****************************************************************************** ** ** ** The Story of Polly Nomial ** ** ** ** Wherein it is related how that paragon of womanly virtue, young ** ** Polly Nomial (our heroine) is accosted by that notorious villain Curly ** ** Pi, and factored (oh, horror!). ** ** ** ** Once upon a time (1/t) pretty Polly Nomial was strolling across a ** ** field of vectors when she came upon the boundary of a singularly large ** ** matrix. Now Polly was convergent, and her mother had made it an ** ** absolute condition that she never enter an array without her brackets ** ** on. Polly, however, who had changed her variables that morning and was ** ** feeling particularly badly behaved, ignored this condition on the basis ** ** that it was insufficient, and made her way in amongst the complex ** ** elements. Rows and columns closed in from all sides. Tangents ** ** approached her surface. She became tensor and tensor. Quite suddenly, ** ** two branches of a hyperbola touched her at a single point. She ** ** oscillated violently, lost all sense of directrix, and went completely ** ** divergent. As she reached a turning point, she tripped over a square ** ** root that was protruding from the erf and plunged headlong down a steep ** ** gradient. When she rounded off once more, she found herslef inverted, ** ** apparently alone, in a non-euclidean space. ** ** ** ** She was being watched, however,. That smooth operator, Curly Pi ** ** was lurking innerproduct. As his eyes devoured her curvilinear ** ** coordinates, a singular expression crossed his face. He wondered, ** ** was she still convergent. He decided to integrate improperly at once. ** ** ** ** Hearing a common fraction behind her, Polly rotated 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. ** ** ** ** "Arcsinh," she gasped. ** ** ** ** "Ho, ho," he said. "What a symmetric little asymptote you have. I ** ** can see your angles have a lot of 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 not normal but homologous. ** ** ** ** "What order are you?" the brute demanded. ** ** ** ** "Seventeen," replied Polly. ** ** ** ** Curly leered. "I suppose you've never been operated on." ** ** ** ** "Of course not!" Polly replied, quite properly. "I'm absolutely ** ** convergent." ** ** ** ** "Come, come" said Curly. "Let's off to a decimal place I know and ** ** I'll take you to the limit." ** ** ** ** "Never!" gasped Polly. ** ** ** ** "Abscissa!" he swore, using the vilest oath he knew. His patience ** ** was gone. Coshing her oever the coefficient with a log until she was ** ** powerless, Curly removed her discontinuities. He started at her ** ** significant places, and began smoothing out her points of inflection. ** ** Poor Polly. The algorithmic method was now her only hope. She felt his ** ** hand tending toward her asymptotic limit. Her convergence would soon be ** ** gone forever. ** ** ** ** There was no mercy, for Curly was a heavyside operator. Curly's ** ** radius squared itself. Polly's loci quivered. He integrated by parts. ** ** He integrated by partial fractions. After he cofactored, he performed ** ** Runge-Kutta on her. The complex beast even went all the way around and ** ** did a contour integration. Curly went on operating until he had ** ** satisfied her hypothesis, then he exponentiated and became completely ** ** orthogonal. ** ** ** ******************************************************************************