Index: Tst/Buch/Example_1_9_13.res.gz.uu
===================================================================
--- Tst/Buch/Example_1_9_13.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_13.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,15 @@
+begin 640 Example_1_9_13.res.gz
+M'XL(",]!CD8``T5X86UP;&5?,5\Y7S$S+G)E<P#=E5U+PS`4AN_[*P[#BTVZ
+M;FGWX5:,X.J%(-[HG<A:NW0+KNE(,YW_WM.O="I*=7IC*#3DXWW><TY(;FZ]
+MRVL`(!2N+L^AI5)EK?E#RS5NRAF;`@[.N>"JW7&-[`^4PL4NB#=K-B?SR9PX
+MEF#/5JH"I;<Y%'1_8,'IYPU8(07$FEC.5ROK9J#J&3`I$PE)&&ZE9`O@`@KB
+MF@L&@RGXOPOU,VKZR#<;+I:@V$Y!)),XP_A5J$,+9#8KX13Z9IN9D;GJF(N-
+M:^ALC"C$@9)\![,[YQX_MXA&),76(%3\B15C?K'2!Y["5BQ8A)$M&@0_FE9;
+M-<37!L84!XEIWZ-'XN9]1_=MW2\=S'*X2!0TQX\1WP3A_QM&E=L375SOSXI[
+M4A?7^U#<"<7!TG%WI:OH_2#Z"7+>:&D*Z1>4/'Z;'40A_1*CQ6H,R3!EFKMV
+MY!Z"(3EF3ZS&X!4GPF"]9`\R:,],K^,><&:(C:!W<C4*KT59J<MO5YXXJ"WW
+MY`84(LQ8KP>M,(GC+=[`>+Q:D+X(%>S,W'J8H%*HJAI%[/O8["YMS*G=#='=
+M<;&MFA2)Z.XIE`*5M9^D>YAY:T2IC8WJQXF,K?Q]RQZO;=HF'??(>`6-GMB(
+$%0<`````
+`
+end
Index: Tst/Buch/Example_1_9_13.stat
===================================================================
--- Tst/Buch/Example_1_9_13.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_13.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728079:2007070609:3-0-3:ix86-Linux:nepomuck:158364
+1 >> tst_memory_1 :: 1183728079:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728079:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728079:2007070609:3-0-3:ix86-Linux:nepomuck:4
Index: Tst/Buch/Example_1_9_13.tst
===================================================================
--- Tst/Buch/Example_1_9_13.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_13.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,18 @@
+LIB "tst.lib";
+tst_init();
+
+=========================== example 1.9.3 =====================================
+ring r = 0,(e,f,h),dp;
+matrix C[3][3];
+C[1,2] = 1; C[1,3] = 1; C[2,3] = 1; 
+matrix D[3][3];
+D[1,2] = -h; 
+D[1,3] = 2e; 
+D[2,3] = -2f;
+ncalgebra(C,D);
+r;
+fe; // "commutative" syntax, not correct 
+f*e; // correct non-commutative syntax
+
+tst_status(1);$
+
Index: Tst/Buch/Example_1_9_20.res.gz.uu
===================================================================
--- Tst/Buch/Example_1_9_20.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_20.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,14 @@
+begin 640 Example_1_9_20.res.gz
+M'XL(",]!CD8``T5X86UP;&5?,5\Y7S(P+G)E<P"M5,]OFS`4OO-7?*IV`*DB
+M@:1;4U2F5.L!*>HE[1D<>&FM@LVP:;K_?C80Z&&KTJH^`/)[[_LE[.W]K^0.
+M0!!CD]S@3"OMEWQW%CG;H1+&,)LI%UR[7N38-^(8MZ^LJDM*@W25AG-?T,%7
+MFNEQ;!%C_%[ZN/[O`O5("/R5'\[Q3NMQ.0;S)ZAI9`.9YVW34`$NT/.57!"6
+M5\B^E#.SI.J9US47C]#TJK%O9&59LJ//"W_R_-WO`Q4Y*Q_[2.&,U1\Q9C.4
+MDA703V0D[QK6_,&!ZZ=NHZ"]#9I+`;G'@^NJ,@V]<?S2MQU8XQH5>Z8'5;JA
+M%UE(11IM;2;Z@2ZH;.K)P!5:T<%3<4*.ER;'DZBR4=PJMJ7&QK2.>HJUI142
+M@E5D#3'8\NRW?9X@8F5$3)`C4S"/(6L;DFMFMC=&UIA_$+RMW3->]J(/9$)6
+M)F2)7%9UJPFFWN:&<\<4J7'>_/:\(%8B,<XI/-\/5HR+3@?+-7^A(>"N\\/9
+M!N'5,#J13.861P$;6U2Z<!/O4QK^U?V^KL6HZRWW)&UI+XM!2[9)/F[<GDZ#
+=,"%>3+=%8$Z.O7#L;=(J-_"B;\Y?,A4;V:8$````
+`
+end
Index: Tst/Buch/Example_1_9_20.stat
===================================================================
--- Tst/Buch/Example_1_9_20.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_20.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728080:2007070609:3-0-3:ix86-Linux:nepomuck:158360
+1 >> tst_memory_1 :: 1183728080:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728080:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728080:2007070609:3-0-3:ix86-Linux:nepomuck:3
Index: Tst/Buch/Example_1_9_20.tst
===================================================================
--- Tst/Buch/Example_1_9_20.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_20.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,17 @@
+LIB "tst.lib";
+tst_init();
+
+========================== example 1.9.20  ==================================
+
+LIB "ncalg.lib"; 
+// load the library with the definition of U((sl_2)
+def A = makeUsl(2); // set up U(sl_2)
+setring A;
+option(redSB);  
+option(redTail); // we wish to compute reduced bases
+ideal I = e2,f;
+ideal LI = std(I);
+LI;
+
+tst_status(1);$
+
Index: Tst/Buch/Example_1_9_22.res.gz.uu
===================================================================
--- Tst/Buch/Example_1_9_22.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_22.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,15 @@
+begin 640 Example_1_9_22.res.gz
+M'XL("-!!CD8``T5X86UP;&5?,5\Y7S(R+G)E<P"ME$%OHS`4A._Y%:.J!Y!6
+MI-"D:1J%5:K=0Z1H#TU[#BZ8U"K8+#:;_/Q])@17W2IJH^4`R,]^W\P8O'[\
+ML?P%((RQ6M[CPF@3%.+Y8C98=Y4H!@UNA!3&\V<#^T0<X^>>E57!-^%FNHFB
+M0/)=H`TS_;+K&/W[*,#\U`7P0S>$P32((IR>/A]0S^_@=:UJJ#1MZIIG$!('
+M7B$DQ^@.R7]E)A:J7T55";F%X7N#O%:EI21'G^/`>;X)#H'*E!7;+M*^.(F1
+M\1P+S%&R5_ZD"R^B;%M;B1M)(#0:25/)4O8)UQ-R_4'CI`??QM#<U-;"HN,M
+M+$0J2%9RJ!P,MCS\;>^?0-X2TK5TI&D,51FAI$=KUO?^#'TVX=7;VB,3!56'
+M0^PX=D*_P"BDJJP:PT'U)B7F,]-<]^OI8Q499P66Y)-'W_+."KEH=;#4B#^\
+MB[.=^>4DP_"N6^H@O;DP.@I8V:(VF;?TS]+PT>S3NJ)>UUNVDT;_744MC5<R
+MVI2]MUKZ-GN*E[6I$@FYJLMVJ^7!QKE:KDG+EV%.ZNB8XH-U4HOMBUF?'^5I
+MJ:,^MG]@3M#X778/ULZYX8S?A]-V<[`;=T"&DZ`]8^T!VF@O]&>7@[_!K_9W
+$F04`````
+`
+end
Index: Tst/Buch/Example_1_9_22.stat
===================================================================
--- Tst/Buch/Example_1_9_22.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_22.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728080:2007070609:3-0-3:ix86-Linux:nepomuck:158380
+1 >> tst_memory_1 :: 1183728080:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728080:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728080:2007070609:3-0-3:ix86-Linux:nepomuck:3
Index: Tst/Buch/Example_1_9_22.tst
===================================================================
--- Tst/Buch/Example_1_9_22.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_22.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,18 @@
+LIB "tst.lib";
+tst_init();
+
+=============================  example 1.9.22  ==============================
+
+LIB "ncalg.lib";
+def A = makeUsl(2);
+setring A;
+option(redSB);  
+option(redTail); // we wish to compute reduced bases
+ideal I = e2,f;
+ideal LI = std(I);
+print(matrix(LI));  // a compact form of an ideal
+ideal RI = rightStd(I);
+print(matrix(RI));
+
+tst_status(1);$
+
Index: Tst/Buch/Example_1_9_23.res.gz.uu
===================================================================
--- Tst/Buch/Example_1_9_23.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_23.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,12 @@
+begin 640 Example_1_9_23.res.gz
+M'XL("-!!CD8``T5X86UP;&5?,5\Y7S(S+G)E<P"M4TUK@S`8OOLK'LH."B-M
+M;+?6B@[&=A#*+NU=G<81IHG$=.W/GQ^MLK()ZY:+(3[O\P7O=O<4O`"@/C;!
