8 @@
/arg1 set
[/vars /n /i /xList /dList /param] pushVariables
[
+ (This is an obsolete macro. Use ring_of_differential_difference_operators)
+ error
(mmLarger) (matrix) switch_function
(mpMult) (difference) switch_function
(red@) (module1) switch_function
@@ -266,7 +269,7 @@
vars reverse /xList set %[z y x]
vars {@@@.diffEsymbol 2 1 roll 2 cat_n} map
reverse /dList set %[Dz Dy Dx]
- [(H)] xList join [@@@.esymbol] join /xList set
+ [@@@.Hsymbol] xList join [@@@.esymbol] join /xList set
[(h)] dList join [@@@.Esymbol] join /dList set
[0 1 1 << xList length >> << xList length >>
1 1 << xList length 1 sub >> << xList length >> ] /param set
@@ -277,7 +280,44 @@
} 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]
+ [@@@.Hsymbol] 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 {
/arg1 set
arg1 length 1 lt
@@ -321,6 +361,8 @@
[
/mat arg1 def
/m mat length def
+ {
+ m 0 eq { /ans [ ] def exit } { } ifelse
mat 0 get isArray
{ }
{ (transpose: Argument must be an array of arrays.) error }
@@ -334,6 +376,8 @@
ans [ j i ] << mat i get j get >> put
} for
} for
+ exit
+ } loop
/arg1 ans def
] pop
popVariables
@@ -1288,6 +1332,7 @@
/univ vars 0 get reverse
vars 1 get reverse join
def
+ w-vectors to_int32 /w-vectors set
[
0 1 << w-vectors length 1 sub >>
{
@@ -1310,7 +1355,8 @@
/arg2 set /arg1 set
[/univ /www /k /vname /vweight /ans] pushVariables
/univ arg1 def /www arg2 def
- [
+ [
+ www to_int32 /www set
/ans << univ length >> -1 0 evecw def
0 2 << www length 2 sub >>
{
@@ -1473,6 +1519,13 @@
(type?) data_conversion RationalFunctionP eq
} def
+[(isRing)
+ [(obj isRing bool) ]
+] putUsages
+/isRing {
+ (type?) data_conversion RingP eq
+} def
+
/toString.tmp {
/arg1 set
[/obj /fname] pushVariables
@@ -1527,7 +1580,7 @@
/obj arg1 def
obj isArray
{
- ( [ )
+ [(LeftBracket)] system_variable %%( [ )
obj {toString.tmp2} map /r set
/n r length 1 sub def
[0 1 n {
@@ -1539,7 +1592,7 @@
ifelse
} for
] aload length cat_n
- ( ] )
+ [(RightBracket)] system_variable %%( ] )
3 cat_n
}
{
@@ -1719,7 +1772,11 @@
/arg1 set
[/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
k 0 lt {
1 1 << 0 k sub >> {
@@ -1732,7 +1789,8 @@
/ans f ans {mul} sendmsg2 def
} for
} ifelse
- /arg1 ans def
+ } ifelse
+ /arg1 ans def
] pop
popVariables
arg1
@@ -1871,8 +1929,8 @@ newline
} def
%%end of function
-/rest { % returns remainder of a given list
- [ 2 1 roll aload length -1 roll pop ]
+/rest {
+ /arg1 set [(Krest) arg1] extension
} def
[(rest)
[(array rest the-rest-of-the-array)
@@ -2275,7 +2333,7 @@ newline
/tolower.aux {
/arg1 set
- arg1 64 gt arg1 96 lt and
+ arg1 64 gt arg1 91 lt and
{ arg1 32 add }
{ arg1 } ifelse
} def
@@ -2459,7 +2517,7 @@ newline
[(ord_w)
[(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 ...])
+ (order of the initial of ff by the weight vector [w1 w2 ...])
(Example: [(x,y) ring_of_polynomials 0] define_ring )
( (x^2 y^3-x). [(x) 2 (y) 1] ord_w ::)
]
@@ -2470,6 +2528,7 @@ newline
[
/fff arg1 def
/www arg2 def
+ www to_int32 /www set
fff (0). eq { /ddd -intInfinity def /ord_w.LLL goto} { } ifelse
fff (ring) dc /rrr set
fff init /fff set
@@ -2487,6 +2546,47 @@ newline
arg1
} 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
+ www to_int32 /www set
+ 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)
[
(f [v1 ... vn] laplace0 g)
@@ -2675,6 +2775,7 @@ newline
[/in-ngcd /nlist /g.ngcd /ans] pushVariables
[
/nlist arg1 def
+ nlist to_univNum /nlist set
nlist length 2 lt
{ /ans nlist 0 get def /L.ngcd goto }
{
@@ -3027,6 +3128,50 @@ newline
arg1
} 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 {
@@@.quiet { pop } { message } ifelse
} def
@@ -3191,6 +3336,10 @@ newline
]] putUsages
/cancelCoeff {
+ /arg1 set
+ [(reduceContent) arg1] gbext 0 get
+} def
+/cancelCoeff_org {
/arg1 set
[/in-cancelCoeff /ff /gg /dd /dd2] pushVariables
[ /ff arg1 def
@@ -3487,6 +3636,618 @@ $ [ff ff] fromVectors :: $
[(nl)
[(nl is the newline character.)
