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 she 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.