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 a 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.

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