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;;; (c) Copyright 1982 Massachusetts Institute of Technology ;;;
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(macsyma-module risch)
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(LOAD-MACSYMA-MACROS RZMAC RATMAC)
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(DECLARE-TOP(SPECIAL PROB ROOTFAC PARNUMER PARDENOM LOGPTDX WHOLEPART $RATALGDENOM
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EXPEXPFLAG $LOGSIMP SWITCH1 DEGREE CARY $RATFAC $LOGEXPAND
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RATFORM GENVAR *VAR VAR ROOTFACTOR EXPINT $KEEPFLOAT
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TRIGINT OPERATOR $EXPONENTIALIZE $GCD $LOGARC CHANGEVP
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KLTH R S BETA GAMMA B MAINVAR EXPFLAG EXPSTUFF LIFLAG
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INTVAR SWITCH VARLIST NOGOOD GENVAR $ERFFLAG $LIFLAG
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RISCHP $FACTORFLAG ALPHAR M SIMP GENPAIRS HYPERTRIGINT
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*MOSESFLAG YYY *EXP Y $ALGEBRAIC IMPLICIT-REAL
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ERRRJFFLAG $%E/_TO/_NUMLOG GENERATE-ATAN2 CONTEXT
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BIGFLOATZERO RP-POLYLOGP)
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(*EXPR $EXPONENTIALIZE SUBFUNSUBS SUBFUNNAME SRATSIMP PARTFRAC MQAPPLYP)
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(*LEXPR CONTEXT POLYLOGP)
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(DEFMVAR $LIFLAG T "Controls whether RISCH generates polylogs")
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(DEFMVAR $ERFFLAG T "Controls whether RISCH generates ERFS")
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(DEFVAR CHANGEVP T #-LISPM "When nil prevents changevar hack")
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(DEFMACRO PAIR (AL BL) `(MAPCAR (FUNCTION CONS) ,AL ,BL))
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(DEFMACRO RISCHZERO () ''((0 . 1) 0))
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(DEFUN RISCHNOUN (EXP1 &OPTIONAL (EXP2 EXP1 EXP2P))
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(UNLESS EXP2P (SETQ EXP1 (RZERO)))
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`(,EXP1 ((%INTEGRATE) ,(DISREP EXP2) ,INTVAR)))
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(DO ((VL VARLIST (CDR VL))
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((NULL (CDR VL)) (CAR GL))))
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(DEFUN RISCH-PCONSTP (P)
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(OR (PCOEFP P) (POINTERGP MAINVAR (CAR P))))
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(DEFUN RISCH-CONSTP (R)
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(AND (RISCH-PCONSTP (CAR R)) (RISCH-PCONSTP (CDR R))))
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(LET (((A . B) X) ((C . D) Y))
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(CONS (R+ A C) (APPEND B D))))
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(DEFMFUN $RISCH (EXP VAR)
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;; Get RATINT from SININT
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(FIND-FUNCTION 'RATINT)
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(WITH-NEW-CONTEXT (CONTEXT)
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(DEFUN SPDERIVATIVE (P VAR)
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(COND ((PCOEFP P) '(0 . 1))
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((NULL (CDR P)) '(0 . 1))
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((OR (NOT (ATOM (CAR P))) (NUMBERP (CAR P))) ;P IS A RATFORM
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(LET ((DENPRIME (SPDERIVATIVE (CDR P) VAR)))
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(COND ((RZEROP DENPRIME)
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(RATQU (SPDERIVATIVE (CAR P) VAR) (CDR P)))
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(T (RATQU (R- (R* (SPDERIVATIVE (CAR P) VAR)
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(R* (CAR P) DENPRIME))
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(R* (CDR P) (CDR P)))))))
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(T (R+ (SPDERIVATIVE1 (CAR P)
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(SPDERIVATIVE (CONS (CAR P) (CDDDR P))
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(DEFUN SPDERIVATIVE1 (VAR1 DEG COEFF VAR)
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(R* (RATEXPT (CONS (LIST VAR 1 1) 1) (SUB1 DEG))
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((POINTERGP VAR VAR1) '(0 . 1))
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((EQUAL DEG 0) (SPDERIVATIVE COEFF VAR))
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(T (R+ (R* (RATEXPT (CONS (LIST VAR1 1 1) 1) DEG)
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(SPDERIVATIVE COEFF VAR))
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(R* (COND ((EQUAL DEG 1) COEFF)
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(RATEXPT (CONS (LIST VAR1 1 1) 1)
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(GET VAR1 'RISCHDIFF) )))))
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(DEFUN POLYLOGP (EXP &OPTIONAL SUB)
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(AND (MQAPPLYP EXP) (EQ (SUBFUNNAME EXP) '$LI)
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(OR (NULL SUB) (EQUAL SUB (CAR (SUBFUNSUBS EXP))))))
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(DEFUN RISCHINT (EXP INTVAR &AUX ($LOGARC NIL) ($EXPONENTIALIZE NIL)
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($GCD '$ALGEBRAIC) ($ALGEBRAIC T) (IMPLICIT-REAL T))
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(PROG ($%E/_TO/_NUMLOG $LOGSIMP TRIGINT OPERATOR Y Z VAR RATFORM LIFLAG
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MAINVAR VARLIST GENVAR HYPERTRIGINT $RATFAC $RATALGDENOM )
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(IF (SPECREPP EXP) (SETQ EXP (SPECDISREP EXP)))
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(IF (SPECREPP INTVAR) (SETQ INTVAR (SPECDISREP INTVAR)))
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(MERROR "Attempt to integrate wrt a number: ~:M" INTVAR))
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(IF (AND (ATOM INTVAR) (ISINOP EXP INTVAR)) (GO NOUN))
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(COND (TRIGINT (RETURN (TRIGIN1 EXP INTVAR)))
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(HYPERTRIGINT (RETURN (HYPERTRIGINT1 EXP INTVAR T)))
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(OPERATOR (GO NOUN)))
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(SETQ Y (INTSETUP EXP INTVAR))
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(IF OPERATOR (GO NOUN))
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(SETQ RATFORM (CAR Y))
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(SETQ VARLIST (CADDR RATFORM))
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(SETQ MAINVAR (CAADR (RATF INTVAR)))
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(SETQ GENVAR (CADDDR RATFORM))
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(UNLESS (ORMAPC (FUNCTION ALGPGET) VARLIST)
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(SETQ $ALGEBRAIC NIL)
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(SETQ $GCD (CAR *GCDL*)))
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(SETQ VAR (GETRISCHVAR))
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(SETQ Z (TRYRISCH (CDR Y) MAINVAR))
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(SETF (CADDR RATFORM) VARLIST)
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(SETF (CADDDR RATFORM) GENVAR)
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(RETURN (COND ((ATOM (CDR Z)) (DISREP (CAR Z)))
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(T (LET (($LOGSIMP T) ($%E/_TO/_NUMLOG T))
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(SIMPLIFY (LIST* '(MPLUS)
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NOUN (RETURN (LIST '(%INTEGRATE) EXP INTVAR))))
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(COND ((OR (ATOM L) (ALIKE1 INTVAR L) (FREEOF INTVAR L)) NIL)
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(IF (AND (INTEGERP (CAR (SUBFUNSUBS L)))
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(SIGNP G (CAR (SUBFUNSUBS L))))
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(RISCHFORM (CAR (SUBFUNARGS L)))
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((%SIN %COS %TAN %COT %SEC %CSC)
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(SETQ TRIGINT T $EXPONENTIALIZE T)
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(RISCHFORM (CADR L)))
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((%ASIN %ACOS %ATAN %ACOT %ASEC %ACSC)
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(SETQ TRIGINT T $LOGARC T)
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(RISCHFORM (CADR L)))
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((%SINH %COSH %TANH %COTH %SECH %CSCH)
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(SETQ HYPERTRIGINT T $EXPONENTIALIZE T)
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(RISCHFORM (CADR L)))
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((%ASINH %ACOSH %ATANH %ACOTH %ASECH %ACSCH)
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(SETQ HYPERTRIGINT T $LOGARC T)
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(RISCHFORM (CADR L)))
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((MTIMES MPLUS MEXPT RAT %ERF %LOG)
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(MAPC #'RISCHFORM (CDR L)))
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(T (SETQ OPERATOR (CAAR L)))))
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(T (SETQ OPERATOR (CAAR L)))))
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(DEFUN HYPERTRIGINT1 (EXP VAR HYPERFUNC)
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(IF HYPERFUNC (INTEGRATOR (RESIMPLIFY EXP) VAR)
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(RISCHINT (RESIMPLIFY EXP) VAR)))
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(DEFUN TRIGIN1 (*EXP VAR)
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(LET ((YYY (HYPERTRIGINT1 *EXP VAR NIL)))
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(SETQ YYY (DIV ($EXPAND ($NUM YYY))
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($EXPAND ($DENOM YYY))))
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(LET ((RISCHP VAR) (RP-POLYLOGP T) $LOGARC $EXPONENTIALIZE)
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(SRATSIMP (IF (AND (FREEOF '$%I *EXP) (FREEOF '$LI YYY))
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(DEFUN TRYRISCH (EXP MAINVAR)
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(PROG (WHOLEPART ROOTFACTOR PARNUMER PARDENOM
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SWITCH1 LOGPTDX EXPFLAG EXPSTUFF EXPINT Y)
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(SETQ EXPSTUFF '(0 . 1))
