O-/𖣠⚪ᗩ∣ᗝ∣Ẏ⚪𖡼𖡼𖡼𖡼⚪𔗢⚪🞋⚪𔗢⚪𖡼𖡼𖡼𖡼⚪Ẏ∣ᗝ∣ᗩ⚪𖣠/𖣠⚪✤ᴥᗩ⚪𖡼𖡼𖡼𖡼⚪𔗢⚪🞋⚪𔗢⚪𖡼𖡼𖡼𖡼⚪ᗩᴥ✤⚪𖣠/𖣠⚪ᗱᗴᴥᗩᗯ✤ꗳⓄᔓᔕ⚪𖡼𖡼𖡼𖡼⚪𔗢⚪🞋⚪𔗢⚪𖡼𖡼𖡼𖡼⚪ᔓᔕⓄꗳ✤ᗯᗩᴥᗱᗴ⚪𖣠/𖣠⚪ЭЄᗩНߦᗱᗴᙏЭЄⓄߦ✤⚪𖡼𖡼𖡼𖡼⚪𔗢⚪🞋⚪𔗢⚪𖡼𖡼𖡼𖡼⚪✤ߦⓄЭЄᙏᗱᗴߦНᗩЭЄ⚪𖣠/𖣠⚪ᔓᔕⓄᴥᗱᗴᑐᑕⓄИNꖴ옷ᴥ⚪𖡼𖡼𖡼𖡼⚪𔗢⚪🞋⚪𔗢⚪𖡼𖡼𖡼𖡼⚪ᴥ옷ꖴИNⓄᑐᑕᗱᗴᴥⓄᔓᔕ⚪𖣠/𖣠⚪ᴥᗱᗴߦⓄ옷ᔓᔕᗩᴥᕤᕦ⚪𖡼𖡼𖡼𖡼⚪𔗢⚪🞋⚪𔗢⚪𖡼𖡼𖡼𖡼⚪ᕤᕦᴥᗩᔓᔕ옷Ⓞߦᗱᗴᴥ⚪𖣠/XHꓨ..⚪ᗩ⚪ᑐᑕ⚪ꖴ⚪✤⚪ᗩ⚪ᙏ⚪ᗱᗴ⚪옷⚪✤⚪ᗩ⚪ᙏ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ᙏ⚪ᗩ⚪✤⚪옷⚪ᗱᗴ⚪ᙏ⚪ᗩ⚪✤⚪ꖴ⚪ᑐᑕ⚪ᗩ⚪..GHX
2024-04-05 11:00:36 +00:00

2446 lines
153 KiB
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<item name="UserText" type_name="gh_string" type_code="10">ClearAll[iCurvaturePlotHelper, CurvaturePlot]
iCurvaturePlotHelper[
f_?(Head[#] =!= List &amp;), {t_, tmin_,
tmax_}, {{x0_, y0_}, \[Theta]0_}, opts : OptionsPattern[]] :=
Module[{sol, \[Theta], x, y, if},
sol = NDSolve[{
\[Theta]'[t] == f,
x'[t] == Cos[\[Theta][t]],
y'[t] == Sin[\[Theta][t]],
\[Theta][tmin] == \[Theta]0,
x[tmin] == x0,
y[tmin] == y0
}, {x, y}, {t, tmin, tmax}, opts];
if = {x[#], y[#]} &amp; /. First[sol];
if
]
CurvaturePlot[f_, {t_, tmin_, tmax_}, opts : OptionsPattern[]] :=
CurvaturePlot[f, {t, tmin, tmax}, {{0, 0}, 0}, opts]
CurvaturePlot[f_, {t_, tmin_, tmax_}, p : {{x0_, y0_}, \[Theta]0_},
opts : OptionsPattern[]] :=
Module[{\[Theta], x, y, sol, rlsplot, rlsndsolve, if, ifs},
rlsplot = FilterRules[{opts}, Options[ParametricPlot]];
rlsndsolve = FilterRules[{opts}, Options[NDSolve]];
If[Head[f] === List,
ifs =
iCurvaturePlotHelper[#, {t, tmin, tmax}, p,
Evaluate@(Sequence @@ rlsndsolve)] &amp; /@ f;
ParametricPlot[
Evaluate[#[tplot] &amp; /@ ifs], {tplot, tmin, tmax},
Evaluate@(Sequence @@ rlsplot)]
,
if =
iCurvaturePlotHelper[f, {t, tmin, tmax}, p,
Evaluate@(Sequence @@ rlsndsolve)];
ParametricPlot[Evaluate[if[tplot]], {tplot, tmin, tmax},
Evaluate@(Sequence @@ rlsplot)]
]
];
ariasD[0] = 1;
ariasD[n_Integer?Positive] := ariasD[n] = Sum[2^((k (k - 1) - n (n - 1))/2) ariasD[k]/(n - k + 1)!, {k, 0, n - 1}]/(2^n - 1);
iFabiusF[x_]:=Module[{prec=Precision[x],n,p,q,s,tol,w,y,z},If[x&lt;0,Return[0,Module]];tol=10^(-prec);
z=SetPrecision[x,Infinity];s=1;y=0;
z=If[0&lt;=z&lt;=2,1-Abs[1-z],q=Quotient[z,2];
If[ThueMorse[q]==1,s=-1];
1-Abs[1-z+2 q]];
While[z&gt;0,n=-Floor[RealExponent[z,2]];p=2^n;
z-=1/p;w=1;
Do[w=ariasD[m]+p z w/(n-m+1);p/=2,{m,n}];
y=w-y;
If[Abs[w]&lt;Abs[y] tol,Break[]]];
SetPrecision[s Abs[y],prec]];
FabiusF[Infinity] = Interval[{-1, 1}];
FabiusF[x_?NumberQ] /; If[Im[x] == 0, TrueQ[Composition[BitAnd[#, # - 1] &amp;, Denominator][x] == 0], False] := iFabiusF[x];
Derivative[n_Integer][FabiusF] := 2^(n (n + 1)/2) FabiusF[2^n #] &amp;;
SetAttributes[FabiusF, {NumericFunction, Listable}];//Timing//AbsoluteTiming;
