version 1.9, 2020/02/25 02:21:53 |
version 1.10, 2020/10/27 02:44:16 |
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/*$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 $ */ |
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/*&C |
/*&C |
@c DO NOT EDIT THIS FILE |
@c DO NOT EDIT THIS FILE |
Line 1165 the inputs @var{f} and @var{g} are left ideals of D. |
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Line 1165 the inputs @var{f} and @var{g} are left ideals of D. |
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@item sm1.reduction([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p}) |
@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},@var{v}]|proc=@var{p}) |
@item sm1.reduction([@var{f},@var{g}]|proc=@var{p},ring_var=@var{r}) |
@item sm1.reduction([@var{f},@var{g}]|proc=@var{p},ring_var=@var{r}) |
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@item sm1.reduction_verbose([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p}) |
:: |
:: |
@end table |
@end table |
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Line 1196 sm1.reduction_d(P,F,G) and sm1.reduction_noH_d(P,F,G) |
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Line 1197 sm1.reduction_d(P,F,G) and sm1.reduction_noH_d(P,F,G) |
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are for distributed polynomials. |
are for distributed polynomials. |
@item When the arguments are two, the function mod_reduction is called. It uses the ring |
@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. |
structure saved in the global variable ring_var in the ox_sm1 server. |
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@item The return value of reduction_verbose is of the form |
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[r,c0,[c1,...,cm],[g1,...gm],init,order] where init is the initial of r and order is the order structure used. |
@end itemize |
@end itemize |
*/ |
*/ |
/*&ja |
/*&ja |
Line 1206 structure saved in the global variable ring_var in the |
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Line 1209 structure saved in the global variable ring_var in the |
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@item sm1.reduction([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p}) |
@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},@var{v}]|proc=@var{p}) |
@item sm1.reduction([@var{f},@var{g}]|proc=@var{p},ring_var=@var{r}) |
@item sm1.reduction([@var{f},@var{g}]|proc=@var{p},ring_var=@var{r}) |
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@item sm1.reduction_verbose([@var{f},@var{g},@var{v},@var{w}]|proc=@var{p}) |
:: |
:: |
@end table |
@end table |
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Line 1240 sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_ |
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Line 1244 sm1.reduction_d(P,F,G) $B$*$h$S(B sm1.reduction_noH_ |
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@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 |
@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$*$$$F4JLs$r9T$&(B. auto_reduce(1) $B$,<+F0$G%;%C%H$5$l$k(B. |
ring_var $BJQ?t$KJ]B8$5$l$?(B ring $B$K$*$$$F4JLs$r9T$&(B. auto_reduce(1) $B$,<+F0$G%;%C%H$5$l$k(B. |
gb $B$r;2>H(B. |
gb $B$r;2>H(B. |
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@item reduction_verbose $B$NLa$jCM$O(B |
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[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 |
@end itemize |
*/ |
*/ |
/*&C |
/*&C |
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[[0,0,0],-1,[[x^2+1,0,0],[1,0,0]],[[-x^2-x-1,x+1,0],[x^2+1,0,-1]]] |
[[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 |
@end example |
*/ |
*/ |
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/*&C |
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@example |
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XM_debug=0$ |
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sm1.auto_reduce(1)$ |
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F=[x*y-1,x^2+y^2-4]$ |
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Weight_vec=[[x,10,y,1]]$ |
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printf("\n\nsyz----\n")$ |
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S=sm1.syz([F,[x,y],Weight_vec]); // When Weight_vec is given, the TOP order is used. |
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// 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. |
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Sgb=sm1.gb([S[0],[x,y],Weight_vec]); |
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R0=[x+y,x^2*y+x]; |
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P=R0[0]*F[0]+R0[1]*F[1]; |
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R=sm1.reduction_verbose([R0,Sgb[0],[x,y],Weight_vec]); |
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printf("\nMinimal representation=%a\n",R[0])$ |
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printf("The initial of minimal rep=%a\n",R[4])$ |
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printf("Order=%a\n",R[5][1][1])$ |
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@end example |
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*/ |
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/*&en |
/*&en |
@table @t |
@table @t |
@item Reference |
@item Reference |