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(COND ((EQ MAINVAR VAR)
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(RETURN (RISCHFPROG EXP)))
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((EQ (GET VAR 'LEADOP)
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(SETQ Y (RISCHLOGDPROG EXP))
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(DOLIST (RAT LOGPTDX)
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(SETQ Y (RISCHADD (RISCHLOGEPROG RAT) Y)))
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(SETQ Y (RISCHADD (TRYRISCH1 EXPSTUFF MAINVAR) Y))
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(RETURN (IF EXPINT (RISCHADD (RISCHEXPPOLY EXPINT VAR) Y)
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(DEFUN TRYRISCH1 (EXP MAINVAR)
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(LET* ((VARLIST (REVERSE (CDR (REVERSE VARLIST))))
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(TRYRISCH EXP MAINVAR)))
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(DEFUN RISCHFPROG (RAT)
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(LET (ROOTFACTOR PARDENOM PARNUMER LOGPTDX WHOLEPART SWITCH1)
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(CONS (CDR (RATREP* (DPROG RAT)))
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(LET ((VARLIST VARLIST)
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(GENVAR (FIRSTN (LENGTH VARLIST) GENVAR)))
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(MAPCAR 'EPROG LOGPTDX)))))
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(DEFUN RISCHLOGDPROG (RATARG)
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(PROG (KLTH AROOTF DERIV THEBPG THETOP THEBOT PROD1 PROD2 ANS)
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(COND ((OR (PCOEFP (CDR RATARG))
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(POINTERGP VAR (CADR RATARG)))
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(RETURN (RISCHLOGPOLY RATARG))))
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(APROG (RATDENOMINATOR RATARG))
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(CPROG (RATNUMERATOR RATARG) (RATDENOMINATOR RATARG))
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(DO ((ROOTFACTOR (REVERSE ROOTFACTOR) (CDR ROOTFACTOR))
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(PARNUMER (REVERSE PARNUMER) (CDR PARNUMER))
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(KLTH (LENGTH ROOTFACTOR) (f1- KLTH)))
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(SETQ AROOTF (CAR ROOTFACTOR))
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((AND (EQ (GET (CAR AROOTF) 'LEADOP) 'MEXPT)
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(NULL (CDDDR AROOTF)))
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(COND ((AND (NOT (ATOM (CAR PARNUMER)))
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(NOT (ATOM (CAAR PARNUMER)))
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(EQ (CAAAR PARNUMER) (CAR AROOTF)))
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(GENNEGS AROOTF (CDAAR PARNUMER) (CDAR PARNUMER)))
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(LIST 'NEG (CAR PARNUMER)
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(CAR AROOTF) KLTH (CADR AROOTF)))))
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((NOT (ZEROP (PDEGREE AROOTF VAR)))
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(SETQ DERIV (SPDERIVATIVE AROOTF MAINVAR))
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(SETQ THEBPG (BPROG AROOTF (RATNUMERATOR DERIV)))
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(SETQ THETOP (CAR PARNUMER))
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(DO ((KX (f1- KLTH) (f1- KX))) ((= KX 0))
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(SETQ PROD1 (R* THETOP (CAR THEBPG)))
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(SETQ PROD2 (R* THETOP (CDR THEBPG) (RATDENOMINATOR DERIV)))
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(SETQ THEBOT (PEXPT AROOTF KX))
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(SETQ ANS (R+ ANS (RATQU (R- PROD2) (R* KX THEBOT))))
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(R+ PROD1 (RATQU (SPDERIVATIVE PROD2 MAINVAR) KX)))
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(SETQ THETOP (CDR (RATDIVIDE THETOP THEBOT))))
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(PUSH (RATQU THETOP AROOTF) LOGPTDX))))
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(PUSH (RATQU (CAR PARNUMER) (CAR ROOTFACTOR)) LOGPTDX)
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(COND ((OR (PZEROP ANS) (PZEROP (CAR ANS)))
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(RETURN (RISCHLOGPOLY WHOLEPART))))
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(SETQ THETOP (CADR (PDIVIDE (RATNUMERATOR ANS)
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(RATDENOMINATOR ANS))))
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(RETURN (RISCHADD (NCONS (RATQU THETOP (RATDENOMINATOR ANS)))
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(RISCHLOGPOLY WHOLEPART)))))
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(DEFUN GENNEGS (DENOM NUM NUMDENOM)
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(COND ((NULL NUM) NIL)
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(T (CONS (LIST 'NEG (CADR NUM)
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(DIFFERENCE KLTH (CAR NUM))
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(R* NUMDENOM (CADDR DENOM) ))
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(GENNEGS DENOM (CDDR NUM) NUMDENOM)))))
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(DEFUN RISCHLOGEPROG (P)
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(PROG (P1E P2E P2DERIV LOGCOEF NCC DCC ALLCC EXPCOEF)
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(IF (OR (PZEROP P) (PZEROP (CAR P))) (RETURN (RISCHZERO)))
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(SETQ P1E (RATNUMERATOR P))
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(DESETQ (DCC P2E) (OLDCONTENT (RATDENOMINATOR P)))
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(COND ((AND (NOT SWITCH1)
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(CDR (SETQ PARDENOM (INTFACTOR P2E))))
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(DESETQ (NCC P1E) (OLDCONTENT P1E))
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(SETQ ALLCC (RATQU NCC DCC))
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(RETURN (DO ((PNUM PARNUMER (CDR PNUM))
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(PDEN PARDENOM (CDR PDEN))
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((OR (NULL PNUM) (NULL PDEN))
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(SETQ SWITCH1 NIL) ANS)
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(R* ALLCC (RATQU (CAR PNUM) (CAR PDEN))))
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(WHEN (AND EXPFLAG (NULL (P-RED P2E)))
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(PUSH (CONS 'NEG P) EXPINT)
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(RETURN (RISCHZERO)))
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(IF EXPFLAG (SETQ EXPCOEF (R* (P-LE P2E) (RATQU (GET VAR 'RISCHDIFF)
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(SETQ P1E (RATQU P1E (PTIMES DCC (P-LC P2E)))
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P2E (RATQU P2E (P-LC P2E))) ;MAKE DENOM MONIC
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(SETQ P2DERIV (SPDERIVATIVE P2E MAINVAR))
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(SETQ LOGCOEF (RATQU P1E
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(IF EXPFLAG (R- P2DERIV (R* P2E EXPCOEF))
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(WHEN (RISCH-CONSTP LOGCOEF)
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(SETQ EXPSTUFF (R- EXPSTUFF (R* EXPCOEF LOGCOEF))))
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(LOGMABS (DISREP P2E))))))
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(if (and expflag $liflag changevp)
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(let* ((newvar (gensym))
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`((%integrate) ,(simplify (disrep p)) ,intvar)
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(sub newvar (get var 'rischexpr))
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(changevp nil)) ;prevents recursive changevar
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(if (and (freeof intvar new-int)
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(setq new-int (rischint (sdiff new-int newvar)
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(MAXIMA-SUBSTITUTE (get var 'rischexpr) newvar new-int))))))
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(RETURN (RISCHNOUN P))))
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(load-macsyma-macros rzmac ratmac)
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(declare-top(special prob rootfac parnumer pardenom logptdx wholepart $ratalgdenom
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expexpflag $logsimp switch1 degree cary $ratfac $logexpand
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ratform genvar *var var rootfactor expint $keepfloat
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trigint operator $exponentialize $gcd $logarc changevp
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klth r s beta gamma b mainvar expflag expstuff liflag
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intvar switch varlist nogood genvar $erfflag $liflag
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rischp $factorflag alphar m simp genpairs hypertrigint
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*mosesflag yyy *exp y $algebraic implicit-real
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errrjfflag $%e/_to/_numlog generate-atan2 context
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bigfloatzero rp-polylogp)
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(*expr $exponentialize subfunsubs subfunname sratsimp partfrac mqapplyp)
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(*lexpr context polylogp)
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(defmvar $liflag t "Controls whether `risch' generates polylogs")
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(defmvar $erfflag t "Controls whether `risch' generates `erfs'")
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(defvar changevp t #-lispm "When nil prevents changevar hack")
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(defmacro pair (al bl) `(mapcar (function cons) ,al ,bl))
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(defmacro rischzero () ''((0 . 1) 0))
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(defun rischnoun (exp1 &optional (exp2 exp1 exp2p))
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(unless exp2p (setq exp1 (rzero)))
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`(,exp1 ((%integrate) ,(disrep exp2) ,intvar)))
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(do ((vl varlist (cdr vl))
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((null (cdr vl)) (car gl))))