$Example: [(You can break line) nl (here.)] cat message$
+]] 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
+
+/to_int32 {
+ /arg1 set
+ [/to-int32 /ob /ans] pushVariables
+ [
+ /ob arg1 def
+ /ans ob def
+ ob isArray {
+ ob {to_int32} map /ans set
+ /LLL.to_int32 goto
+ } { } ifelse
+ ob isUniversalNumber {
+ ob (integer) dc /ans set
+ /LLL.to_int32 goto
+ } { } ifelse
+ /LLL.to_int32
+ /arg1 ans def
+ ] pop
+ popVariables
+ arg1
+} def
+[(to_int32)
+[(obj to_int32 obj2)
+ $All universalNumber in obj are changed to integer (int32).$
+ (Example: /ff [1 (2).. [(hello) (0).]] def ff { tag } map ::)
+ ( ff to_int32 { tag } map :: )
+ (cf. to_int, to_univNum )
+]] 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 <> in the current ring to the sm1 variable <>.)
+ (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
+
+/to_univNum {
+ /arg1 set
+ [/rr ] pushVariables
+ [
+ /rr arg1 def
+ rr isArray {
+ rr { to_univNum } map /rr set
+ } {
+ } ifelse
+ rr isInteger {
+ rr (universalNumber) dc /rr set
+ } {
+ } ifelse
+ /arg1 rr def
+ ] pop
+ popVariables
+ arg1
+} def
+[(to_univNum)
+[(obj to_univNum obj2)
+ (Example. [ 2 (3).. ] to_univNum)
+ $cf. to_int32. (to_int)$
+]] putUsages
+
+[(lcm)
+ [ ([a b c ...] lcm r)
+ (cf. polylcm, mpzext)
+ ]
+] putUsages
+/lcm {
+ /arg1 set
+ [/aa /bb /rr /pp /i] pushVariables
+ [
+ /aa arg1 def
+ /rr (1).. def
+ /pp 0 def % isPolynomial array?
+ 0 1 aa length 1 sub {
+ /i set
+ aa i get isPolynomial {
+ /pp 1 def
+ exit
+ } { } ifelse
+ } for
+
+ 0 1 aa length 1 sub {
+ /i set
+ pp {
+ [rr aa i get] polylcm /rr set
+ } {
+ [(lcm) rr aa i get ] mpzext /rr set
+ } ifelse
+ } for
+
+ /arg1 rr def
+ ] pop
+ popVariables
+ arg1
+} def
+[(gcd)
+ [ ([a b c ...] gcd r)
+ (cf. polygcd, mpzext)
+ ]
+] putUsages
+/gcd {
+ /arg1 set
+ [/aa /bb /rr /pp /i] pushVariables
+ [
+ /aa arg1 def
+ /rr (1).. def
+ /pp 0 def % isPolynomial array?
+ 0 1 aa length 1 sub {
+ /i set
+ aa i get isPolynomial {
+ /pp 1 def
+ /rr aa i get def
+ exit
+ } { } ifelse
+ } for
+
+ pp {
+ 0 1 aa length 1 sub {
+ /i set
+ [rr aa i get] polygcd /rr set
+ } for
+ } {
+ aa ngcd /rr set
+ } ifelse
+
+ /arg1 rr def
+ ] pop
+ popVariables
+ arg1
+} def
+
+[(denominator)
+ [ ([a b c ...] denominator r)
+ ( a denominator r )
+ (cf. dc, numerator)
+ (Output is Z or a polynomial.)
+ ]
+] putUsages
+% test data.
+% [(1).. (2).. div (1).. (3).. div ] denominator
+% [(2).. (3).. (4).. ] denominator
+/denominator {
+ /arg1 set
+ [/pp /dd /ii /rr] pushVariables
+ [
+ /pp arg1 def
+ pp to_univNum /pp set
+ {
+ pp isArray {
+ pp { denominator } map /dd set
+ /rr dd lcm def % rr = lcm(dd[0], dd[1], ... )
+ rr /dd set
+ exit
+ } { } ifelse
+
+ pp (denominator) dc /dd set
+ exit
+
+ } loop
+ /arg1 dd def
+ ] pop
+ popVariables
+ arg1
+} def
+
+[(numerator)
+ [ ([a b c ...] numerator r)
+ ( a numerator r )
+ (cf. dc, denominator)
+ (Output is a list of Z or polynomials.)
+ ]
+] putUsages
+% test data.