+M(R:ZTB3GKQ/7V)[^V#[JQY`+KDW+-9HO?!_/Q[@H<Q;2T`GM.1'L0"H=ZWYL
+M[J._+PB\L0.PC@V4.,2>8QSN>49-^@"FE%202;)7BJ7@`IU@S@7#8HWH?T6C
+M1K5ZYV7)Q1LT.VID2A:-3'1.>D>&U/<$/&5QC@`>F'V;N9UM(:$:ACC1_(,9
+M/7[IG_";9J#2J1E8WX^T;U$+CL`K[$7*LCIT^C-ZM*OE^L3V13KJG:U\E#6C
+M-HM8*WXT-X%EN<!TBAB)+,I:")E4!62&6'0IKK2RJJW\6FMPZIP[W#5!]$'^
+MH<91GTY?V852[X7.+EK;-4FNK(7.+GMIV08Q.JP;M4F[L<TZ[BN36NZ-\0DC
+'1R:1YP,`````
+`
+end
Index: Tst/Buch/Example_1_9_23.stat
===================================================================
--- Tst/Buch/Example_1_9_23.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_23.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728080:2007070609:3-0-3:ix86-Linux:nepomuck:158364
+1 >> tst_memory_1 :: 1183728080:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728080:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728080:2007070609:3-0-3:ix86-Linux:nepomuck:2
Index: Tst/Buch/Example_1_9_23.tst
===================================================================
--- Tst/Buch/Example_1_9_23.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_23.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,13 @@
+LIB "tst.lib";
+tst_init();
+
+=============================  example 1.9.23  ===============================
+
+ideal I = e2,f;
+ideal LI = std(I);
+print(matrix(LI));  // a compact form of an ideal
+ideal TI = twostd(I);
+print(matrix(TI));
+
+tst_status(1);$
+
Index: Tst/Buch/Example_1_9_24.res.gz.uu
===================================================================
--- Tst/Buch/Example_1_9_24.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_24.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,15 @@
+begin 640 Example_1_9_24.res.gz
+M'XL("-%!CD8``T5X86UP;&5?,5\Y7S(T+G)E<P"ME%UOFS`8A>_S*XZJ781T
+M([5#FB8H3)FV"Z1HTE1Z6V!@6JM@,G#6_OS:?+F5HBBIR@4@7OL\Y[S&O@U^
+M^K\!$`];_P<N9"WMG/^]<$>W785Z4!]#+K@<6^Y(/^%Y^/42%[N<A21<AM2Q
+M!7NV:QG+8=K,P_#NV%@?NP#6JH'82YLZ.#Y\/5*:W\&JJJQ0)LF^JE@*+M#R
+M<BX8G!6B3V5&&EH_\=V.BP=(]B*1566A*5&?<VZ;S-=VVU"1Q/E#U]*AN/"0
+ML@P;K%'$3^RNSJGN;1,KZK]$X#5$*?50%2D](?5"I3X@'`W@&P\UDY6.L.EX
+MFQ8#$1<,9888NCS]I^\G(&\4TD@:TM(#3UF<(U!>G`F;9)>/]_0;G3RZF$Z1
+M,"$K564Y*]2K%KT;UWE(K9:I##62<2+Y?]9UIA%LVK(7IS=EN>IFGFUE2$.N
+MO&:R?"YKF8X#RX6^.EO!V9;(E?)T0-``U7X,W(_K$ZUO5H.H3=PL*/Z\@[X#
+MG/>K$:H0AS0-=-;_`KX:P.C7S/WTM26S87$'B#'@]`:VNJC]^=:'/!P:?=R7
+M,_AZRS;6YOJ\[?N_]<\//E_I>6\4K\V!2Q9V<V;K`WE?CXGE?AF]`B3<9PKI
+#!0``
+`
+end
Index: Tst/Buch/Example_1_9_24.stat
===================================================================
--- Tst/Buch/Example_1_9_24.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_24.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728081:2007070609:3-0-3:ix86-Linux:nepomuck:158584
+1 >> tst_memory_1 :: 1183728081:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728081:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728081:2007070609:3-0-3:ix86-Linux:nepomuck:3
Index: Tst/Buch/Example_1_9_24.tst
===================================================================
--- Tst/Buch/Example_1_9_24.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_24.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,18 @@
+LIB "tst.lib";
+tst_init();
+
+=============================  example 1.9.24  ==============================
+
+LIB "ncalg.lib";
+def A = makeUsl2();
+setring A;
+ideal T = 4*e*f+h^2-2*h; // central element in U(sl_2)
+T = twostd(T);     
+T;
+qring Q = twostd(T);
+ideal I = e2,f;
+ideal LI = std(I);
+LI;
+
+tst_status(1);$
+
Index: Tst/Buch/Example_1_9_25.res.gz.uu
===================================================================
--- Tst/Buch/Example_1_9_25.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_25.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,18 @@
+begin 640 Example_1_9_25.res.gz
+M'XL("-%!CD8``T5X86UP;&5?,5\Y7S(U+G)E<P"U5DUOVD`0O?,K1E$/H+8&
+M+RS!0;A*:0^1JDA1R(5#\<8,L(JQZ7H)47Y]9_VMM!`@P`$L/#/OS9N/W?O1
+MCYM;`+!=^'7S'2YTK*U`/E[T:_?9&^8"_3F1H=3U1K]F?L%UX>>+6*X"G-@3
+M9\*X%>+&BK70A5O;A>*Y8\%@UP<P#0:VY5B,PV[KP:!&,;\!*A4IB'Q_K11.
+M08:0X@4R1.A<@7=23,^`QD]RM9+A'#2^:)BI:&E0O#Q/;I4Y=ZU4T-`7P3R3
+MM'AYF:GM8ZA1O1&\Y\(49W#=@@$LQ1,^Q`$CY:'9A(=Z'$Q8`Z)G5*`7"$IH
+M&84BB%-)O-S>`QE#&&D3B>28[J%8CQ0['-<K:#LNQ*B54>>ZU4\!*5;"`T*Q
+M1(AF(,`8-/^8[STX.<2I$K0`LUNNH>5'R]5:8\+(2*E$(%^)(0'-?C-8KT!'
+MI,!<(4*W\+4MD%,4`0PIT8I;G7R^="GA8<:>>"?(PM?R&3.%$]=$WG6XO[BV
+M?96Y[D#U,HCAN<+G"M!(I\;CS)CL.-F,SY`X*YC]`Y;G.SYQU#S-=C9(O-K0
+M_#\=/6[R\9L!(KO#6;7S$=H+L23:J8P.ST>'?VQT[$YU=GA%%KZE^J>O/=]6
+MI9),URVZ[I@^Z!)"M>27Y:EC]RPC^P9!*#1^9DO0+L9')4B0PLS)U\&(..I-
+M%.MIO8.SSPOVE2V(ZQET<0I=MF$6&3':=*-<H-'!4*Q%4*-2($;G?-)!<$?(
+M'PEL-DXU4@G!CM_-K/W>;CYY,5C[W=59ID:#FA\.1VQI9D:RLH<9+[N5T7W!
