> The Rape of the Polynomial > > > -------------------------------------------------------------- > > > UNDER THE DOUBLE INTEGRAL >once upon a time, pretty Polly Nomial was strolling across a feild of vectors >when she came to the edge of a singularly large matrix. >Now Polly was convergent and her mother had made it an absolute condition that >she must never enter such an array without her brackets on. Polly, however, >who had changed her variable that morning and was feeling particularly badly >behaved, ignored this condition on the grounds that it was insufficient and >made her way among the complex elements. > >Rows and columns enveloped her on all sides. Tangents approached her surface. >She became tensor and tensor. Quite suddenly three branches of a hyperbol >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 which was protruding from the erf and plunged >headlong down a steep gradient. > >When she was differenciated once more, she found herself apparently alone in a >non-euclidean space. > >She was being watched however. That smooth operator, Curley Pi, was lurking >inner product. 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 round and saw Curly Pi >approaching her with his power series extrapolated. She could see at once, by >his degenerate conic and his dissipative terms, that he was bent on no good. > >"Ho, ho," he said, "What a symmetrical little polynomial you are. I can see >youre absolutly bubbling over with secs." > >"Oh, Sir," she protested, "keep away from me, I havent got my brackets on." > >"Calm yourself, my dear," said the suave operator, "your fears are purely >imaginary." > >"I, I," she thought, "Perhaps he is homogenous then." > >"What order are you ?" the brute demanded. > >"Seventeen, " replied Polly. > >Curly leered, "I suppose you have never been operated on yet ?" > >"Of Course not," replied Polly indignantly, "I'm absolutely convergent." > >"Come, come" said Curly, "Lets off to a decimal place I know and I'll take you >to the limit." > >"Never," gasped Polly. > >"BODMAS," he swore using the vilest oath he knew. > >His patience was gone. Coshing her over the the coefficient with a log until >she was powerless, Curly removed her discontinuities. He stared at her points >of inflexion. > >Poor Polly! All was up! She felt his hand tending to her asymptotic limit. Her >convergence would soon be gone forever. > >There was no mercy, for Curly was a heavyside operator. He integrated by >parts, he integrated by partial fractions. The complex beast even went all the >way round and did a contour integration. > >What an indignity. To be multiply connected on her first integration. Curly >went on operating until he was absolutely and completely orthogonal. > >When Polly got home that evening, her mother noticed that she had been >truncated in several places. But it was too late to differenciate now. > >As the months went by, Polly increased monotonically. Finally she generated a >small but pathological function, which left surds all over the plane until she >was driven to distraction.