Once upon a time, pretty little Polly Nomial was strolling across
a field of vectors when she came to the boundary of a singularly
large matrix.  Now Polly was convergent and her mother had made it an absolute
condition that she never enter such an array with 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
sufficient, and made her way amongst the complex elements.
   Rows and columns closed in on her from all sides.  Tangents approached
her surface.  She had become 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 herself inverted, apparently alone, in a non-euclidean space.
   She was being watched, however.  That smooth operator, Curly Pi, was
lurking inner product.  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 his 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
that your angles have lots of secs."
   "Oh, sir." she protested, "Keep away from me.  I haven't got any 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 homotopic."
   "What order are you?" he demanded.
   "Seventeen." replied Polly.
   Curly leered.  "I suppose you've never been operated on?"
   "Of course not." Polly replied quite promptly.  "I'm absolutely
convergent."
   "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.
   "Abscissa!" he swore using the vilest oath he knew.  His patience was gone.
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 point of inflexions.  Poor, poor Polly!  The algorithmic method
was her only hope.  She felt his hand tending to her asymptotic limit.  Soon
her convergence would 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.
What an indignity, to be multiply connected on her very first integration.
Curly went on operating until he had 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.  But it was too
late to differentiate now.  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 surds all over the place and drove Polly to
deviation.
   The moral of our sad story is this: "If you want to keep your expressions
convergent, never allow them a single degree of freedom."