ToString[DecimalForm[N[Table[{ToString[DecimalForm[N[X],256]],ToString[DecimalForm[N[FabiusF[X]],256]],ToString[DecimalForm[N[0],256]]},{X,0,N[1],N[1/16]}]],256]]</item>
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<item name="MarginRight" type_name="gh_int32" type_code="3">0</item>
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<item name="Colour" type_name="gh_drawing_color" type_code="36">
<ARGB>255;255;255;255</ARGB>
</item>
<item name="DrawIndices" type_name="gh_bool" type_code="1">true</item>
<item name="DrawPaths" type_name="gh_bool" type_code="1">true</item>
<item name="Multiline" type_name="gh_bool" type_code="1">true</item>
<item name="SpecialCodes" type_name="gh_bool" type_code="1">false</item>
<item name="Stream" type_name="gh_bool" type_code="1">false</item>
<item name="Wrap" type_name="gh_bool" type_code="1">true</item>
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<item name="UserText" type_name="gh_string" type_code="10">ariasD[0] = 1;
ariasD[n_Integer?Positive] := ariasD[n] = Sum[2^((k (k - 1) - n (n - 1))/2) ariasD[k]/(n - k + 1)!, {k, 0, n - 1}]/(2^n - 1);
iFabiusF[x_]:=Module[{prec=Precision[x],n,p,q,s,tol,w,y,z},If[x&lt;0,Return[0,Module]];tol=10^(-prec);
z=SetPrecision[x,Infinity];s=1;y=0;
z=If[0&lt;=z&lt;=2,1-Abs[1-z],q=Quotient[z,2];
If[ThueMorse[q]==1,s=-1];
1-Abs[1-z+2 q]];
While[z&gt;0,n=-Floor[RealExponent[z,2]];p=2^n;
z-=1/p;w=1;
Do[w=ariasD[m]+p z w/(n-m+1);p/=2,{m,n}];
y=w-y;
If[Abs[w]&lt;Abs[y] tol,Break[]]];
SetPrecision[s Abs[y],prec]];
FabiusF[Infinity] = Interval[{-1, 1}];
FabiusF[x_?NumberQ] /; If[Im[x] == 0, TrueQ[Composition[BitAnd[#, # - 1] &amp;, Denominator][x] == 0], False] := iFabiusF[x];
Derivative[n_Integer][FabiusF] := 2^(n (n + 1)/2) FabiusF[2^n #] &amp;;
SetAttributes[FabiusF, {NumericFunction, Listable}];//Timing//AbsoluteTiming;
ToString[DecimalForm[N[Table[{ToString[DecimalForm[N[t],256]],ToString[DecimalForm[N[FabiusF[t]],256]],ToString[DecimalForm[N[0],256]]},{t,0,N[1],N[1/32]}]],256]]</item>
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</item>
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<item name="Multiline" type_name="gh_bool" type_code="1">true</item>
<item name="SpecialCodes" type_name="gh_bool" type_code="1">false</item>
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<item name="Name" type_name="gh_string" type_code="10">Culture</item>
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<item name="InstanceGuid" type_name="gh_guid" type_code="9">c12585f7-fe64-4c0f-869d-d10df254cf72</item>
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</items>
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<chunk name="Container">
