= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
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 L u ibU\R`^
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 	 	 L u pe<P{ibU\R`^L u M a t h 3 2 . d l l 
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 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
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 # L u M a t h O(uf{ 
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 [ L u M a t h 3 2 . d l l ]   L u M a t h O(uf
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         L u M a t h 3 2 . d l l /f N*NL u pe<P{ibU\R`^勓^N~'`Npeyr+R/fw5Џ{:NW@x0
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         (WL u M a t h -NvQpe/fǏN~Qpe}T
Tzz m a t h  Qv@b	gQpeGWwQ	g{|<O m a t h : : m a t r i x ( . . . )  v<h_0O(u! ! ! u s i n g ( " m a t h " ) ; S{SL u M a t h -NvQpe0
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         L u M a t h ^vpe~/fC <h_vCQ }^S/fWN0 v0
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         L u M a t h ^QpewQ	gQX[mNO0gbLHesؚ0Nx{m0[(u'`:_vyrp0
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         L u M a t h vnNx/f _>evnNxN}h t t p : / / w w w . f o r c a l . n e t / x i a z a i / l u 1 / l u 1 c o d e . r a r 
 
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         L u M a t h ^-N@b(uv{lb
N/f g}YvYg`	g}Yv{lSNeO0WۏLfbccGSL u M a t h v'`0
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         L u M a t h ^S(uN _Sg'`v^(uz^/fq`C / C + + 0F o r t r a n vpef[1r}YvgsOv~Kb]wQTe_Ngg[ N,vpe<P{(u7bcOegYveO0
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         PN\O4ls^g_NgSNqQT[UL u M a t h Yg`	gNHN}Yv{lNUO9eۏvab^N\OT|0
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         ,g^N/fbx_sNUOU"kL u M a t h v*NN0VbFUNlQSSWNdk^ _SFUNz^0
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 } # 
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 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
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 # L u M a t h pe~w5	[aW,g(ul{ 
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 [ L u M a t h 3 2 . d l l ]   L u M a t h pe~w5	[aW,g(ul
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         PRL u ыhVv/ecL u M a t h -Nvpe~w5	[a	gNN{mv(ul0
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         A 0B /fL u M a t h pe~w5	[a
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             A . = B                                   / / \[aB K<P~[aA 
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             A . = A + B                               / / \[aA + B K<P~[aA 
 
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             A [ 2 ] = A [ 2 ] + 1                     / / \ N~pe~A ,{2 *NUSCQv<PR1 
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             A [ 2 , 3 , 5 ] = A [ 3 , 1 , 2 ] + 1     / / \	N~pe~A v,{[ 2 , 3 , 5 ] *NUSCQv<PK<P:NA [ 3 , 1 , 2 ] + 1 
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         A /f N*NL u M a t h w5
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             A ( a l l : j )                           / / Sw5A ,{j R@b	gCQ }0a l l /f N*N8^ϑ(Wُ̑h:yS@b	gL
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             A ( i : a l l )                           / / Sw5A ,{i L@b	gCQ }0a l l /f N*N8^ϑ(Wُ̑h:yS@b	gR
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             A ( i , i + m : a l l )                   / / Sw5A ,{i ^i + m L@b	gCQ }0a l l /f N*N8^ϑ(Wُ̑h:yS@b	gR
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             A ( a l l : j , j + m )                   / / Sw5A ,{j ^j + m R@b	gCQ }0a l l /f N*N8^ϑ(Wُ̑h:yS@b	gL
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 
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             A ( a l l : j ) = B                       / / nw5A ,{j R@b	gCQ }B /f N*Npe~0a l l /f N*N8^ϑ(Wُ̑h:yS@b	gL
 
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 
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 
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             A ( a l l : j , j + m ) = B               / / nw5A ,{j ^j + m R@b	gCQ }B /f N*Nw50a l l /f N*N8^ϑ(Wُ̑h:yS@b	gL
 
