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/*-*-MACSYMA-*-*/
EVAL_WHEN(BATCH,TTYOFF:TRUE)$
/* Or use the BATCHLOAD command to load this with TTYOFF:TRUE */
/* NOTE: THE CURRENT VERSION OF VECT IS THE ONE DUE TO STOUTEMYER.
IT WILL BE REPLACED SOON BY AN EXTENDED VERSION WHICH HANDLES BOTH
VECTORS AND DYADICS.
MICHAEL C. WIRTH (MCW)
12/18/78
Style changes made in order to TRANSLATE, 3/1/81 George Carrette (GJC)
*/
HERALD_PACKAGE('VECT)$
PUT('VECT,TRUE,'VERSION);
EVAL_WHEN([TRANSLATE,batch,demo,load,loadfile],
/* trgsmp is in the standard Maxima image but check anyway */
if get('sin,'complement_function)=false then load("trgsmp"),
MATCHDECLARE([ETRUE,TTRUE,VTRUE], TRUE,
LESSP, BEFORE, SCALARM, VSCALARP),
TR_BOUND_FUNCTION_APPLYP:FALSE
/* we do not want FOO(F):=F(1) to mean APPLY(F,[1]) */
)$
INFIX("~", 134, 133, EXPR, EXPR, EXPR) $
PREFIX("GRAD", 142, EXPR, EXPR) $
PREFIX("DIV", 142, EXPR, EXPR) $
PREFIX("CURL", 142, EXPR, EXPR) $
PREFIX("LAPLACIAN", 142, EXPR, EXPR) $
DECLARE([".",ORDER],COMMUTATIVE,
ORDERN,NARY,
["GRAD","DIV","CURL","LAPLACIAN"],OUTATIVE,
"CURL",NONSCALAR)$
TELLSIMPAFTER(0~ETRUE, 0) $
TELLSIMPAFTER(ETRUE~0, 0) $
TELLSIMPAFTER(ETRUE~ETRUE, 0)$
TELLSIMPAFTER(ETRUE~TTRUE.VTRUE, ETRUE.TTRUE~VTRUE)$
TELLSIMP(ETRUE~LESSP, -LESSP~ETRUE) $
TELLSIMPAFTER(DIV (CURL( ETRUE)), 0) $
TELLSIMPAFTER(CURL (GRAD( ETRUE)), 0) $
TELLSIMPAFTER(VECTORPOTENTIAL(ETRUE,TTRUE),
(SCALEFACTORS(TTRUE), VPOT(ETRUE))) $
TELLSIMPAFTER(VECTORPOTENTIAL(ETRUE), VPOT(ETRUE)) $
TELLSIMPAFTER(EXPRESS(ETRUE), EXPRESS1(ETRUE)) $
TELLSIMPAFTER(EXPRESS(ETRUE,TTRUE),
(SCALEFACTORS(TTRUE), EXPRESS(ETRUE))) $
TELLSIMPAFTER(POTENTIAL(ETRUE, TTRUE),
(SCALEFACTORS(TTRUE), POTENTIAL1(ETRUE))) $
TELLSIMPAFTER(POTENTIAL(ETRUE), POTENTIAL1(ETRUE)) $
/* Variables and switches */
DEFINE_VARIABLE(COORDINATES, '[X, Y, Z],ANY)$
DEFINE_VARIABLE(DIMENSION,3,FIXNUM)$
DEFINE_VARIABLE(DIMENIMBED,1,FIXNUM)$
DEFINE_VARIABLE(TRYLENGTH,1,FIXNUM)$
DEFINE_VARIABLE(BESTLENGTH,1,FIXNUM)$
DEFINE_VARIABLE(SFPROD,1,any)$
DEFINE_VARIABLE(SF,[1,1,1],list)$
