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71 lines
1.8 KiB
Typst
71 lines
1.8 KiB
Typst
#let bgBlock(body, fill: color, width: 100%) = block(body, fill:fill.lighten(80%), width: width, inset: (bottom: 2mm))
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#let SeperatorLine = line(length: 100%, stroke: (paint: black, thickness: 0.3mm))
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#let MathAlignLeft(e) = {
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align(left, block(e))
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}
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#let subHeading(body, fill: color) = {
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box(
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align(
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top+center,
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text(
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body,
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size: 8pt,
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weight: "bold",
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style: "italic",
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)
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),
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fill: fill,
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width: 100%,
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inset: 1mm,
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height: auto
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)
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}
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#let MathAlignLeft(e) = {
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align(left, block(e))
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}
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#let tableFillHigh = white
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#let tableFillLow = color.lighten(gray, 50%)
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#let sinTable = [
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#let data = json("../sintable.json")
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#table(
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columns: data.len(),
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rows: data.keys().len(),
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stroke: none,
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table.hline(stroke: (thickness: 0.3mm)),
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fill: (x, y) => if (calc.rem(y, 2) == 0) { tableFillLow } else { tableFillHigh },
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table.vline(),
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..for (i, label) in data.keys().enumerate() {
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([*#eval(label, mode: "math")*], if i > 0 { table.vline() } else { table.vline(stroke: none) })
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},
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table.hline(stroke: (thickness: 0.3mm)),
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..for (i, v) in data.at("x").enumerate() {
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for (col) in data.keys() {
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(eval(data.at(col).at(i), mode: "math"),)
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}
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},
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table.hline(stroke: (thickness: 0.3mm)),
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)
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]
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#let ComplexNumbersSection(i: $i$) = [
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$1/#i = #i^(-1) = -#i quad quad #i^2=-1 quad quad sqrt(#i) = 1/sqrt(2) + 1/sqrt(2)#i$
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$z in CC = a + b #i quad quad quad z = r dot e^(phi #i)$ \
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$z_0 + z_1 = (a_0 + a_1) + (b_0 + b_1) #i$\
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$z_0 dot z_1 = (a_1 a_2 - b_1 b_2) + #i (a_1b_2 + a_2 b_1) = r_0 r_1 e^(#i (phi_0 + phi_1))$\
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$z^x = r^x dot e^(phi #i dot x) quad x in RR$ \
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$z_0/z_1 = r_0/r_1 e^(#i (phi_0 - phi_1)) quad quad quad$
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$r = abs(z) quad phi = cases(
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+ arccos(a/r) space : space b >= 0,
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- arccos(a/r) space : space b < 0,
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)$
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] |