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             A ( i , i + m : j , j + n ) = B           / / nw5A ,{i ^i + m Lv^(W,{j ^j + n Rv@b	gCQ }B /f N*Nw50
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 
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 ! ! ! u s i n g [ " m a t h " ] ; 
 
 m a i n ( : t 0 , k , i , a , b ) = 
 
 { 
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         t 0 = c l o c k ( ) , 
 
         k = z e r o s ( 5 , 5 ) ,                   / / ub5  5 w5k RYS:N0 
 
         i = 0 , ( + + i < = 1 0 0 0 ) . w h i l e { / / _s{1 0 0 0 !k
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                 a = r a n d ( 5 , 7 ) ,   b = r a n d ( 7 , 5 ) ,   / / ub5  7 w5a 7  5 w5b (u0 ^1 KNv:gpeRYS
 
                 k . = k + a * b + a ( 0 , 4 : 1 , 5 ) * b ( 1 , 5 : 0 , 4 ) + a ( a l l : 6 ) * b ( 3 : a l l ) 
 
         } , 
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         k . o u t a ( ) ,                           / / Qw5k 
 
         [ c l o c k ( ) - t 0 ] / 1 0 0 0 .         / / _0R{ey
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 } ; 
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 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : r e a l _ s { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : r e a l _ s (u(WQpen e w [ m a t h : : r e a l _ s , . . .   . . . ] -N3upe~bw50[avW,g{|W:Nr e a l s ibU\{|W:Nr e a l _ s 0  
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : p i { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : p i = 3 . 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h   + { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h   + pe~w5	Rl0ЏL1 
NSƋ+R[a2 pe~
NX[(W3 pe~w5	
N9SM4 QX[0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h   - { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h   - pe~w5	Ql0ЏL1 
NSƋ+R[a2 pe~
NX[(W3 pe~w5	
N9SM4 QX[0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h   * { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h   * w5XNl0ЏL1 
NSƋ+R[a2 w5
NX[(W3 w5
N9SM4 QX[0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h   ' { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h   ' w5ln0ЏL1 
NSƋ+R[a2 w5
NX[(W3 QX[0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h   . * { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h   . * pe~pXN0ЏL1 
NSƋ+R[a2 pe~
NX[(W3 pe~
N9SM4 QX[0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h   . / { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h   . / pe~p]d0ЏL1 
NSƋ+R[a2 pe~
NX[(W3 pe~
N9SM4 QX[0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h   . ^ { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h   . ^ pe~pXNe0ЏL1 
NSƋ+R[a2 pe~
NX[(W3 pe~
N9SM4 QX[0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h   ͑}Qpe{ 
 
 [ L u M a t h 3 2 . d l l ]   m a t h   ͑}Qpe勓^[NNQpeۏLN͑}/ecr e a l _ s {|W[avvsQЏ{n e w 0c o p y 0l e n 0o s e t 0o g e t 0o 0s q r t 0e x p 0l n 0l g 0s i n 0c o s 0t a n 0a s i n 0a c o s 0a t a n 0s i n h 0c o s h 0t a n h 0a b s 0f l o o r 0c e i l 0a t a n 2 0f m o d 0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : r a 1 { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : r a 1 [ 2 , 3 . 5 , - 5 ] 3u N~pe~v^RYS0  ЏL1 
NSƋ+RSpeScS[pebtepeSpe0  
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : S e t A r r a y { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : S e t A r r a y ( a   :   x 1 , x 2 , . . .   . . . ) [pe~bw5ۏLRYS
 
 
 
         (ul1 m a t h : : S e t A r r a y ( a   :   x 1 , x 2 , . . .   . . . ) [pe~bw5a ۏLRYSN0W@W0  _YX[>epencx 1 , x 2 , . . .   . . . RYSpencSN\NbYNpe~'Y\YYOvpenc_eu0
 
 
 
         (ul2 m a t h : : S e t A r r a y ( a   :   " 1     - 2   3   2 . 3   . . .   . . . " ) [pe~bw5a ۏLRYSN0W@W0  _YX[>epencpencX[>e(WW[&{2N" 1     - 2   3   2 . 3   . . .   . . . " -NRYSpencSN\NbYNpe~'Y\YYOvpenc_eu0
 