+57+/,'6H=U^U&_U/M+]8LGJ><"0``
+`
+end
Index: Tst/Buch/Example_1_9_25.stat
===================================================================
--- Tst/Buch/Example_1_9_25.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_25.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728081:2007070609:3-0-3:ix86-Linux:nepomuck:204564
+1 >> tst_memory_1 :: 1183728081:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728081:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728081:2007070609:3-0-3:ix86-Linux:nepomuck:10
Index: Tst/Buch/Example_1_9_25.tst
===================================================================
--- Tst/Buch/Example_1_9_25.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_25.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,27 @@
+LIB "tst.lib";
+tst_init();
+
+============================= example 1.9.25  ===============================
+
+LIB "ncalg.lib";
+LIB "center.lib";
+def A0 = makeUsl2(); // U(sl_2) over the rationals
+setring A0;
+// compute the centralizer of f^2 up to degree 6
+ideal C = centralizer(f^2,6); C;
+ideal Z = center(5); Z;
+def A5 = makeUsl2(5); // U(sl_2) over Z/5Z
+setring A5;
+ideal Z = center(5); 
+Z;
+
+// we are in the algebra A5
+ideal T = twostd(4ef+h2-2h);  
+T;
+qring Q = T;
+// compute the centralizer of f^2 up to degree 6
+ideal C = centralizer(f^2,6); 
+C;
+
+tst_status(1);$
+
Index: Tst/Buch/Example_1_9_28.res.gz.uu
===================================================================
--- Tst/Buch/Example_1_9_28.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_28.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,18 @@
+begin 640 Example_1_9_28.res.gz
+M'XL("-)!CD8``T5X86UP;&5?,5\Y7S(X+G)E<P"M55UOVC`4?>=7'%63"A12
+M;&B!H69B6A]@TUZZ/$TK\>#26`U.EIBU_?>S"3A9MZXMC(<0N-?GR[[RU9</
+MD\\`F(]/D_<XTKGV8OG]:%2[VE:X#_/G3"JIZXU1S7[#]W%Y+U9I3#,V&\[X
+MP%-TY^5::+>LZ\.]]SQ<//L!%8A@WM#C@[^NJ!FP=Z`L2S(D\_DZRV@!J5`0
+MQ5(1>F\1_A^RT++EMS)-I;J!IGN-99:L+'RX<W;FE2[/O2)"-1?QS39$5^S[
+M6-`2"'"!E;BE((^YB1.GIPCJ>3SC#20_*8..")G0,E$BS@N[X:X_A,RA$FV1
+MC-7%"]+HFS1>SQLZV0,?.>G,!A","KZ@4`$E5H1D"0%;/OUAGR]0-#"*2LB2
+M:>AO<#`V0CNMNFBT%JD[A*RSB\^6`YQ@/,(VG6"/6%C'Y5(!=&(8J]@>[WR/
+M#S/.6-7YN+3.>#DJK.LA3>('(#6Z>DUJ+D^B:][FS0AMB*V4D/;QW#7\_\(.
+MMR#W*<VU66Y[V^971GENSH4'_9`2CB.*TTUM=.Q4]WQ[H%(K2F!.2F<B!L6T
+M,J\VJF#L6LW$R`69\L2(H.MN"TO[B*Z[[5XS:B%U&[N7R3-C\CG\QT8W_4\Y
+MW10K5L\W5J72E.5FN:&YDSHJYL?N[,>OXIMK[N_,3JV86*ZD$IKJDY;)OADU
+M#MK.OG/Z!/A!-LW@3W?RIAMY:_4*<7;*IY4C/BR/..]XOZDM8YCL$0.WD_P(
+MSM%R5J'EWA\AB8-V@/-'U%O(DKYR!W)S!]IKU-Z1Z[S.&J,WM5]5@"5T?`<`
+!````
+`
+end
Index: Tst/Buch/Example_1_9_28.stat
===================================================================
--- Tst/Buch/Example_1_9_28.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_28.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728082:2007070609:3-0-3:ix86-Linux:nepomuck:159920
+1 >> tst_memory_1 :: 1183728082:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728082:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728082:2007070609:3-0-3:ix86-Linux:nepomuck:3
Index: Tst/Buch/Example_1_9_28.tst
===================================================================
--- Tst/Buch/Example_1_9_28.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_28.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,25 @@
+LIB "tst.lib";
+tst_init();
+
+================================== example 1.9.28 ====================
+
+LIB "ncalg.lib";
+def  U = makeUsl2(); // U(sl_2) over the rationals
+setring U;
+ring A = 0,(a),dp;
+def  UA = U + A; 
+setring UA;
+
+poly  p = 4*e*f+h^2-2*h - a;
+// p is a central element of UA
+ideal I = e^3, f^3, h^3-4*h, p; 
+// intersect I with the ring K[a]
+ideal J = eliminate(I,e*f*h);
+J;
+
+eliminate(I,h);
+
+eliminate(I,e*f*a);
+
+tst_status(1);$
+
Index: Tst/Buch/Example_1_9_29.res.gz.uu
===================================================================
--- Tst/Buch/Example_1_9_29.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_29.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,12 @@
+begin 640 Example_1_9_29.res.gz
+M'XL("-)!CD8``T5X86UP;&5?,5\Y7S(Y+G)E<P"MDT]O@C`8QN]\BB=F!XBD
+M6MRF2&3)LAU(EEW<>8!073,LI=3-CS_^.'0>U)CUTJ9]^OZ>YTT[?WL*7@%0
+M'R_!(WJZU"3CBYYGS'<GCH]J,^2":]/RC'J&[^-Y&Z]EQD(:NJ'C$L&^2:EC
+MW5T;^>C6MP2S,X.UY4")2QSWG-RHBCZ`*94KY$FR48JEX`(M,.."X7:*Z'^A
+M44TM/[F47*R@V59CJ?)UC8E^D]Z1?>I[`E4K2\PPM$UI%Y:=2L_H!&,?(HFS
+M%5NHV*1V\>Y8'@8#E$SK!O'!H%@6:YX+%+(J(POT4>G:_%$1@9<0N4;*EE7H
+M](*^C*N^7$F-.N<3'SQE<8:@/NX7-J33+QROY8N\#1XGFG^QG==&W_C=B,O=
+M3J:[F\>DO1?7!\OXFHM8,S.HFGS"Q4F66[&.*G44.MP_9TK)'Z*\FDCI$5(>
+:(IT#Y(@TG[#^89O2I)9W8_P`KW7""[H#````
+`
+end
Index: Tst/Buch/Example_1_9_29.stat
===================================================================
--- Tst/Buch/Example_1_9_29.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_29.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728082:2007070609:3-0-3:ix86-Linux:nepomuck:158364
+1 >> tst_memory_1 :: 1183728082:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728082:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728082:2007070609:3-0-3:ix86-Linux:nepomuck:2
Index: Tst/Buch/Example_1_9_29.tst
===================================================================
--- Tst/Buch/Example_1_9_29.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_29.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,14 @@
+LIB "tst.lib";
+tst_init();
+
+================================example 1.9.29 ===============================
+
+ring s = 0,(p,q),dp;
+ncalgebra(1,q^2); // setting the relation qp = pq + q^2
+ideal I = p+q, p2+q2;
+eliminate(I,q);
+
+eliminate(I,p);
+
+tst_status(1);$
+
Index: Tst/Buch/Example_1_9_3.res.gz.uu
===================================================================
--- Tst/Buch/Example_1_9_3.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_3.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,14 @@
+begin 640 Example_1_9_3.res.gz
+M'XL("-)!CD8``T5X86UP;&5?,5\Y7S,N<F5S`+64WTO#,!#'W_M7'.)#*[4N
+M[7ZX%2.X^B"(,.:;C+5NF02W="295O]ZDZ5MYF`PK89"2^[N^\G=I3=^3.X>
+M``!AN+^[@1,I9+"DSR>Q,RXM(0:U.:6,2M>+'?T&C.&VR%;K)9FB:7\:!8R\
+M!T)FLHZ*,-3?[0"N#BX`8I0`!?V@K=P/^YKE*)]K()SG'/+9;,,YF0-E8'!+
+MR@BT!Y#^)3+53/%*UVO*7D"20L*"YRL-2:LL.P%P;15*#MR6/_)\M_`__$_/
+MGZ]CIZY&%\,JDYP6,'R*)NJ)34(L-_'93-(W8O92XYD"%;!A<[)0R<V/R+\[
+MJ$)K2%H?H(?5)O+#B3KG*"SIZ7`+8;F$XS$]A=F5LHQ+PXBT`5TTHUR6%"MF
+M.7W-"8VI&:6_I5BIFH%:=<.2?VL8:MF.)?L=0^KG3*HRGX_./JL\DU_DB9`B
+M?5>SH-"`JDJ??30BA25I1\ZB(HTJRZU.430B15O2KIH%M3&P6;9\(<\\<X=^
+MXC6Y)4A/ECTYB^I@$)6Z^/D=Z"AML2/7M3,4]8+M%-8S=B-<Y,6GSA=N%U8O
+$NP4`````
+`
+end
Index: Tst/Buch/Example_1_9_3.stat
===================================================================
--- Tst/Buch/Example_1_9_3.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_3.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728082:2007070609:3-0-3:ix86-Linux:nepomuck:158436
+1 >> tst_memory_1 :: 1183728082:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728082:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728082:2007070609:3-0-3:ix86-Linux:nepomuck:3
Index: Tst/Buch/Example_1_9_3.tst
===================================================================
--- Tst/Buch/Example_1_9_3.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_3.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,18 @@
+LIB "tst.lib";
+tst_init();
+
+==========================  example 1.9.4   ================================
+ring s  = (0,Q),(x,y,z),dp;
+matrix C[3][3];
+C[1,2] = Q2;
+C[1,3] = 1/Q2;
+C[2,3] = Q2;
+matrix D[3][3];
+D[1,2] = -Q*z;
+D[1,3] = 1/Q*y;
+D[2,3] = -Q*x;
+ncalgebra(C,D);
+s;
+
+tst_status(1);$
+
Index: Tst/Buch/Example_1_9_30.res.gz.uu
===================================================================
--- Tst/Buch/Example_1_9_30.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_30.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,18 @@
+begin 640 Example_1_9_30.res.gz
+M'XL("--!CD8``T5X86UP;&5?,5\Y7S,P+G)E<P"]5DUOVD`0O?,K1E$/1H7%
+M-M^@NDK4JK*H>BCI&38PA!6VU[&7@/+K.^NO39O6`91V#QB8V??>O)FU/;_]
+MY'\#`,>#K_X-7*E4L4#<74T;\R+B>D!_+D0DE-6<-O05/`\^'WD8![AP%N-%
+MUV81'EBJN*JV=3VHOO<8?*A?@#D<.&S,NO8KZ0W"_`B8)#(!N5KMDP37("+(
+M^0(1(?0FL'Q3SJ4F37<BCD5T#PJ/"C:)##7+LJRSSTS-`Y8;&JUX<%]86@6'
+M'JQQ`]=$"B'?X8\T<,E<(D"5:/QK>YH7N2S#2Q`I1%+IC53@^@0/AN3!JS3+
+M'(AR,GR(>(@@-\!!9W0>].?;<94&C#R0L1(RL@AJ?J/SS.];+H*F&<"Q!V*-
+M/`"?H-%M;=S6UFT[A4$D.8/G*R4>L3`MR\\<VT>G^S6>%#M_9ZIT.[:7Q=1!