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(defun risch-pconstp (p)
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(or (pcoefp p) (pointergp mainvar (car p))))
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(defun risch-constp (r)
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(and (risch-pconstp (car r)) (risch-pconstp (cdr r))))
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(destructuring-let (((a . b) x) ((c . d) y))
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(cons (r+ a c) (append b d))))
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(defmfun $risch (exp var)
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;; Get RATINT from SININT
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(find-function 'ratint)
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(with-new-context (context)
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(defun spderivative (p var)
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(cond ((pcoefp p) '(0 . 1))
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((null (cdr p)) '(0 . 1))
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((or (not (atom (car p))) (numberp (car p))) ;P IS A RATFORM
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(let ((denprime (spderivative (cdr p) var)))
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(cond ((rzerop denprime)
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(ratqu (spderivative (car p) var) (cdr p)))
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(t (ratqu (r- (r* (spderivative (car p) var)
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(r* (car p) denprime))
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(r* (cdr p) (cdr p)))))))
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(t (r+ (spderivative1 (car p)
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(spderivative (cons (car p) (cdddr p))
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(defun spderivative1 (var1 deg coeff var)
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(r* (ratexpt (cons (list var 1 1) 1) (sub1 deg))
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((pointergp var var1) '(0 . 1))
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((equal deg 0) (spderivative coeff var))
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(t (r+ (r* (ratexpt (cons (list var1 1 1) 1) deg)
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(spderivative coeff var))
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(r* (cond ((equal deg 1) coeff)
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(ratexpt (cons (list var1 1 1) 1)
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(get var1 'rischdiff) )))))
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(defun polylogp (exp &optional sub)
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(and (mqapplyp exp) (eq (subfunname exp) '$li)
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(or (null sub) (equal sub (car (subfunsubs exp))))))
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(defun rischint (exp intvar &aux ($logarc nil) ($exponentialize nil)
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($gcd '$algebraic) ($algebraic t) (implicit-real t))
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(prog ($%e/_to/_numlog $logsimp trigint operator y z var ratform liflag
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mainvar varlist genvar hypertrigint $ratfac $ratalgdenom )
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(if (specrepp exp) (setq exp (specdisrep exp)))
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(if (specrepp intvar) (setq intvar (specdisrep intvar)))
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(merror "Attempt to integrate wrt a number: ~:M" intvar))
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(if (and (atom intvar) (isinop exp intvar)) (go noun))
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(cond (trigint (return (trigin1 exp intvar)))
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(hypertrigint (return (hypertrigint1 exp intvar t)))
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(operator (go noun)))
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(setq y (intsetup exp intvar))
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(if operator (go noun))
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(setq ratform (car y))
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(setq varlist (caddr ratform))
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(setq mainvar (caadr (ratf intvar)))
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(setq genvar (cadddr ratform))
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(unless (ormapc (function algpget) varlist)
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(setq $algebraic nil)
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(setq $gcd (car *gcdl*)))
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(setq var (getrischvar))
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(setq z (tryrisch (cdr y) mainvar))
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(setf (caddr ratform) varlist)
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(setf (cadddr ratform) genvar)
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(return (cond ((atom (cdr z)) (disrep (car z)))
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(t (let (($logsimp t) ($%e/_to/_numlog t))
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(simplify (list* '(mplus)
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noun (return (list '(%integrate) exp intvar))))
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(cond ((or (atom l) (alike1 intvar l) (freeof intvar l)) nil)
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(if (and (integerp (car (subfunsubs l)))
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(signp g (car (subfunsubs l))))
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(rischform (car (subfunargs l)))
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((%sin %cos %tan %cot %sec %csc)
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(setq trigint t $exponentialize t)
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(rischform (cadr l)))
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((%asin %acos %atan %acot %asec %acsc)
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(setq trigint t $logarc t)
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(rischform (cadr l)))
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((%sinh %cosh %tanh %coth %sech %csch)
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(setq hypertrigint t $exponentialize t)
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(rischform (cadr l)))
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((%asinh %acosh %atanh %acoth %asech %acsch)
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(setq hypertrigint t $logarc t)
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(rischform (cadr l)))
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((mtimes mplus mexpt rat %erf %log)
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(mapc #'rischform (cdr l)))
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(t (setq operator (caar l)))))
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(t (setq operator (caar l)))))
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(defun hypertrigint1 (exp var hyperfunc)
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(if hyperfunc (integrator (resimplify exp) var)
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(rischint (resimplify exp) var)))
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(defun trigin1 (*exp var)
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(let ((yyy (hypertrigint1 *exp var nil)))
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(setq yyy (div ($expand ($num yyy))
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($expand ($denom yyy))))
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(let ((rischp var) (rp-polylogp t) $logarc $exponentialize)
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(sratsimp (if (and (freeof '$%i *exp) (freeof '$li yyy))
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(defun tryrisch (exp mainvar)
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(prog (wholepart rootfactor parnumer pardenom
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switch1 logptdx expflag expstuff expint y)
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(setq expstuff '(0 . 1))
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(cond ((eq mainvar var)
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(return (rischfprog exp)))
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((eq (get var 'leadop)
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(setq y (rischlogdprog exp))
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(dolist (rat logptdx)
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(setq y (rischadd (rischlogeprog rat) y)))
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(setq y (rischadd (tryrisch1 expstuff mainvar) y))
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(return (if expint (rischadd (rischexppoly expint var) y)
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(defun tryrisch1 (exp mainvar)
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(let* ((varlist (reverse (cdr (reverse varlist))))
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(tryrisch exp mainvar)))
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(defun rischfprog (rat)
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(let (rootfactor pardenom parnumer logptdx wholepart switch1)
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(cons (cdr (ratrep* (dprog rat)))
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(let ((varlist varlist)
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(genvar (firstn (length varlist) genvar)))
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(mapcar 'eprog logptdx)))))
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(defun rischlogdprog (ratarg)
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(prog (klth arootf deriv thebpg thetop thebot prod1 prod2 ans)
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(cond ((or (pcoefp (cdr ratarg))
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(pointergp var (cadr ratarg)))
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(return (rischlogpoly ratarg))))
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(aprog (ratdenominator ratarg))
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(cprog (ratnumerator ratarg) (ratdenominator ratarg))
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(do ((rootfactor (reverse rootfactor) (cdr rootfactor))
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(parnumer (reverse parnumer) (cdr parnumer))
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(klth (length rootfactor) (f1- klth)))