 
 
         ЏL1 ^lvpe~[a2 ^lvL u W[&{2NSvQNSpe3 ^lvpeW[W[&{2N0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : o u t a { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : o u t a ( a ,   p r e c i s i o n ,   r l ,   i n d e x ) Qpe~bw5
 
 
 
         a pe~bw5	cRhe_Q0
 
         p r e c i s i o n 	gHepeW[MOpe2 ^1 8 	:w/f6 MO	gHepeW[0
 
         r l ][PbS[PQ^0 h:yS[P0:w/fS[P0
 
         i n d e x i n d e x ^0 eQpe~CQ }Nh0:w/f
NQpe~CQ }Nh0
 
 
 
         ЏL1 Spe*YYb*Y\2 Spe
N&{TBl3 pe~
NX[(W3 QX[0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : S u m { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : S u m ( a , i ) pe~CQ }BlT
 
 
 
         	gm ~pe~+Tw5	a ( n 1 , n 2 , . . .   . . . , n m ) RS u m ( a , i ) [,{i ~BlTԏV N*Nm - 1 ~pe~0a /f N~pe~01  k w50k  1 w50i < 1 bi > m RS u m QpeԏV@b	gpe~CQ }vT0S u m ( a ) vS_NS u m ( a , m ) 0
 
 
 
         ЏL1 Spe*YYb*Y\2 pe~
NX[(W3 pe~~pe*YY4 QX[0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h   s u m { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h   s u m ( a , i ) Qpe/f͑}QpegbLNm a t h : : S u m [hQvTvЏ{0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : n d g r i d { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : n d g r i d ( x 1 , x 2 , . . . , x n   :   & y 1 , & y 2 , . . . , y n ) ubn ~QpevR<hp5R
 
 
 
         x 1 , x 2 , . . . , x n GW/f N~pe~0
 
         & y 1 , & y 2 , . . . , y n ԏVn ~QpevR<hp5R0
 
         ԏV<PeaIN0
 
 
 
         ЏL1 Spe*YYb*Y\2 pe~
NX[(W3 
N/f N~pe~4 QX[0
 
 
 
         OP[
 
 
 
 ! ! ! u s i n g [ " m a t h " ] ; 
 
 m v a r : 
 
 n d g r i d [ l i n s p a c e ( 0 . 0 , 1 . 0 , 0 . 0 0 1 1 ) , l i n s p a c e ( 1 . 0 , 2 . 0 , 0 . 0 0 0 9 ) , & x , & y ] , 
 
 S u m [ c o s ( 1 . 0 - s i n ( ( 1 . 2 ) . * x . ^ ( y . / 2 . 0 ) + c o s ( 1 . 0 - s i n ( ( 1 . 2 ) . * y . ^ ( x . / 2 . 0 ) ) ) ) ) , 0 ] ; 
 
 
 
         vS_N
 
 
 
 f ( x , y ) = c o s ( 1 . 0 - s i n ( 1 . 2 * x ^ ( y / 2 . 0 ) + c o s ( 1 - s i n ( 1 . 2 * y ^ ( x / 2 . 0 ) ) ) ) ) ; 
 
