MATH08068 Facets of Mathematics: Cubic Curves
Facets of Mathematics: Cubic Curves
End of theme assessment
Your completed assessment should consist of
1. This completed Jupyter notebook, including all requested code.
In-code comments should be included to explain the steps of your code.
If you use code adapted from a worksheet or another source, then this should be clearly
cited in an adjacent markdown cell.
2. A LaTeX document containing the requested explanations. You can use CC_eot.tex as a starting point.
The final document must be no longer than two pages.
For each question, you should provide explicit computations for solving the problems.
Whenever appropriate, you should also provide theoretical justification for your
results, quoting lemmas, theorems, etc from the lectures, tutorial worksheets and/or
references.
The Latex document should showcase the ideas and methodology that go into solving
the problems. For instance, some questions require repeating the same computations
over and over again. In such cases, it may be desireable to describe a single example in
the Latex document, rather than spelling out every single calculation.
You can get a feel for what is required by considering the markdown text in the tutorial
worksheets and solutions.
Submission
Please upload both your final compiled PDF, and your completed Jupyter notebook, via
Learn.
You can download your completed Jupyter notebook from Noteable using File
Download as Notebook (.ipynb) .
Marking
This assessment is marked out of 15. Marks will be based on 10 marks Completeness and correctness.
Questions should be answered fully and correctly.
The discussion should be complete, relevant, and correct.
You should correctly describe the methods used, and where appropriate relate the
discussion to the theoretic background.
All code should be clear, correct, and appropriately commented.
5 marks Presentation and use of LaTeX.
LaTeX should be used correctly and appropriately.
Text should be in grammatical sentences and free of typographical errors.
Any formulae should be appropriately typeset.
Question
Consider the following points in the complex projective plane , ,,.
a) Is there a conic in that passes through these points?
b) Is it unique? Explain your answer.
c) Find an equation of a conic passing through these points, where the coefficient of
d) Is this conic irreducible? Explain your answer.
In [ ]:
In [ ]:
In [ ]:
In [ ]:is 1.
2𝑥
CP
2
CP∈]4:3:2[= 5𝑃]0:2:1−[= 4𝑃 ]2:6:3[= 3𝑃 ]1:2:1[= 2𝑃
]20 : 2 : 1[ = 1𝑃
from sympy import * import itertools
# Add code here
