TTYOFF: NOLABELS: TRUE $
%SIGNUMDISTRIBUTE:%ABSDISTRIBUTE:FALSE $
%ELIGIBLE:'[SINH,ATAN,TANH,ATANH,ERF,ASINH,CSCH,COTH,ASIN] $
UNITSTEP(U) := (1+SIGNUM(U))/2 $
UNITRAMP(U) := (U+ABS(U))/2 $

MATCHDECLARE([UTRUE, VTRUE], TRUE,  EVENINTEGER, EVENINTEGERP) $
ODDINTEGERP(U):=
   IF INTEGERP(U) AND INTEGERP((U+1)/2) OR ?MODDP(U)
      THEN TRUE ELSE FALSE $
EVENINTEGERP(U):=
   IF INTEGERP(U) AND INTEGERP(U/2) OR ?MEVENP(U)
     THEN TRUE ELSE FALSE $
TELLSIMPAFTER(ABS(UTRUE)^EVENINTEGER, UTRUE^EVENINTEGER) $
TELLSIMPAFTER('DIFF(ABS(UTRUE),VTRUE),SIGNUM(UTRUE)*DIFF(UTRUE,VTRUE))$
TELLSIMPAFTER(COSH(ABS(UTRUE)), COSH(UTRUE)) $
TELLSIMPAFTER(SECH(ABS(UTRUE)), SECH(UTRUE)) $
TELLSIMPAFTER(COS(ABS(UTRUE)), COS(UTRUE)) $
TELLSIMPAFTER(SEC(ABS(UTRUE)), SEC(UTRUE)) $
TELLSIMPAFTER(ABS(UTRUE),  ABSIMP(UTRUE)) $
ABSIMP(UT) :=BLOCK(
   [PARTSWITCH, PREDERROR, U, V, W, B, NOMATCH],
   PARTSWITCH:TRUE, PREDERROR:FALSE,
   IF ATOM(UT) OR INPART(UT,0)="+"  THEN
      IF IS(UT>0 or ut=0)=TRUE THEN RETURN(UT)
      ELSE IF IS(UT<0 or ut=0)=TRUE THEN RETURN(-UT)
      ELSE RETURN(ABS(UT)),
   IF PIECE="*" THEN(U:V:1,
      W:[],
      FOR J:1 STEP 1 WHILE(B:INPART(UT,J))#END DO
         IF IS(B>0 or b=0)=TRUE THEN U:U*B
         ELSE IF IS(B<0 or b=0)=TRUE THEN U:-U*B
         ELSE IF ATOM(B) OR NOT(MEMBER(INPART(B,0), %ELIGIBLE) OR
            PIECE="^" AND ODDINTEGERP(INPART(B,2))) THEN(NOMATCH:TRUE,
            FOR WW IN W WHILE NOMATCH DO
               IF B=FIRST(WW) THEN (NOMATCH:FALSE,
                  U: U*B*FIRST(REST(WW)),
                  W:DELETE(WW,W)),
            IF NOMATCH THEN W:CONS([B,B],W))
         ELSE (NOMATCH:TRUE,
            INPART(B,1),
            FOR WW IN W WHILE NOMATCH DO
               IF PIECE=FIRST(WW) THEN (NOMATCH:FALSE,
                  U: U*B*FIRST(REST(WW)),
                  W:DELETE(WW,W)),
            IF NOMATCH THEN W: CONS([PIECE,B], W)),
         IF W=[] THEN RETURN(U),
      IF %ABSDISTRIBUTE THEN FOR WW IN W DO U:U*ABSIMP(FIRST(REST(WW)))
      ELSE (FOR WW IN W DO V:V*FIRST(REST(WW)),
         U:U*(IF REST(W)=[] THEN ABSIMP(V) ELSE 'ABS(V))),
      RETURN(U)),
   IF PIECE="^" THEN (U:INPART(UT,1),
      IF IS(U>0 or u=0)=TRUE THEN RETURN(UT),
      V:INPART(UT,2),
      IF EVENINTEGERP(V) THEN RETURN(UT),
      IF ODDINTEGERP(V) AND IS(U<0 or u=0) THEN RETURN(-UT),
      RETURN(ABS(UT))),
   IF PIECE='LOG THEN(B:INPART(UT,1),
      IF IS(B>1 or b=1)=TRUE THEN RETURN(UT),
      IF IS(B<1 or b=1)=TRUE THEN RETURN(-UT),
      RETURN(ABS(UT))),
   IF PIECE='COSH OR PIECE='SECH OR PIECE='ABS THEN RETURN(UT),
   IF MEMBER(PIECE, %ELIGIBLE)
      then RETURN(APPLY(PIECE, [ABSIMP(INPART(UT,1))])),
   RETURN(ABS(UT))) $

