---------- Forwarded message ---------- From: Michael Becker <michael.bec...@coconet.de> Date: Mon, Jan 11, 2010 at 10:18 PM Subject: Re: [Axiom-developer] sum(binomial(t+i,i),i=0..k) To: Bill Page <bill.p...@newsynthesis.org>
Am Dienstag, 12. Januar 2010 00:46 schrieb Bill Page: > What in particular do you think requires explanation? It looks ok to me. > E.g. > > (1) -> ex1:=sum(binomial(t+i,i),i=0..k) > > t + k t - 1 > (t + k + 1)( ) - t( ) > k - 1 > (1) ----------------------------- > t + 1 > Type: Expression a) i do not understand the meaning of binomial(t-1,-1): (2) -> kernels(ex1).2 t - 1 (2) ( ) - 1 b) i did expect: binomial(t+k+1, t+1) (3) -> eval(binomial(t+k+1, t+1),[t=10,k=31]) (3) 4280561376 c) axiom does not like binomial(t-1,-1) (4) -> normalize (ex1 - binomial(t+k+1, t+1)) >> Error detected within library code: factorial not defined for negative integers d) t*binomial(t-1,-1) is really = 0 in ex1 : (4) -> normalize ( (t+k+1)*binomial(t+k,k)/ (t+1) - binomial(t+k+1, t+1)) (4) 0 > Integer (2) -> eval(ex1,[t=10,k=31]) > > (2) 4280561376 > Type: Expression > Integer (3) -> [binomial(10+i,i) for i in 0..31] > > (3) > [1, 11, 66, 286, 1001, 3003, 8008, 19448, 43758, 92378, 184756, 352716, > 646646, 1144066, 1961256, 3268760, 5311735, 8436285, 13123110, > 20030010, 30045015, 44352165, 64512240, 92561040, 131128140, 183579396, > 254186856, 348330136, 472733756, 635745396, 847660528, 1121099408] > Type: List > Integer (4) -> reduce(+,%) > > (4) 4280561376 > Type: > PositiveInteger > > 2010/1/11 Michael Becker <michael.bec...@coconet.de>: > > can someone explain the following answer of axiom? > > > > (12) -> sum(binomial(t+i,i),i=0..k) > > > > t + k t - 1 > > (t + k + 1)( ) - t( ) > > k - 1 > > (12) ----------------------------- > > t + 1 > > Type: > > Expression(Integer) ------------------------------------------------------------------------------------ Diese Nachricht könnte vertrauliche und/oder rechtlich geschützte Informationen enthalten. Wenn Sie nicht der Adressat dieser Email sind oder nicht autorisiert sind, diese für den Adressaten entgegenzunehmen, so ist es untersagt, diese Nachricht oder in ihr enthaltene Informationen zu nutzen, zu kopieren, offen zu legen oder anderweitig weiterzuverarbeiten. Sollten Sie diese Nachricht fälschlicherweise erhalten haben, verständigen Sie den Absender bitte unverzüglich per Antwort auf diese Mail und löschen sie diese anschließend. Vielen Dank für Ihre Kooperation. ------------------------------------------------------------------------------------ This message may contain confidential and/or privileged information. If you are not the addressee or authorized to receive this for the addressee, you must not use, copy, disclose or take any action based on this message or any information herein. If you have received this message in error, please advise the sender immediately by reply e-mail and delete this message. Thank you for your co-operation. ------------------------------------------------------------------------------------ We make your business move. _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer
