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authorNguyễn Gia Phong <mcsinyx@disroot.org>2021-11-14 12:15:17 +0700
committerNguyễn Gia Phong <mcsinyx@disroot.org>2021-11-14 12:15:17 +0700
commitf0f838c13f4a552dca7b5dbaca066a382c1145f8 (patch)
treee9c5ceb32aea9035c535e9dcb336066b19d6a6cd /blog/conseq.md
parent6add857c033e6f836257f2b6bc659ec23b1cf74a (diff)
downloadsite-f0f838c13f4a552dca7b5dbaca066a382c1145f8.tar.gz
Update Franklin
Diffstat (limited to 'blog/conseq.md')
-rw-r--r--blog/conseq.md18
1 files changed, 9 insertions, 9 deletions
diff --git a/blog/conseq.md b/blog/conseq.md
index c4d98ad..27dada3 100644
--- a/blog/conseq.md
+++ b/blog/conseq.md
@@ -12,7 +12,7 @@ whose domain is a subset of the set of all integers.  Such sequences will be
 using functional programming paradigm, where functions are more similar
 to the ones in math (in contrast to imperative style with side effects
 confusing to inexperenced coders).  The idea is taken from [subsection 3.5.2
-of SICP][] and adapted to Python, which, compare to Scheme, is significantly
+of SICP] and adapted to Python, which, compare to Scheme, is significantly
 more popular: Python is pre-installed on almost every modern Unix-like system,
 namely macOS, GNU/Linux and the \*BSDs; and even at MIT, the new 6.01 in Python
 has recently replaced the legendary 6.001 (SICP).
@@ -37,12 +37,12 @@ can be imported directly from ``itertools``:
 ```
 
 To open a Python emulator, simply lauch your terminal and run `python`.
-If that is somehow still too struggling, navigate to [the interactive shell][]
+If that is somehow still too struggling, navigate to [the interactive shell]
 on Python.org.
 
 *Let's get it started* with somethings everyone hates: recursively defined
 sequences, e.g. the famous Fibonacci ($F_n = F_{n-1} + F_{n-2}$,
-$F_1 = 1$ and $F_0 = 0$).  Since [Python does not support][] [tail recursion][],
+$F_1 = 1$ and $F_0 = 0$).  Since [Python does not support] [tail recursion],
 it's generally **not** a good idea to define anything recursively (which is,
 ironically, the only trivial *functional* solution in this case)
 but since we will only evaluate the first few terms
@@ -82,7 +82,7 @@ It is noticable that the elements having been iterated through (using `next`)
 will disappear forever in the void (oh no!), but that is the cost we are
 willing to pay to save some memory, especially when we need to evaluate a
 member of (arbitrarily) large index to estimate the sequence's limit.
-One case in point is estimating a definite integral using [left Riemann sum][].
+One case in point is estimating a definite integral using [left Riemann sum].
 
 ```python
 def integral(f, a, b):
@@ -123,8 +123,8 @@ the result is somewhat acceptable:
 Since we are comfortable with sequence of sums, let's move on to sums of
 a sequence, which are called series.  For estimation, again, we are going to
 make use of infinite sequences of partial sums, which are implemented as
-`itertools.accumulate` by thoughtful Python developers.  [Geometric][] and
-[p-series][] can be defined as follow:
+`itertools.accumulate` by thoughtful Python developers.  [Geometric] and
+[p-series] can be defined as follow:
 
 ```python
 from itertools import accumulate as partial_sums
@@ -161,7 +161,7 @@ We can observe that it takes quite a lot of steps to get the precision we would
 generally expect ($s_{11}$ is only precise to the first decimal place;
 second decimal places: $s_{101}$; third: $s_{2304}$).
 Luckily, many techniques for series acceleration are available.
-[Shanks transformation][] for instance, can be implemented as follow:
+[Shanks transformation] for instance, can be implemented as follow:
 
 ```python
 from itertools import islice, tee
@@ -176,7 +176,7 @@ the anonymous function $(x, y, z) \mapsto \frac{xz - y^2}{x + z - 2y}$
 and `map` is a higher order function applying that function to
 respective elements of subsequences starting from index 1, 2 and 3 of `seq`.
 On Python 2, one should import `imap` from `itertools` to get the same
-[lazy][] behavior of `map` on Python 3.
+[lazy] behavior of `map` on Python 3.
 
 ```python
 >>> s = shanks(p_series(2))
@@ -251,7 +251,7 @@ def power_series(c, start=0, a=0):
 ```
 
 We can use this to compute functions that can be written as
-[Taylor series][]:
+[Taylor series]:
 
 ```python
 from math import factorial