OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw - diff

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Diff for /OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw between version 1.9 and 1.10

version 1.9, 2020/02/25 02:21:53

version 1.10, 2020/10/27 02:44:16

Line 1

/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v 1.8 2019/09/13 05:21:33 takayama Exp $ */

/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1/sm1.oxw,v 1.9 2020/02/25 02:21:53 takayama Exp $ */

/*&C

@c DO NOT EDIT THIS FILE

Line 1165 the inputs @var{f} and @var{g} are left ideals of D.

@item sm1.reduction([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p})

@item sm1.reduction([@var{f},@var{g},@var{v}]|proc=@var{p})

@item sm1.reduction([@var{f},@var{g}]|proc=@var{p},ring_var=@var{r})

@item sm1.reduction_verbose([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p})

@end table

Line 1196 sm1.reduction_d(P,F,G) and sm1.reduction_noH_d(P,F,G)

Line 1197 sm1.reduction_d(P,F,G) and sm1.reduction_noH_d(P,F,G)

are for distributed polynomials.

@item When the arguments are two, the function mod_reduction is called. It uses the ring

structure saved in the global variable ring_var in the ox_sm1 server.

@item The return value of reduction_verbose is of the form

[r,c0,[c1,...,cm],[g1,...gm],init,order] where init is the initial of r and order is the order structure used.

@end itemize

/*&ja

Line 1206 structure saved in the global variable ring_var in the

Line 1209 structure saved in the global variable ring_var in the

@item sm1.reduction([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p})

@item sm1.reduction([@var{f},@var{g},@var{v}]|proc=@var{p})

@item sm1.reduction([@var{f},@var{g}]|proc=@var{p},ring_var=@var{r})

@item sm1.reduction_verbose([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p})

@end table

Line 1240 sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_

Line 1244 sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_

@item $B0z?t$,#2$D$N;~$O(B mod_reduction $B4X?t$,8F$P$l$k(B. $B$3$l$O(B ox_sm1 $B$NBg0hJQ?t(B

ring_var $BJQ?t$KJ]B8$5$l$?(B ring $B$K$*$$$F4JLs$r9T$&(B. auto_reduce(1) $B$,<+F0$G%;%C%H$5$l$k(B.

gb $B$r;2>H(B.

@item reduction_verbose $B$NLa$jCM$O(B

[r,c0,[c1,...,cm],[g1,...gm],init,order] $B$3$3$G(B init $B$O(B $B=g=x(B order $B$K$h$k(B r $B$N(B initial.

@end itemize

/*&C

Line 1258 gb $B$r;2>H(B.

Line 1264 gb $B$r;2>H(B.

[[0,0,0],-1,[[x^2+1,0,0],[1,0,0]],[[-x^2-x-1,x+1,0],[x^2+1,0,-1]]]

@end example

/*&C

@example

XM_debug=0$

sm1.auto_reduce(1)$

F=[x*y-1,x^2+y^2-4]$

Weight_vec=[[x,10,y,1]]$

printf("\n\nsyz----\n")$

S=sm1.syz([F,[x,y],Weight_vec]); // When Weight_vec is given, the TOP order is used.

// If the Weight_vec is not given, the POT order (e.g., (1,0,0)<(0,1,0)<(0,0,1)) with grlex is used.

Sgb=sm1.gb([S[0],[x,y],Weight_vec]);

R0=[x+y,x^2*y+x];

P=R0[0]*F[0]+R0[1]*F[1];

R=sm1.reduction_verbose([R0,Sgb[0],[x,y],Weight_vec]);

printf("\nMinimal representation=%a\n",R[0])$

printf("The initial of minimal rep=%a\n",R[4])$

printf("Order=%a\n",R[5][1][1])$

@end example

/*&en

@table @t

@item Reference

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