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Update cetz & ci

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Mark
2025-09-23 23:29:06 -07:00
parent 121780df6c
commit e5b0053465
17 changed files with 393 additions and 483 deletions
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22
src/Advanced/Tropical Polynomials/parts/02 cubic.typ
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@ -1,6 +1,6 @@
#import "@local/handout:0.1.0": *
#import "../macros.typ": *
#import "@preview/cetz:0.3.1"
#import "@preview/cetz:0.4.2"
= Tropical Cubic Polynomials
@ -131,15 +131,12 @@ Using the last three problems, find formulas for $B$ and $C$ in terms of $a$, $b
#problem()
What are the roots of the following polynomial?
#align(
center,
box(
inset: 3mm,
$
3 x^6 #tp 4 x^5 #tp 2 x^4 #tp x^3 #tp x^2 #tp 4 x #tp 5
$,
),
)
#align(center, box(
inset: 3mm,
$
3 x^6 #tp 4 x^5 #tp 2 x^4 #tp x^3 #tp x^2 #tp 4 x #tp 5
$,
))
#solution([
We have
@ -169,9 +166,8 @@ Find a formula for each $C_i$ in terms of $c_0, c_1, ..., c_n$.
#solution([
$
A_j
&= min_(l<=j<k)( (a_l - a_k) / (k-l) (k-j) + a_k ) \
&= min_(l<=j<k)( a_l (k-j) / (k-l) + a_k (j-l) / (k-l) )
A_j & = min_(l<=j<k)( (a_l - a_k) / (k-l) (k-j) + a_k ) \
& = min_(l<=j<k)( a_l (k-j) / (k-l) + a_k (j-l) / (k-l) )
$
#v(2mm)