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(setq arootf (car rootfactor))
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((and (eq (get (car arootf) 'leadop) 'mexpt)
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(null (cdddr arootf)))
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(cond ((and (not (atom (car parnumer)))
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(not (atom (caar parnumer)))
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(eq (caaar parnumer) (car arootf)))
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(gennegs arootf (cdaar parnumer) (cdar parnumer)))
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(list 'neg (car parnumer)
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(car arootf) klth (cadr arootf)))))
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((not (zerop (pdegree arootf var)))
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(setq deriv (spderivative arootf mainvar))
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(setq thebpg (bprog arootf (ratnumerator deriv)))
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(setq thetop (car parnumer))
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(do ((kx (f1- klth) (f1- kx))) ((= kx 0))
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(setq prod1 (r* thetop (car thebpg)))
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(setq prod2 (r* thetop (cdr thebpg) (ratdenominator deriv)))
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(setq thebot (pexpt arootf kx))
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(setq ans (r+ ans (ratqu (r- prod2) (r* kx thebot))))
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(r+ prod1 (ratqu (spderivative prod2 mainvar) kx)))
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(setq thetop (cdr (ratdivide thetop thebot))))
246
(push (ratqu thetop arootf) logptdx))))
247
(push (ratqu (car parnumer) (car rootfactor)) logptdx)
248
(cond ((or (pzerop ans) (pzerop (car ans)))
249
(return (rischlogpoly wholepart))))
250
(setq thetop (cadr (pdivide (ratnumerator ans)
251
(ratdenominator ans))))
252
(return (rischadd (ncons (ratqu thetop (ratdenominator ans)))
253
(rischlogpoly wholepart)))))
255
(defun gennegs (denom num numdenom)
256
(cond ((null num) nil)
257
(t (cons (list 'neg (cadr num)
259
(difference klth (car num))
260
(r* numdenom (caddr denom) ))
261
(gennegs denom (cddr num) numdenom)))))
263
(defun rischlogeprog (p)
264
(prog (p1e p2e p2deriv logcoef ncc dcc allcc expcoef)
265
(if (or (pzerop p) (pzerop (car p))) (return (rischzero)))
266
(setq p1e (ratnumerator p))
267
(desetq (dcc p2e) (oldcontent (ratdenominator p)))
268
(cond ((and (not switch1)
269
(cdr (setq pardenom (intfactor p2e))))
272
(desetq (ncc p1e) (oldcontent p1e))
274
(setq allcc (ratqu ncc dcc))
275
(return (do ((pnum parnumer (cdr pnum))
276
(pden pardenom (cdr pden))
278
((or (null pnum) (null pden))
279
(setq switch1 nil) ans)
282
(r* allcc (ratqu (car pnum) (car pden))))
284
(when (and expflag (null (p-red p2e)))
285
(push (cons 'neg p) expint)
286
(return (rischzero)))
287
(if expflag (setq expcoef (r* (p-le p2e) (ratqu (get var 'rischdiff)
289
(setq p1e (ratqu p1e (ptimes dcc (p-lc p2e)))
290
p2e (ratqu p2e (p-lc p2e))) ;MAKE DENOM MONIC
291
(setq p2deriv (spderivative p2e mainvar))
292
(setq logcoef (ratqu p1e
293
(if expflag (r- p2deriv (r* p2e expcoef))
295
(when (risch-constp logcoef)
297
(setq expstuff (r- expstuff (r* expcoef logcoef))))
303
(logmabs (disrep p2e))))))
304
(if (and expflag $liflag changevp)
305
(let* ((newvar (gensym))
307
`((%integrate) ,(simplify (disrep p)) ,intvar)
308
(sub newvar (get var 'rischexpr))
310
(changevp nil)) ;prevents recursive changevar
311
(if (and (freeof intvar new-int)
313
(setq new-int (rischint (sdiff new-int newvar)
317
(maxima-substitute (get var 'rischexpr) newvar new-int))))))
318
(return (rischnoun p))))
321
(DEFUN FINDINT (EXP) (COND ((ATOM EXP) NIL)
322
((ATOM (CAR EXP)) (FINDINT (CDR EXP)))
323
((EQ (CAAAR EXP) '%INTEGRATE) T)
324
(T (FINDINT (CDR EXP)))))
326
(DEFUN LOGEQUIV (FN1 FN2)
327
(FREEOF INTVAR ($RATSIMP (DIV* (REMABS (LEADARG FN1))
328
(REMABS (LEADARG FN2))))))
331
(COND ((ATOM EXP) EXP)
332
((EQ (CAAR EXP) 'MABS) (CADR EXP))
335
(DECLARE-TOP(SPECIAL VLIST LIANS DEGREE))
337
(DEFUN GETFNSPLIT (L &AUX COEF FN)
338
(MAPC #'(LAMBDA (X) (IF (FREE X INTVAR) (PUSH X COEF) (PUSH X FN))) L)
339
(CONS (MULN COEF NIL) (MULN FN NIL)))
341
(DEFUN GETFNCOEFF (A FORM)
343
((EQUAL (CAR A) 0) (GETFNCOEFF (CDR A) FORM))
344
((EQ (CAAAR A) 'MPLUS) (RATPL (GETFNCOEFF (CDAR A) FORM)
345
(GETFNCOEFF (CDR A) FORM)))
346
((EQ (CAAAR A) 'MTIMES)
347
(LET (((COEF . NEWFN) (GETFNSPLIT (CDAR A))))
348
(SETF (CDAR A) (LIST COEF NEWFN))
349
(COND ((ZEROP1 COEF) (GETFNCOEFF (CDR A) FORM))
350
((AND (MATANP NEWFN) (MEMQ '$%I VARLIST))
351
(LET (($LOGARC T) ($LOGEXPAND '$ALL))
352
(RPLACA A ($EXPAND (RESIMPLIFY (CAR A)))))
354
((AND (ALIKE1 (LEADOP NEWFN) (LEADOP FORM))
355
(OR (ALIKE1 (LEADARG NEWFN) (LEADARG FORM))
357
(LOGEQUIV FORM NEWFN))))
360
(GETFNCOEFF (CDR A) FORM))))
361
((DO ((VL VARLIST (CDR VL))) ((NULL VL))
362
(AND (NOT (ATOM (CAR VL)))
363
(ALIKE1 (LEADOP (CAR VL)) (LEADOP NEWFN))
365
(LOGEQUIV (CAR VL) NEWFN)
366
(ALIKE1 (CAR VL) NEWFN))
367
(RPLACA (CDDAR A) (CAR VL))
369
((LET (VLIST) (NEWVAR1 (CAR A)) (NULL VLIST))
371
(RATPL (CDR (RATREP* (CAR A)))
374
(GETFNCOEFF (CDR A) FORM))
378
(PUSH (DILOG (CONS (CAR A) FORM)) LIANS)
380
(GETFNCOEFF (CDR A) FORM))
384
(LOGEQUIV FORM NEWFN))
385
(PUSH (MUL* (CADAR A) (MAKE-LI (f1+ (CAR (SUBFUNSUBS FORM)))
389
(GETFNCOEFF (CDR A) FORM))
390
(T (SETQ NOGOOD T) 0))))
391
(T (RPLACA A (LIST '(MTIMES) 1 (CAR A)))
392
(GETFNCOEFF A FORM))))
395
(DEFUN RISCHLOGPOLY (EXP)
396
(COND ((EQUAL EXP '(0 . 1)) (RISCHZERO))
397
(EXPFLAG (PUSH (CONS 'POLY EXP) EXPINT)
399
((NOT (AMONG VAR EXP)) (TRYRISCH1 EXP MAINVAR))
400
(T (DO ((DEGREE (PDEGREE (CAR EXP) VAR) (f1- DEGREE))
406
(Y) (Z) (AK) (NOGOOD) (LBKPL1))
407
((MINUSP DEGREE) (CONS SUM (APPEND LIANS (CDR Y))))
408
(SETQ AK (R- (RATQU (POLCOEF P DEGREE) DEN)
409
(R* (CONS (ADD1 DEGREE) 1)
411
(GET VAR 'RISCHDIFF))))
412
(IF (NOT (PZEROP (POLCOEF P DEGREE)))
413
(SETQ P (IF (PCOEFP P) (PZERO) (PSIMP VAR (P-RED P)))))
414
(SETQ Y (TRYRISCH1 AK MAINVAR))
416
(AND (> DEGREE 0) (SETQ LIFLAG $LIFLAG))
417
(SETQ Z (GETFNCOEFF (CDR Y) (GET VAR 'RISCHEXPR)))
419
(COND ((AND (GREATERP DEGREE 0)
420
(OR NOGOOD (FINDINT (CDR Y))))
421
(RETURN (RISCHNOUN SUM (R+ (R* AK
422
(MAKE-POLY VAR DEGREE 1))
424
(SETQ LBKPL1 (RATQU Z (CONS (f1+ DEGREE) 1)))
425
(SETQ SUM (R+ (R* LBKPL1 (MAKE-POLY VAR (ADD1 DEGREE) 1))
426
(R* CARY (IF (ZEROP DEGREE) 1
427
(MAKE-POLY VAR DEGREE 1)))
430
(DEFUN MAKE-LI (SUB ARG)
431
(SUBFUNMAKE '$LI (NCONS SUB) (NCONS ARG)))
433
;integrates log(ro)^degree*log(rn)' in terms of polylogs
434
;finds constants c,d and integers j,k such that
435
;c*ro^j+d=rn^k If ro and rn are poly's then can assume either j=1 or k=1
437
(LET* ((((nil COEF NLOG) . OLOG) L)
438
(NARG (REMABS (CADR NLOG)))
442
(RO (RFORM (CADR OLOG)))
444
((J . K) (RATREDUCE (PDEGREE (CAR RN) VAR) (PDEGREE (CAR RO) VAR)))
447
(COND ((AND (= J 1) (> K 1))
448
(SETQ RN (RATEXPT RN K)
451
((AND (= K 1) (> J 1))
452
(SETQ RO (RATEXPT RO J)
453
COEF (DIV COEF (f* J DEGREE))
455
(DESETQ (RC . RD) (RATDIVIDE RN RO))
456
(COND ((AND (RISCH-CONSTP RC)
458
(SETQ NARG ($RATSIMP (SUB 1 (DIV NARG (RDIS RD)))))
459
(MUL* COEF (POWER -1 (f1+ DEGREE))
460
`((MFACTORIAL) ,DEGREE)
461
(DOSUM (MUL* (POWER -1 IDX)
462
(DIV* (POWER OLOG IDX)
463
`((MFACTORIAL) ,IDX))
464
(MAKE-LI (ADD DEGREE (NEG IDX) 1) NARG))
466
(T (SETQ NOGOOD T) 0))))
468
(DEFUN EXPPOLYCONTROL (FLAG F A EXPG N)
469
(LET (Y L VAR (VARLIST VARLIST) (GENVAR GENVAR))
470
(SETQ VARLIST (REVERSE (CDR (REVERSE VARLIST))))
471
(SETQ VAR (GETRISCHVAR))
472
(SETQ Y (GET VAR 'LEADOP))
473
(COND ((AND (NOT (PZEROP (RATNUMERATOR F)))
474
(RISCH-CONSTP (SETQ L (RATQU A F))))
476
(LIST (R* L (CONS (LIST EXPG N 1) 1)) 0))
479
(RISCHEXPVAR NIL FLAG (LIST F A EXPG N)))
480
(T (RISCHEXPLOG (EQ Y 'MEXPT) FLAG F A
481
(LIST EXPG N (GET VAR 'RISCHARG)
482
VAR (GET VAR 'RISCHDIFF)))))))
484
(DEFUN RISCHEXPPOLY (EXPINT VAR)
485
(LET (Y W NUM DENOM TYPE (ANS (RISCHZERO))
486
(EXPDIFF (RATQU (GET VAR 'RISCHDIFF) (LIST VAR 1 1))))
487
(DO ((EXPINT EXPINT (CDR EXPINT)))
489
(DESETQ (TYPE . Y) (CAR EXPINT))
490
(DESETQ (NUM . DENOM) (RATFIX Y))
491
(COND ((EQ TYPE 'NEG)
492
(SETQ W (EXPPOLYCONTROL T
493
(R* (MINUS (CADR DENOM))
495
(RATQU NUM (CADDR DENOM))
497
(MINUS (CADR DENOM)))))
498
((OR (NUMBERP NUM) (NOT (EQ (CAR NUM) VAR)))
499
(SETQ W (TRYRISCH1 Y MAINVAR)))
500
(T (SETQ W (RISCHZERO))
501
(DO ((NUM (CDR NUM) (CDDR NUM))) ((NULL NUM))
502
(COND ((EQUAL (CAR NUM) 0)
504
(TRYRISCH1 (RATQU (CADR NUM) DENOM) MAINVAR)
506
(T (SETQ W (RISCHADD (EXPPOLYCONTROL
508
(R* (CAR NUM) EXPDIFF)
509
(RATQU (CADR NUM) DENOM)
513
(SETQ ANS (RISCHADD W ANS)))))
515
(DEFUN RISCHEXPVAR (EXPEXPFLAG FLAG L)
516
(PROG (LCM Y M P ALPHAR BETA GAMMA DELTA R S
517
TT DENOM K WL WV I YTEMP TTEMP YALPHA F A EXPG N YN YD)
518
(DESETQ (F A EXPG N) L)
519
(COND ((OR (PZEROP A) (PZEROP (CAR A)))
520
(RETURN (COND ((NULL FLAG) (RZERO))
522
(SETQ DENOM (RATDENOMINATOR F))
523
(SETQ P (FINDPR (CDR (PARTFRAC A MAINVAR))
524
(CDR (PARTFRAC F MAINVAR))))
525
(SETQ LCM (PLCM (RATDENOMINATOR A) P))
526
(SETQ Y (RATPL (SPDERIVATIVE (CONS 1 P) MAINVAR)
528
(SETQ LCM (PLCM LCM (RATDENOMINATOR Y)))
529
(SETQ R (CAR (RATQU LCM P)))
530
(SETQ S (CAR (R* LCM Y)))
531
(SETQ TT (CAR (R* A LCM)))
532
(SETQ BETA (PDEGREE R MAINVAR))
533
(SETQ GAMMA (PDEGREE S MAINVAR))
534
(SETQ DELTA (PDEGREE TT MAINVAR))
535
(SETQ ALPHAR (MAX (DIFFERENCE (ADD1 DELTA) BETA)
536
(DIFFERENCE DELTA GAMMA)))
538
(COND ((EQUAL (SUB1 BETA) GAMMA)
540
(RATQU (POLCOEF S GAMMA)
542
(AND (EQUAL (CDR Y) 1)
545
(SETQ ALPHAR (MAX ALPHAR M))
547
(RETURN (IF FLAG (CXERFARG (RZERO) EXPG N A) NIL)))
548
(COND ((NOT (AND (EQUAL ALPHAR M) (NOT (ZEROP M))))
550
(SETQ K (PLUS ALPHAR BETA -2))
552
L2 (SETQ WV (LIST (CONS (POLCOEF TT K) 1)))
555
(CONS (R+ (R* (CONS I 1)
556
(POLCOEF R (PLUS K 1 (MINUS I))))
557
(CONS (POLCOEF S (PLUS K (MINUS I))) 1))
560
(COND ((GREATERP I -1) (GO L1)))
561
(SETQ WL (CONS WV WL))
563
(COND ((GREATERP K -1) (GO L2)))
565
(IF (OR (EQ Y 'SINGULAR) (EQ Y 'INCONSISTENT))
566
(COND ((NULL FLAG) (RETURN NIL))
567
(T (RETURN (CXERFARG (RZERO) EXPG N A)))))
572
(R+ (R* (CAR Y) (PEXPT (LIST MAINVAR 1 1) K))
577
(RETURN (COND ((NULL FLAG) (RATQU LCM P))
578
(T (LIST (R* (RATQU LCM P)
579
(CONS (LIST EXPG N 1) 1))
582
DOWN2(COND ((GREATERP (SUB1 BETA) GAMMA)
583
(SETQ K (PLUS ALPHAR (SUB1 BETA)))
584
(SETQ DENOM '(RATTI ALPHAR (POLCOEF R BETA) T)))
585
((LESSP (SUB1 BETA) GAMMA)
586
(SETQ K (PLUS ALPHAR GAMMA))
587
(SETQ DENOM '(POLCOEF S GAMMA)))
588
(T (SETQ K (PLUS ALPHAR GAMMA))
590
'(RATPL (RATTI ALPHAR (POLCOEF R BETA) T)
591
(POLCOEF S GAMMA)))))
593
LOOP (SETQ YN (POLCOEF (RATNUMERATOR TT) K)
594
YD (R* (RATDENOMINATOR TT) ;DENOM MAY BE 0
595
(COND ((ZEROP ALPHAR) (POLCOEF S GAMMA))
598
(COND ((PZEROP YN) (SETQ K (f1- K) ALPHAR (f1- ALPHAR))
599
(GO LOOP)) ;need more constraints?
