===================================================================
RCS file: /home/cvs/OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave,v
retrieving revision 1.14
retrieving revision 1.18
diff -u -p -r1.14 -r1.18
--- OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave	2004/03/05 15:30:50	1.14
+++ OpenXM/src/asir-contrib/packages/doc/Attic/sm1.oxweave	2004/05/28 01:22:13	1.18
@@ -1,9 +1,9 @@
-/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.13 2003/07/28 01:36:36 takayama Exp $ */
+/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.17 2004/05/14 01:25:03 takayama Exp $ */
 
-/*&C-texi
+/*&C
 @c DO NOT EDIT THIS FILE   oxphc.texi
 */
-/*&C-texi
+/*&C
 @node SM1 Functions,,, Top
 
 */
@@ -68,7 +68,7 @@ Hence, the dimension of the first de Rham cohomology g
 cohomology groups.
 @end tex
 */
-/*&C-texi
+/*&C
 @example
 
 @include opening.texi
@@ -77,7 +77,7 @@ cohomology groups.
 [1,2]
 @end example
 */
-/*&C-texi
+/*&C
 @noindent
 The author of @code{sm1} : Nobuki Takayama, @code{takayama@@math.sci.kobe-u.ac.jp} @*
 The author of sm1 packages : Toshinori Oaku, @code{oaku@@twcu.ac.jp} @*
@@ -87,7 +87,7 @@ Grobner Deformations of Hypergeometric Differential Eq
 See the appendix.
 */
 
-/*&C-texi
+/*&C
 @menu
 * ox_sm1_forAsir::
 * sm1.start::
@@ -279,7 +279,7 @@ The descriptor can be obtained by the function
 $B$3$N<1JLHV9f$O4X?t(B @code{sm1.get_Sm1_proc()} $B$G$H$j$@$9$3$H$,$G$-$k(B.
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [260] ord([da,a,db,b]);
 [da,a,db,b,dx,dy,dz,x,y,z,dt,ds,t,s,u,v,w, 
@@ -361,7 +361,7 @@ to execute the command string @var{s}.
  ($B<!$NNc$G$O(B, $B<1JLHV9f(B 0)
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [261] sm1.sm1(0," ( (x-1)^2 ) . ");
 0
@@ -604,7 +604,7 @@ List
     $BLa$jB?9`<0$O(B dehomogenize $B$5$l$k(B ($B$9$J$o$A(B h $B$K(B 1 $B$,BeF~$5$l$k(B).
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [293] sm1.gb([[x*dx+y*dy-1,x*y*dx*dy-2],[x,y]]);
 [[x*dx+y*dy-1,y^2*dy^2+2],[x*dx,y^2*dy^2]]
@@ -633,7 +633,7 @@ graded reverse lexicographic order $B$K4X$9$k%0%l%V%J
 $BBP$9$k(B leading monomial (initial monomial) $B$G$"$k(B.
 @end tex
 */
-/*&C-texi
+/*&C
 @example
 [294] sm1.gb([[dx^2+dy^2-4,dx*dy-1],[x,y],[[dx,50,dy,2,x,1]]]);
 [[dx+dy^3-4*dy,-dy^4+4*dy^2-1],[dx,-dy^4]]
@@ -666,14 +666,14 @@ $m' = x^{a'} y^{b'} \partial_x^{c'} \partial_y^{d'}$
 $B$5$l$k(B).
 @end tex
 */
-/*&C-texi
+/*&C
 @example
 [294] F=sm1.gb([[dx^2+dy^2-4,dx*dy-1],[x,y],[[dx,50,dy,2,x,1]]]|sorted=1);
       map(print,F[2][0])$
       map(print,F[2][1])$
 @end example
 */
-/*&C-texi
+/*&C
 @example
 [595]
    sm1.gb([["dx*(x*dx +y*dy-2)-1","dy*(x*dx + y*dy -2)-1"],
@@ -804,7 +804,7 @@ mode. So, it is strongly recommended to execute the co
   $B$r0l;~(B shutdown $B$7$F%j%9%?!<%H$7$?J}$,0BA4$G$"$k(B.
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [332] sm1.deRham([x^3-y^2,[x,y]]);
 [1,1,0]
@@ -917,7 +917,7 @@ List
 @end itemize
 */
 