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<item name="Description" type_name="gh_string" type_code="10">A panel for custom notes and text values</item>
<item name="InstanceGuid" type_name="gh_guid" type_code="9">32ca42c3-b85d-40fc-b02f-a79187312f7b</item>
<item name="Name" type_name="gh_string" type_code="10">Panel</item>
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<item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
<item name="UserText" type_name="gh_string" type_code="10">ClearAll[iCurvaturePlotHelper, CurvaturePlot]
iCurvaturePlotHelper[
f_?(Head[#] =!= List &amp;), {t_, tmin_,
tmax_}, {{x0_, y0_}, \[Theta]0_}, opts : OptionsPattern[]] :=
Module[{sol, \[Theta], x, y, if},
sol = NDSolve[{
\[Theta]'[t] == f,
x'[t] == Cos[\[Theta][t]],
y'[t] == Sin[\[Theta][t]],
\[Theta][tmin] == \[Theta]0,
x[tmin] == x0,
y[tmin] == y0
}, {x, y}, {t, tmin, tmax}, opts];
if = {x[#], y[#]} &amp; /. First[sol];
if
]
CurvaturePlot[f_, {t_, tmin_, tmax_}, opts : OptionsPattern[]] :=
CurvaturePlot[f, {t, tmin, tmax}, {{0, 0}, 0}, opts]
CurvaturePlot[f_, {t_, tmin_, tmax_}, p : {{x0_, y0_}, \[Theta]0_},
opts : OptionsPattern[]] :=
Module[{\[Theta], x, y, sol, rlsplot, rlsndsolve, if, ifs},
rlsplot = FilterRules[{opts}, Options[ParametricPlot]];
rlsndsolve = FilterRules[{opts}, Options[NDSolve]];
If[Head[f] === List,
ifs =
iCurvaturePlotHelper[#, {t, tmin, tmax}, p,
Evaluate@(Sequence @@ rlsndsolve)] &amp; /@ f;
ParametricPlot[
Evaluate[#[tplot] &amp; /@ ifs], {tplot, tmin, tmax},
Evaluate@(Sequence @@ rlsplot)]
,
if =
iCurvaturePlotHelper[f, {t, tmin, tmax}, p,
Evaluate@(Sequence @@ rlsndsolve)];
ParametricPlot[Evaluate[if[tplot]], {tplot, tmin, tmax},
Evaluate@(Sequence @@ rlsplot)]
]
];
ariasD[0] = 1;
ariasD[n_Integer?Positive] := ariasD[n] = Sum[2^((k (k - 1) - n (n - 1))/2) ariasD[k]/(n - k + 1)!, {k, 0, n - 1}]/(2^n - 1);
iFabiusF[x_]:=Module[{prec=Precision[x],n,p,q,s,tol,w,y,z},If[x&lt;0,Return[0,Module]];tol=10^(-prec);
z=SetPrecision[x,Infinity];s=1;y=0;
z=If[0&lt;=z&lt;=2,1-Abs[1-z],q=Quotient[z,2];
If[ThueMorse[q]==1,s=-1];
1-Abs[1-z+2 q]];
While[z&gt;0,n=-Floor[RealExponent[z,2]];p=2^n;
z-=1/p;w=1;
Do[w=ariasD[m]+p z w/(n-m+1);p/=2,{m,n}];
y=w-y;
If[Abs[w]&lt;Abs[y] tol,Break[]]];
SetPrecision[s Abs[y],prec]];
FabiusF[Infinity] = Interval[{-1, 1}];
FabiusF[x_?NumberQ] /; If[Im[x] == 0, TrueQ[Composition[BitAnd[#, # - 1] &amp;, Denominator][x] == 0], False] := iFabiusF[x];
Derivative[n_Integer][FabiusF] := 2^(n (n + 1)/2) FabiusF[2^n #] &amp;;
SetAttributes[FabiusF, {NumericFunction, Listable}];//Timing//AbsoluteTiming;