+MIFIM^<VR2_[99(Y-;+]B&1HZC3%5I:R0DWE'"FJ':'4ZA1<$QF$EPYCJAHU,
+MPK^[42_#(1GG<AFAKCGE3I?!0]YIH++\'"3'.2"$\A%!24+Z\KW=IC.!=PF'
+MZ\O]ZY+P\_F,]%XY5C/4(RO7^T!:V+*;%PW6^<;WJFE[(<"(['MY5$_(#-_K
+MBZW[0S5&U`@>B"?4&0>6,,5`;1$V)(%H,^A"]0Q/E7Q^&?V)QK]<HJEUH&N=
+MUDJNES+(I#QS;_AL.D>L;/?6N+UM._^OX2/3\)<2C&BZW67QS,]MY6?IR_;?
+MM5+?__Y$76ES;:VM.FAF4:]U7W>81!CHIP=552NX5HAK9T).Y#'J'--NUV79
+56XM^)=FGEM.<OFO\!/#,%*WK"```
+`
+end
Index: Tst/Buch/Example_1_9_30.stat
===================================================================
--- Tst/Buch/Example_1_9_30.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_30.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728083:2007070609:3-0-3:ix86-Linux:nepomuck:158640
+1 >> tst_memory_1 :: 1183728083:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728083:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728083:2007070609:3-0-3:ix86-Linux:nepomuck:3
Index: Tst/Buch/Example_1_9_30.tst
===================================================================
--- Tst/Buch/Example_1_9_30.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_30.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,23 @@
+LIB "tst.lib";
+tst_init();
+
+=============================== example 1.9.30 ==============================
+
+LIB "ncalg.lib";
+def A0 = makeUsl2();  setring A0;
+option(redSB);  option(redTail);
+ideal I = e2,f2,h2-1;
+I = twostd(I);
+print(matrix(I));     // ideal in a compact form
+
+qring A  = I;        // we move to a GR--algebra A
+ideal Ke = modulo(e,0);
+Ke = std(Ke+std(0)); // normalize Ke w.r.t. the factor ideal
+Ke;
+
+ideal Kh = modulo(h-1,0);
+Kh = std(Kh+std(0));
+Kh;                  // the kernel of h-1
+
+tst_status(1);$
+
Index: Tst/Buch/Example_1_9_31.res.gz.uu
===================================================================
--- Tst/Buch/Example_1_9_31.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_31.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,17 @@
+begin 640 Example_1_9_31.res.gz
+M'XL("--!CD8``T5X86UP;&5?,5\Y7S,Q+G)E<P"M55]OFS`0?\^G.%5]@+4B
+M,21-DZA,JK:'BFG20M^#1YS,*M@,S!;RZ7<.!+,US9(J2`E@GW]_CO,Y?/[T
+M]!4`B`]?GA[A2A7*2?CWJUDO;&9<'W!PP057ECWKZ3OX/GS>T#1+V((L)@N/
+M.(+]=@I%5;O,\Z%]'CKP</P"5L,!<2:.1_X3WD/,C\#R7.8@X[C,<[8$+J#F
+M2[A@,)Q"=%'.2),6+SS+N%B#8AL%JURFFB7:^QPYQO.=4R=4Q#19-REM)\<^
+M+-D*YO``*7UAWPKI61XF=^<KZ@Q%P`LH!0:CJ>4)OL?H^Q!TU'+?^U`PE6L7
+M\X9QKEF$!$%3!G(%%/1T_Z?^/X'S'CD-I&&:^"`SQ:6P<$WX:,\ZK\^4)SC0
+M[\,*@7&@C!%7EBHKVQHB`Q_XDM$$`G2SN:ENMK?ZMVUDH^(=)XT5_\6:Y.T6
+MG)TV,I@V2U]QM7X([I%4+DNLF!!CBFIK!6BAN=")^L'`2MA*V7JR6E?[<$QI
+M<$1R'75(\Z'PXS[(=(_W'I'&*^[Z#*F5%9K5_UR]*#3QG>U.<+O7J<2^@1IV
+MSY;*J2@R63!$_&!>`MM^U]<\/S/#]@N?*,N8&^V3D5*L\HV%`$=E'Q<R0B$'
+MX`S=72>78Z<NR-NJ+?LH.+^\=5LP.(8*FT&G3!K\\#()UVVA`VY()YW:ZA:1
+M.S#&7>*8;J'*7.C^T4ZZ_NOJOJAXU_U;?$UAE'IO61AV+.!QH$].?2R6A47L
+,V77O#PM`[V]O!P``
+`
+end
Index: Tst/Buch/Example_1_9_31.stat
===================================================================
--- Tst/Buch/Example_1_9_31.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_31.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728083:2007070609:3-0-3:ix86-Linux:nepomuck:158496
+1 >> tst_memory_1 :: 1183728083:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728083:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728083:2007070609:3-0-3:ix86-Linux:nepomuck:3
Index: Tst/Buch/Example_1_9_31.tst
===================================================================
--- Tst/Buch/Example_1_9_31.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_31.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,26 @@
+LIB "tst.lib";
+tst_init();
+
+=============================== example 1.9.31 ==============================
+
+LIB "ncalg.lib";
+def R = makeQso3(3);
+setring R;
+option(redSB); option(redTail); // for reduced output
+ideal K = x+y+z,y+z,z;
+module S = syz(K);        // the (left) syzygy module of K
+print(S);                       
+
+ideal tst = ideal(transpose(S)*transpose(K));
+print(matrix(tst));
+
+K = x,y,z;
+S = syz(K);
+print(S);
+
+option(returnSB);
+S = syz(K);      
+print(S);
+
+tst_status(1);$
+
Index: Tst/Buch/Example_1_9_32.res.gz.uu
===================================================================
--- Tst/Buch/Example_1_9_32.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_32.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,17 @@
+begin 640 Example_1_9_32.res.gz
+M'XL("--!CD8``T5X86UP;&5?,5\Y7S,R+G)E<P"]EE]OVC`4Q=_Y%%?5'H)4
+M!>+00D!DHMHB4:U[H7N:)I(20ZTF3N:8C8_?:_+'0")&`2T/0&+[_,X]NC:9
+M/7^9?@<`RX5OTP>XD9DT(_9R,VK-BA'B`CZ<,\ZDT1ZUU#>X+GS=!'$:T;DU
+M=^8V,3G]:V8RD-4RVX7J=\^$\;$+:"X&ENF8-H'CL\<ME/P,5(A$0+)8K(6@
+M(3`..2YBG$)O"/XUD;YB9F\L31E?@:0;"4N1Q`KBEU7>F;KB>S./DR^":%4$
+M6@WV70CI$B8PACAXHS^RB&"RJ$^E4/*345ZA7X[ZP#+@B53+L+KPA`#Z&,`_
+M('XN,\G%@0<QA60)`:CQSF_U>2U06?G`A225+.$&"LT>U#1]_QRPJ*W[SG&!