-/*&C-texi
+/*&C
 @example
 
 [346] load("katsura")$
@@ -1020,7 +1020,7 @@ List
     @var{f} $B$OJQ?t(B @code{rest}(@var{v}) $B>e$NB?9`<0$G$"$k(B.
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [595] sm1.genericAnn([x^3+y^3+z^3,[s,x,y,z]]);
 [-x*dx-y*dy-z*dz+3*s,z^2*dy-y^2*dz,z^2*dx-x^2*dz,y^2*dx-x^2*dy]
@@ -1122,7 +1122,7 @@ the inputs @var{f} and @var{g} are left ideals of D.
 $B0lHL$K(B, $B=PNO$O<+M32C72(B D^r $B$NItJ,2C72$G$"$k(B.
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [258]  sm1.wTensor0([[x*dx -1, y*dy -4],[dx+dy,dx-dy^2],[x,y],[1,2]]);
 [[-y*x*dx-y*x*dy+4*x+y],[5*x*dx^2+5*x*dx+2*y*dy^2+(-2*y-6)*dy+3],
@@ -1210,7 +1210,7 @@ sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_
 $B$O(B, $BJ,;6B?9`<0MQ$G$"$k(B.
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [259] sm1.reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y]]);
 [x^2+y^2-4,1,[0,0],[y^4-4*y^2+1,x+y^3-4*y]]
@@ -1287,7 +1287,7 @@ String
 ($B$?$H$($P(B, /usr/local/jdk1.1.8/bin $B$r%3%^%s%I%5!<%A%Q%9$KF~$l$k$J$I(B.)
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [263] load("om");
 1
@@ -1405,7 +1405,7 @@ syzygy $B$G$"$k(B.
 $BF1<!2=JQ?t(B @code{h} $B$,7k2L$K2C$o$k(B.
 @end itemize
 */
-/*&C-texi
+/*&C
 @example
 [293] sm1.syz([[x*dx+y*dy-1,x*y*dx*dy-2],[x,y]]);
 [[[y*x*dy*dx-2,-x*dx-y*dy+1]],    generators of the syzygy
@@ -1414,7 +1414,7 @@ syzygy $B$G$"$k(B.
  [[y*x*dy*dx-2,-x*dx-y*dy+1]]]]
 @end example
 */
-/*&C-texi
+/*&C
 @example
 [294]sm1.syz([[x^2*dx^2+x*dx+y^2*dy^2+y*dy-4,x*y*dx*dy-1],[x,y],[[dx,-1,x,1]]]);
 [[[y*x*dy*dx-1,-x^2*dx^2-x*dx-y^2*dy^2-y*dy+4]], generators of the syzygy
@@ -1450,6 +1450,10 @@ List
 @itemize @bullet
 @item Ask the sm1 server to multiply @var{f} and @var{g} in the ring of differential operators over @var{v}.
 @item @code{sm1.mul_h} is for homogenized Weyl algebra.
+@item BUG: @code{sm1.mul(p0*dp0,1,[p0])} returns
+@code{dp0*p0+1}.
+A variable order such that d-variables come after non-d-variables
+is necessary for the correct computation.
 @end itemize
 */
 
@@ -1478,10 +1482,13 @@ List
 @item   sm1$B%5!<%P(B $B$K(B @var{f} $B$+$1$k(B @var{g} $B$r(B @var{v}
 $B>e$NHyJ,:nMQAG4D$G$d$C$F$/$l$k$h$&$KMj$`(B.
 @item @code{sm1.mul_h} $B$O(B homogenized Weyl $BBe?tMQ(B.
+@item BUG: @code{sm1.mul(p0*dp0,1,[p0])} $B$O(B
+@code{dp0*p0+1} $B$rLa$9(B.  
+d$BJQ?t$,8e$m$K$/$k$h$&$JJQ?t=g=x$,$O$$$C$F$$$J$$$H(B, $B$3$N4X?t$O@5$7$$Ez$($rLa$5$J$$(B.
 @end itemize
 */
 