601
((NULL FLAG) (RETURN NIL))
602
(T (RETURN (CXERFARG (RZERO) EXPG N A)))))))
603
(T (SETQ YALPHA (RATQU YN YD))))
604
(SETQ YTEMP (R+ Y (R* YALPHA
605
(CONS (LIST MAINVAR ALPHAR 1) 1) )))
606
(SETQ TTEMP (R- TT (R* YALPHA
607
(R+ (R* S (CONS (LIST MAINVAR ALPHAR 1) 1))
609
(LIST MAINVAR (SUB1 ALPHAR) 1))))))
611
(SETQ ALPHAR (SUB1 ALPHAR))
617
((NULL FLAG) (RETURN (RATQU YTEMP P)))
618
(T (RETURN (LIST (RATQU (R* YTEMP (CONS (LIST EXPG N 1) 1))
321
(defun findint (exp) (cond ((atom exp) nil)
322
((atom (car exp)) (findint (cdr exp)))
323
((eq (caaar exp) '%integrate) t)
324
(t (findint (cdr exp)))))
326
(defun logequiv (fn1 fn2)
327
(freeof intvar ($ratsimp (div* (remabs (leadarg fn1))
328
(remabs (leadarg fn2))))))
331
(cond ((atom exp) exp)
332
((eq (caar exp) 'mabs) (cadr exp))
335
(declare-top(special vlist lians degree))
337
(defun getfnsplit (l &aux coef fn)
338
(mapc #'(lambda (x) (if (free x intvar) (push x coef) (push x fn))) l)
339
(cons (muln coef nil) (muln fn nil)))
341
(defun getfncoeff (a form)
343
((equal (car a) 0) (getfncoeff (cdr a) form))
344
((eq (caaar a) 'mplus) (ratpl (getfncoeff (cdar a) form)
345
(getfncoeff (cdr a) form)))
346
((eq (caaar a) 'mtimes)
347
(destructuring-let (((coef . newfn) (getfnsplit (cdar a))))
348
(setf (cdar a) (list coef newfn))
349
(cond ((zerop1 coef) (getfncoeff (cdr a) form))
350
((and (matanp newfn) (memq '$%i varlist))
351
(let (($logarc t) ($logexpand '$all))
352
(rplaca a ($expand (resimplify (car a)))))
354
((and (alike1 (leadop newfn) (leadop form))
355
(or (alike1 (leadarg newfn) (leadarg form))
357
(logequiv form newfn))))
360
(getfncoeff (cdr a) form))))
361
((do ((vl varlist (cdr vl))) ((null vl))
362
(and (not (atom (car vl)))
363
(alike1 (leadop (car vl)) (leadop newfn))
365
(logequiv (car vl) newfn)
366
(alike1 (car vl) newfn))
367
(rplaca (cddar a) (car vl))
369
((let (vlist) (newvar1 (car a)) (null vlist))
371
(ratpl (cdr (ratrep* (car a)))
374
(getfncoeff (cdr a) form))
378
(push (dilog (cons (car a) form)) lians)
380
(getfncoeff (cdr a) form))
384
(logequiv form newfn))
385
(push (mul* (cadar a) (make-li (f1+ (car (subfunsubs form)))
389
(getfncoeff (cdr a) form))
390
(t (setq nogood t) 0))))
391
(t (rplaca a (list '(mtimes) 1 (car a)))
392
(getfncoeff a form))))
395
(defun rischlogpoly (exp)
396
(cond ((equal exp '(0 . 1)) (rischzero))
397
(expflag (push (cons 'poly exp) expint)
399
((not (among var exp)) (tryrisch1 exp mainvar))
400
(t (do ((degree (pdegree (car exp) var) (f1- degree))
406
(y) (z) (ak) (nogood) (lbkpl1))
407
((minusp degree) (cons sum (append lians (cdr y))))
408
(setq ak (r- (ratqu (polcoef p degree) den)
409
(r* (cons (add1 degree) 1)
411
(get var 'rischdiff))))
412
(if (not (pzerop (polcoef p degree)))
413
(setq p (if (pcoefp p) (pzero) (psimp var (p-red p)))))
414
(setq y (tryrisch1 ak mainvar))
416
(and (> degree 0) (setq liflag $liflag))
417
(setq z (getfncoeff (cdr y) (get var 'rischexpr)))
419
(cond ((and (greaterp degree 0)
420
(or nogood (findint (cdr y))))
421
(return (rischnoun sum (r+ (r* ak
422
(make-poly var degree 1))
424
(setq lbkpl1 (ratqu z (cons (f1+ degree) 1)))
425
(setq sum (r+ (r* lbkpl1 (make-poly var (add1 degree) 1))
426
(r* cary (if (zerop degree) 1
427
(make-poly var degree 1)))
430
(defun make-li (sub arg)
431
(subfunmake '$li (ncons sub) (ncons arg)))
433
;;integrates log(ro)^degree*log(rn)' in terms of polylogs
434
;;finds constants c,d and integers j,k such that
435
;;c*ro^j+d=rn^k If ro and rn are poly's then can assume either j=1 or k=1
437
(destructuring-let* ((((nil coef nlog) . olog) l)
438
(narg (remabs (cadr nlog)))
442
(ro (rform (cadr olog)))
444
((j . k) (ratreduce (pdegree (car rn) var) (pdegree (car ro) var)))
447
(cond ((and (= j 1) (> k 1))
448
(setq rn (ratexpt rn k)
451
((and (= k 1) (> j 1))
452
(setq ro (ratexpt ro j)
453
coef (div coef (f* j degree))
455
(desetq (rc . rd) (ratdivide rn ro))
456
(cond ((and (risch-constp rc)
458
(setq narg ($ratsimp (sub 1 (div narg (rdis rd)))))
459
(mul* coef (power -1 (f1+ degree))
460
`((mfactorial) ,degree)
461
(dosum (mul* (power -1 idx)
462
(div* (power olog idx)
463
`((mfactorial) ,idx))
464
(make-li (add degree (neg idx) 1) narg))
466
(t (setq nogood t) 0))))
468
(defun exppolycontrol (flag f a expg n)
469
(let (y l var (varlist varlist) (genvar genvar))
470
(setq varlist (reverse (cdr (reverse varlist))))
471
(setq var (getrischvar))
472
(setq y (get var 'leadop))
473
(cond ((and (not (pzerop (ratnumerator f)))
474
(risch-constp (setq l (ratqu a f))))
476
(list (r* l (cons (list expg n 1) 1)) 0))
479
(rischexpvar nil flag (list f a expg n)))
480
(t (rischexplog (eq y 'mexpt) flag f a
481
(list expg n (get var 'rischarg)
482
var (get var 'rischdiff)))))))
484
(defun rischexppoly (expint var)
485
(let (y w num denom type (ans (rischzero))
486
(expdiff (ratqu (get var 'rischdiff) (list var 1 1))))
487
(do ((expint expint (cdr expint)))
489
(desetq (type . y) (car expint))
490
(desetq (num . denom) (ratfix y))
491
(cond ((eq type 'neg)
492
(setq w (exppolycontrol t
493
(r* (minus (cadr denom))
495
(ratqu num (caddr denom))
497
(minus (cadr denom)))))
498
((or (numberp num) (not (eq (car num) var)))
499
(setq w (tryrisch1 y mainvar)))
500
(t (setq w (rischzero))
501
(do ((num (cdr num) (cddr num))) ((null num))
502
(cond ((equal (car num) 0)
504
(tryrisch1 (ratqu (cadr num) denom) mainvar)
506
(t (setq w (rischadd (exppolycontrol
508
(r* (car num) expdiff)
509
(ratqu (cadr num) denom)
513
(setq ans (rischadd w ans)))))
515
(defun rischexpvar (expexpflag flag l)
516
(prog (lcm y m p alphar beta gamma delta r s
517
tt denom k wl wv i ytemp ttemp yalpha f a expg n yn yd)
518
(desetq (f a expg n) l)
519
(cond ((or (pzerop a) (pzerop (car a)))
520
(return (cond ((null flag) (rzero))
522
(setq denom (ratdenominator f))
523
(setq p (findpr (cdr (partfrac a mainvar))
524
(cdr (partfrac f mainvar))))
525
(setq lcm (plcm (ratdenominator a) p))
526
(setq y (ratpl (spderivative (cons 1 p) mainvar)
528
(setq lcm (plcm lcm (ratdenominator y)))
529
(setq r (car (ratqu lcm p)))
530
(setq s (car (r* lcm y)))
531
(setq tt (car (r* a lcm)))
532
(setq beta (pdegree r mainvar))
533
(setq gamma (pdegree s mainvar))
534
(setq delta (pdegree tt mainvar))
535
(setq alphar (max (difference (add1 delta) beta)
536
(difference delta gamma)))
538
(cond ((equal (sub1 beta) gamma)
540
(ratqu (polcoef s gamma)
542
(and (equal (cdr y) 1)
545
(setq alphar (max alphar m))
547
(return (if flag (cxerfarg (rzero) expg n a) nil)))
548
(cond ((not (and (equal alphar m) (not (zerop m))))
550
(setq k (plus alphar beta -2))
552
l2 (setq wv (list (cons (polcoef tt k) 1)))
555
(cons (r+ (r* (cons i 1)
556
(polcoef r (plus k 1 (minus i))))
557
(cons (polcoef s (plus k (minus i))) 1))
560
(cond ((greaterp i -1) (go l1)))
561
(setq wl (cons wv wl))
563
(cond ((greaterp k -1) (go l2)))
565
(if (or (eq y 'singular) (eq y 'inconsistent))
566
(cond ((null flag) (return nil))
567
(t (return (cxerfarg (rzero) expg n a)))))
572
(r+ (r* (car y) (pexpt (list mainvar 1 1) k))
577
(return (cond ((null flag) (ratqu lcm p))
578
(t (list (r* (ratqu lcm p)
579
(cons (list expg n 1) 1))
582
down2(cond ((greaterp (sub1 beta) gamma)
583
(setq k (plus alphar (sub1 beta)))
584
(setq denom '(ratti alphar (polcoef r beta) t)))
585
((lessp (sub1 beta) gamma)
586
(setq k (plus alphar gamma))
587
(setq denom '(polcoef s gamma)))
588
(t (setq k (plus alphar gamma))
590
'(ratpl (ratti alphar (polcoef r beta) t)
591
(polcoef s gamma)))))
593
loop (setq yn (polcoef (ratnumerator tt) k)
594
yd (r* (ratdenominator tt) ;DENOM MAY BE 0
595
(cond ((zerop alphar) (polcoef s gamma))
598
(cond ((pzerop yn) (setq k (f1- k) alphar (f1- alphar))
599
(go loop)) ;need more constraints?
601
((null flag) (return nil))
602
(t (return (cxerfarg (rzero) expg n a)))))))
603
(t (setq yalpha (ratqu yn yd))))
604
(setq ytemp (r+ y (r* yalpha
605
(cons (list mainvar alphar 1) 1) )))
606
(setq ttemp (r- tt (r* yalpha
607
(r+ (r* s (cons (list mainvar alphar 1) 1))
609
(list mainvar (sub1 alphar) 1))))))
611
(setq alphar (sub1 alphar))
617
((null flag) (return (ratqu ytemp p)))
618
(t (return (list (ratqu (r* ytemp (cons (list expg n 1) 1))
621
((NULL FLAG) (RETURN NIL))
622
((AND (RISCH-CONSTP (SETQ TTEMP (RATQU TTEMP LCM)))
624
(EQUAL (PDEGREE (CAR (GET EXPG 'RISCHARG)) MAINVAR) 2)
625
(EQUAL (PDEGREE (CDR (GET EXPG 'RISCHARG)) MAINVAR) 0))
626
(RETURN (LIST (RATQU (R* YTEMP (CONS (LIST EXPG N 1) 1)) P)
627
(ERFARG2 (R* N (GET EXPG 'RISCHARG)) TTEMP))))
630
(RATQU (R* Y (CONS (LIST EXPG N 1) 1)) P)
621
((null flag) (return nil))
622
((and (risch-constp (setq ttemp (ratqu ttemp lcm)))
624
(equal (pdegree (car (get expg 'rischarg)) mainvar) 2)
625
(equal (pdegree (cdr (get expg 'rischarg)) mainvar) 0))
626
(return (list (ratqu (r* ytemp (cons (list expg n 1) 1)) p)
627
(erfarg2 (r* n (get expg 'rischarg)) ttemp))))
630
(ratqu (r* y (cons (list expg n 1) 1)) p)
639
639
;; *JM should be declared as an array, although it is not created
640
640
;; by this file. -- cwh
644
(PROG (D *MOSESFLAG M M2)
645
(SETQ D (LENGTH (CAR MM)))
646
;; MTOA stands for MATRIX-TO-ARRAY. An array is created and
647
;; associated functionally with the symbol *JM. The elements
648
;; of the array are initialized from the matrix MM.
649
(MTOA '*JM* (LENGTH MM) D MM)
650
(SETQ M (TFGELI '*JM* (LENGTH MM) D))
651
(COND ((OR (AND (NULL (CAR M)) (NULL (CADR M)))
653
(> (LENGTH (CAR M)) (f- (LENGTH MM) (f1- D)))))
655
((CADR M) (RETURN 'INCONSISTENT)))
657
(PTORAT '*JM* (f1- D) D)
658
(SETQ M2 (XRUTOUT '*JM* (f1- D) D NIL NIL))
659
(SETQ M2 (LSAFIX (CDR M2) (CADDR M)))
644
(prog (d *mosesflag m m2)
645
(setq d (length (car mm)))
646
;; MTOA stands for MATRIX-TO-ARRAY. An array is created and
647
;; associated functionally with the symbol *JM. The elements
648
;; of the array are initialized from the matrix MM.
649
(mtoa '*jm* (length mm) d mm)
650
(setq m (tfgeli '*jm* (length mm) d))
651
(cond ((or (and (null (car m)) (null (cadr m)))
653
(> (length (car m)) (f- (length mm) (f1- d)))))
655
((cadr m) (return 'inconsistent)))
657
(ptorat '*jm* (f1- d) d)
658
(setq m2 (xrutout '*jm* (f1- d) d nil nil))
659
(setq m2 (lsafix (cdr m2) (caddr m)))
664
664
(declare (special *jm*))
668
;(STORE (*JM 1 (CAR N)) (CAR L))
669
(STORE (aref *JM* 1 (CAR N)) (CAR L))
671
(DO ((S (LENGTH L) (f1- S))
673
((= S 0) (CONS '(LIST) ANS))
674
(SETQ ANS (CONS (aref *JM* 1 S) ANS))))
677
(DEFUN FINDPR (ALIST FLIST &AUX (P 1) ALPHAR FTERM)
678
(DO ((ALIST ALIST (CDR ALIST))) ((NULL ALIST))
679
(SETQ FTERM (FINDFLIST (CADAR ALIST) FLIST))
680
(IF FTERM (SETQ FLIST (REMQ Y FLIST 1)))
682
(COND ((NULL FTERM) (CADDAR ALIST))
683
((EQUAL (CADDR FTERM) 1)
684
(FPR-DIF (CAR FLIST) (CADDAR ALIST)))
685
(T (MAX (f- (CADDAR ALIST) (CADDR FTERM)) 0))))
686
(IF (NOT (ZEROP ALPHAR))
687
(SETQ P (PTIMES P (PEXPT (CADAR ALIST) ALPHAR)))))
688
(DO ((FLIST FLIST (CDR FLIST))) ((NULL FLIST))
689
(WHEN (EQUAL (CADDAR FLIST) 1)
690
(SETQ ALPHAR (FPR-DIF (CAR FLIST) 0))
691
(SETQ P (PTIMES P (PEXPT (CADAR FLIST) ALPHAR)))))
694
(DEFUN FPR-DIF (FTERM ALPHA)
695
(LET* (((NUM DEN MULT) FTERM)
696
(M (SPDERIVATIVE DEN MAINVAR))
698
(COND ((RZEROP M) ALPHA)
699
(T (SETQ N (RATQU (CDR (RATDIVIDE NUM DEN))
701
(IF (AND (EQUAL (CDR N) 1) (NUMBERP (CAR N)))
705
(DEFUN FINDFLIST (A LLIST) (COND ((NULL LLIST) NIL)
706
((EQUAL (CADAR LLIST) A) (CAR LLIST))
707
(T (FINDFLIST A (CDR LLIST)))))
710
(DEFUN RISCHEXPLOG (EXPEXPFLAG FLAG F A L)
668
;(STORE (*JM 1 (CAR N)) (CAR L))
669
(store (aref *jm* 1 (car n)) (car l))
671
(do ((s (length l) (f1- s))
673
((= s 0) (cons '(list) ans))
674
(setq ans (cons (aref *jm* 1 s) ans))))
677
(defun findpr (alist flist &aux (p 1) alphar fterm)
678
(do ((alist alist (cdr alist))) ((null alist))
679
(setq fterm (findflist (cadar alist) flist))
680
(if fterm (setq flist (remq y flist 1)))
682
(cond ((null fterm) (caddar alist))
683
((equal (caddr fterm) 1)
684
(fpr-dif (car flist) (caddar alist)))
685
(t (max (f- (caddar alist) (caddr fterm)) 0))))
686
(if (not (zerop alphar))
687
(setq p (ptimes p (pexpt (cadar alist) alphar)))))
688
(do ((flist flist (cdr flist))) ((null flist))
689
(when (equal (caddar flist) 1)
690
(setq alphar (fpr-dif (car flist) 0))
691
(setq p (ptimes p (pexpt (cadar flist) alphar)))))
694
(defun fpr-dif (fterm alpha)
695
(destructuring-let* (((num den mult) fterm)
696
(m (spderivative den mainvar))
698
(cond ((rzerop m) alpha)
699
(t (setq n (ratqu (cdr (ratdivide num den))
701
(if (and (equal (cdr n) 1) (numberp (car n)))
705
(defun findflist (a llist) (cond ((null llist) nil)
706
((equal (cadar llist) a) (car llist))
707
(t (findflist a (cdr llist)))))
710
(defun rischexplog (expexpflag flag f a l)
711
711
(declare (special var))
712
(PROG (LCM Y YY M P ALPHAR BETA GAMMA DELTA
713
MU R S TT DENOM YMU RBETA EXPG N ETA LOGETA LOGDIFF
714
TEMP CARY NOGOOD VECTOR AARRAY RMU RRMU RARRAY)
715
(DESETQ (EXPG N ETA LOGETA LOGDIFF) L)
716
(COND ((OR (PZEROP A) (PZEROP (CAR A)))
717
(RETURN (COND ((NULL FLAG) (RZERO))
719
(SETQ P (FINDPR (CDR (PARTFRAC A VAR)) (CDR (PARTFRAC F VAR))))
720
(SETQ LCM (PLCM (RATDENOMINATOR A) P))
721
(SETQ Y (RATPL (SPDERIVATIVE (CONS 1 P) MAINVAR)
723
(SETQ LCM (PLCM LCM (RATDENOMINATOR Y)))
724
(SETQ R (CAR (RATQU LCM P)))
725
(SETQ S (CAR (R* LCM Y)))
726
(SETQ TT (CAR (R* A LCM)))
727
(SETQ BETA (PDEGREE R VAR))
728
(SETQ GAMMA (PDEGREE S VAR))
729
(SETQ DELTA (PDEGREE TT VAR))
730
(COND (EXPEXPFLAG (SETQ MU (MAX (f- DELTA BETA)
733
(SETQ MU (MAX (f- (f1+ DELTA) BETA)
734
(f- (f1+ DELTA) GAMMA)))
735
(COND ((< BETA GAMMA) (GO BACK))
736
((= (SUB1 BETA) GAMMA) (GO DOWN1)))
737
(SETQ Y (TRYRISCH1 (RATQU (R- (R* (POLCOEF R (f1- BETA))
740
(POLCOEF S (f1- GAMMA))))
745
(SETQ YY (GETFNCOEFF (CDR Y) (GET VAR 'RISCHEXPR)))
746
(COND ((AND (NOT (FINDINT (CDR Y)))
751
(GREATERP (CAR YY) MU))
755
(COND ((NOT (EQUAL BETA GAMMA)) (GO BACK)))
756
(SETQ Y (TRYRISCH1 (RATQU (POLCOEF S GAMMA) (POLCOEF R BETA))
758
(COND ((FINDINT (CDR Y)) (GO BACK)))
759
(SETQ YY (RATQU (R* -1 (CAR Y)) ETA))
760
(COND ((AND (EQUAL (CDR YY) 1)
762
(GREATERP (CAR YY) MU))
765
DOWN1(SETQ Y (TRYRISCH1 (RATQU (POLCOEF S GAMMA) (POLCOEF R BETA))
768
(SETQ YY (GETFNCOEFF (CDR Y) (GET VAR 'RISCHEXPR)))
769
(COND ((AND (NOT (FINDINT (CDR Y)))
773
(GREATERP (MINUS (CAR YY)) MU))
774
(SETQ MU (MINUS (CAR YY)))))
776
(RETURN (IF FLAG (CXERFARG (RZERO) EXPG N A) NIL)))
777
(COND ((> BETA GAMMA)(GO LSACALL))
780
(SETQ DENOM (POLCOEF S GAMMA))
783
(SETQ YMU (RATQU (POLCOEF (RATNUMERATOR TT) (f+ MU GAMMA))
784
(R* (RATDENOMINATOR TT) DENOM)))
785
(SETQ Y (R+ Y (SETQ YMU (R* YMU (PEXPT (LIST LOGETA 1 1) MU) ))))
788
(R* R (SPDERIVATIVE YMU MAINVAR))))
791
((NOT (< MU 0)) (GO LINEARLOOP))
792
((NOT FLAG) (RETURN (COND ((RZEROP TT) (RATQU Y P)) (T NIL))))
794
(RETURN (CONS (RATQU (R* Y (CONS (LIST EXPG N 1) 1)) P) '(0))))
795
(T (RETURN (CXERFARG (RATQU (R* Y (CONS (LIST EXPG N 1) 1)) P)
800
(SETQ RBETA (POLCOEF R BETA))
803
(SETQ F (R+ (RATQU (POLCOEF S GAMMA) RBETA)
804
(COND (EXPEXPFLAG (R* MU (SPDERIVATIVE ETA MAINVAR)))
806
(SETQ YMU (EXPPOLYCONTROL NIL
808
(RATQU (POLCOEF (RATNUMERATOR TT)
810
(R* (RATDENOMINATOR TT) RBETA))
817
(T (RETURN (CXERFARG (RATQU (R* Y (CONS (LIST EXPG N 1) 1)) P)
818
EXPG N (RATQU TT LCM))))))))
819
(SETQ Y (R+ Y (SETQ YMU (R* YMU (PEXPT (LIST LOGETA 1 1) MU)))))
822
(R* R (SPDERIVATIVE YMU MAINVAR))))
825
((NOT (< MU 0)) (GO RECURSELOOP))
827
(RETURN (COND ((RZEROP TT) (RATQU Y P)) (T NIL))))
829
(RETURN (CONS (RATQU (R* Y (CONS (LIST EXPG N 1) 1)) P) '(0))))
830
(T (RETURN (CXERFARG (RATQU (R* Y (CONS (LIST EXPG N 1) 1)) P)
837
(SETQ TEMP (R* (RATEXPT (CONS (LIST LOGETA 1 1) 1) (f1- MU))
838
(R+ (R* S (CONS (LIST LOGETA 1 1) 1))
839
(R* MU R LOGDIFF ))))
840
MU1 (SETQ VECTOR NIL)
841
(SETQ RMU (f+ RRMU BETA))
843
(SETQ VECTOR (CONS (RATQU (POLCOEF (RATNUMERATOR TEMP) RMU)
844
(RATDENOMINATOR TEMP)) VECTOR))
846
(COND ((NOT (< RMU 0)) (GO RMULOOP)))
848
(SETQ AARRAY (APPEND AARRAY (LIST (REVERSE VECTOR))))
849
(COND ((NOT (< MU 0)) (GO MULOOP))
850
((EQUAL MU -2) (GO SKIPMU)))
857
(SETQ VECTOR (MAPCAR 'CAR AARRAY))
