| blob | d43c7f01098742835d2aa1070edd0e3f67d934ed |
1 ;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*- ;;;;
2 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
3 ;;; The data in this file contains enhancements. ;;;;;
4 ;;; ;;;;;
5 ;;; Copyright (c) 1984,1987 by William Schelter,University of Texas ;;;;;
6 ;;; All rights reserved ;;;;;
7 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
8 ;;; (c) Copyright 1981 Massachusetts Institute of Technology ;;
9 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
17 ;;; The properties NOUN and VERB give correct linear display
26 ;;COMPUTES %E**Z WHERE Z IS AN ARBITRARY EXPRESSION TAKING SOME OF THE WORK AWAY FROM SIMPEXPT
32 ;;REST IS A PRODUCT WITHOUT THE MTIMES.FIXUPREST PUTS BACK THE MTIMES
44 ;;;INITIALIZES SOME GLOBAL VARIABLES THEN CALLS THE DISPATCHING FUNCTION
52 ;;;LAMBDA BINDS SOME SPECIAL VARIABLES TO NIL AND DISPATCHES
56 e
62 ;; Handles easy cases and calls appropriate function on others.
115 ;; Laplace has not found a result but returns a definit
116 ;; integral. This integral can contain internal integration
117 ;; variables. Replace such a result with the noun form.
119 ;; Check if we have a result, when not call $specint.
122 ;;; Check if laplace has found a result, when not try $specint.
129 ;; laplace returns a noun form or a result which contains %limit or %at.
130 ;; We pass the function to $specint to look for more results.
132 ;; laplace assumes the parameter s to be positive and does a
133 ;; declaration before an integration is done. Therefore we declare
134 ;; the parameter of the Laplace transform to be positive before
135 ;; we call $specint too.
141 ;; $specint has not found a result.
142 result
143 ;; $specint has found a result
144 res)))
151 ;;EXPECTS A LIST (PERHAPS EMPTY) OF FUNCTIONS MULTIPLIED TOGETHER WITHOUT THE MTIMES
152 ;;SEES IF IT CAN APPLY THE FIRST AS A TRANSFORMATION ON THE REST OF THE FUNCTIONS
159 1
160 t))
163 1
164 t))
187 ;;HANDLES %E**(A*T+B)*REST(T), %E**(A*T**2+B*T+C),
188 ;; 1/SQRT(A*T+B), OR T**K*REST(T)
195 ab
199 power
201 base-of-fun))
202 1
203 nil)))
204 time-var)))
219 parm))
223 1
225 -1
229 result
230 parm)
234 %e-case-lin
239 parm
241 parm
243 nil))))))
246 parm
251 result)
252 1
253 nil))
254 %e-case-quad
257 result
267 1
269 -1
273 2
275 result
277 ))))
281 parm
283 -1
285 parm
286 result)))
290 var-case
296 parm
297 power))
302 parm parm)))
304 var-easy-case
310 parm
314 noluck
323 base-of-fun
325 rest))
326 time-var parm))
329 ;;;INTEGRAL FROM A TO INFINITY OF F(X)
332 ;; We don't want any errors thrown by $defint to propagate,
333 ;; so we set errset, errcatch, $errormsg and *mdebug*. If
334 ;; $defint throws a error, then no error message is printed
335 ;; and errset simply returns nil below.