+MA32(8(K*E-PNBU30ZE8W6$CVAQ9);6=N8UKSTT-RAL5*S:B\6MV2_XAC*Y'0
+M%TZ%,6U?WX;5K7P<LK0=W*""9DFT5G&!A_,XWAN/M]VCCO2:)EM-2XY;M8:[
+MF@<^M%L\-+RRB[V/!T*0XNW(X6&2HE%IQ`$VU<;P?EJ_VJI[=JY.!]1CQ9*O
+M%"*ZE-B0Z;F%VFCA7*8VWJL9)\TBI!*)61CBN72!]5[=^@>HVOQ=S;S=+&-7
+M,H*M7B^*_:[N_72HMGZO_WVLOKF[<YY4R\9LV[3>?]TZ_?VM<V!$>Q\<Q/Y4
+M=-ZYW,%AI*6@1CIU)+D$Z30@R1Z2=.M(^P(DZ38@[7VDI9N"$'/[5J->6=:9
+.8;5'GUKOSLT!O@L)````
+`
+end
Index: Tst/Buch/Example_1_9_32.stat
===================================================================
--- Tst/Buch/Example_1_9_32.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_32.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728083:2007070609:3-0-3:ix86-Linux:nepomuck:158452
+1 >> tst_memory_1 :: 1183728083:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728083:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728083:2007070609:3-0-3:ix86-Linux:nepomuck:3
Index: Tst/Buch/Example_1_9_32.tst
===================================================================
--- Tst/Buch/Example_1_9_32.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_32.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,23 @@
+LIB "tst.lib";
+tst_init();
+
+============================= example 1.9.32  ==============================
+
+LIB "ncalg.lib";
+def A = makeUsl2();  setring A;
+option(redSB);  option(redTail);
+ideal I = e2,f;
+ideal J = groebner(I);
+resolution F = nres(J,0);
+F;
+print(matrix(F[1]));             // F[1] is the left map
+print(matrix(F[2]));             // F[2] is the middle map
+print(matrix(F[3]));             // F[3] is the right map
+
+resolution MF = minres(F);
+print(matrix(MF[1]));
+print(matrix(MF[2]));
+print(matrix(MF[3]));
+
+tst_status(1);$
+
Index: Tst/Buch/Example_1_9_33.res.gz.uu
===================================================================
--- Tst/Buch/Example_1_9_33.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_33.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,14 @@
+begin 640 Example_1_9_33.res.gz
+M'XL("-1!CD8``T5X86UP;&5?,5\Y7S,S+G)E<P"ME$]K@T`0Q>]^BD?H04$D
+M&],_B60+)3T$2@]);J6-)F["4K/:==/FXW?45$-I):$5P=UUYOW>#,S.YN/)
+M(P#&\3"Y0\?DQDODLA-8L\.?'@<=+J22QG8"J_B"<]SOHVV6B`5;#!:^[RGQ
+MX>4F,G6:SU&O^QY&K0]$I0;F#3S?;X^V2/$60NM4(UVM=EJ+&%*AHB52"?2'
+M"/^1&!;(_%5FF50;&+$W6.MT6S#"KQHOO:;>*P^ZB-08H>O:>S=VWQPWS@*K
+M#KGFV$9&RSW&3_XSO4%5EDJKU&AEY+NHSL(J,H3,L5.Q6%.)\0E=N!Y^I=:0
+ML#9PP^F0N;WGT=M+[P`/QR5#I0:G4VZ(<J34$`8<:A4E&['4D<W<L?,7RH`H
+MW]1J$NMRR%A$"2;4\++;;=TL0\]N)NL.#ZE'E,8"S4^:&9DJFU)G=TYPM)U'
+M,G'J@6(T4%KD:;(K_F-*8EO:VQ.WZ[39;G)^\OY32GL]O>&QYC<?36$TQ].`
+MY`XNIN<WSB=0*=&(]CDRLFOLI3!&VE/'[92K3EL'VBG%R/^FV8`OFUN)T906
+4%UMQ:^URFSG!A?4)N2WNZPX%````
+`
+end
Index: Tst/Buch/Example_1_9_33.stat
===================================================================
--- Tst/Buch/Example_1_9_33.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_33.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728084:2007070609:3-0-3:ix86-Linux:nepomuck:158412
+1 >> tst_memory_1 :: 1183728084:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728084:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728084:2007070609:3-0-3:ix86-Linux:nepomuck:3
Index: Tst/Buch/Example_1_9_33.tst
===================================================================
--- Tst/Buch/Example_1_9_33.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_33.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,17 @@
+LIB "tst.lib";
+tst_init();
+
+============================== example 1.9.33 =============================
+
+ring r = 0,(x,d,q),dp;
+matrix D[3][3];
+D[1,2]=q^2;
+ncalgebra(1,D);
+ideal I = x,d,q;
+option(redSB); option(redTail);
+resolution R = mres(I,0);
+R;   
+print(betti(R),"betti");
+
+tst_status(1);$
+
Index: Tst/Buch/Example_1_9_34.res.gz.uu
===================================================================
--- Tst/Buch/Example_1_9_34.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_34.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,17 @@
+begin 640 Example_1_9_34.res.gz
+M'XL("-5!CD8``T5X86UP;&5?,5\Y7S,T+G)E<P"ME=UNXC`0A>]YBE&U%X&&
+ME-B!0E&S@FZ["HOVIO2&58&4.,0B/R@QHH^_8T+LM*JZ*U&$"/%DYGQS/%8>
+M9S^\WP!@NS#UQG`A"F'%_.5BV'@\18@+N+CD*1=&<]B05W!=N'_UDUW,EO9R
+ML*2.E;*#50A?J#3J@OKO6'#[CP^PLA[8UL"BSJ?/-[#D=V!YGN60K=?[/&<!
+M\!1*N9BG#)P;6'VEY$IJ%EN^V_%T`X*]"@CS+)$BJZK+KJ4[[EFEG9MMP).3
+MH2IX??(Z7?OQYIW;?1<"%L((;B'QM^RIB`W2',+5%11,P'X'3T81+TE3)0Q<
+M&<DEUDB5L3LN\(#Y,7B`E1@Q0QVSJ]C4PU@A`L-KZBAN]\]?"&U,Y>K1Z=5Q
+M806\@#03D@\M#OYC%VQR<TH^5ELI$5HAS"2".&3O*9R*8O8%%(ZBF+VAZ%84
+M<X1P6JP5PB5$"P)MO(LT3,\]/B$9YS7&ZXIQ?C[BM4*<UPEQ&HX[.T;YCFGX
+M33/8:8!!.2MPA]$1HH]5B'3T5-SI55M/!0[%@IH0RI]H0=O8L%EZ<(D.M$DK
+M0A=\G8IC\<&T$%IY</XV$:H\J.\2<2KHB82.><)37S##,Y&U%=58NA7+Y'R6
+MKF*9U%EZ'QTV@H.0LR*+]X)G*3P@9HKW./)FISRZ!P;K+-GMA102\,+"+&<J
+MO5]Q/_RQG\L$$2$R?O&$<E&P.#RWG[[JYQ,1W>=`(Y'G\]T<U-1E/25$.UJ(
+DGB]$.S4A^D;(UJ\C2JSC&TV^KO:%83>'WQI_`7PH,*,'!P``
+`
+end
Index: Tst/Buch/Example_1_9_34.stat
===================================================================
--- Tst/Buch/Example_1_9_34.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_34.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728085:2007070609:3-0-3:ix86-Linux:nepomuck:327328
+1 >> tst_memory_1 :: 1183728085:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728085:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728085:2007070609:3-0-3:ix86-Linux:nepomuck:23
Index: Tst/Buch/Example_1_9_34.tst
===================================================================
--- Tst/Buch/Example_1_9_34.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_1_9_34.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,33 @@
+LIB "tst.lib";
+tst_init();
+
+================================ example 1.9.34 ============================
+
+LIB "gkdim.lib";
+LIB "ncalg.lib";
+def A = makeUsl(2); // set up U(sl_2)
+setring A;
+ideal I  = e2,f;
+ideal LI = std(I);
+GKdim(LI);
+ideal TI = twostd(I);
+GKdim(TI);
+ideal Z = 4*e*f + h^2 - 4*h;
+Z = std(Z);
+GKdim(Z);
+ring B = 0,(a),dp;
+def  C = A + B;
+setring C;
+ideal I = e^3, f^3, h^3-4*h, 4*e*f+h^2-2*h - a;
+I = std(I);
+GKdim(I);
+ideal J = eliminate(I,e*f*h);
+GKdim(J);
