vsn@CC.IMPERIAL.AC.UK (V S Narinian) (02/09/90)
Loipon kyrioi epeidh parathrhsa oti osa anekdota kai asteia emfanisthkan htan arketa kakogousta, sas stelno ena poly eksypno keimenaki pou mou arese poly. Elpizo na sas aresei kai esas. ------------------------------------------------------------------------ Once upon a time (1/T) pretty little Polly Nomial was strolling through a field of Vectors when she came to the edge of a singu- larly large matrix. Now Polly was convergent and her mother had made it an absolute condition that she must never enter an array without her brackets on. Polly however, who had changed her variables that morning, was feeling particularly badly behaved and ignored this boundary condition on the grounds that it was insufficient and made her way in among the complex elements. Rows and columns enveloped her on all sides and tangents ap- proached her surface. She became tensor and tensor until, quite suddenly, three branches of a hyperbola touched her at a single point. She oscillated violently, lost all sense directrix, and went completely divergent. As she reached a turning point, she tripped over s square root which was protruding from the erf and plunged headlong down a steep gradient. When she was differen- tiated once more she found herself apparently alone in a non- euclidean space. She was being watched; that smooth operator, Curly Pi, was lurk- ing inner product and as his eyes devoured her curvilinear co- ordinates a singular expression crossed his face. "Was she still convergent?" he wondered. He decided to integrate improperly at once. Hearing a vulgar fraction behind her, Polly turned around and saw Curly Pi approaching with his power series extrapolated. She could see at once by his degenerate conic and dissipative terms that he was bent on no good. "Eureka!" she gasped. "HO ho" he said, "What a symmetric little polynomial you are. I can see your just bubbling over with secs." "Oh sir" she protested, "keep away from me - I haven't got my brackets on." "Calm yourself, my dear," said our suave operator, "your fears are purely imaginary." "I, I" she thought, "perhaps he's homogenous then?" "What order are you ?" the brute demanded. "Seventeen" she replied. "I suppose you've never been operated on before," he leered. "Of course not!" Polly cried indignantly. "I'm absolutely conver- gent." "Come, come," said Curly, "lets off to a decimal place I know and I'll take you to the limit." "Never!" gasped Polly. "Fortran!" he swore using the most debase oath he knew. His pati- ence had gone, so, coshing her over the coefficient with a log until she was powerless, Curly removed her discontinuities. He stared at her significant places and began smoothing her points of inflection. Poor Polly, all was up. She felt his hand tending to her asymptotic limit. Her convergence would soon be gone for- ever! There was no mercy, for Curly was a heavy side operator. He in- tegrated by parts, he integrated by partial fractions, and then the complete beast went all the round and integrated over the surface. Curly went on operating until he was absolutely and com- pletely orthogonal. When Polly got home that evening, her mother noticed that she had been truncated in several places. But it was too late to dif- ferentiate now, and as the months went by, Polly increased mono- tonically. Finally she generated a small but pathological func- tion that left surds all over the place until she was driven to distraction. The moral to the story is this: If you want your expressions to remain convergent, never allow them a single degree of freedom. -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- Vartan <vsn@cc.ic.ac.uk>