;;; calc-arith.el --- arithmetic functions for Calc
-;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
+;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
+;; 2005, 2006 Free Software Foundation, Inc.
;; Author: David Gillespie <daveg@synaptics.com>
;; Maintainer: Jay Belanger <belanger@truman.edu>
(real number)
(number)
(scalar)
+ (sqmatrix matrix vector)
(matrix vector)
(vector)
(const)))
(and (not (Math-scalarp a))
(not (math-known-scalarp a t))))
+(defun math-known-square-matrixp (a)
+ (and (math-known-matrixp a)
+ (math-check-known-square-matrixp a)))
+
;;; Try to prove that A is a scalar (i.e., a non-vector).
(defun math-check-known-scalarp (a)
(cond ((Math-objectp a) t)
(let ((decl (if (eq (car a) 'var)
(or (assq (nth 2 a) math-decls-cache)
math-decls-all)
- (assq (car a) math-decls-cache))))
- (memq 'scalar (nth 1 decl))))))
+ (assq (car a) math-decls-cache)))
+ val)
+ (cond
+ ((memq 'scalar (nth 1 decl))
+ t)
+ ((and (eq (car a) 'var)
+ (boundp (nth 2 a))
+ (setq val (symbol-value (nth 2 a))))
+ (math-check-known-scalarp val))
+ (t
+ nil))))))
;;; Try to prove that A is *not* a scalar.
(defun math-check-known-matrixp (a)
(let ((decl (if (eq (car a) 'var)
(or (assq (nth 2 a) math-decls-cache)
math-decls-all)
- (assq (car a) math-decls-cache))))
- (memq 'vector (nth 1 decl))))))
-
+ (assq (car a) math-decls-cache)))
+ val)
+ (cond
+ ((memq 'matrix (nth 1 decl))
+ t)
+ ((and (eq (car a) 'var)
+ (boundp (nth 2 a))
+ (setq val (symbol-value (nth 2 a))))
+ (math-check-known-matrixp val))
+ (t
+ nil))))))
+
+;;; Given that A is a matrix, try to prove that it is a square matrix.
+(defun math-check-known-square-matrixp (a)
+ (cond ((math-square-matrixp a)
+ t)
+ ((eq (car-safe a) '^)
+ (math-check-known-square-matrixp (nth 1 a)))
+ ((or
+ (eq (car-safe a) '*)
+ (eq (car-safe a) '+)
+ (eq (car-safe a) '-))
+ (and
+ (math-check-known-square-matrixp (nth 1 a))
+ (math-check-known-square-matrixp (nth 2 a))))
+ (t
+ (let ((decl (if (eq (car a) 'var)
+ (or (assq (nth 2 a) math-decls-cache)
+ math-decls-all)
+ (assq (car a) math-decls-cache)))
+ val)
+ (cond
+ ((memq 'sqmatrix (nth 1 decl))
+ t)
+ ((and (eq (car a) 'var)
+ (boundp (nth 2 a))
+ (setq val (symbol-value (nth 2 a))))
+ (math-check-known-square-matrixp val))
+ ((and (or
+ (integerp calc-matrix-mode)
+ (eq calc-matrix-mode 'sqmatrix))
+ (eq (car-safe a) 'var))
+ t)
+ ((memq 'matrix (nth 1 decl))
+ nil)
+ (t
+ nil))))))
;;; Try to prove that A is a real (i.e., not complex).
(defun math-known-realp (a)
(and (math-known-scalarp b)
(math-add (nth 1 a) b))))
(and (eq (car-safe b) 'calcFunc-idn)
- (= (length a) 2)
+ (= (length b) 2)
(or (and (math-square-matrixp a)
(math-add a (math-mimic-ident (nth 1 b) a)))
(and (math-known-scalarp a)
(and (eq (car-safe b) '^)
(Math-looks-negp (nth 2 b))
(not (and (eq (car-safe a) '^) (Math-looks-negp (nth 2 a))))
+ (not (math-known-matrixp (nth 1 b)))
(math-div a (math-normalize
(list '^ (nth 1 b) (math-neg (nth 2 b))))))
(and (eq (car-safe a) '/)
(list 'calcFunc-idn (math-mul a (nth 1 b))))
(and (math-known-matrixp a)
(math-mul a (nth 1 b)))))
+ (and (math-identity-matrix-p a t)
+ (or (and (eq (car-safe b) 'calcFunc-idn)
+ (= (length b) 2)
+ (list 'calcFunc-idn (math-mul
+ (nth 1 (nth 1 a))
+ (nth 1 b))
+ (1- (length a))))
+ (and (math-known-scalarp b)
+ (list 'calcFunc-idn (math-mul
+ (nth 1 (nth 1 a)) b)
+ (1- (length a))))
+ (and (math-known-matrixp b)
+ (math-mul (nth 1 (nth 1 a)) b))))
+ (and (math-identity-matrix-p b t)
+ (or (and (eq (car-safe a) 'calcFunc-idn)
+ (= (length a) 2)
+ (list 'calcFunc-idn (math-mul (nth 1 a)
+ (nth 1 (nth 1 b)))
+ (1- (length b))))
+ (and (math-known-scalarp a)
+ (list 'calcFunc-idn (math-mul a (nth 1 (nth 1 b)))
+ (1- (length b))))
+ (and (math-known-matrixp a)
+ (math-mul a (nth 1 (nth 1 b))))))
(and (math-looks-negp b)
(math-mul (math-neg a) (math-neg b)))
(and (eq (car-safe b) '-)
(math-div-new-non-trig term))))
(defun math-div-symb-fancy (a b)
- (or (and math-simplify-only
+ (or (and (math-known-matrixp b)
+ (math-mul a (math-pow b -1)))
+ (and math-simplify-only
(not (equal a math-simplify-only))
(list '/ a b))
(and (Math-equal-int b 1) a)
(math-mul-zero b a))))
(list '/ a b)))
+;;; Division from the left.
+(defun calcFunc-ldiv (a b)
+ (if (math-known-scalarp a)
+ (math-div b a)
+ (math-mul (math-pow a -1) b)))
(defun calcFunc-mod (a b)
(math-normalize (list '% a b)))
(cond ((and math-simplify-only
(not (equal a math-simplify-only)))
(list '^ a b))
+ ((and (eq (car-safe a) '*)
+ (or
+ (and
+ (math-known-matrixp (nth 1 a))
+ (math-known-matrixp (nth 2 a)))
+ (and
+ calc-matrix-mode
+ (not (eq calc-matrix-mode 'scalar))
+ (and (not (math-known-scalarp (nth 1 a)))
+ (not (math-known-scalarp (nth 2 a)))))))
+ (if (and (= b -1)
+ (math-known-square-matrixp (nth 1 a))
+ (math-known-square-matrixp (nth 2 a)))
+ (math-mul (math-pow-fancy (nth 2 a) -1)
+ (math-pow-fancy (nth 1 a) -1))
+ (list '^ a b)))
((and (eq (car-safe a) '*)
(or (math-known-num-integerp b)
(math-known-nonnegp (nth 1 a))
HCoop / bpt / emacs.git / blobdiff