+setring A;
+resolution F = nres(LI,0); // we computed it before
+GKdim(F[1]); // this is LI itself
+GKdim(F[2]);
+GKdim(F[3]);
+
+tst_status(1);$
+
Index: Tst/Buch/Example_4_6_26.res.gz.uu
===================================================================
--- Tst/Buch/Example_4_6_26.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_4_6_26.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,15 @@
+begin 640 Example_4_6_26.res.gz
+M'XL("-5!CD8``T5X86UP;&5?-%\V7S(V+G)E<P"M5,MNG#`4W?,55U&E0`.>
+MX1':!D&EJEV,5+J8R;I`P2E6&1O9GH;^?6T>9M0D:E+5"VSL>\ZYQ]?VX?;C
+M[@L`^!E\WGV`"RDDZLBWB\0ZS"M!!FJR()1(VTDLW4.6P:>A.O8=+J(B+H(8
+M47R/A*RD@849F'&$(/U;`\`3HXJ.41##TQ!+4;X'S#GCP.KZQ#EN@%"8Y#I"
+M%<<-E/]3LM2:X@?I>T*_@\2#A#O.CEJD7%Q>H]5QC(#K2(!]NG4'.T+(=]RF
+M3RP3\B8#TN"J`]BEWF#[SNO!#IRK>13I4>BXDU?*)KJJEN0GGN;*$5T"$7"B
+M#;Y3MAM#_A:!:2NY%XS=UV#D'E4\WS6@=X^"EF3FM$;PPF?6%PY_>\9Q-<>'
+M8W#RC++Y6U6WI_"E$5&']5A)3@;(T[JM>"$P)UC8NT7DT?V:(']LV#-R\F\6
+M[$.Y-2=U3>:*'U)[++GCJ*^/4#@6?K.1#`3&(%L,'(M3)^&>R%:-/4,2GADC
+MQZJW]V[N).N.;C:BQ[4$1:5IZI8Q@2DPWF`M/AO=CQXID_`"E^&YRW_0+F>1
+M00<I^HG+4__*K"",(I"_>@R7+>[Z>36Y-,ZC#/*Y>&7^\AKI^YZ?5>-Z?7U\
+7=1?U`Z9?IY-01S=Y9?T&D0S\-/8$````
+`
+end
Index: Tst/Buch/Example_4_6_26.stat
===================================================================
--- Tst/Buch/Example_4_6_26.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_4_6_26.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728085:2007070609:3-0-3:ix86-Linux:nepomuck:161548
+1 >> tst_memory_1 :: 1183728085:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728085:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728085:2007070609:3-0-3:ix86-Linux:nepomuck:3
Index: Tst/Buch/Example_4_6_26.tst
===================================================================
--- Tst/Buch/Example_4_6_26.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_4_6_26.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,17 @@
+LIB "tst.lib";
+tst_init();
+
+=================================  example 4.6.26  =========================
+
+ring   R=0,x(4..1),dp;
+ideal  I=-x(1)*x(2)+x(1)*x(4)+x(3),
+         -x(1)*x(2)-2*x(2)^2+x(3)*x(4)-1,
+         -x(1)*x(2)*x(4)+x(1)*x(4)^2+x(1)*x(2)-x(2)*x(4)
+         +x(4)^2+3*x(2);
+matrix M=char_series(I);
+ring   S=(0,x(4)),x(1..3),dp;//to see the result with re-
+matrix M=imap(R,M);          //spect to the choosen ordering
+M;
+
+tst_status(1);$
+
Index: Tst/Buch/Example_4_7_7.res.gz.uu
===================================================================
--- Tst/Buch/Example_4_7_7.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_4_7_7.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,16 @@
+begin 640 Example_4_7_7.res.gz
+M'XL("-5!CD8``T5X86UP;&5?-%\W7S<N<F5S`*U438^;,!"]YU>,5CU`(1!(
+MNC2)H.JJU2Y2MX=F3ZVB0,#)6G5L:HP*_/J.-^&CAW975>?"X/&\-_,\]N;A
+M0_P9`+P(/L4W<*5*Y3"ZOUI/-I>('P$N[BBGRC#7$_V%*(*/=7HJ&-DM=L$N
+M<#CYZ90J57W6/(+>7S@0/F=`SGBX.7""O^Z?(.0[(%(*"2++*BE)#I3#F8Y1
+MCB`K2/XG9:(YR^^T*"@_@B*U@H,4)TV2=%V^<8:.KQVMYE4AZ2DGV470/AI$
+M(#7.EW!F&[7=V*UILV)0_&T$-"<I@SAL_:EO0^-;?C/U;#`:J[4\\W5M-2UZ
+M&*I]"W^FWI"]C.!$^?NRO'WX:L1X8D]R)?U:`K0$+A3DY(!:Y2^0<[D:Y6O,
+MI&/S9L,Y>YX#HE!4<`,A-C?F&B[FNBG@4I4A,B,UW$I!]IQ(V*<E%J/K(23'
+M4CHDG+DX+%6NN6!LB(3[>5'A`6"]2M*4'^_OP$C944BJ'D\]!DY@%S9BVQ]7
+M(PYP+PAC1-IP1_&[ERG/S8M27=8_".7-5T/^"UD'+1<C+7&:=/\_*J$HX0JQ
+MSD>O`5U7/1(H229X?NFQ8JG$%379??.V3U.#GK\-FRDFH3O?AK75]NC7(Z;@
+MS-01K'^76S,=J"S5<T360(0C.6TQT#'@//_17!>')4L9`\UT(BG7-P.E.M<$
+A!]/L<9;##?-G(Q_G3K]0^OVI2@-;>#7Y!2(LOE37!```
+`
+end
Index: Tst/Buch/Example_4_7_7.stat
===================================================================
--- Tst/Buch/Example_4_7_7.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_4_7_7.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728085:2007070609:3-0-3:ix86-Linux:nepomuck:160448
+1 >> tst_memory_1 :: 1183728085:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728085:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728085:2007070609:3-0-3:ix86-Linux:nepomuck:3
Index: Tst/Buch/Example_4_7_7.tst
===================================================================
--- Tst/Buch/Example_4_7_7.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_4_7_7.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,22 @@
+LIB "tst.lib";
+tst_init();
+
+================================= example 4.7.7 ============================
+
+LIB"primdec.lib";
+ring R=0,(x,y,z),lp;
+ideal I=z2-2, y2+2y-1, (y+z+1)*x+yz+z+2, x2+x+y-1;
+minAssGTZ(I);
+
+option(redSB);        //a reduced lex Groebner basis is needed
+I=std(I);             //as input for triangMH (algorithm
+triangMH(I,2);        //of Moeller, Hillebrand)
+
+std(quotient(I,y+z+1));  //the second triangular set
+
+std(I,y+z+1);            //the first triangular set
+                         //(recall the meaning of std(I, f))
+
+
+tst_status(1);$
+
Index: Tst/Buch/Example_B_5_10.res.gz.uu
===================================================================
--- Tst/Buch/Example_B_5_10.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_5_10.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,32 @@
+begin 640 Example_B_5_10.res.gz
+M'XL("-9!CD8``T5X86UP;&5?0E\U7S$P+G)E<P"M6%UOXC@4?>^OL$8K36@R
+M`3L)E$')2M6N1DBK?6CG;;6"##@0;4BRCIE"?OU<Y\,.%"@)\-"F=7S/N5_'
+M%[]^_V/Z-T((>^BOZ3/ZQ#-N1N&/3Y.'UVJ%>`C^.0OCD&N]R8/XC3P/_;GS
+M-VE$9\\S9X8'9DS?S(S[7&ZS/"2?;1.Y'WT0+0VB9],Q\>#"A@>P^#NBC"4,
+M)8O%EC&Z1&&,2K0HC"FROZ+Y'1'G`C+[+TS3,%XA3G<<!2S9"(QY[:-C(B96
+M7UQB:+FQ,_8](THG#S((0P^E2;1'@;LC^D['$R0__?X&PKKQH^*-.-F$\)@$
+MB*\I"D(:+4N7XZ2$\!<\_$G+_\W%CCD*,[2-ES0`YY=7Q&?XM=S8B<Q<NC3R
+MT+E/OP]1HG$6)K%\_<DL([!R<Z+G1Z`-,)Z@`'Q,6)C3>WO^5'O>AH3R>.PA
+M1K-MQ/V8:X&Q,G;0$B6=H.`2)QQ=SV8,;-[9DVAX<(B6;7]D7%L9N9'KNYZ"
+M/A6=B[!X<(3[WK(B@54C8U)E<.WN'7UOZ7NB[ZL0]ONB0$Z43@`\Q!(H!+IW
+M-C&IT]F5D?+3NE3,1>&C=R6-[2H@W]R#$.Y[DPJ>,S_.`'`#W!6%#G%HGV2[
+MCDU+<BHD3B59S&T6RS=1'^C^N71JOB?A%"L04C8YEZ@BK^`18K5F-9VL^+'V
+MY(1B=D55U"\*9J,\ZO=!,>7S6#V3055V62-2:X/!F7-!$KJEA0SJM)P`DYX1
+M4(GLX_!`<%A%)FO/!`.3*T$4,:+DBUBFTG0MD\J==5!N8@&9`V,*TFY`UF/!
+MJZL1,1*(T:`<#.HWH)Q!HT2$#R5,OC"270A"EFHO!I/,7[HP'ZD^4P;GU<Y=
+M2A>\DH,O\!>D7`B>B?@^I>CSFD9IL3;Y+/D]U8,-=E>+I<:,'`_T?*SG(ST?
