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Tropical typos #9

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Mark merged 1 commits from typos into main 2025-01-25 09:41:12 -08:00
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2 changed files with 5 additions and 5 deletions
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src/Advanced/Tropical Polynomials/parts/00 arithmetic.typ
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@ -104,7 +104,7 @@ Is there a tropical multiplicative identity? \
Do tropical multiplicative inverses always exist? \ Do tropical multiplicative inverses always exist? \
#note([ #note([
For every $x != #sym.infinity$, does there exist an inverse $y$ so that $x #tm y = i$, \ For every $x != #sym.infinity$, does there exist an inverse $y$ so that $x #tm y = i$, \
where $i$ is the additive identity? where $i$ is the multiplicative identity?
]) ])
#solution([Yes, it is $-x$. For $x != 0$, $x #tm (-x) = 0$]) #solution([Yes, it is $-x$. For $x != 0$, $x #tm (-x) = 0$])

8
src/Advanced/Tropical Polynomials/parts/02 cubic.typ
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@ -5,7 +5,7 @@
= Tropical Cubic Polynomials = Tropical Cubic Polynomials
#problem() #problem()
Consider the polynomial $f(x) = x^3 #tp x^2 #tp 3x #tp 6$. \ Consider the polynomial $f(x) = x^3 #tp 1x^2 #tp 3x #tp 6$. \
- sketch a graph of this polynomial - sketch a graph of this polynomial
- use this graph to find the roots of $f$ - use this graph to find the roots of $f$
- write (and expand) a product of linear factors with the same graph as $f$. - write (and expand) a product of linear factors with the same graph as $f$.
@ -43,7 +43,7 @@ Consider the polynomial $f(x) = x^3 #tp x^2 #tp 3x #tp 6$. \
#pagebreak() // MARK: page #pagebreak() // MARK: page
#problem() #problem()
Consider the polynomial $f(x) = x^3 #tp x^2 #tp 6x #tp 6$. \ Consider the polynomial $f(x) = x^3 #tp 1x^2 #tp 6x #tp 6$. \
- sketch a graph of this polynomial - sketch a graph of this polynomial
- use this graph to find the roots of $f$ - use this graph to find the roots of $f$
- write (and expand) a product of linear factors with the same graph as $f$. - write (and expand) a product of linear factors with the same graph as $f$.
@ -118,10 +118,10 @@ Using the last three problems, find formulas for $B$ and $C$ in terms of $a$, $b
#solution([ #solution([
$ $
B = min(b, (a+c)/2, (2a+d)/2) B = min(b, (a+c)/2, (2a+d)/3)
$ $
$ $
C = min(c, (b+d)/2, (a+2d)/2) C = min(c, (b+d)/2, (a+2d)/3)
$ $
]) ])