/*************** -*- Mode: MACSYMA; Package: MAXIMA -*- ******************/ /*************************************************************************** *** ***** *** Copyright (c) 1984 by William Schelter,University of Texas ***** *** All rights reserved ***** ***************************************************************************/ /* -*- Package: CL-MAXIMA; Mode: MACSYMA -*-*/ (KILL(ALL),clear_rules(),MATCHDECLARE(A,TRUE)); DONE$ TELLSIMP(SIN(A)^2,1-COS(A)^2); ["^RULE1",?SIMPEXPT]$ SIN(Y)^2; 1-COS(Y)^2$ KILL(RULES); DONE$ NONZEROANDFREEOF(X,E):=IS(E # 0 AND FREEOF(X,E)); NONZEROANDFREEOF(X,E):=IS(E # 0 AND FREEOF(X,E))$ MATCHDECLARE(A,NONZEROANDFREEOF(X),B,FREEOF(X)); DONE$ DEFMATCH(LINEAR,A*X+B,X); LINEAR$ LINEAR(3*Z+(Y+1)*Z+Y^2,Z); [B = Y^2,A = Y+4,X = Z]$ MATCHDECLARE([A,F],TRUE); DONE$ CONSTINTERVAL(L,H):=CONSTANTP(H-L); CONSTINTERVAL(L,H):=CONSTANTP(H-L)$ MATCHDECLARE(B,CONSTINTERVAL(A)); DONE$ MATCHDECLARE(X,ATOM); DONE$ BLOCK(REMOVE(INTEGRATE,OUTATIVE),DEFMATCH(CHECKLIMITS,'INTEGRATE(F,X,A,B)), DECLARE(INTEGRATE,OUTATIVE)); DONE$ 'INTEGRATE(SIN(T),T,X+%PI,X+2*%PI); 'INTEGRATE(SIN(T),T,X+%PI,X+2*%PI)$ CHECKLIMITS(%); [B = X+2*%PI,A = X+%PI,X = T,F = SIN(T)]$ 'INTEGRATE(SIN(T),T,0,X); 'INTEGRATE(SIN(T),T,0,T)$ CHECKLIMITS(%); FALSE$ (KILL(ALL),MATCHDECLARE(X,FREEOF(%I))); DONE$ %IARGS:FALSE; FALSE$ TELLSIMP(SIN(%I*X),%I*SINH(X)); [SINRULE1,?SIMP\-%SIN]$ TRIGEXPAND(SIN(X+%I*Y)); SIN(X)*COS(%I*Y)+%I*COS(X)*SINH(Y)$ %IARGS:TRUE; TRUE$ ERRCATCH(0^0); []$ EV(TELLSIMP(0^0,1),SIMP:FALSE); ["^RULE2",?SIMPEXPT]$ 0^0; 1$ REMRULE("^","^RULE2"); "^"$ TELLSIMP(SIN(X)^2,1-COS(X)^2); ["^RULE3",?SIMPEXPT]$ (SIN(X)+1)^2; (SIN(X)+1)^2$ EXPAND(%); 2*SIN(X)-COS(X)^2+2$ SIN(X)^2; 1-COS(X)^2$ KILL(RULES); DONE$ MATCHDECLARE(A,TRUE); DONE$ TELLSIMP(SIN(A)^2,1-COS(A)^2); ["^RULE4",?SIMPEXPT]$ SIN(Y)^2; 1-COS(Y)^2$ KILL(RULES); DONE$ (KILL(ALL),NONZEROANDFREEOF(X,E):=IS(E # 0 AND FREEOF(X,E))); NONZEROANDFREEOF(X,E):=IS(E # 0 AND FREEOF(X,E))$ MATCHDECLARE(A,NONZEROANDFREEOF(X),B,FREEOF(X)); DONE$ DEFMATCH(LINEAR,A*X+B,X); LINEAR$ LINEAR(3*Z+(Y+1)*Z+Y^2,Z); [B = Y^2,A = Y+4,X = Z]$ MATCHDECLARE([A,F],TRUE); DONE$ CONSTINTERVAL(L,H):=CONSTANTP(H-L); CONSTINTERVAL(L,H):=CONSTANTP(H-L)$ MATCHDECLARE(B,CONSTINTERVAL(A)); DONE$ MATCHDECLARE(X,ATOM); DONE$ BLOCK(REMOVE(INTEGRATE,OUTATIVE),DEFMATCH(CHECKLIMITS,'INTEGRATE(F,X,A,B)), DECLARE(INTEGRATE,OUTATIVE)); DONE$ 'INTEGRATE(SIN(T),T,X+%PI,X+2*%PI); 'INTEGRATE(SIN(T),T,X+%PI,X+2*%PI)$ CHECKLIMITS(%); [B = X+2*%PI,A = X+%PI,X = T,F = SIN(T)]$ 'INTEGRATE(SIN(T),T,0,X); 'INTEGRATE(SIN(T),T,0,T)$ CHECKLIMITS(%); FALSE$ REMVALUE(A,B,F,X); [A,B,F,X]$ (KILL(ALL),MATCHDECLARE([A,A1,A2],TRUE)); DONE$ ONELESS(X,Y):=IS(X = Y-1); ONELESS(X,Y):=IS(X = Y-1)$ LET(A1*A2!,A1!,ONELESS,A2,A1); ?MTEXT(A1*A2!,?\ \-\-\>\ ,A1!,?\ WHERE\ ,ONELESS(A2,A1))$ EV(LET(A1!/A1,(A1-1)!),LETRAT); ?MTEXT(A1!/A1,?\ \-\-\>\ ,(A1-1)!)$ EV(LETSIMP(N*M!*(N-1)!/M),LETRAT); (M-1)!*N!$ LET(SIN(A)^2,1-COS(A)^2); ?MTEXT(SIN(A)^2,?\ \-\-\>\ ,1-COS(A)^2)$ SIN(X)^4; SIN(X)^4$ LETSIMP(%); COS(X)^4-2*COS(X)^2+1$ MATCHDECLARE([A,A1,A2],TRUE); DONE$ ONELESS(X,Y):=IS(X = Y-1); ONELESS(X,Y):=IS(X = Y-1)$ LET(A1*A2!,A1!,ONELESS,A2,A1); ?MTEXT(A1*A2!,?\ \-\-\>\ ,A1!,?\ WHERE\ ,ONELESS(A2,A1))$ EV(LET(A1!/A1,(A1-1)!),LETRAT); ?MTEXT(A1!/A1,?\ \-\-\>\ ,(A1-1)!)$ EV(LETSIMP(N*M!*(N-1)!/M),LETRAT); (M-1)!*N!$ LET(SIN(A)^2,1-COS(A)^2); ?MTEXT(SIN(A)^2,?\ \-\-\>\ ,1-COS(A)^2)$ SIN(X)^4; SIN(X)^4$ LETSIMP(%); COS(X)^4-2*COS(X)^2+1$ PFEFORMAT:TRUE; TRUE$ POISSIMP(SIN(X)^2); 1/2-1/2*COS(2*X)$ (2*A^2-B)*COS(X+2*Y)-(A*B+5)*SIN(U-4*X); (2*A^2-B)*COS(2*Y+X)+(A*B+5)*SIN(4*X-U)$ EXP1:outofpois(POISEXPT(%,2)); 1/2*(2*A^2-B)^2*COS(4*Y+2*X)-(2*A^2-B)*(-A*B-5)*SIN(2*Y+5*X-U) +(2*A^2-B)*(-A*B-5)*SIN(2*Y-3*X+U) -1/2*(-A*B-5)^2*COS(8*X-2*U)+1/2*(-A*B-5)^2 +1/2*(2*A^2-B)^2$ PRINTPOIS(%); DONE$ outofpois(POISINT(EXP1,Y)); 1/8*(2*A^2-B)^2*SIN(4*Y+2*X)+1/2*(2*A^2-B)*(-A*B-5)*COS(2*Y+5*X-U) -1/2*(2*A^2-B)*(-A*B-5)*COS(2*Y-3*X+U)$ outofpois(POISSIMP(%)); 1/8*(2*A^2-B)^2*SIN(4*Y+2*X)+1/2*(2*A^2-B)*(-A*B-5)*COS(2*Y+5*X-U) -1/2*(2*A^2-B)*(-A*B-5)*COS(2*Y-3*X+U)$ POISSIMP(SIN(X)^5+COS(X)^5); 1/16*SIN(5*X)+1/16*COS(5*X)-5/16*SIN(3*X)+5/16*COS(3*X)+5/8*SIN(X)+5/8*COS(X)$ PFEFORMAT:FALSE; FALSE$