DEFINE_VARIABLE(EXPANDALL,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDDOT,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDDOTPLUS,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDGRAD,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDPLUS,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDALL,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDGRADPLUS,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDDIV,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDDIVPLUS,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDCURL,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDCURLPLUS,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDLAPLACIAN,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDLAPLACIANPLUS,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDPROD,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDGRADPROD,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDDIVPROD,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDCURLCURL,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDLAPLACIANTODIVGRAD,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDLAPLACIANPROD,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDCROSS,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDCROSSCROSS,false,BOOLEAN)$
DEFINE_VARIABLE(EXPANDCROSSPLUS,false,BOOLEAN)$
DEFINE_VARIABLE(FIRSTCROSSSCALAR,false,BOOLEAN)$
EV_DIFF(X):=APPLY('EV,[X,'DIFF])$
declare(jacobian,special)$
SCALEFACTORS(TRANSFORMATION) := BLOCK(
IF LISTP(FIRST(TRANSFORMATION)) THEN (
COORDINATES: REST(TRANSFORMATION),
TRANSFORMATION: FIRST(TRANSFORMATION))
ELSE COORDINATES: LISTOFVARS(TRANSFORMATION),
DIMENSION: LENGTH(COORDINATES),
DIMENIMBED: LENGTH(TRANSFORMATION),
FOR ROW:1 THRU DIMENSION DO
FOR COL:1 THRU DIMENIMBED DO JACOBIAN[ROW,COL]:
TRIGSIMP(RATSIMP(DIFF(TRANSFORMATION[COL],
COORDINATES[ROW]))),
SFPROD:1,
FOR ROW:1 THRU DIMENSION DO (
FOR COL:1 THRU ROW-1 DO (
SF[ROW]: GCOV(ROW,COL),
IF SF[ROW]#0 THEN PRINT("WARNING: COORDINATE SYSTEM IS NONORTHOGONAL UNLESS FOLLOWING SIMPLIFIES TO ZERO:", SF[ROW])),
SF[ROW]: RADCAN(SQRT(GCOV(ROW,ROW))),
SFPROD: SFPROD*SF[ROW])) $
GCOV(II,JJ) := TRIGSIMP(RATSIMP(SUM(
JACOBIAN[II,KK]*JACOBIAN[JJ,KK], KK, 1, DIMENIMBED))) $
EXPRESS1(EXPN) := BLOCK(
[ANS],
IF MAPATOM(EXPN) THEN
IF NONSCALARP(EXPN) THEN (ANS:[],
FOR JJ: DIMENSION STEP -1 THRU 1 DO
ANS: CONS(EXPN[COORDINATES[JJ]], ANS),
RETURN(ANS))
ELSE RETURN(EXPN),
EXPN: MAP('EXPRESS1, EXPN),
IF MAPATOM(EXPN) OR LISTP(EXPN) THEN RETURN(EXPN),
IF INPART(EXPN,0)="GRAD" THEN (ANS:[],
EXPN: INPART(EXPN,1),
FOR JJ: DIMENSION STEP -1 THRU 1 DO ANS:
CONS('DIFF(EXPN,COORDINATES[JJ])/SF[JJ], ANS),
RETURN(ANS)),
IF PIECE="DIV" THEN (EXPN: INPART(EXPN,1),
IF NOT LISTP(EXPN) THEN ERROR("DIV CALLED ON SCALAR ARG:",
EXPN),
