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From: Daphne Xu <daphne@nym.alias.net>
Subject: REPOST: Little Polly Nomial (silly math puns)
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Hello All

This hasn't been posted in a while.  I didn't write it, and I have
no idea who did.  I understand it's an oldy --- older than me
perhaps?  <*Giggle*> --- but probably not quite old enough to have
passed into the Public Domain.  Celeste reviewed it a few years
back, but I only saw her rating; I never saw the actual review.

Kiddies, I think you can read this.  It's not so perverted as to
warp your mind --- at least not THAT way.

				Daphne

PS.  I think something strange is happening with my reply block;
I'm not sure.  I might not be receiving anything at the moment.

			Polynomials

Once upon a time (1/t), pretty little Polly Nomial was strolling
across a field 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
variables that morning and was feeling particularly badly behaved,
ignored this condition on the grounds that it was insufficient, and
made her way in amongst the complex elements.
 
Rows and columns enveloped her on all sides.  Tangents approached
her surface.  She became tensor and tensor.  Suddenly two branches
of a hyperbola touched her at a single point.  She oscillated
violently, lost all sense of direction, and went completely
divergent.  As she reached a turning point she tripped over a
square root that was protruding from the erf, and she plunged
headlong down a steep gradient.  When she was differentiated once
more, she found herself, apparently alone, in a non-Euclidean
space.
 
She was being watched, however.  That smooth operator, Curly Pi,
was lurking inner product.  As he numerically analyzed her, his
eyes devoured her curvilinear coordinates, and a singular
expression crossed his face.  Was she still convergent, he
wondered.  He decided to integrate improperly at once.  Hearing a
common fraction behind her, Polly rotated and saw Curly approaching
her with his power series expanding.  She could see by his
degenerate conic that he was up to no good.
 
"What a symmetric little polynomial you are," he said.  "I can see
that your angles have lots 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 homogeneous."
 
"What order are you?" the brute demanded.
 
"Seventeen," replied Polly.
 
"I suppose you've never been operated on?"
 
"Of course not," Polly cried indignantly.  "I'm absolutely
convergent."
 
"Come, come," said Curly.  "Let's go off to a decimal place, 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 over the head 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.  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.  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 satisfied her hypothesis, then he exponentiated
and became completely orthogonal.
 
When Polly got home that night her mother noticed that she was no
longer piecewise continuous, but had been truncated in several
places.  As the months went by, Polly's denominator increased
monotonically.  Finally she went to l'Hospital and generated a
small but pathological function which left little surds all over
the place and drove Polly to deviation.

The moral of the story is, "If you want to keep your expressions
convergent, never allow them a single degree of freedom."

-- 
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