| blob | e290d0157242f4323a880fd84d69a9ff2c812504 |
1 ;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*- ;;;;
2 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
3 ;;; The data in this file contains enhancments. ;;;;;
4 ;;; ;;;;;
5 ;;; Copyright (c) 1984,1987 by William Schelter,University of Texas ;;;;;
6 ;;; All rights reserved ;;;;;
7 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
8 ;;; (c) Copyright 1982 Massachusetts Institute of Technology ;;;
9 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
22 ;; Compute the poles (roots) of the polynomial D and return them.
23 ;; Divide these roots into several parts: Those in REGION, REGION1,
24 ;; and everywhere else. These are returned in a list. (In a more
25 ;; modern style, we'd probably return them in 4 different values.)
26 ;;
27 ;; The regions are determined by functions REGION and REGION1, which
28 ;; should return non-NIL if the root is in the given region.
29 ;;
30 ;; The description below applies if *SEMIRAT* is NIL. If *SEMIRAT* is
31 ;; non-NIL, somewhat different results are returned. I (rtoy) am not
32 ;; exactly sure what *SEMIRAT* is intended to mean.
33 ;;
34 ;; The first part of the list of the form ((r1 (x - r1)^d1) (r2 (x -
35 ;; r2)^d2) ...) where r1, r2 are the roots, d1, d2 are the
36 ;; multiplicity of each root, and x is the variable.
37 ;;
38 ;; The second part is a list of the repeated roots in REGION. Each
39 ;; element of the list is of the form (r d) where r is the root and d
40 ;; is the multiplicity.
41 ;;
42 ;; The third part is a list of the simple roots in REGION.
43 ;;
44 ;; Finally, the fourth part is NIL, unless *semirat* is T.
51 ;; Loop over all the roots. SOLVECASE returns the roots in the form
52 ;; ((x = r1) mult1
53 ;; (x = r2) mult2
54 ;; ...)
56 loop1
61 ;; Return CF, repeated roots (*semirat*), simple
62 ;; roots (*semirat*), roots in region 1.
65 ;; Return CF, repeated roots, simple roots, roots in region 1.
68 ;; Set POLE to the actual root and set D to the
69 ;; multiplicity of the root.
73 ;; Is it possible for LEADCOEF to be NIL ever?
74 ;;
75 ;; Push (pole (x - pole)^d) onto the list CF.
79 d)
80 cf)))))))
81 ;; Don't change the order of clauses here. We want to call REGION and then REGION1.
83 ;; The pole is in REGION
85 ;; A simple pole, so just push the pole onto the list S.
88 ;; A multiple pole, so push (pole d) onto the list R.
91 ;; The pole is in REGION1
93 ;; Put the pole onto the R1 list. (Don't know what
94 ;; $NOPRINCIPAL is.)
97 ;; Return NIL if we get here.
100 ;; (What does *SEMIRAT* mean?) Anyway if we're here, the
101 ;; pole is not in REGION or REGION1, so push the pole onto
102 ;; SS or RR depending if the pole is repeated or not.
106 ;; Pop this root and multiplicity and move on.
118 ;; Compute the sum of the residues of n/d.
121 dp a b c factors leadcoef)
127 ;; PL now contains the list of the roots in region, roots in
128 ;; region1, and everything else.
133 ;; Compute the sum of the residues of n/d for the
134 ;; multiple roots in REGION.
140 ;; Compute the sum of the residues of n/d for the simple
141 ;; roots in REGION1. Since the roots are simple, we can
142 ;; use RES1 to compute the residues instead of the more
143 ;; complicated $RESIDUE. (This works around a bug
144 ;; described in bug 1073338.)
145 #+nil
152 ;; Compute the sum of the residues of n/d for the roots
153 ;; not in REGION nor REGION1.
158 ;; Return the sum of the residues in the two regions and the
159 ;; sum of the residues outside the two regions.
167 pl))
170 pl))))
172 ;; Compute the residues of zn/d for the simple poles in the list PL1.
173 ;; The poles must be simple because ZD must be the derivative of
174 ;; denominator. For simple poles the residue can be computed as
175 ;; limit(n(z)/d(z)*(z-a),z,a). Since the pole is simple we have the
176 ;; indeterminate form (z-a)/d(z). Use L'Hospital's rule to get
177 ;; 1/d'(z). Hence, the residue is easily computed as n(a)/d'(a).
181 ;; In case the pole is messy, call $RECTFORM. This
182 ;; works around some issues with gcd bugs in certain
183 ;; cases. (See bug 1073338.)
185 pl1))
248 ;;;Looks for polynomials. puts polys^(pos-num) in sn* polys^(neg-num) in sd*.
260 sd*)))
279 ;; Call taylor with silent-taylor-flag t and catch an error.
283 ;; Things like residue(s/(s^2-a^2),s,a) fails if use -1.