Added if_solutions methods
			#5
		
		
	| @ -137,7 +137,11 @@ | ||||
|   } | ||||
| } | ||||
|  | ||||
| #let notsolution(content) = { | ||||
| #let if_solutions(content) = { | ||||
|   if show_solutions { content } | ||||
| } | ||||
|  | ||||
| #let if_no_solutions(content) = { | ||||
|   if not show_solutions { content } | ||||
| } | ||||
|  | ||||
|  | ||||
| @ -126,7 +126,7 @@ Fill the following tropical addition and multiplication tables | ||||
|  | ||||
| #let col = 10mm | ||||
|  | ||||
| #notsolution( | ||||
| #if_no_solutions( | ||||
|   table( | ||||
|     columns: (1fr, 1fr), | ||||
|     align: center, | ||||
|  | ||||
| @ -63,7 +63,7 @@ where all exponents represent repeated tropical multiplication. | ||||
| Draw a graph of the tropical polynomial $f(x) = x^2 #tp 1x #tp 4$. \ | ||||
| #hint([$1x$ is not equal to $x$.]) | ||||
|  | ||||
| #notsolution(graphgrid(none)) | ||||
| #if_no_solutions(graphgrid(none)) | ||||
|  | ||||
| #solution([ | ||||
|   $f(x) = min(2x , 1+x, 4)$, which looks like: | ||||
| @ -132,7 +132,7 @@ How can we use the graph to determine these roots? | ||||
| Graph $f(x) = -2x^2 #tp x #tp 8$. \ | ||||
| #hint([Use half scale. 1 box = 2 units.]) | ||||
|  | ||||
| #notsolution(graphgrid(none)) | ||||
| #if_no_solutions(graphgrid(none)) | ||||
|  | ||||
| #solution([ | ||||
|   #graphgrid({ | ||||
| @ -210,7 +210,7 @@ and always produces $7$ for sufficiently large inputs. | ||||
| #problem() | ||||
| Graph $f(x) = 1x^2 #tp 3x #tp 5$. | ||||
|  | ||||
| #notsolution(graphgrid(none)) | ||||
| #if_no_solutions(graphgrid(none)) | ||||
|  | ||||
| #solution([ | ||||
|   The graphs of all three terms intersect at the same point: | ||||
| @ -261,7 +261,7 @@ How are the roots of $f$ related to its coefficients? | ||||
| #problem() | ||||
| Graph $f(x) = 2x^2 #tp 4x #tp 4$. | ||||
|  | ||||
| #notsolution(graphgrid(none)) | ||||
| #if_no_solutions(graphgrid(none)) | ||||
|  | ||||
| #solution( | ||||
|   graphgrid({ | ||||
|  | ||||
| @ -10,7 +10,7 @@ Consider the polynomial $f(x) = x^3 #tp x^2 #tp 3x #tp 6$. \ | ||||
| - use this graph to find the roots of $f$ | ||||
| - write (and expand) a product of linear factors with the same graph as $f$. | ||||
|  | ||||
| #notsolution(graphgrid(none)) | ||||
| #if_no_solutions(graphgrid(none)) | ||||
|  | ||||
| #solution([ | ||||
|   - Roots are 1, 2, and 3. | ||||
| @ -48,7 +48,7 @@ Consider the polynomial $f(x) = x^3 #tp x^2 #tp 6x #tp 6$. \ | ||||
| - use this graph to find the roots of $f$ | ||||
| - write (and expand) a product of linear factors with the same graph as $f$. | ||||
|  | ||||
| #notsolution(graphgrid(none)) | ||||
| #if_no_solutions(graphgrid(none)) | ||||
|  | ||||
| #solution([ | ||||
|   - Roots are 1, 2.5, and 2.5. | ||||
| @ -82,7 +82,7 @@ Consider the polynomial $f(x) = x^3 #tp 6x^2 #tp 6x #tp 6$. \ | ||||
| - use this graph to find the roots of $f$ | ||||
| - write (and expand) a product of linear factors with the same graph as $f$. | ||||
|  | ||||
| #notsolution(graphgrid(none)) | ||||
| #if_no_solutions(graphgrid(none)) | ||||
|  | ||||
| #solution([ | ||||
|   - Roots are 2, 2, and 2. | ||||
|  | ||||
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