   D    Once upon a time, pretty little Polly Nomial was strolling across@ a field of vectors when she came to the boundary of a singularlyN large matrix.  Now Polly was convergent and her mother had made it an absoluteJ condition that she never enter such an array with her brackets on.  Polly,C however, who had changed her variables that morning and was feeling K particularly badly behaved, ignored this condition on the basis that it was : sufficient, and made her way amongst the complex elements.I    Rows and columns closed in on her from all sides.  Tangents approached M her surface.  She had become tensor and tensor.  Quite suddenly, two branches M of a hyperbola touched her at a single point.  She oscillated violently, lost H all sense of directrix, and went completely divergent.  As she reached aN turning point, she tripped over a square root that was protruding from the erfL and plunged headlong down a steep gradient.  When she rounded off once more,G she found herself inverted, apparently alone, in a non-euclidean space. G    She was being watched, however.  That smooth operator, Curly Pi, was K lurking inner product.  As his eyes devoured her curvilinear coordinates, a N singular expression crossed his face.  He wondered "Was she still convergent?"+ He decided to integrate improperly at once. G    Hearing a common fraction behind her, Polly rotated and saw Curly Pi M approaching with his power series extrapolated.  She could see at once by his G degenerate conic and his dissipative terms that he was bent on no good.     "Arcsinh!" she gasped. M    "Ho, ho." he said, "What a symmetric little asymptote you have.  I can see $ that your angles have lots of secs."L    "Oh, sir." she protested, "Keep away from me.  I haven't got any brackets on."F    "Calm yourself, my dear." said our suave operator.  "Your fears are purely imaginary."A    "I, i." she thought.  "Perhaps he's not normal but homotopic." %    "What order are you?" he demanded.     "Seventeen." replied Polly.<    Curly leered.  "I suppose you've never been operated on?"B    "Of course not." Polly replied quite promptly.  "I'm absolutely convergent."M    "Come, come." said Curly, "Let's go off to a decimal place I know and I'll  take you to the limit."     "Never!" gasped Polly. N    "Abscissa!" he swore using the vilest oath he knew.  His patience was gone.J Coshing her over the coefficient with a log until she was powerless, CurlyK removed her discontinuities.  He stared at her significant places and began M smoothing her point of inflexions.  Poor, poor Polly!  The algorithmic method L was her only hope.  She felt his hand tending to her asymptotic limit.  Soon& her convergence would be gone forever.J    There was no mercy, for Curly was a heavyside operator.  Curly's radiusN squared itself; Polly's loci quivered.  He integrated by parts.  He integratedL by partial fractions.  After he cofactored, he performed Runge-Kutta on her.M The complex beast even went all the way around and did a contour integration. J What an indignity, to be multiply connected on her very first integration.F Curly went on operating until he had satisfied her hypothesis; then he/ exponentiated and became completely orthogonal. L    When Polly got home that night, her mother noticed that she was no longerN piecewise continuous but had been truncated in several places.  But it was tooO late to differentiate now.  As the months went by Polly's denominator increased H monotonically.  Finally she went to L'Hospital and generated a small butL pathological function which left surds all over the place and drove Polly to
 deviation.L    The moral of our sad story is this: "If you want to keep your expressions9 convergent, never allow them a single degree of freedom."    