 s u m [ @ f : 0 . 0 , 1 . 0 , 0 . 0 0 1 1 : 1 . 0 , 2 . 0 , 0 . 0 0 0 9 ] ; 
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h   c o p y { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h   c o p y Qpe/f͑}Qpe0c o p y ( a ) \ub[aa voR,gc o p y ( a , b ) \pe~b 
Y6R0Rpe~a $Npe~_{I{v^\Y~pe~Ɖ:N N~~pec o p y ( a , a b e g i n , b , b b e g i n , k ) \pe~b N0W@Wb b e g i n  _Yvk *NCQ }
Y6R0Rpe~a v0W@Wa b e g i n  _YvUSCQ0ЏL1 Spe*YYb*Y\2 pe~
NX[(W3 pe~
N9SM  4 QX[0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h   o s e t { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h   o s e t Qpe/f͑}Qpe0a /f N*NN~pe~[aRgbLb_Ya [ i , j ] = 2 . 0 vK<PSe\(uQpe0ЏL1 Spe*Y\2 
NSƋ+R[a3 pe~
N9SM4 Spe
N&{TBl0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h   o g e t { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h   o g e t Qpe/f͑}Qpe0a /f N*NN~pe~[aRgbLb_Ya [ i , j ] vSe\_[aCQ }v<P0ЏL1 Spe*Y\2 
NSƋ+R[a3 pe~
N9SM4 CQ }0W@W0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : a r r a y f u n { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : a r r a y f u n ( h F o r : x 1 , x 2 , . . . , x n   :   x x ) N[pepe~CQ }:NSϑۏLQpe(u0
 
 
 
         h F o r :NQpeSgx 1 , x 2 , . . . , x n   :   x x :NI{v[pepe~_eu~pe	x x (uNX[>e~gS:w0:wx x ԏV N*N[pepe~X[>e~g&TRQpeԏVx x 0QpeNpe~x 1 , x 2 , . . . , x n v,{i *NCQ }:NSϑ(uQpeh F o r ۏL{~gX[eQx x v,{i *NUSCQ0
 
 
 
         ЏL1 \ 2 *NSpe2 c[vh_
NX[(W3 pe~*NpeNSϑ*Npe
NvI{4 
N/f[pepe~5 pe~^
N9SM6 QX[7 Qpe^ԏV N*N[pe0
 
 
 
         OP[
 
 
 
 ! ! ! u s i n g [ " m a t h " ] ; 
 
 f ( x , y ) = x + y ; 
 
 a r r a y f u n [ @ f , l i n s p a c e ( 1 . , 5 . , 5 ) , l i n s p a c e ( 1 . , 5 . , 5 ) ] . o [ ] ; 
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : r e s h a p e { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : r e s h a p e ( a , . . .   . . . ) 9eSpe~w5	b_r
 
 
 
         <h_1 m a t h : : r e s h a p e ( a ) \w5͑n:N N~pe~0
 
         <h_2 m a t h : : r e s h a p e ( a , i , j ) \w5a b N~pe~	͑n:Ni  j w5Oc;`CQ }
NS0
 
         <h_3 m a t h : : r e s h a p e ( a , i , j , k , . . . ) 9eSY~pe~v~pe'Y\Oc~peT;`CQ }
NS0
 
 
 
         ЏLNx1 Spe*YYb*Y\2 [pepe~
NX[(W3 pe~~pe\N1 4 pe~
N9SM0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : m a t r i x { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : m a t r i x ( m , n : x 1 1 , x 1 2 , . . .   . . . ) bm a t h : : m a t r i x ( s t r ) 3um  n w5v^RYS0
 
 
 
         m , n w5vLTR0RYSpenc  x 1 1 , x 1 2 , . . . , x 1 n , x 2 1 , x 2 2 , . . . , x 2 n , . . .   . . . , x m 1 , x m 2 , . . . , x m n   SN:wRShQYYOvpenc_eu0
 
         s t r W[&{2NS+Tw5pencpencKNSN(uzz<hbSR0dke\ꁨRnx[w5vLTR0OYNN/f N*N2  3 w5W[&{2N
 
 
 
 	 " 1         1 . 2     3 , 
 
 	   2 . 2     3 ,       5 " 
 
 
 
         ЏL1 Spe
N&{TBl2 W[&{2Nw5kL-Npenc*Npe
NT3 W[&{2N-Npenc^l0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : s u b g { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : s u b g ( a ,   . . .   . . . ) ԏV N*Nw5vP[w5
 