RETURN(SUM('DIFF(SFPROD*EXPN[JJ]/SF[JJ],
COORDINATES[JJ]), JJ, 1, DIMENSION)/SFPROD)),
IF PIECE="LAPLACIAN" THEN RETURN(SUM('DIFF(SFPROD*'DIFF(
INPART(EXPN,1),COORDINATES[JJ])/SF[JJ]**2,
COORDINATES[JJ]), JJ, 1, DIMENSION) / SFPROD),
IF PIECE="CURL" THEN (EXPN:INPART(EXPN,1),
IF LISTP(EXPN) THEN (
IF LENGTH(EXPN)=2 THEN RETURN(('DIFF(SF[2]*EXPN[2],
COORDINATES[1])-'DIFF(SF[1]*EXPN[1],
COORDINATES[2]))/ SF[1]/SF[2]),
IF DIMENSION=3 THEN RETURN([
('DIFF(SF[3]*EXPN[3],COORDINATES[2])-
'DIFF(SF[2]*EXPN[2],COORDINATES[3]))/
SF[2]/SF[3],
('DIFF(SF[1]*EXPN[1],COORDINATES[3])-
'DIFF(SF[3]*EXPN[3],COORDINATES[1]))/
SF[1]/SF[3],
('DIFF(SF[2]*EXPN[2],COORDINATES[1]) -
'DIFF(SF[1]*EXPN[1],COORDINATES[2]))/
SF[1]/SF[2]])),
ERROR("CURL USED IN SPACE OF WRONG DIMENSION")),
IF PIECE="~" THEN (
ANS: INPART(EXPN,1), EXPN:INPART(EXPN,2),
IF LISTP(ANS) AND LISTP(EXPN) AND LENGTH(ANS)=LENGTH(EXPN)
THEN (IF LENGTH(ANS)=2 THEN RETURN(ANS[1]*EXPN[2]
-ANS[2]*EXPN[1]),
IF LENGTH(ANS)=3 THEN RETURN([ANS[2]*EXPN[3]-
ANS[3]*EXPN[2], ANS[3]*EXPN[1]-ANS[1]*EXPN[3],
ANS[1]*EXPN[2]-ANS[2]*EXPN[1]])),
ERROR("~ USED WITH IMPROPER ARGUMENTS:",ANS,EXPN)),
EXPN) $
DOTASSOC: DOTEXPTSIMP: FALSE$
DOTSCRULES: TRUE $
define_variable(EXPANDFLAGS, '[
EXPANDALL,
EXPANDDOT,
EXPANDDOTPLUS,
EXPANDCROSS,
EXPANDCROSSPLUS,
EXPANDCROSSCROSS,
EXPANDGRAD,
EXPANDGRADPLUS,
EXPANDGRADPROD,
EXPANDDIV,
EXPANDDIVPLUS,
EXPANDDIVPROD,
EXPANDCURL,
EXPANDCURLPLUS,
EXPANDCURLCURL,
EXPANDLAPLACIAN,
EXPANDLAPLACIANPLUS,
EXPANDLAPLACIANPROD,
EXPANDLAPLACIANTODIVGRAD,
EXPANDPLUS,
EXPANDPROD ],list) $
APPLY('DECLARE, ['EXPANDFLAGS, 'EVFLAG]) $
VECTORSIMP(EXPN) := BLOCK(
[DOTDISTRIB, DOTSCRULES, INFLAG, FIRSTCROSSSCALAR],
INFLAG: FIRSTCROSSSCALAR: TRUE,
DOTDISTRIB: EXPANDALL OR EXPANDDOT OR EXPANDDOTPLUS
OR EXPANDPLUS,
IF EXPANDALL OR EXPANDGRAD OR EXPANDGRADPLUS OR EXPANDPLUS
THEN DECLARE("GRAD",ADDITIVE),
IF EXPANDALL OR EXPANDDIV OR EXPANDDIVPLUS OR EXPANDPLUS
THEN DECLARE("DIV",ADDITIVE),
IF EXPANDALL OR EXPANDCURL OR EXPANDCURLPLUS OR EXPANDPLUS
THEN DECLARE("CURL",ADDITIVE),
IF EXPANDALL OR EXPANDLAPLACIAN OR EXPANDLAPLACIANPLUS OR
EXPANDPLUS THEN DECLARE("LAPLACIAN",ADDITIVE),
EXPN: VSIMP(EXPN),
IF EXPANDALL THEN EXPN: RATEXPAND(EXPN),
IF EXPANDALL OR EXPANDGRAD OR EXPANDGRADPLUS OR EXPANDPLUS
THEN REMOVE("GRAD",ADDITIVE),
IF EXPANDALL OR EXPANDDIV OR EXPANDDIVPLUS OR EXPANDPLUS
THEN REMOVE("DIV",ADDITIVE),
