The Perils of Pretty Miss Poly Nomial...

Once upon a time (1/t), pretty little Polly Nomial was walking across a field of vectors, when she came to the edge of a singular sparse 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 amongst 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 hyperpola toched her at a single point. She oscillated violently, lost all sense of directrix and went completley divergent. As she reached the turning point, she tripped over a square root which was protruding from the Erf and 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 his eyes devoured her curvilinear coordinates, a singular expression crossed his face. Was she still convergent?, he wondered? He decided to intergrate improperly at once.

Hearing a vulgar fraction behind her, Polly turned round and saw Curly Pi approching with his power series extrapolated. She could see at once, by his degenerate conic and his dissapative terms, that he was bent on no good.

"Eureka," she gasped.

"Ho, Ho!" he said. "What a symetric little polynomial you are. I can see that you are bubbling over with secs." "Calm yourself, my dear," said our suave operator, "your fears are purely imaginarey."

"I, I," she thought. "Perhaps he's homogenous then."

"What order are you?" the brute demanded.

"Seventeen," replied Polly.

Curly leered. "I suppose you've never been operated on yet?" he asked.

"Of course not," Polly cried indignantly. "I'm absolutely convergent."

"Come, come," said Curly. "Lets go off to a decimal place I know and I'll take you to the limit."

"Never," gasped Polly.

"EXCHLF!" he swore, using the vilest oath he knew. His patience was gone.

Coshing her over the coeffiecient with a log until she was powerless, Curly removed her discontinuities. He stared at her signigicant bits and began smoothing her points of inflexion. Poor Polly. All was up. She felt him 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 intergrated by partial fractions. The complex beast even did a contour integration. What an indignity! To be multiply connected on her first integration! Curly went on operating until he was absolutley orthogonal.

When Polly got home that evening, her mother noticed that she had been truncated in several places. It was too late to differentiate now. As time went by, Polly increased monotonically. Finally, she generated a small but pathological function which left surds all over the place until she was driven to diffraction.

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

Once upon a time (1/t), pretty little Polly Nomial was walking across a field of vectors, when she came to the edge of a singular sparse 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 amongst 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 hyperpola toched her at a single point. She oscillated violently, lost all sense of directrix and went completley divergent. As she reached the turning point, she tripped over a square root which was protruding from the Erf and 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 his eyes devoured her curvilinear coordinates, a singular expression crossed his face. Was she still convergent?, he wondered? He decided to intergrate improperly at once.

Hearing a vulgar fraction behind her, Polly turned round and saw Curly Pi approching with his power series extrapolated. She could see at once, by his degenerate conic and his dissapative terms, that he was bent on no good.

"Eureka," she gasped.

"Ho, Ho!" he said. "What a symetric little polynomial you are. I can see that you are bubbling over with secs." "Calm yourself, my dear," said our suave operator, "your fears are purely imaginarey."

"I, I," she thought. "Perhaps he's homogenous then."

"What order are you?" the brute demanded.

"Seventeen," replied Polly.

Curly leered. "I suppose you've never been operated on yet?" he asked.

"Of course not," Polly cried indignantly. "I'm absolutely convergent."

"Come, come," said Curly. "Lets go off to a decimal place I know and I'll take you to the limit."

"Never," gasped Polly.

"EXCHLF!" he swore, using the vilest oath he knew. His patience was gone.

Coshing her over the coeffiecient with a log until she was powerless, Curly removed her discontinuities. He stared at her signigicant bits and began smoothing her points of inflexion. Poor Polly. All was up. She felt him 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 intergrated by partial fractions. The complex beast even did a contour integration. What an indignity! To be multiply connected on her first integration! Curly went on operating until he was absolutley orthogonal.

When Polly got home that evening, her mother noticed that she had been truncated in several places. It was too late to differentiate now. As time went by, Polly increased monotonically. Finally, she generated a small but pathological function which left surds all over the place until she was driven to diffraction.

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

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