858
(SETQ AARRAY (MAPCAR 'CDR AARRAY))
859
(SETQ RARRAY (APPEND RARRAY (LIST VECTOR)))
860
(COND ((NOT (NULL (CAR AARRAY))) (GO ARRAYLOOP)))
861
(SETQ RMU (f1+ RRMU))
864
(SETQ VECTOR (CONS '(0 . 1) VECTOR))
866
(COND ((NOT (< RMU 0)) (GO ARRAY1LOOP)))
869
(COND ((EQUAL (CAR RARRAY) VECTOR) NIL)
870
(T (SETQ AARRAY (CONS (CAR RARRAY) AARRAY))))
871
(SETQ RARRAY (CDR RARRAY))
872
(COND (RARRAY (GO ARRAY2LOOP)))
873
(SETQ RARRAY (REVERSE AARRAY))
874
(SETQ TEMP (LSA RARRAY))
875
(COND ((OR (EQ TEMP 'SINGULAR) (EQ TEMP 'INCONSISTENT))
877
(COND ((NULL FLAG) NIL)
878
(T (CXERFARG (RZERO) EXPG N A))))))
879
(SETQ TEMP (reverse (CDR TEMP)))
882
L3 (SETQ Y (R+ Y (R* (CAR TEMP) (PEXPT (LIST LOGETA 1 1) RMU))))
883
(SETQ TEMP (CDR TEMP))
885
(COND ((NOT (> RMU RRMU)) (GO L3)))
886
(RETURN (COND ((NULL FLAG) (RATQU Y P))
887
(T (CONS (R* (LIST EXPG N 1) (RATQU Y P)) '(0)))))))
890
(DEFUN ERFARG (EXPARG COEF)
891
(PROG (NUM DENOM ERFARG)
892
(SETQ EXPARG (R- EXPARG))
893
(UNLESS (AND (SETQ NUM (PNTHROOTP (RATNUMERATOR EXPARG) 2))
894
(SETQ DENOM (PNTHROOTP (RATDENOMINATOR EXPARG) 2)))
896
(SETQ ERFARG (CONS NUM DENOM))
898
(SETQ COEF (RATQU COEF (SPDERIVATIVE ERFARG MAINVAR))))
899
(RETURN (SIMPLIFY `((MTIMES) ((RAT) 1 2)
900
((MEXPT) $%PI ((RAT) 1 2))
902
((%ERF) ,(DISREP ERFARG))))))))
904
(DEFUN ERFARG2 (EXPARG COEFF &AUX (VAR MAINVAR) A B C D)
905
(WHEN (AND (= (PDEGREE (CAR EXPARG) VAR) 2)
906
(EQ (CAAR EXPARG) VAR)
907
(RISCH-PCONSTP (CDR EXPARG))
908
(RISCH-CONSTP COEFF))
909
(SETQ A (RATQU (R* -1 (CADDAR EXPARG))
911
(SETQ B (DISREP (RATQU (R* -1 (POLCOEF (CAR EXPARG) 1))
913
(SETQ C (DISREP (RATQU (R* (POLCOEF (CAR EXPARG) 0))
919
((MEXPT) $%E ((MPLUS) ,C
920
((MQUOTIENT) ((MEXPT) ,B 2)
925
((MEXPT) $%PI ((RAT) 1 2)))
927
((MTIMES) ,D ,INTVAR)
928
((MTIMES) ,B ((RAT) 1 2) ((MEXPT) ,D -1))))))))
931
(DEFUN CXERFARG (ANS EXPG N NUMDENOM &AUX (ARG (R* N (GET EXPG 'RISCHARG)))
933
(PROG (DENOM ERFANS NUM NERF)
934
(DESETQ (NUM . DENOM) NUMDENOM)
935
(UNLESS $ERFFLAG (SETQ FAILS NUM) (GO LOSE))
936
(IF (SETQ ERFANS (ERFARG ARG NUMDENOM))
937
(RETURN (LIST ANS ERFANS)))
938
AGAIN (WHEN (AND (NOT (PCOEFP DENOM))
940
(EQ (GET (CAR DENOM) 'LEADOP) 'MEXPT))
941
(SETQ ARG (R+ ARG (R* (f- (P-LE DENOM))
942
(GET (P-VAR DENOM) 'RISCHARG)))
945
(SLOOP FOR (COEF EXPARG EXPPOLY) IN (EXPLIST NUM ARG 1)
946
DO (SETQ COEF (RATQU COEF DENOM)
947
NERF (OR (ERFARG2 EXPARG COEF) (ERFARG EXPARG COEF)))
948
(IF NERF (PUSH NERF ERFANS) (SETQ FAILS
949
(PPLUS FAILS EXPPOLY))))
951
(IF (PZEROP FAILS) (CONS ANS ERFANS)
952
(RISCHADD (CONS ANS ERFANS)
953
(RISCHNOUN (R* (RATEXPT (CONS (MAKE-POLY EXPG) 1) N)
954
(RATQU FAILS (CDR NUMDENOM)))))))))
956
(DEFUN EXPLIST (P OARG EXPS)
957
(COND ((OR (PCOEFP P) (NOT (EQ 'MEXPT (GET (P-VAR P) 'LEADOP))))
958
(LIST (LIST P OARG (PTIMES P EXPS))))
959
(T (SLOOP WITH NARG = (GET (P-VAR P) 'RISCHARG)
960
FOR (EXP COEF) ON (P-TERMS P) BY 'PT-RED
962
(R+ OARG (R* EXP NARG))
964
(MAKE-POLY (P-VAR P) EXP 1)))))))
967
(declare-top (SPECIAL *FNEWVARSW))
712
(prog (lcm y yy m p alphar beta gamma delta
713
mu r s tt denom ymu rbeta expg n eta logeta logdiff
714
temp cary nogood vector aarray rmu rrmu rarray)
715
(desetq (expg n eta logeta logdiff) l)
716
(cond ((or (pzerop a) (pzerop (car a)))
717
(return (cond ((null flag) (rzero))
719
(setq p (findpr (cdr (partfrac a var)) (cdr (partfrac f var))))
720
(setq lcm (plcm (ratdenominator a) p))
721
(setq y (ratpl (spderivative (cons 1 p) mainvar)
723
(setq lcm (plcm lcm (ratdenominator y)))
724
(setq r (car (ratqu lcm p)))
725
(setq s (car (r* lcm y)))
726
(setq tt (car (r* a lcm)))
727
(setq beta (pdegree r var))
728
(setq gamma (pdegree s var))
729
(setq delta (pdegree tt var))
730
(cond (expexpflag (setq mu (max (f- delta beta)
733
(setq mu (max (f- (f1+ delta) beta)
734
(f- (f1+ delta) gamma)))
735
(cond ((< beta gamma) (go back))
736
((= (sub1 beta) gamma) (go down1)))
737
(setq y (tryrisch1 (ratqu (r- (r* (polcoef r (f1- beta))
740
(polcoef s (f1- gamma))))
745
(setq yy (getfncoeff (cdr y) (get var 'rischexpr)))
746
(cond ((and (not (findint (cdr y)))
751
(greaterp (car yy) mu))
755
(cond ((not (equal beta gamma)) (go back)))
756
(setq y (tryrisch1 (ratqu (polcoef s gamma) (polcoef r beta))
758
(cond ((findint (cdr y)) (go back)))
759
(setq yy (ratqu (r* -1 (car y)) eta))
760
(cond ((and (equal (cdr yy) 1)
762
(greaterp (car yy) mu))
765
down1(setq y (tryrisch1 (ratqu (polcoef s gamma) (polcoef r beta))
768
(setq yy (getfncoeff (cdr y) (get var 'rischexpr)))
769
(cond ((and (not (findint (cdr y)))
773
(greaterp (minus (car yy)) mu))
774
(setq mu (minus (car yy)))))
776
(return (if flag (cxerfarg (rzero) expg n a) nil)))
777
(cond ((> beta gamma)(go lsacall))
780
(setq denom (polcoef s gamma))
783
(setq ymu (ratqu (polcoef (ratnumerator tt) (f+ mu gamma))
784
(r* (ratdenominator tt) denom)))
785
(setq y (r+ y (setq ymu (r* ymu (pexpt (list logeta 1 1) mu) ))))
788
(r* r (spderivative ymu mainvar))))
791
((not (< mu 0)) (go linearloop))
792
((not flag) (return (cond ((rzerop tt) (ratqu y p)) (t nil))))
794
(return (cons (ratqu (r* y (cons (list expg n 1) 1)) p) '(0))))
795
(t (return (cxerfarg (ratqu (r* y (cons (list expg n 1) 1)) p)
800
(setq rbeta (polcoef r beta))
803
(setq f (r+ (ratqu (polcoef s gamma) rbeta)
804
(cond (expexpflag (r* mu (spderivative eta mainvar)))
806
(setq ymu (exppolycontrol nil
808
(ratqu (polcoef (ratnumerator tt)
810
(r* (ratdenominator tt) rbeta))
817
(t (return (cxerfarg (ratqu (r* y (cons (list expg n 1) 1)) p)
818
expg n (ratqu tt lcm))))))))
819
(setq y (r+ y (setq ymu (r* ymu (pexpt (list logeta 1 1) mu)))))
822
(r* r (spderivative ymu mainvar))))
825
((not (< mu 0)) (go recurseloop))
827
(return (cond ((rzerop tt) (ratqu y p)) (t nil))))
829
(return (cons (ratqu (r* y (cons (list expg n 1) 1)) p) '(0))))
830
(t (return (cxerfarg (ratqu (r* y (cons (list expg n 1) 1)) p)
837
(setq temp (r* (ratexpt (cons (list logeta 1 1) 1) (f1- mu))
838
(r+ (r* s (cons (list logeta 1 1) 1))
839
(r* mu r logdiff ))))
840
mu1 (setq vector nil)
841
(setq rmu (f+ rrmu beta))
843
(setq vector (cons (ratqu (polcoef (ratnumerator temp) rmu)
844
(ratdenominator temp)) vector))
846
(cond ((not (< rmu 0)) (go rmuloop)))
848
(setq aarray (append aarray (list (reverse vector))))
849
(cond ((not (< mu 0)) (go muloop))
850
((equal mu -2) (go skipmu)))
857
(setq vector (mapcar 'car aarray))
858
(setq aarray (mapcar 'cdr aarray))
859
(setq rarray (append rarray (list vector)))
860
(cond ((not (null (car aarray))) (go arrayloop)))
861
(setq rmu (f1+ rrmu))
864
(setq vector (cons '(0 . 1) vector))
866
(cond ((not (< rmu 0)) (go array1loop)))
869
(cond ((equal (car rarray) vector) nil)
870
(t (setq aarray (cons (car rarray) aarray))))
871
(setq rarray (cdr rarray))
872
(cond (rarray (go array2loop)))
873
(setq rarray (reverse aarray))
