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;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*- ;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; The data in this file contains enhancments. ;;;;;
;;; ;;;;;
;;; Copyright (c) 1984,1987 by William Schelter,University of Texas ;;;;;
;;; All rights reserved ;;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; (c) Copyright 1980 Massachusetts Institute of Technology ;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(in-package :maxima)
(macsyma-module opers)
;; This file is the run-time half of the OPERS package, an interface to the
;; Macsyma general representation simplifier. When new expressions are being
;; created, the functions in this file or the macros in MOPERS should be called
;; rather than the entrypoints in SIMP such as SIMPLIFYA or SIMPLUS. Many of
;; the functions in this file will do a pre-simplification to prevent
;; unnecessary consing. [Of course, this is really the "wrong" thing, since
;; knowledge about 0 being the additive identity of the reals is now
;; kept in two different places.]
;; The basic functions in the virtual interface are ADD, SUB, MUL, DIV, POWER,
;; NCMUL, NCPOWER, NEG, INV. Each of these functions assume that their
;; arguments are simplified. Some functions will have a "*" adjoined to the
;; end of the name (as in ADD*). These do not assume that their arguments are
;; simplified. In addition, there are a few entrypoints such as ADDN, MULN
;; which take a list of terms as a first argument, and a simplification flag as
;; the second argument. The above functions are the only entrypoints to this
;; package.
;; The functions ADD2, ADD2*, MUL2, MUL2*, and MUL3 are for use internal to
;; this package and should not be called externally. Note that MOPERS is
;; needed to compile this file.
;; Addition primitives.
(defmfun add2 (x y)
(cond ((numberp x)
(cond ((numberp y) (+ x y))
((=0 x) y)
(t (simplifya `((mplus) ,x ,y) t))))
((=0 y) x)
(t (simplifya `((mplus) ,x ,y) t))))
(defmfun add2* (x y)
(cond
((and (numberp x) (numberp y)) (+ x y))
((=0 x) (simplifya y nil))
((=0 y) (simplifya x nil))
(t (simplifya `((mplus) ,x ,y) nil))))
;; The first two cases in this cond shouldn't be needed, but exist
;; for compatibility with the old OPERS package. The old ADDLIS
;; deleted zeros ahead of time. Is this worth it?
(defmfun addn (terms simp-flag)
(cond ((null terms) 0)
(t (simplifya `((mplus) . ,terms) simp-flag))))
(declare-top (special $negdistrib))
(defmfun neg (x)
(cond ((numberp x) (- x))
(t (let (($negdistrib t))
(simplifya `((mtimes) -1 ,x) t)))))
(defmfun sub (x y)
(cond
((and (numberp x) (numberp y)) (- x y))
((=0 y) x)
((=0 x) (neg y))
(t (add x (neg y)))))
(defmfun sub* (x y)
(cond
((and (numberp x) (numberp y)) (- x y))
((=0 y) x)
((=0 x) (neg y))
(t
(add (simplifya x nil) (mul -1 (simplifya y nil))))))
;; Multiplication primitives -- is it worthwhile to handle the 3-arg
;; case specially? Don't simplify x*0 --> 0 since x could be non-scalar.
(defmfun mul2 (x y)
(cond
((and (numberp x) (numberp y)) (* x y))
((=1 x) y)
((=1 y) x)
(t (simplifya `((mtimes) ,x ,y) t))))
(defmfun mul2* (x y)
(cond
((and (numberp x) (numberp y)) (* x y))
((=1 x) (simplifya y nil))
((=1 y) (simplifya x nil))
(t (simplifya `((mtimes) ,x ,y) nil))))
(defmfun mul3 (x y z)
(cond ((=1 x) (mul2 y z))
((=1 y) (mul2 x z))
((=1 z) (mul2 x y))
(t (simplifya `((mtimes) ,x ,y ,z) t))))
;; The first two cases in this cond shouldn't be needed, but exist
;; for compatibility with the old OPERS package. The old MULSLIS
;; deleted ones ahead of time. Is this worth it?
(defmfun muln (factors simp-flag)
(cond ((null factors) 1)
((atom factors) factors)
(t (simplifya `((mtimes) . ,factors) simp-flag))))
(defmfun div (x y)
(if (=1 x)
(inv y)
(mul x (inv y))))
(defmfun div* (x y)
(if (=1 x)
(inv* y)
(mul (simplifya x nil) (inv* y))))
(defmfun ncmul2 (x y)
(simplifya `((mnctimes) ,x ,y) t))
(defmfun ncmuln (factors flag)
(simplifya `((mnctimes) . ,factors) flag))
;; Exponentiation
;; Don't use BASE as a parameter name since it is special in MacLisp.
(defmfun power (*base power)
(cond ((=1 power) *base)
(t (simplifya `((mexpt) ,*base ,power) t))))
(defmfun power* (*base power)
(cond ((=1 power) (simplifya *base nil))
(t (simplifya `((mexpt) ,*base ,power) nil))))
(defmfun ncpower (x y)
(cond ((=0 y) 1)
((=1 y) x)
(t (simplifya `((mncexpt) ,x ,y) t))))
;; [Add something for constructing equations here at some point.]
;; (ROOT X N) takes the Nth root of X.
;; Warning! Simplifier may give a complex expression back, starting from a
;; positive (evidently) real expression, viz. sqrt[(sinh-sin) / (sin-sinh)] or
;; something.
(defmfun root (x n)
(cond ((=0 x) 0)
((=1 x) 1)
(t (simplifya `((mexpt) ,x ((rat simp) 1 ,n)) t))))
;; (Porm flag expr) is +expr if flag is true, and -expr
;; otherwise. Morp is the opposite. Names stand for "plus or minus"
;; and vice versa.
(defmfun porm (s x) (if s x (neg x)))
(defmfun morp (s x) (if s (neg x) x))
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