 
 
         s u b g ( a ) ԏVw5a voR,g0
 
         s u b g ( a : t y p e ) ԏVNw5a T7h'Y\vw5v^9hnct y p e v<PۏLRYS0t y p e vS	<P:Nz e r o s hQ0 w5	0o n e s hQ1 w5	0e y e USMOw5	0r a n d 0 ^1 KNGW SR^v:gpe	0r a n d n GW<P:N0 e]:N1 vhQck`R^v:gpe	0
 
         s u b g ( a : a l l : j ) Sw5a ,{j R@b	gCQ }0a l l /f N*N8^ϑ(Wُ̑h:yS@b	gL0  
 
         s u b g ( a : i : a l l ) Sw5a ,{i L@b	gCQ }0a l l /f N*N8^ϑ(Wُ̑h:yS@b	gR0
 
         s u b g ( a : i , i + m : a l l ) Sw5a ,{i ^i + m L@b	gCQ }0a l l /f N*N8^ϑ(Wُ̑h:yS@b	gR0
 
         s u b g ( a : a l l : j , j + m ) Sw5a ,{j ^j + m R@b	gCQ }0a l l /f N*N8^ϑ(Wُ̑h:yS@b	gL0
 
         s u b g ( a : i , i + m : j , j + n ) Sw5a ,{i ^i + m Lv^(W,{j ^j + n Rv@b	gCQ }0
 
 
 
         ЏL1 Spe*YYb*Y\2 pe~
NX[(W3 
N/fN~pe~w5	4 
NSƋ+Rv{|WhƋt y p e 5 el[MOw5vLbR6 QX[0
 
 
 
         [ OP[] 
 
 
 
 ! ! ! u s i n g [ " m a t h " ] ; 
 
 m a i n ( : a ) = 
 
         a = m a t r i x [ 6 , 5 ] . r a n d ( ) , 
 
         a . o u t a ( ) , 
 
         a . s u b g ( a l l : 3 ) . o u t a ( ) , 
 
         a . s u b g ( 3 : a l l ) . o u t a ( ) , 
 
         a . s u b g ( 3 , 5 : 2 , 3 ) . o u t a ( ) ;   
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : s u b s { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : s u b s ( a ,   . . .   . . . , b ) n N*Nw5vP[w5
 
 
 
         s u b s ( a : b ) \w5b K<P~w5a a Nb ^wQ	gvTv~g0
 
         s u b s ( a : a l l : j , b ) [w5a ,{j R@b	gCQ }K<Pb /f N*NI{v N~pe~0a l l /f N*N8^ϑ(Wُ̑h:yS@b	gL0  
 
         s u b s ( a : i : a l l , b ) [w5a ,{i L@b	gCQ }K<Pb /f N*NI{v N~pe~0a l l /f N*N8^ϑ(Wُ̑h:yS@b	gR0
 
         s u b s ( a : i , i + m : a l l , b ) [w5a ,{i ^i + m L@b	gCQ }K<Pb /f N*NvT'Y\vw50a l l /f N*N8^ϑ(Wُ̑h:yS@b	gR0
 
         s u b s ( a : a l l : j , j + m , b ) [w5a ,{j ^j + m R@b	gCQ }K<Pb /f N*NvT'Y\vw50a l l /f N*N8^ϑ(Wُ̑h:yS@b	gL0
 
         s u b s ( a : i , i + m : j , j + n , b ) [w5a ,{i ^i + m Lv^(W,{j ^j + n Rv@b	gCQ }K<Pb /f N*NvT'Y\vw50
 
         ԏV<PԏVa 0
 
 
 