IF EXPANDALL OR EXPANDCURL OR EXPANDCURLPLUS OR EXPANDPLUS
THEN REMOVE("CURL",ADDITIVE),
IF EXPANDALL OR EXPANDLAPLACIAN OR EXPANDLAPLACIANPLUS OR
EXPANDPLUS THEN REMOVE("LAPLACIAN",ADDITIVE),
EXPN) $
BEFORE(ARG) := INPART(ORDER(ETRUE,ARG),1)#ETRUE$
VSCALARP(ARG) := NOT NONSCALARP(ARG)$
VSIMP(EXPN) :=
IF MAPATOM(EXPN) THEN EXPN
ELSE BLOCK([PV, QV, RV, SV],
EXPN: MAP('VSIMP, EXPN),
IF MAPATOM(EXPN) THEN RETURN(EXPN),
IF INPART(EXPN,0)="~" THEN EXPN:REMOVECROSSSC1(EXPN,pv,rv,sv)
ELSE IF PIECE="GRAD" THEN (
IF (EXPANDALL OR EXPANDGRAD OR EXPANDGRADPROD OR
EXPANDPROD) AND
NOT MAPATOM(PV:INPART(EXPN,1)) AND INPART(PV,0)="*"
THEN EXPN:APPLY("+", MAPLIST(lambda([u],GRADPROD(u,pv)), PV)))
ELSE IF PIECE="DIV" THEN(
IF (EXPANDALL OR EXPANDDIV OR EXPANDDIVPROD OR
EXPANDPROD) AND NOT
MAPATOM(PV:INPART(EXPN,1)) AND INPART(PV,0)="*" THEN
EXPN: APPLY("+", MAPLIST(lambda([u],DIVPROD(u,pv)), PV)))
ELSE IF PIECE="CURL" THEN (
IF (EXPANDALL OR EXPANDCURL OR EXPANDCURLCURL) AND NOT
MAPATOM(PV:INPART(EXPN,1)) AND INPART(PV,0)="CURL"
THEN EXPN: GRAD( DIV(PV:INPART(PV,1))) - LAPLACIAN( PV))
ELSE IF PIECE="LAPLACIAN" THEN
IF EXPANDLAPLACIANTODIVGRAD THEN
EXPN: DIV (GRAD( INPART(EXPN,1)))
ELSE IF (EXPANDALL OR EXPANDLAPLACIAN OR
EXPANDLAPLACIANPROD OR EXPANDPROD) AND NOT MAPATOM
(PV:INPART(EXPN,1)) AND INPART(PV,0)="*" THEN(
QV: INPART(PV,1),
RV: DELETE(QV,PV),
EXPN: RV*LAPLACIAN(QV) + 2*GRAD (RV) * GRAD( QV) + QV*
LAPLACIAN(RV)),
EXPN) $
CROSSSIMP(EX,pv,rv,sv) :=
IF NOT MAPATOM(EX) AND INPART(EX,0)="~" THEN (
IF EXPANDALL OR EXPANDCROSS OR EXPANDCROSSCROSS THEN
EX: TRYCROSSCROSS(EX,pv,rv,sv),
IF NOT MAPATOM(EX) AND INPART(EX,0)="~" AND(
EXPANDALL OR EXPANDCROSS OR EXPANDCROSSPLUS OR
EXPANDPLUS) THEN EX: TRYCROSSPLUS(EX,pv,rv,sv),
EX)
ELSE EX $
REMOVECROSSSC(EXPN,pv,rv,sv) :=
IF NOT MAPATOM(EXPN) AND INPART(EXPN,0)="~" THEN
REMOVECROSSSC1(EXPN,pv,rv,sv)
ELSE EXPN $
REMOVECROSSSC1(EXPN,pv,rv,sv) := BLOCK(
[LEFT, RIGHT],
LEFT: PARTITIONSC(INPART(EXPN,1)),
RIGHT: PARTITIONSC(INPART(EXPN,2)),
IF FIRSTCROSSSCALAR AND (LEFT[2]=1 OR RIGHT[2]=1)
THEN( PRINT("WARNING: DECLARE VECTOR INDETERMINANTS
NONSCALAR TO AVOID ERRORS & TO GET FULL SIMPLIFICATION"),
FIRSTCROSSSCALAR:FALSE,
RETURN(EXPN)),
LEFT[1]*RIGHT[1]*CROSSSIMP(LEFT[2]~RIGHT[2],pv,rv,sv))$
PARTITIONSC(EX) :=
IF MAPATOM(EX) THEN
IF NONSCALARP(EX) THEN [1,EX]
ELSE [EX,1]
ELSE IF INPART(EX,0)="*" THEN BLOCK([SC,NONSC],
SC: NONSC: 1,
FOR FACT IN EX DO