-/*&C-texi
+/*&C
 
 @example
 [277] sm1.mul(dx,x,[x]);
@@ -1559,7 +1566,7 @@ See Saito, Sturmfels, Takayama : Grobner Deformations 
 @end itemize
 */
 
-/*&C-texi
+/*&C
 
 @example
 [280] sm1.distraction([x*dx,[x],[x],[dx],[x]]);
@@ -1639,7 +1646,7 @@ List
 @end itemize
 */
 
-/*&C-texi
+/*&C
 
 @example
 
@@ -1679,6 +1686,9 @@ F_D(a,b1,b2,...,bn,c;x1,...,xn)
 where @var{a} =(a,c,b1,...,bn).
 When n=2, the Lauricella function is called the Appell function F_1.
 The parameters a, c, b1, ..., bn may be rational numbers.
+@item It does not call sm1 function appell1. As a concequence,
+when parameters are rational or symbolic, this function also works
+as well as integral parameters.
 @end itemize
 */
 
@@ -1706,10 +1716,12 @@ F_D(a,b1,b2,...,bn,c;x1,...,xn)
 $B$N$_$?$9HyJ,J}Dx<07O$rLa$9(B. $B$3$3$G(B,
 @var{a} =(a,c,b1,...,bn).
 $B%Q%i%a!<%?$OM-M}?t$G$b$h$$(B.
+@item sm1 $B$N4X?t(B appell1 $B$r$h$V$o$1$G$J$$$N$G(B, $B%Q%i%a!<%?$,M-M}?t$dJ8;z<0$N>l9g$b(B
+$B@5$7$/F0$/(B.
 @end itemize
 */
 
-/*&C-texi
+/*&C
 
 @example
 
@@ -1728,7 +1740,7 @@ F_D(a,b1,b2,...,bn,c;x1,...,xn)
  [x1*dx1*dx2,-x1^2*dx1^2,-x2^2*dx1*dx2,-x1*x2^2*dx2^2]]
 
 [283] sm1.rank(sm1.appell1([1/2,3,5,-1/3]));
-1
+3
 
 [285] Mu=2$ Beta = 1/3$
 [287] sm1.rank(sm1.appell1([Mu+Beta,Mu+1,Beta,Beta,Beta]));
@@ -1763,6 +1775,9 @@ F_4(a,b,c1,c2,...,cn;x1,...,xn)
 where @var{a} =(a,b,c1,...,cn).
 When n=2, the Lauricella function is called the Appell function F_4.
 The parameters a, b, c1, ..., cn may be rational numbers.
+@item @item It does not call sm1 function appell4. As a concequence,
+when parameters are rational or symbolic, this function also works
+as well as integral parameters.
 @end itemize
 */
 
@@ -1790,10 +1805,12 @@ F_C(a,b,c1,c2,...,cn;x1,...,xn)
 $B$N$_$?$9HyJ,J}Dx<07O$rLa$9(B. $B$3$3$G(B,
 @var{a} =(a,b,c1,...,cn).
 $B%Q%i%a!<%?$OM-M}?t$G$b$h$$(B.
+@item sm1 $B$N4X?t(B appell1 $B$r$h$V$o$1$G$J$$$N$G(B, $B%Q%i%a!<%?$,M-M}?t$dJ8;z<0$N>l9g$b(B
+$B@5$7$/F0$/(B.
 @end itemize
 */
 
-/*&C-texi
+/*&C
 
 @example
 
@@ -1870,7 +1887,7 @@ holonomic. It is generally faster than @code{sm1.rank}
 @end itemize
 */
 
-/*&C-texi
+/*&C
 
 @example
 
@@ -2035,7 +2052,7 @@ Slope $B$NK\Mh$NDj5A$G$O(B, $BId9f$,Ii$H$J$k$,(B, 
 Slope $B$N@dBPCM$rLa$9(B.
 */
 
-/*&C-texi
+/*&C
 
 @example
 
@@ -2069,11 +2086,11 @@ Slope $B$N@dBPCM$rLa$9(B.
 
 
 /*&en
-@include sm1-auto-en.texi
+@include sm1-auto.en
 */
 
 /*&ja
-@include sm1-auto-ja.texi
+@include sm1-auto.ja
 */