         ЏL1 Spe*YYb*Y\2 pe~
NX[(W3 
N/fN~pe~w5	4 pe~
N9SM5 el[MOw5vLbR0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : r o w { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : r o w ( a , b , n ) Nu N*NUSLw5LTϑ	0a 0b 0x :N[pen :Ntepe0a Tb /fLTϑv,{ N*NT gT N*NCQ }CQ };`pe/fn 0ba /f,{ N*NCQ }TbvCQ }	cx X gT N*NCQ }
NǏb 0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : c o l { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : c o l ( a , b , n ) Nu N*NUSRw5RTϑ	0a 0b 0x :N[pen :Ntepe0a Tb /fRTϑv,{ N*NT gT N*NCQ }CQ };`pe/fn 0ba /f,{ N*NCQ }TbvCQ }	cx X gT N*NCQ }
NǏb 0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : l i n s p a c e { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : l i n s p a c e ( a , b , n ) Nu N*N N~pe~0a 0b 0x :N[pen :Ntepe0a Tb /fpe~v,{ N*NT gT N*NCQ }CQ };`pe/fn 0ba /f,{ N*NCQ }TbvCQ }	cx X gT N*NCQ }
NǏb 0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : z e r o s { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : z e r o s ( a )   b  m a t h : : z e r o s ( i , j ) \w5a ͑eRYS:NhQ0 w5bub N*Ni  j hQ0 w50ЏL1 pe~
NX[(W2 
N/fN~pe~w5	3 QX[4 Spe*YYb*Y\0  
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : o n e s { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : o n e s ( a )   b  m a t h : : o n e s ( i , j ) \w5a ͑eRYS:NhQ1 w5bub N*Ni  j hQ1 w50ЏL1 pe~
NX[(W2 
N/fN~pe~w5	3 QX[4 Spe*YYb*Y\0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : e y e { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : e y e ( a )   b  m a t h : : e y e ( i , j ) \w5a ͑eRYS:NUSMOw5bub N*Ni  j USMOw50ЏL1 pe~
NX[(W2 
N/fN~pe~w5	3 QX[4 Spe*YYb*Y\0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : r a n d { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : r a n d ( a )   b  m a t h : : r a n d ( i , j ) \w5a ͑eRYS:N0 ^1 KNGW SR^v:gpew5bub N*Ni  j w5v^(u0 ^1 KNGW SR^v:gpeRYS0  ЏL1 pe~
NX[(W2 
N/fN~pe~w5	3 QX[4 Spe*YYb*Y\0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : r a n d n { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : r a n d n ( a )   b  m a t h : : r a n d n ( i , j ) \w5a ͑eRYS:NGW<P:N0 e]:N1 vhQck`R^v:gpew5bub N*Ni  j w5v^(uGW<P:N0 e]:N1 vhQck`R^v:gpeRYS0  ЏL1 pe~
NX[(W2 
N/fN~pe~w5	3 QX[4 Spe*YYb*Y\0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : i n v { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : i n v ( a ) w5Bl0ЏL1 
NSƋ+R[a2 
N/fn  n w53 QX[4 w5GY_0
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : n e t n { 
 
 [ L u M a t h 3 2 . d l l ]   m a t h : : n e t n ( f , x , e p s , t , h , k ) Bl^~'`ez~ N~[9hvb[rl
 
 
 
 f ꁚ[INNCQb2 n ( n > 1 ) CQQpeSgFO_{1uN~QpeH F o r _Sg01u(u7b0
 
 
 
         Ygf /fNCQQpeR$N*NSpe:NI{v N~pe~
 
 
 
 f ( x , y ) =         / / NCQQpex [ i ] :NSϑy [ i ] :NezSzpQpe<P
 
 { 
 
         y [ 0 ] = f 1 ( x [ 0 ] , x [ 1 ] , . . . , x [ n - 1 ] ) , 
 
         y [ 1 ] = f 2 ( x [ 0 ] , x [ 1 ] , . . . , x [ n - 1 ] ) , 
 
         . . .   . . . 
 
         y [ n - 1 ] = f n ( x [ 0 ] , x [ 1 ] , . . . , x [ n - 1 ] ) 
 
 } ; 
 
 
 
         b
 
 
 
 f ( x 1 , x 2 , . . . , x n , y 1 , y 2 , . . . , y n ) =         / / 2 n CQQpex i :NSϑy i :NezSzpQpe<P
 