+MZKFEPT&+I>;`*^@MY.MJGF`9/^S*EL[(\[PS^@V>C\^W\U%QEI52;[2@?P,L
+M!P?<NA4LT91@0=:<!?T'$<A"&&C#8*\%V!!.GZ+R5K:)'T'=PIX;2.""1!=0
+MQ9MX-T:"'$?"JLN1O"\(1R^'OM/UD-%%$B]O*4?+DN78%;U[.5KV=>585Z,4
+M*0M$"OBJ/!*1QSHGI'U.Q$G^WJ!*$4A>0&X!&!8`#8LC);D6')KL2X`?X853
+MSG,*32\"7IYFAZ77,MU"?5I@*;YCQ=<NQ*`:T:"%BAGM<5\U4EDH8?R3LJPQ
+M5?A<3*&=N\8>5*W;'E3Z8)^4G!LXG983A7>K5-C'4F%;7E'W91!(A\BW+UW;
+MJGJC/:CB;7MW[5?;OMROMG-CO]K.4;_:PT;]CTS0/EY>GE0@+V4OHMC?4#'/
+M^<40U?]?_+P&3XPXRJ:"A5$E7%+X"CAU,[[4BF?XBK'NW?0MWA8R<,[NL9X7
+M:^<$O5A4BFZ#3!0^H^_NM&8X;1]^<<V@[,AP.`,/):DH+0TVO3[WY,SI8#73
+M%3/BJQ'@QC)19VR]3!K+]1&\J@?,U4T3JV.I2QMEL/M!Z4#_--*$P9H<6_I]
+M<2A#R:V.Y\1JA"M`RYVF:?9J;[)MFB:,7^>/Z+>N!"JWWU@BKB*%BTNZB'Q6
+M2,2E8G(<U7/.T&Q&@'Q$H)I-[AB"X6$(VC'H'H/&G.`\E3'0=L5,]BA^]Y0,
+I'TT)LW_PO^6-H;@PE38:Y_@0SG%Q42YNP;>9!NWRV\,O'(B-.%X7````
+`
+end
Index: Tst/Buch/Example_B_5_10.stat
===================================================================
--- Tst/Buch/Example_B_5_10.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_5_10.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728086:2007070609:3-0-3:ix86-Linux:nepomuck:162456
+1 >> tst_memory_1 :: 1183728086:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728086:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728086:2007070609:3-0-3:ix86-Linux:nepomuck:2
Index: Tst/Buch/Example_B_5_10.tst
===================================================================
--- Tst/Buch/Example_B_5_10.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_5_10.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,61 @@
+LIB "tst.lib";
+tst_init();
+
+================================= example B.5.10 ==========================
+ring R=2,(z,x,y),lp;
+poly f=x2+x+1;          //minimal polynomial of the field
+                        //extension
+poly g=z2+z+1;          //polynomial to factorize
+resultant(f,g,x);
+resultant(f,subst(g,z,z+x),x);
+
+poly h=y5+y3+y2+y+1;    //the minimal polynomial for the new 
+                        //field extension
+poly G=subst(g,z,z+xy); //the transformed polynomial
+poly r=resultant(f,G,x);  
+r;                      //the norm r of the transformed 
+                        //polynomial
+
+
+poly s=resultant(h,r,y);
+s;                      //the norm of r
+
+factorize(s);
+
+ring S=(2,y),(z,x),lp;
+minpoly=y5+y3+y2+y+1;
+poly r=imap(R,r);
+poly f1=gcd(r,z10+z9+z7+z6+z3+z2+1); //the gcd with the first 
+                                     //factor
+f1;
+f1=simplify(f1,1);                   //we normalize f1
+f1;
+poly f2=gcd(r,z10+z9+z7+z5+z2+z+1); //the gcd with the second 
+                                    //factor 
+f2=simplify(f2,1);
+f2;
+
+r-f1*f2;                  //test the result
+
+f1=subst(f1,z,z+x*y);     //the inverse transformation
+f1=simplify(f1,1);
+f1;
+f2=subst(f2,z,z+x*y);     //the inverse transformation
+f2=simplify(f2,1);
+f2;
+
+setring R;
+ideal I=std(ideal(f,h));
+qring T=I;
+option(redSB);
+poly f1=imap(S,f1);
+poly f2=imap(S,f2);
+poly g=imap(R,g);
+std(ideal(f1,g));       //gcd of g with the first factor
+
+std(ideal(f2,g));       //gcd of g with the second factor
+
+std((x+z+1)*(x+z));     //test the result
+
+tst_status(1);$
+
Index: Tst/Buch/Example_B_6_12.res.gz.uu
===================================================================
--- Tst/Buch/Example_B_6_12.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_6_12.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,22 @@
+begin 640 Example_B_6_12.res.gz
+M'XL("-9!CD8``T5X86UP;&5?0E\V7S$R+G)E<P#-5UUOVC`4?>=77%63"@)2
+M8B=`&R73JDT34M6'T#T3/AP:#9(L-FOR[V>3#YN,5A!X:!]H',?GW'ON\4T\
+M??D^>08`W8&GR2/<,,JT3;"XL5K38@8YP&_.@C!@[8[5$O_!<>!'.M_&&S)[
+MG`UG.M)"\J91-F?5,NQ`=6UH8)_V!R2'A4=MJ.GHR+(6Q_L*)$FB!*+E<I<D
+M9`5!"#G7)@@)&`_@78W/$X3T=Q#'0;@&1E(&?A)M!8-7YF=J,M>A!HEXTK4'
+MO7;:RSJ]56RUJNF1`W&TR<"W<8JRKI%FJ)OA+A]TAVG6Y2.<6GF.890CS9<L
+M^$OR>YY8[$%`81>NB,^S79T@R.@A7_@QJU<%.2Z"7-M(/,Z?[F>XSZ_[_`I=
+M/[YQ&=][A#*T>VDK?5!(/;7;`R%TNI>ZG-4KI8/M/&Z[/;]CE6D5=]:=(A7/
+MW<<<1@Q.CUK7I:P?47@%5AJ3)>,HXH$^'R6$TB`*-6!93.#VE6SB_9QU^SF#
+M*H7E#<$O=?//KK6.>("^K*C.&\6ZA%N?#X<YW%J!,Q2#F(5!7G3;K+ECZ`#7
+M`N+7P';YU,"JZ2'6]</YEIP2PY#'<(A6EY?/OJ<NGU+$E?V!@[65THFA]"L?
+M-3&'T@B.PS?VZB<*J)1R?)E/QS6?WE_FT_M#GZ*!]"G22Y\B>W3H4X0*G](K
+M^!2ATJ?T4I\B+'U*#^M&#WQ*F]@"8<461^&;^_3S!%1*:5SD4V0<^A29%_D4
+MF36?#A6?CC2@A!4M57I4?"X4G0_5&]19W/OO@`I)QL"WGNP/56O@@'=W;P3H
+M;D%9P':,0`:+#%!S+<4F/8?):Z[S^52%&IAWCO5RU?:5SQ>_@:?Q0%2Z!)+P
+MNBPX1DK!455P+#8_K1><GE]PO-]6]+^"8\-1-EJ]IYQ?5VSD8M<!FY?O?<0R
+M!?-*53*/5TG9EEC9EF[!Y>9,(-X,$/DPW[\H[OZ(WU-8Q7M98DK:L9(5P-ZL
+M[)7`=/+\\]?3-Q<6NV##^AS,WX7\6!"%EZ0^5E,_B4T&JIP3#'Y.$"=8<3S=
+0T;;>L;ZT_@%R^__%]PX`````
+`
+end
Index: Tst/Buch/Example_B_6_12.stat
===================================================================
--- Tst/Buch/Example_B_6_12.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_6_12.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728086:2007070609:3-0-3:ix86-Linux:nepomuck:162668
+1 >> tst_memory_1 :: 1183728086:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728086:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728086:2007070609:3-0-3:ix86-Linux:nepomuck:3
Index: Tst/Buch/Example_B_6_12.tst
===================================================================
--- Tst/Buch/Example_B_6_12.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_6_12.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,41 @@
+LIB "tst.lib";
+tst_init();
+
+======================================= example B.6.12 ==================
+
+ring R=0,(x,y),dp;
+poly f=3x2y+4xy2+y3+3x2+6xy+y2+3x;
+poly g=2x2y+xy2-y3-2x2-y2-2x;
+
+ring S=(0,y),x,dp;
+poly f=imap(R,f); poly g=imap(R,g);
+f;
+g;
+
+ring T1=5,x,dp;
+map phi=R,x,0;
+poly f=phi(f); poly g=phi(g);
+f;
+g;
+
+ring T2=7,x,dp;
+map psi=R,x,0;
+poly f=psi(f); poly g=psi(g);
+f;
+g;
+
+setring T1;
+phi=R,x,2;
+f=phi(f); g=phi(g);   //we substitute y by 2
+gcd(f,g);
+
+setring T2;
+psi=R,x,2;
+f=psi(f); g=psi(g);
+gcd(f,g);
+
+setring R;
+gcd(f,g);     //the SINGULAR built-in function
+
+tst_status(1);$
+
Index: Tst/Buch/Example_B_6_2.res.gz.uu
===================================================================
--- Tst/Buch/Example_B_6_2.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_6_2.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,12 @@
+begin 640 Example_B_6_2.res.gz
+M'XL("-=!CD8``T5X86UP;&5?0E\V7S(N<F5S`*V244^#,!2%W_D5-XL/,*"A
+MA:&3#)-%'Y88'YSO,$<QC:R0TBGEU]N.C6EBXAYLTM!>3L_7T]SUR_WJ"0!P
+M"H^K)4QD*U'%7B>)M3[^(2GH8L8XD[:36.8+:0H/W6;75#1;9G%&$*>?J)4;
+M.9X*4QC7$8+%90/HX`I+%"/RVRE+^]T!%:(64&^W>R%H`8S#P*H8IQ#=0OYO
+MO-P`VW?6-(R_@:2=A%+4.T/(3_EFZ)PU1B",\GD1>';G*:]WO*))K%%PG4)3
+M5PK*11>YMM^[H3/M0M?N]52^WO2^(CXV53*$Y?5@N=E*]D&'6FX\<F`M['E!