874
(setq temp (lsa rarray))
875
(cond ((or (eq temp 'singular) (eq temp 'inconsistent))
877
(cond ((null flag) nil)
878
(t (cxerfarg (rzero) expg n a))))))
879
(setq temp (reverse (cdr temp)))
882
l3 (setq y (r+ y (r* (car temp) (pexpt (list logeta 1 1) rmu))))
883
(setq temp (cdr temp))
885
(cond ((not (> rmu rrmu)) (go l3)))
886
(return (cond ((null flag) (ratqu y p))
887
(t (cons (r* (list expg n 1) (ratqu y p)) '(0)))))))
890
(defun erfarg (exparg coef)
891
(prog (num denom erfarg)
892
(setq exparg (r- exparg))
893
(unless (and (setq num (pnthrootp (ratnumerator exparg) 2))
894
(setq denom (pnthrootp (ratdenominator exparg) 2)))
896
(setq erfarg (cons num denom))
898
(setq coef (ratqu coef (spderivative erfarg mainvar))))
899
(return (simplify `((mtimes) ((rat) 1 2)
900
((mexpt) $%pi ((rat) 1 2))
902
((%erf) ,(disrep erfarg))))))))
904
(defun erfarg2 (exparg coeff &aux (var mainvar) a b c d)
905
(when (and (= (pdegree (car exparg) var) 2)
906
(eq (caar exparg) var)
907
(risch-pconstp (cdr exparg))
908
(risch-constp coeff))
909
(setq a (ratqu (r* -1 (caddar exparg))
911
(setq b (disrep (ratqu (r* -1 (polcoef (car exparg) 1))
913
(setq c (disrep (ratqu (r* (polcoef (car exparg) 0))
919
((mexpt) $%e ((mplus) ,c
920
((mquotient) ((mexpt) ,b 2)
925
((mexpt) $%pi ((rat) 1 2)))
927
((mtimes) ,d ,intvar)
928
((mtimes) ,b ((rat) 1 2) ((mexpt) ,d -1))))))))
931
(defun cxerfarg (ans expg n numdenom &aux (arg (r* n (get expg 'rischarg)))
933
(prog (denom erfans num nerf)
934
(desetq (num . denom) numdenom)
935
(unless $erfflag (setq fails num) (go lose))
936
(if (setq erfans (erfarg arg numdenom))
937
(return (list ans erfans)))
938
again (when (and (not (pcoefp denom))
940
(eq (get (car denom) 'leadop) 'mexpt))
941
(setq arg (r+ arg (r* (f- (p-le denom))
942
(get (p-var denom) 'rischarg)))
945
(loop for (coef exparg exppoly) in (explist num arg 1)
946
do (setq coef (ratqu coef denom)
947
nerf (or (erfarg2 exparg coef) (erfarg exparg coef)))
948
(if nerf (push nerf erfans) (setq fails
949
(pplus fails exppoly))))
951
(if (pzerop fails) (cons ans erfans)
952
(rischadd (cons ans erfans)
953
(rischnoun (r* (ratexpt (cons (make-poly expg) 1) n)
954
(ratqu fails (cdr numdenom)))))))))
956
(defun explist (p oarg exps)
957
(cond ((or (pcoefp p) (not (eq 'mexpt (get (p-var p) 'leadop))))
958
(list (list p oarg (ptimes p exps))))
959
(t (loop with narg = (get (p-var p) 'rischarg)
960
for (exp coef) on (p-terms p) by #'pt-red
962
(r+ oarg (r* exp narg))
964
(make-poly (p-var p) exp 1)))))))
967
(declare-top (special *fnewvarsw))
969
(DEFUN INTSETUP (EXP *VAR)
970
(PROG (VARLIST CLIST $FACTORFLAG DLIST GENPAIRS OLD Y Z $RATFAC $KEEPFLOAT
972
Y (SETQ EXP (RADCAN1 EXP))
979
(COND ((FREEOF *VAR Y) (PUSH Y CLIST))
982
(NOT (EQ (CADR Y) '$%E)))
983
(COND ((NOT (FREEOF *VAR (CADDR Y)))
984
(SETQ DLIST `((MEXPT SIMP)
987
`((%LOG) ,(CADR Y)))))
988
(SETQ EXP (MAXIMA-SUBSTITUTE DLIST Y EXP))
989
(SETQ VARLIST NIL) (GO Y))
991
(COND ((NUMBERP (CADDR Y)) (PUSH Y DLIST))
992
(T (SETQ OPERATOR T)(RETURN NIL))))
996
(IF (MEMQ '$%I CLIST) (SETQ CLIST (CONS '$%I (zl-DELETE '$%I CLIST))))
997
(SETQ VARLIST (APPEND CLIST
999
(NREVERSE (SORT (APPEND DLIST NIL) 'INTGREAT)))))
1000
(ORDERPOINTER VARLIST)
1002
(MAPC (FUNCTION INTSET1) (CONS *VAR DLIST))
1003
(COND ((ALIKE OLD VARLIST) (RETURN (RATREP* EXP)))
969
(defun intsetup (exp *var)
970
(prog (varlist clist $factorflag dlist genpairs old y z $ratfac $keepfloat
972
y (setq exp (radcan1 exp))
979
(cond ((freeof *var y) (push y clist))
982
(not (eq (cadr y) '$%e)))
983
(cond ((not (freeof *var (caddr y)))
984
(setq dlist `((mexpt simp)
987
`((%log) ,(cadr y)))))
988
(setq exp (maxima-substitute dlist y exp))
989
(setq varlist nil) (go y))
991
(cond ((numberp (caddr y)) (push y dlist))
992
(t (setq operator t)(return nil))))
996
(if (memq '$%i clist) (setq clist (cons '$%i (zl-delete '$%i clist))))
997
(setq varlist (append clist
999
(nreverse (sort (append dlist nil) 'intgreat)))))
1000
(orderpointer varlist)
1002
(mapc (function intset1) (cons *var dlist))
1003
(cond ((alike old varlist) (return (ratrep* exp)))
1008
(COND ((ATOM EXP) EXP)
1009
((MQAPPLYP EXP) (CADR EXP))
1012
(DEFUN LEADARG (EXP)
1013
(COND ((ATOM EXP) 0)
1014
((AND (MEXPTP EXP) (EQ (CADR EXP) '$%E)) (CADDR EXP))
1015
((MQAPPLYP EXP) (CAR (SUBFUNARGS EXP)))
1021
(SETQ D (IF (MEXPTP B) ;needed for radicals
1024
,(RADCAN1 (SDIFF (SIMPLIFY (CADDR B)) *VAR)))
1025
(RADCAN1 (SDIFF (SIMPLIFY B) *VAR)))))
1026
(SETQ D (RATREP* D))
1027
(SETQ C (RATREP* (LEADARG B)))
1028
(SETQ E (CDR (zl-ASSOC B (PAIR VARLIST GENVAR))))
1029
(PUTPROP E (LEADOP B) 'LEADOP)
1030
(PUTPROP E B 'RISCHEXPR)
1031
(PUTPROP E (CDR D) 'RISCHDIFF)
1032
(PUTPROP E (CDR C) 'RISCHARG)))
1034
(DEFUN INTGREAT (A B)
1035
(COND ((AND (NOT (ATOM A)) (NOT (ATOM B)))
1036
(COND ((AND (NOT (FREEOF '%ERF A)) (FREEOF '%ERF B)) T)
1037
((AND (NOT (FREEOF '$LI A)) (FREEOF '$LI B)) T)
1038
((AND (FREEOF '$LI A) (NOT (FREEOF '$LI B))) NIL)
1039
((AND (FREEOF '%ERF A) (NOT (FREEOF '%ERF B))) NIL)
1040
((NOT (FREE B A)) NIL)
1041
((NOT (FREE A B)) T)
1042
(T (GREAT (RESIMPLIFY (FIXINTGREAT A))
1043
(RESIMPLIFY (FIXINTGREAT B))))))
1044
(T (GREAT (RESIMPLIFY (FIXINTGREAT A))
1045
(RESIMPLIFY (FIXINTGREAT B))))))
1047
(DEFUN FIXINTGREAT (A) (SUBST '/_101X *VAR A))
1050
(DECLARE-TOP(UNSPECIAL B BETA CARY CONTEXT *EXP DEGREE GAMMA
1051
KLTH LIFLAG M NOGOOD OPERATOR PROB
1052
R S SIMP SWITCH SWITCH1 *VAR VAR Y YYY))
1008
(cond ((atom exp) exp)
1009
((mqapplyp exp) (cadr exp))
1012
(defun leadarg (exp)
1013
(cond ((atom exp) 0)
1014
((and (mexptp exp) (eq (cadr exp) '$%e)) (caddr exp))
1015
((mqapplyp exp) (car (subfunargs exp)))
1021
(setq d (if (mexptp b) ;needed for radicals
1024
,(radcan1 (sdiff (simplify (caddr b)) *var)))
1025
(radcan1 (sdiff (simplify b) *var)))))
1026
(setq d (ratrep* d))
1027
(setq c (ratrep* (leadarg b)))
1028
(setq e (cdr (zl-assoc b (pair varlist genvar))))
1029
(putprop e (leadop b) 'leadop)
1030
(putprop e b 'rischexpr)
1031
(putprop e (cdr d) 'rischdiff)
1032
(putprop e (cdr c) 'rischarg)))
1034
(defun intgreat (a b)
1035
(cond ((and (not (atom a)) (not (atom b)))
1036
(cond ((and (not (freeof '%erf a)) (freeof '%erf b)) t)
1037
((and (not (freeof '$li a)) (freeof '$li b)) t)
1038
((and (freeof '$li a) (not (freeof '$li b))) nil)
1039
((and (freeof '%erf a) (not (freeof '%erf b))) nil)
1040
((not (free b a)) nil)
1041
((not (free a b)) t)
1042
(t (great (resimplify (fixintgreat a))
1043
(resimplify (fixintgreat b))))))
1044
(t (great (resimplify (fixintgreat a))
1045
(resimplify (fixintgreat b))))))
1047
(defun fixintgreat (a) (subst '/_101x *var a))
1050
(declare-top(unspecial b beta cary context *exp degree gamma
1051
klth liflag m nogood operator prob
1052
r s simp switch switch1 *var var y yyy))
added
removed
src/risch.lisp