+/numerator {
+ /arg1 set
+ [/pp /dd /ii /rr] pushVariables
+ [
+ /pp arg1 def
+ pp to_univNum /pp set
+ {
+ pp isArray {
+ pp denominator /dd set
+ pp dd mul /rr set
+ rr cancel /rr set
+ exit
+ } { } ifelse
+
+ pp (numerator) dc /rr set
+ exit
+
+ } loop
+ /arg1 rr def
+ ] pop
+ popVariables
+ arg1
+} def
+
+/cancel.Q {
+ /arg1 set
+ [/aa /rr /nn /dd /gg] pushVariables
+ [
+ /aa arg1 def
+ {
+ aa isRational {
+ [(cancel) aa] mpzext /rr set
+ rr (denominator) dc (1).. eq {
+ /rr rr (numerator) dc def
+ exit
+ } { } ifelse
+ rr (denominator) dc (-1).. eq {
+ /rr rr (numerator) dc (-1).. mul def
+ } { } ifelse
+ exit
+ } { } ifelse
+
+ /rr aa def
+ exit
+ } loop
+ /arg1 rr def
+ ] pop
+ popVariables
+ arg1
+} def
+
+/cancel.one {
+ /arg1 set
+ [/aa /rr /nn /dd /gg] pushVariables
+ [
+ /aa arg1 def
+ {
+ aa isRational {
+ aa (numerator) dc /nn set
+ aa (denominator) dc /dd set
+ nn isUniversalNumber dd isUniversalNumber and {
+ /rr aa cancel.Q def
+ exit
+ } { (cancel: not implemented) error } ifelse
+ } { } ifelse
+
+ /rr aa def
+ exit
+ } loop
+ /arg1 rr def
+ ] pop
+ popVariables
+ arg1
+} def
+
+[(cancel)
+ [ (obj cancel r)
+ (Cancel numerators and denominators)
+ (The implementation has not yet been completed. It works only for Q.)
+]] putUsages
+/cancel {
+ /arg1 set
+ [/aa /rr] pushVariables
+ [
+ /aa arg1 def
+ aa isArray {
+ aa {cancel} map /rr set
+ } {
+ aa cancel.one /rr set
+ } ifelse
+ /arg1 rr def
+ ] pop
+ popVariables
+ arg1
+} def
+
+/nnormalize_vec {
+ /arg1 set
+ [/pp /rr /dd ] pushVariables
+ [
+ /pp arg1 def
+ pp denominator /dd set
+ dd (0).. lt { (nnormalize_vec: internal error) error } { } ifelse
+ pp numerator dd mul cancel /pp set
+ /@@@.nnormalize_vec_c dd def
+ pp gcd /dd set
+ dd (0).. lt { (nnormalize_vec: internal error) error } { } ifelse
+ pp (1).. dd div mul cancel /rr set
+ @@@.nnormalize_vec_c dd div cancel /@@@.nnormalize_vec_c set
+ /arg1 rr def
+ ] pop
+ popVariables
+ arg1
+} def
+[(nnormalize_vec)
+[(pp nnormalize_vec npp)
+ (It normalizes a given vector of Q into a vector of Z with relatively prime)
+ (entries by multiplying a postive number.)
+]] putUsages
+
+/getNode {
+ /arg2 set
+ /arg1 set
+ [/in-getNode /ob /key /rr /rr /ii] pushVariables
+ [
+ /ob arg1 def
+ /key arg2 def
+ /rr null def
+ {
+ ob isClass {
+ ob (array) dc /ob set
+ } { exit } ifelse
+ ob 0 get key eq {
+ /rr ob def
+ exit
+ } { } ifelse
+ ob 2 get /ob set
+ 0 1 ob length 1 sub {
+ /ii set
+ ob ii get key getNode /rr set
+ rr tag 0 eq { } { exit } ifelse
+ } for
+ exit
+ } loop
+ /arg1 rr def
+ ] pop
+ popVariables
+ arg1
+} def
+[(getNode)
+[(ob key getNode)
+ (ob is a class object.)
+ (The operator getNode returns the node with the key in ob.)
+ (The node is an array of the format [key attr-list node-list])
+ (Example:)
+ ( /dog [(dog) [[(legs) 4] ] [ ]] [(class) (tree)] dc def)
+ ( /man [(man) [[(legs) 2] ] [ ]] [(class) (tree)] dc def)
+ ( /ma [(mammal) [ ] [man dog]] [(class) (tree)] dc def)
+ ( ma (dog) getNode )
+]] putUsages
+
+/cons {
+ /arg2 set /arg1 set
+ [/aa /bb] pushVariables
+ [
+ /aa arg1 def /bb arg2 def
+ [aa] (list) dc bb join /arg1 set
+ ] pop
+ popVariables
+ arg1
+} def
+[(cons)
+[(obj list cons list)
+]] putUsages
+
+/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
;