 { 
 
         y 1 = f 1 ( x 1 , x 2 , . . . , x n ) , 
 
         y 2 = f 2 ( x 1 , x 2 , . . . , x n ) , 
 
         . . .   . . . 
 
         y n = f n ( x 1 , x 2 , . . . , x n ) 
 
 } ; 
 
 
 
 x S|^[W N~pe~^
N\Nn X[>e N~R<PԏVez~v N~[9h0
 
 e p s c6R|^e p s > 0 	0S:wSpe:w<Pe p s = 1 e - 6 0
 
 t c6Rh 'Y\vSϑ0 < t < 1 0S:wSpe:w<Ph = 0 . 1 0
 
 h XϑR<P(W,gQpe-N\4xOW0S:wSpe:w<Ph = 0 . 1 0
 
 k AQv g'YN!kpe0S:wSpe:w<Pk = 1 0 0 0
 
 
 
 ԏV<PԏV<P:N[EN!kpe0ԏV<P:N- 1 h:yNpeezGY_ԏV<P:N- 2 h:y= 0 ُ$Ny`QS>e[|^Bl09eST*NR<Pb9eST*Nezz^QՋԏV<PI{N0 fNNk !kN*gn|^Blz^]\O1Y%0
 
 
 
 ЏLNx1 Spe*YYb*Y\2 c[vh_
NX[(W3 ezf Spe*Npe
N&{TBl4 [pepe~
NX[(W5 pe~CQ }*Y\6 |^0c6RSϑ0N!kpeI{
N&{TBl7 QX[8 (u7b RdNꁚ[INNCQQpe-Nv]\Ope~0
 
 
 
         [ OP[] 
 
 
 
 f ( x 1 , x 2 , x 3 , y 1 , y 2 , y 3 ) =             / / Qpe[IN
 
 { 
 
         y 1 = x 1 * x 1 + x 2 * x 2 + x 3 * x 3 - 1 . 0 , 
 
         y 2 = 2 . 0 * x 1 * x 1 + x 2 * x 2 - 4 . 0 * x 3 , 
 
         y 3 = 3 . 0 * x 1 * x 1 - 4 . 0 * x 2 + x 3 * x 3 
 
 } ; 
 
 ! ! ! u s i n g [ " m a t h " ] ; 
 
 m a i n ( : x , i ) = { 
 
         x = n e w { r e a l _ s , d a t a   :   1 . 0 , 1 . 0 , 1 . 0 } ,       / / nR<P:N1 . 0 , 1 . 0 , 1 . 0 
 
         i = n e t n [ @ f , x ] ,                     / / b[rl㉹ez
 
         x . o u t a ( ) ,                             / / Q~g
 
         i                                             / / ԏVN!kpe
 
 } ; 
 
 
 
         b
 
 
 
 f ( x , y ) =                                       / / Qpe[IN
 
 { 
 
         y [ 0 ] = x [ 0 ] * x [ 0 ] + x [ 1 ] * x [ 1 ] + x [ 2 ] * x [ 2 ] - 1 . 0 , 
 
         y [ 1 ] = 2 . 0 * x [ 0 ] * x [ 0 ] + x [ 1 ] * x [ 1 ] - 4 . 0 * x [ 2 ] , 
 
         y [ 2 ] = 3 . 0 * x [ 0 ] * x [ 0 ] - 4 . 0 * x [ 1 ] + x [ 2 ] * x [ 2 ] 
 
 } ; 
 
 ! ! ! u s i n g [ " m a t h " ] ; 
 
 m a i n ( : x , i ) = { 
 
         x = n e w { r e a l _ s , d a t a   :   1 . 0 , 1 . 0 , 1 . 0 } ,       / / nR<P:N1 . 0 , 1 . 0 , 1 . 0 
 
         i = n e t n [ @ f , x ] ,                     / / b[rl㉹ez
 
         x . o u t a ( ) ,                             / / Q~g
 
         i                                             / / ԏVN!kpe
 
 } ; 
 
 } # 
 
 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 
 # m a t h : : b t F i n d R o o t { 
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