MATCHDECLARE(NONZERO,NONZEROP, ODDINTEGER,ODDINTEGERP) $
NONZEROP(U) :=
   IF EV(IS(U>0 OR U<0),PREDERROR:FALSE)=TRUE THEN TRUE
   ELSE FALSE $

TELLSIMPAFTER(SIGNUM(UTRUE)^ODDINTEGER, SIGNUM(UTRUE)) $
TELLSIMPAFTER(SIGNUM(NONZERO)^EVENINTEGER, 1) $
TELLSIMPAFTER('DIFF(SIGNUM(UTRUE),VTRUE),
   2*DELTA(UTRUE)*DIFF(UTRUE,VTRUE))$
TELLSIMPAFTER(COSH(SIGNUM(NONZERO)), COSH(1)) $
TELLSIMPAFTER(SECH(SIGNUM(NONZERO)), SECH(1)) $
TELLSIMPAFTER(UTRUE*SIGNUM(UTRUE), ABSIMP(UTRUE)) $
TELLSIMPAFTER(COS(SIGNUM(UTRUE)), COS(1)) $
TELLSIMPAFTER(SEC(SIGNUM(UTRUE)), SEC(1)) $
TELLSIMPAFTER(SIGNUM(UTRUE), SIGNUMSIMP(UTRUE)) $
SIGNUMSIMP(UT) := BLOCK(
   [PARTSWITCH, PREDERROR, U, V, B, NOMATCH],
   PARTSWITCH:TRUE, PREDERROR:FALSE,
   IF ATOM(UT) OR INPART(UT,0)="+" THEN
      IF IS(UT>0)=TRUE THEN RETURN(1)
      ELSE IF IS(UT<0)=TRUE THEN RETURN(-1)
      ELSE RETURN(SIGNUM(UT)),
   IF PIECE="*" THEN(U:V:1, W:[],
      FOR J:1 STEP 1 WHILE(B:INPART(UT,J))#END DO
         IF IS(B<0)=TRUE THEN U:-U
         ELSE IF IS(B>0)#TRUE THEN 
            IF ATOM(B) OR NOT(MEMBER(INPART(B,0),%ELIGIBLE) OR
               PIECE="^" AND ODDINTEGERP(INPART(B,2))) THEN(
               NOMATCH:TRUE,
               FOR WW IN W WHILE NOMATCH DO
                  IF B=FIRST(WW) THEN (NOMATCH:FALSE,
                     W:CONS([B,NOT FIRST(REST(WW))], DELETE(WW,W))),
               IF NOMATCH THEN W:CONS([B,TRUE],W))
            ELSE (NOMATCH:TRUE,
               INPART(B,1),
               FOR WW IN W WHILE NOMATCH DO
                  IF PIECE=FIRST(WW) THEN (NOMATCH:FALSE,
                    W:CONS([PIECE,NOT FIRST(REST(WW))],DELETE(WW,W))),
               IF NOMATCH THEN W:CONS([PIECE,TRUE],W)),
      IF W=[] THEN RETURN(U),
      IF %SIGNUMDISTRIBUTE THEN FOR WW IN W DO U:U*
         (IF FIRST(REST(WW)) THEN SIGNUMSIMP(FIRST(WW))
         ELSE SIGNUMSIMP(FIRST(WW)^2))
      ELSE (
         FOR WW IN W DO V:V*(IF FIRST(REST(WW)) THEN FIRST(WW)
            ELSE FIRST(WW)^2),
         U:U*(IF REST(W)=[] THEN SIGNUMSIMP(V) ELSE 'SIGNUM(V))),
      RETURN(U)),
   IF PIECE="^" THEN(U:INPART(UT,1),
      IF IS(U>0)=TRUE THEN RETURN(1),
      V:INPART(UT,2),
      IF EVENINTEGERP(V) AND NONZEROP(U) THEN RETURN(1),
      IF ODDINTEGERP(V) THEN RETURN(SIGNUMSIMP(U)),
      RETURN(SIGNUM(UT))),
   IF PIECE='LOG THEN(B:INPART(UT,1),
      IF IS(B>1)=TRUE THEN RETURN(1),
      IF IS(B<1)=TRUE THEN RETURN(-1),
      IF IS(B=1)=TRUE THEN RETURN(0),
      RETURN(SIGNUM(UT))),
   IF PIECE='COSH OR PIECE='SECH THEN RETURN(1),
   IF PIECE='SIGNUM THEN RETURN(UT),
   IF MEMBER(PIECE, %ELIGIBLE) THEN RETURN(SIGNUMSIMP(INPART(UT,1))),
   RETURN(SIGNUM(UT))) $
TTYOFF: NOLABELS: FALSE $