349 ;;;CREATES UNIQUE NAMES FOR VARIABLE OF INTEGRATION
353 ;;;REDUCES LAPLACE(F(T)/T**N,T,S) CASE TO LAPLACE(F(T)/T**(N-1),T,S) CASE
364 ;;MULTIPLIES FUNCT BY -1 IF SIGNSWITCH IS NIL
376 time-var parm))
382 time-var parm))))
384 ;;;COMPUTES %E**(W*B*%I)*F(S-W*A*%I) WHERE W=-1 IF SIGN IS T ELSE W=1
388 parm
391 substinfun
394 substinfun))))
396 ;;;IF WHICHSIGN IS NIL THEN SIN TRANSFORM ELSE COS TRANSFORM
402 whichsign)))))
405 result
409 ;;;FUN IS OF THE FORM SIN(A*T+B)*REST(T) OR COS
415 parm
416 trigswitch
428 parm
431 -1
437 parm
451 ;;;FUN IS OF THE FORM SINH(A*T+B)*REST(T) OR IS COSH
460 '$%e
463 rest)
466 '$%e
468 nil))
470 rest)
471 switch))
472 1
473 nil)
474 time-var parm)))
478 ;;;FUN IS OF THE FORM LOG(A*T)
494 fbase
497 ;;TAKES TRANSFORM OF HSTEP(A*T+B)*F(T)
505 ($positive
511 time-var parm))
513 ($negative
520 time-var parm)))
526 ;;TAKES TRANSFORM OF DELTA(A*T+B)*F(T)
539 recipa))
544 recipa)))
545 nil))
555 4
557 parm)
559 1
561 -1
563 1
564 nil))
576 ;; We don't want any errors thrown by $defint to propagate,
577 ;; so we set errset, errcatch, $errormsg and *mdebug*. If
578 ;; $defint throws a error, then no error message is printed
579 ;; and errset simply returns nil below.
589 skip
594 ;;FUN IS OF THE FORM DIFF(F(T),T,N) WHERE N IS A POSITIVE INTEGER
598 a
603 time-var
604 parm)
605 newdlist))))
612 out
619 newdlist))))
622 loop
628 resultlist))
633 resultlist))
640 -1
641 resultlist))
644 ;;;FUN IS OF THE FORM INTEGRATE(F(X)*G(T)*H(T-X),X,0,T)
653 notcon
660 dvar
666 dvar))))
667 giveup
669 convolutiontest
674 gothrulist
680 time-var
681 dvar)
682 time-var
683 f)))
690 parm-list
699 var-parm-list))
700 dvar
701 0
702 time-var))))
703 time-var parm dvar)))
704 convolution
710 dvar
712 time-var parm dvar)
715 time-var parm dvar))
716 1
717 t))))
720 ;;EXP IS F(S)/G(S) WHERE F AND G ARE POLYNOMIALS IN S AND DEGR(F) < DEGR(G)
722 s-var)
723 ;; MAKES ILS THE MAIN VARIABLE
741 nil)
745 ;;;THIS FUNCTION DOES THE PARTIAL FRACTION DECOMPOSITION
748 apart bpart parnumer ratarg laplac-ratform)
775 loop
778 bpart 1
784 skip
788 t)
791 t))))
793 parnumer
797 content
798 t)
799 t))
802 laplac-ratform
803 ils
804 ilt
805 s-var)
806 parnumer))
824 ;;;INVERTS P(S)/Q(S)**K WHERE Q(S) IS IRREDUCIBLE
825 ;;;DOESN'T CALL ILT3 IF Q(S) IS LINEAR
842 k
843 laplac-ratform
844 ils
845 ilt
846 z
847 q
848 s-var)
850 ilt
853 k
854 laplac-ratform
855 ils
856 ilt
857 z
858 q
859 s-var))
860 1
861 t)))
862 1
863 t))))
871 '$%e
873 -1
874 ilt
875 b
877 1
878 nil)
880 a
885 1
886 nil))))
888 ;;(DEFUN COEF MACRO (POL) (SUBST (CADR POL) (QUOTE DEG)
889 ;; '(DISREP (RATQU (POLCOEF (CAR P) DEG) (CDR P)))))
891 ;;;INVERTS P(S)/Q(S) WHERE Q(S) IS IRREDUCIBLE
896 ;; FIXME: Consider replacing these 3 functions with
897 ;; make-mplus-l, make-mtimes-l, and make-expt-l.
913 1
914 nil)))
921 ils ilt))
922 cubic
929 quadratic
936 1
937 nil))
949 ilt)))
963 1
964 nil))
967 ilt
969 c)
970 1
971 t))
978 1
979 nil)))))