IF NONSCALARP(FACT) THEN NONSC:NONSC*FACT
ELSE SC:SC*FACT,
[SC,NONSC])
ELSE [1,EX] $
TRYCROSSPLUS(EXPN,pv,rv,sv) :=(
PV:INPART(EXPN,1), RV:INPART(EXPN,2),
IF NOT MAPATOM(PV) AND INPART(PV,0)="+" THEN
IF NOT MAPATOM(RV) AND INPART(RV,0)="+" THEN
MAP(lambda([u],TRYCROSSPLUS(u,pv,rv,sv)),
MAP(lambda([u],CROSSRV(u,rv,sv)), PV))
ELSE MAP(lambda([u],CROSSRV(u,rv,sv)), PV)
ELSE IF NOT MAPATOM(RV) AND INPART(RV,0)="+" THEN
MAP(lambda([u],PVCROSS(pv,u,sv)), RV)
ELSE EXPN) $
TRYCROSSCROSS(EXPN,pv,rv,sv) := (
PV:INPART(EXPN,1), RV:INPART(EXPN,2),
IF NOT MAPATOM(RV) AND INPART(RV,0)="~" THEN (
SV: INPART(RV,2), RV:INPART(RV,1),
RV*PV.SV - SV*PV.RV)
ELSE IF NOT MAPATOM(PV) AND INPART(PV,0)="~" THEN(
SV:INPART(PV,2), PV:INPART(PV,1),
SV*RV.PV - PV*RV.SV)
ELSE EXPN) $
PVCROSS(pv,RV,sv) := REMOVECROSSSC(PV~RV,pv,rv,sv) $
CROSSRV(PV,rv,sv) := REMOVECROSSSC(PV~RV,pv,rv,sv) $
GRADPROD(UU,pv) := DELETE(UU,PV)*GRAD(UU) $
DIVPROD(UU,pv) := BLOCK([DOTSCRULES],
DOTSCRULES: FALSE,
IF NONSCALARP(UU) THEN DELETE(UU,PV)*DIV(UU)
ELSE DELETE(UU,PV).GRAD(UU) )$
POTENTIAL1(GR) := BLOCK(
[ORIGIN, GRPERM, JJ, RESULT,%dum],
IF NOT LISTP(GR) OR LENGTH(GR)#DIMENSION THEN ERROR(
"1ST ARG OF POTENTIAL MUST BE A LIST OF LENGTH EQUAL TO",
"THE DIMENSIONALITY OF THE COORDINATE SYSTEM"),
ORIGIN: ZEROLOC(),
RESULT: [],
FOR JJ:DIMENSION STEP -1 THRU 1 DO
RESULT: CONS(SF[JJ]*GR[JJ], RESULT),
GRPERM:[],
FOR EQN IN ORIGIN DO (
JJ:1,
WHILE LHS(EQN)#COORDINATES[JJ] DO JJ:JJ+1,
GRPERM: ENDCONS(RESULT[JJ], GRPERM)),
RESULT:SUM(MYINT(SUBLESS(JJ,origin,grperm), %DUM, RHS(ORIGIN[JJ]),
LHS(ORIGIN[JJ])), JJ, 1, DIMENSION),
GR: GR-EXPRESS1(GRAD( RESULT)),
GR: EV_DIFF(GR),
GR: TRIGSIMP(RADCAN(GR)),
ORIGIN:1,
/* Variable name should NOT be re-used! */
WHILE ORIGIN<=DIMENSION AND GR[ORIGIN]=0 DO
(MODE_DECLARE(ORIGIN,FIXNUM),ORIGIN:ORIGIN+1),
IF ORIGIN<=DIMENSION THEN PRINT("UNABLE TO PROVE THAT THE",
"FOLLOWING DIFFERENCE BETWEEN THE INPUT AND THE GRADIENT",
"OF THE RETURNED RESULT IS ZERO", GR),
TRIGSIMP(RADCAN(RESULT))) $
define_variable(POTENTIALZEROLOC, 0, any) $
ZEROLOC() :=
IF NOT LISTP(POTENTIALZEROLOC) THEN
MAP(LAMBDA([UU],UU=POTENTIALZEROLOC), COORDINATES)
ELSE IF DISJUNCT(COORDINATES,MAP('LHS,POTENTIALZEROLOC)) # []
THEN ERROR("POTENTIALZEROLOC MUST BE A LIST OF LENGTH",
"EQUALING THE DIMENSIONALITY OF THE COORDINATE SYSTEM",
"CONTAINING EQUATIONS WITH EACH COORDINATE VARIABLE",
"ON THE LHS OF EXACTLY 1 EQUATION,",
