Shareware Grab Bag/Shareware Grab Bag.iso/090/poly.txt

Text File | 1985-10-31 | 3.6 KB | 80 lines

18-Apr-85 03:22:38-EST,3564;000000000000
Mail-From: EN4.IG-WINOGRAD created at 18-Apr-85 03:22:36
Date: Thu 18 Apr 85 03:22:35-EST
From: Ian G Winograd <EN4.IG-WINOGRAD@CU20C>
Subject: polynomials
To: BBOARD@CU20C



        THE SAGA OF POLLY NOMIAL

    Once upon a time, pretty Polly Nomial was skipping through a
field of vectors when she came to the edge of a singularly large matrix.
Now Polly as convergent, and her mother had made it an absolute condition
that she never enter such an array without her brackets on. But Polly
had changed her variables that morning and had been feeling particularly
badly behaved, so she ignored her mother's 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. Tangents approached
her surface. She grew tensor and tensor.  Quite suddenly, three branches
of a hyperbola touched her at a single point. She oscillated violently and
lost all sense of directrix. She tripped over a square root protruding from
the erf, and tumbled headlong down a steep gradient. When she was once again
in possession of her variables, she found herself apparently in a
non-euclidean space.  She was being watched. However, that smoothe
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 integrate inproperly
at once. Hearing an improper fraction behind her, Polly rotated and saw Curly
approaching with his power series extrapolated.  She could tell at once
from his degenerate conic and his dissipative terms that he was bent
to no good.

    "Eureka!" she gasped.

    "Ho, Ho," said our operator. "What a symmetric little asymptote
you have.  I bet your angles are just dripping with secs."

    "Stay away from me!" she said. "I haven't got my brackets on."

    "Calm yourself, my dear," he said.  "Your fears are purely imaginary."

    "I, I," she thought, "maybe he's not normal...maybe he's even a
homorphism."

    "What order are you?" the brute demanded.

    "Seventeen," she replied.

    Curly leered. "Enough of this idle chatter. Let's go to a decimal
place I know, and I'll take you to the limit."

    "Never!" she gasped.

    "Arcsinh!!!" He swore the vilest oath he knew. 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
out her points of inflection. Poor Polly. She could feel his hand tending
toward her asymptotic limit. The algorithmic method as now her only hope.
Her convergence would sson be gone forever. Curly's radius squared itself.
Polly's loci quivered. He integrated by parts. He integrated by partial
fractions. The complex beast even went all the way around and did a
contour integration. Curly went on operating until he was completely and
totally exhausted of all his primitive roots.

    When Polly arrived home that night, her mother noticed that she had
been truncated in several places. But it was too late to differentiate now.
Nine orders later, she went to L'Hopital and generated a small but
pathological function which left serds and residuess all over the place
and drove poor Polly to deviation.

    The moral of our story is: if you want to keep your expressions
convergent, never allow them any degrees of freedom.


    ---- The above does not necessarily reflect the views of me,
my employer, friends, family, the Mets, the blockaders....
-------