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From: Dan Gildea <dgildea@us...>  20110722 18:24:33

This is an automated email from the git hooks/postreceive script. It was generated because a ref change was pushed to the repository containing the project "Maxima, A Computer Algebra System". The branch, master has been updated via 70d5485d173b6d952af68475bb6948366d02b564 (commit) from 0c6001a9aca21c5694dd7848f9265169e99c761b (commit) Those revisions listed above that are new to this repository have not appeared on any other notification email; so we list those revisions in full, below.  Log  commit 70d5485d173b6d952af68475bb6948366d02b564 Author: Dan Gildea <dgildea> Date: Fri Jul 22 14:17:39 2011 0400 src/defint.lisp: o look for discontinuities in antiderivative, and evaluate on both sides. fixes error in integrating exp(x)*sinh(sqrt(x))  ID: 3292033 integrate(x^m * exp(x^2),x,minf,inf) > 0  ID: 3311145 special case assumed to be general in integration  ID: 3369856 src/solve.lisp: o solve(abs(x), x) now yields [x = 0] tests/rtestint.mac: o add integrate(exp(sqrt(x)x), x, 0, inf); diff git a/src/defint.lisp b/src/defint.lisp index 2849ef7..ee7fcfe 100644  a/src/defint.lisp +++ b/src/defint.lisp @@ 877,10 +877,76 @@ in the interval of integration.") ((eq a '$neg) 1) (t 1.)))) +;; Substitute a and b into integral e +;; +;; Looks for discontinuties in integral, and works around them. +;; For example, in +;; +;; integrate(x^(2*n)*exp((x)^2),x) ==> +;; gamma_incomplete((2*n+1)/2,x^2)*x^(2*n+1)*abs(x)^(2*n1)/2 +;; +;; the integral has a discontinuity at x=0. +;; +(defun intsubs (e a b) + (let ((edges (cond ((not $intanalysis) + '$no) ;don't do any checking. + (t (discontinuitiesininterval + (let (($algebraic t)) + (sratsimp e)) + var a b))))) + + (cond ((or (eq edges '$no) + (eq edges '$unknown)) + (wholeintsubs e a b)) + (t + (do* ((l edges (cdr l)) + (total nil) + (a1 (car l) (car l)) + (b1 (cadr l) (cadr l))) + ((null (cdr l)) (if (every (lambda (x) x) total) + (m+l total))) + (push + (wholeintsubs e a1 b1) + total)))))) + +;; look for terms with a negative exponent +(defun discontinuitiesdenom (exp) + (cond ((atom exp) 1) + ((eq (caar exp) 'mtimes) + (m*l (mapcar #'discontinuitiesdenom (cdr exp)))) + ((and (eq (caar exp) 'mexpt) + (eq ($sign (caddr exp)) '$neg)) + (m^ (cadr exp) (m (caddr exp)))) + (t 1))) + +;; returns list of places where exp might be discontinuous in var. +;; list begins with ll and ends with ul, and include any values between +;; ll and ul. +;; return '$no or '$unknown if no discontinuities found. +(defun discontinuitiesininterval (exp var ll ul) + (let* ((denom (discontinuitiesdenom exp)) + (roots (realroots denom var))) + (cond ((eq roots '$failure) + '$unknown) + ((eq roots '$no) + '$no) + (t (do ((dummy roots (cdr dummy)) + (polelist nil)) + ((null dummy) + (cond (polelist + (append (list ll) + (sortgreat polelist) + (list ul))) + (t '$no))) + (let ((soltn (caar dummy))) + ;; (multiplicity (cdar dummy)) ;; not used + (if (strictlyininterval soltn ll ul) + (push soltn polelist)))))))) + ;; Carefully substitute the integration limits A and B into the ;; expression E. (defun intsubs (e a b) +(defun wholeintsubs (e a b) (cond ((easysubs e a b)) (t (setq *currentassumptions* (makedefintassumptions 'ask)) ;get forceful! @@ 3468,6 +3534,15 @@ in the interval of integration.") (greateqll (askgreateq place ll))) (if (and (eq lessequl '$yes) (eq greateqll '$yes)) '$yes '$no)))) +;; returns true or nil +(defun strictlyininterval (place ll ul) + ;; real values for ll and ul; place can be imaginary. + (and (equal ($imagpart place) 0) + (or (eq ul '$inf) + (eq ($asksign (m+ ul (m place))) '$pos)) + (or (eq ll '$minf) + (eq ($asksign (m+ place (m ll))) '$pos)))) + (defun realroots (exp var) (let (($solvetrigwarn (cond (defintdebug t) ;Rest of the code for (t ()))) ;TRIGS in denom needed. diff git a/src/solve.lisp b/src/solve.lisp index 55aa30f..9c0cdc2 100644  a/src/solve.lisp +++ b/src/solve.lisp @@ 337,6 +337,10 @@ (solve (car terms) *var mult)) 'mtimes) + ((eq (caar *exp) 'mabs) ;; abs(x) = 0 <=> x = 0 + (solve (cadr *exp) *var mult) + 'mabs) + ((eq (caar *exp) 'mexpt) (cond ((and (freeof *var (cadr *exp)) (not (zerop1 (cadr *exp)))) diff git a/tests/rtestint.mac b/tests/rtestint.mac index bbf1eb3..5e7d3ce 100644  a/tests/rtestint.mac +++ b/tests/rtestint.mac @@ 1371,3 +1371,9 @@ integrate(abs(x  1) + abs(x + 1)  2*abs(x),x,minf,inf); /* definite integration  ID: 3315476 */ integrate(1/2^x, x, 0, 1); 1/(2*log(2)); + +/* discontinuities in integral */ +/* error in integrating exp(x)*sinh(sqrt(x))  ID: 3292033 */ +integrate(exp(sqrt(x)x), x, 0, inf); +%e^(1/4)*gamma_incomplete(1,1/4)%e^(1/4)*gamma_incomplete(1/2,1/4)/2 + +%e^(1/4)*sqrt(%pi);  Summary of changes: src/defint.lisp  77 +++++++++++++++++++++++++++++++++++++++++++++++++++ src/solve.lisp  4 +++ tests/rtestint.mac  6 ++++ 3 files changed, 86 insertions(+), 1 deletions() hooks/postreceive  Maxima, A Computer Algebra System 