"OR ELSE POTENTIALZEROLOC MUST NOT BE A LIST")
ELSE POTENTIALZEROLOC$
EVAL_WHEN([TRANSLATE,BATCH,DEMO,load,loadfile],
CYC(II) ::= BUILDQ([II], 1 + REMAINDER(II+SHIFT,3)) )$
VPOT(KURL) := BLOCK(
[ORIGIN, SHIFT],
MODE_DECLARE(SHIFT,FIXNUM),
IF NOT LISTP(KURL) OR LENGTH(KURL)#3 THEN ERROR(
"1ST ARG OF VECTORPOTENTIAL MUST BE A LIST OF LENGTH 3"),
ORIGIN: ZEROLOC(),
SHIFT: 1,
WHILE SHIFT<=3 AND LHS(ORIGIN[1])#COORDINATES[SHIFT] DO
SHIFT:SHIFT+1,
SHIFT: SHIFT+1,
IF SHIFT>4 OR LHS(ORIGIN[2])#COORDINATES[CYC(2)] OR
LHS(ORIGIN[3])#COORDINATES[CYC(3)] THEN ERROR(
"LEFT SIDES OF POTENTIALZEROLOC MUST BE A CYCLIC",
"PERMUTATION OF COORDINATES"),
ORIGIN: [(MYINT(SF[CYC(1)]*SF[CYC(3)]*KURL[CYC(2)],
LHS(ORIGIN[3]),RHS(ORIGIN[3]),LHS(ORIGIN[3])) - MYINT(
SF[CYC(1)]*SF[CYC(2)]*SUBST(ORIGIN[3],KURL[CYC(3)]),
LHS(ORIGIN[2]),RHS(ORIGIN[2]),LHS(ORIGIN[2])))/SF[CYC(1)],
-MYINT(SF[CYC(2)]*SF[CYC(3)]*KURL[CYC(1)],
LHS(ORIGIN[3]),RHS(ORIGIN[3]),LHS(ORIGIN[3]))/SF[CYC(2)],
0],
ORIGIN: [ORIGIN[CYC(CYC(1))], ORIGIN[CYC(CYC(2))],
ORIGIN[CYC(CYC(3))]],
KURL: KURL-EXPRESS1(CURL (ORIGIN)),
KURL: EV_DIFF(KURL),
KURL: TRIGSIMP(RADCAN(KURL)),
FOR JJ:1 THRU 3 DO IF KURL[JJ]#0 THEN PRINT(
"UNABLE TO PROVE THAT THE FOLLOWING DIFFERENCE BETWEEN A",
"COMPONENT OF THE INPUT AND OF THE CURL OUTPUT IS ZERO",
KURL[JJ]),
ORIGIN) $
DISJUNCT(L1,L2) := APPEND(SETDIFF(L1,L2), SETDIFF(L2,L1)) $
SETDIFF(L1,L2) :=
IF L1=[] THEN []
ELSE IF MEMBER(FIRST(L1),L2) THEN SETDIFF(REST(L1),L2)
ELSE CONS(FIRST(L1), SETDIFF(REST(L1),L2)) $
SUBLESS(KK,origin,grperm) := (MODE_DECLARE(KK,FIXNUM),BLOCK([ANS,%dum],
ANS: RATSUBST(%DUM, LHS(ORIGIN[KK]), GRPERM[KK]),
FOR L1:1 THRU KK-1 DO
ANS: RATSUBST(RHS(ORIGIN[L1]), LHS(ORIGIN[L1]),ANS),
ANS)) $
MYINT(FUN,VAR,LOW,HIGH):=BLOCK([RESULT,ATLOW,ATHIGH],
RESULT:INTEGRATE(FUN,VAR),
IF FREEOF(nounify('INTEGRATE),RESULT) THEN (
ATLOW:EVLIMIT(RESULT,VAR,LOW),
IF ATLOW=FALSE THEN GO(NOGOOD),
ATHIGH:EVLIMIT(RESULT,VAR,HIGH),
IF ATHIGH=FALSE THEN GO(NOGOOD),
RETURN(RADCAN(ATHIGH-ATLOW))),
NOGOOD, DEFINT(FUN,VAR,LOW,HIGH))$
EVLIMIT(EXPR,VAR,LIM):=BLOCK([TEMP],
IF LIM='MINF OR LIM='INF THEN GO(USELIMIT),
TEMP:ERRCATCH(SUBST(LIM,VAR,EXPR)),
IF TEMP#[] THEN RETURN(TEMP[1]),
USELIMIT, TEMP:LIMIT(EXPR,VAR,LIM),
IF MEMBER(TEMP,'[INF,MINF,UND,IND,INFINITY]) THEN RETURN(FALSE),
IF FREEOF(nounify('LIMIT),TEMP) THEN TEMP)$
EVAL_WHEN(BATCH,TTYOFF:FALSE)$
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