+M2QV[&`DW",9A"!JCB!LJ%\^TNQMKYU$[_ZY56DKT/?JI[:O0QS/E^$1?)@R2
+M"YY]KI_](J_\1,=!"J5.50O64[MTCI2\/`3CM813M+_I.-#X'V9G##[W(B;H
+4T,VF5_>MC9WDROH"\`!#X0,#````
+`
+end
Index: Tst/Buch/Example_B_6_2.stat
===================================================================
--- Tst/Buch/Example_B_6_2.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_6_2.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728087:2007070609:3-0-3:ix86-Linux:nepomuck:158448
+1 >> tst_memory_1 :: 1183728087:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728087:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728087:2007070609:3-0-3:ix86-Linux:nepomuck:2
Index: Tst/Buch/Example_B_6_2.tst
===================================================================
--- Tst/Buch/Example_B_6_2.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_6_2.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,13 @@
+LIB "tst.lib";
+tst_init();
+
+======================================= example B.6.2 ===================
+
+ring R=0,(x,y,z),dp;
+poly f=x4+(-z+3)*x3+(z3+(y-3)*z-y2-13)*x2
+         +(-z4+(y2+3y+15)*z+6)*x
+         +yz4+2z3+z*(-y3-15y)-2y2-30;
+factorize(f);
+
+tst_status(1);$
+
Index: Tst/Buch/Example_B_6_4.res.gz.uu
===================================================================
--- Tst/Buch/Example_B_6_4.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_6_4.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,11 @@
+begin 640 Example_B_6_4.res.gz
+M'XL("-=!CD8``T5X86UP;&5?0E\V7S0N<F5S`*V2P4^#,!3&[_P57Q8/$+$9
+M&VYSA)H0/2PQ'C;/4H1B&EE+2J?@7R^,R;+$`P=[:?/>^][O?<W;O3QLG@%X
+M%$^;"!-3&5*(MTE@[4Z9&44;C(44QG8"J[M!*1[K9%\6/([B1>P3R;](91(S
+MJ.84P]LG"$<=\+XI(K(@_I\BJ^UW#ZZUTE!I>M":9Q`2/:L0DL-?@_T;CW7`
+MZD.4I9#O,+PVR+7:=P3VZ^^6G+TN"'17N0VGKEV[C>-F96`-Z25%J8H&>5C/
+M;NSFVG->YT'O2:I>F:1&?/(^QKIB!E'A(#.>M^ZR$1^P7/?"2PH;AEA1Y"U%
+M:?'-[=PY\5E^!$EE,!ZU:E$7O<Z4N_,&>%-RW*%N0PZ5[3G!E?4#SK>PY7D"
+"````
+`
+end
Index: Tst/Buch/Example_B_6_4.stat
===================================================================
--- Tst/Buch/Example_B_6_4.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_6_4.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728087:2007070609:3-0-3:ix86-Linux:nepomuck:158336
+1 >> tst_memory_1 :: 1183728087:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728087:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728087:2007070609:3-0-3:ix86-Linux:nepomuck:2
Index: Tst/Buch/Example_B_6_4.tst
===================================================================
--- Tst/Buch/Example_B_6_4.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_6_4.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,11 @@
+LIB "tst.lib";
+tst_init();
+
+====================================== example B.6.4 ====================
+
+ring R=0,(x,y),dp;
+poly f=x2-(y+1)^3;
+factorize(f);
+
+tst_status(1);$
+
Index: Tst/Buch/Example_B_7_5.res.gz.uu
===================================================================
--- Tst/Buch/Example_B_7_5.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_7_5.res.gz.uu	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,14 @@
+begin 640 Example_B_7_5.res.gz
+M'XL("-=!CD8``T5X86UP;&5?0E\W7S4N<F5S`+64S6ZC,!2%]SS%430+TB!/
+M[$!(6X5*45NI4M7%9-8%FIB150(4'(7DZ6O3!-Q?9313%F#9^!Z?\UUY_OOR
+MY@X`#7![,T-/5I*DXJ%W;LWW*RR`F@Q%)J3=/[?T%T&`JSI>%2D/9Z$?>B3C
+M&U+)6+:[1@':L4LP/>(!?RF)&?&)]]D62Q6\`"_+O$2^6*S+DB\A,KR(I2+C
+M<,\0_3_!2"M6CZ(H1/8'DM<229FOM$1T<.B1SNV8Z"1[\4.5Q(M]F(#5KOM&
+M,A."4E?]1:=#QZZ=;=]9%EWTIP&*/-TBF=HU&VQ9_WYT8M>C9N2ID3MP^_>L
+M_9\.`RQY@CG%5,E?*_F\%#MN)XI;$UMD3D<0%;)<ZCTJMN41R=*ABO8SB:@]
+MAVJFBDOMS)[3@[;:TN@ABU<<>8*X\?[S2;^/T:9*VRS;Z:D658?)T[7D8=(<
+MJ3(,OYIO3*^SO[#,SMY7,;2-1J?N`2?;XW1VSN854NJ]03K8*99LL'&[7\9[
+MBNS;*(X/%#^0Z)SY!D764F3_2-$W*3)3;_*=%"=?4SSM*+(A:2X\?9VM*ULU
+,V@_K&=:@D_0F!0``
+`
+end
Index: Tst/Buch/Example_B_7_5.stat
===================================================================
--- Tst/Buch/Example_B_7_5.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_7_5.stat	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,4 @@
+1 >> tst_memory_0 :: 1183728087:2007070609:3-0-3:ix86-Linux:nepomuck:162000
+1 >> tst_memory_1 :: 1183728087:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_memory_2 :: 1183728087:2007070609:3-0-3:ix86-Linux:nepomuck:706180
+1 >> tst_timer_1 :: 1183728087:2007070609:3-0-3:ix86-Linux:nepomuck:2
Index: Tst/Buch/Example_B_7_5.tst
===================================================================
--- Tst/Buch/Example_B_7_5.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
+++ Tst/Buch/Example_B_7_5.tst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -0,0 +1,21 @@
+LIB "tst.lib";
+tst_init();
+
+==================================== example B.7.5 =======================
+
+LIB"absfact.lib";  
+
+ring R1=0,(x,y),dp;
+poly f=(x2+y2)^3*(x3+y2)^5*(x4+4)^2;
+def S1 =absFactorize(f);
+setring(S1);
+absolute_factors;
+
+ring R2=0,(x,y,z,w),dp;
+poly f=(x2+y2+z2)^2+w4;
+def S2 =absFactorize(f);
+setring(S2);
+absolute_factors;
+
+tst_status(1);$
+
Index: Tst/Buch/buch.lst
===================================================================
--- Tst/Buch/buch.lst	(revision b9098a173989c6af6070827d3d7450ac82a9c4a9)
+++ Tst/Buch/buch.lst	(revision a7efa795b51b06ad0b97c4eb3ce0b3b005e0d96f)
@@ -88,2 +88,23 @@
 Proc_3_7_3
 Proc_4_6
+Example_1_9_13
+Example_1_9_20
+Example_1_9_22
+Example_1_9_23
+Example_1_9_24
+Example_1_9_25
+Example_1_9_28
+Example_1_9_29
+Example_1_9_3
+Example_1_9_30
+Example_1_9_31
+Example_1_9_32
+Example_1_9_33
+Example_1_9_34
+Example_4_6_26
+Example_4_7_7
+Example_B_5_10
+Example_B_6_12
+Example_B_6_2
+Example_B_6_4
+Example_B_7_5