ToString[DecimalForm[N[Table[{ToString[DecimalForm[N[X],256]],ToString[DecimalForm[N[FabiusF[X]],256]],ToString[DecimalForm[N[0],256]]},{X,0,N[1],N[1/256]}]],256]];
П = CurvaturePlot[
Evaluate[
SetPrecision[SetAccuracy[Abs[FabiusF[X/Pi*((((4))))/2]], Infinity],
Infinity], {X, 0, 4 \[Pi]}, WorkingPrecision -&gt; ((((10)))),
Accuracy -&gt; Infinity, MaxRecursion -&gt; 0, PlotPoints -&gt; 1 + 2^((((8))))],
Axes -&gt; {True, True}];
Show[П, Frame -&gt; True, FrameTicks -&gt; {{-1, 0, 1}, {-1, 0, 1}},
PlotRange -&gt; Full, AspectRatio -&gt; 1];
ↀПↀ = Flatten[Cases[П, Line[X__] -&gt; X, Infinity], 1];
Export["ↀПↀ", ↀПↀ, "CSV"];
ↀПↀ</item>
</items>
<chunks count="2">
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<item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
<X>-629</X>
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</item>
<item name="MarginLeft" type_name="gh_int32" type_code="3">0</item>
<item name="MarginRight" type_name="gh_int32" type_code="3">0</item>
<item name="MarginTop" type_name="gh_int32" type_code="3">0</item>
<item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
<X>-628.7882</X>
<Y>330.9467</Y>
</item>
</items>
</chunk>
<chunk name="PanelProperties">
<items count="7">
<item name="Colour" type_name="gh_drawing_color" type_code="36">
<ARGB>255;255;255;255</ARGB>
</item>
<item name="DrawIndices" type_name="gh_bool" type_code="1">true</item>
<item name="DrawPaths" type_name="gh_bool" type_code="1">true</item>
<item name="Multiline" type_name="gh_bool" type_code="1">true</item>
<item name="SpecialCodes" type_name="gh_bool" type_code="1">false</item>
<item name="Stream" type_name="gh_bool" type_code="1">false</item>
<item name="Wrap" type_name="gh_bool" type_code="1">true</item>
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<item name="GUID" type_name="gh_guid" type_code="9">59e0b89a-e487-49f8-bab8-b5bab16be14c</item>
<item name="Name" type_name="gh_string" type_code="10">Panel</item>
</items>
<chunks count="1">
<chunk name="Container">
<items count="9">
<item name="Description" type_name="gh_string" type_code="10">A panel for custom notes and text values</item>
<item name="InstanceGuid" type_name="gh_guid" type_code="9">d540c611-1af7-4e7e-9179-d4927d03008d</item>
<item name="Name" type_name="gh_string" type_code="10">Panel</item>
<item name="NickName" type_name="gh_string" type_code="10"></item>
<item name="Optional" type_name="gh_bool" type_code="1">false</item>
<item name="ScrollRatio" type_name="gh_double" type_code="6">0.50049507617950439</item>
<item name="Source" index="0" type_name="gh_guid" type_code="9">b731122a-226d-4448-829a-f10aac320680</item>
<item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
<item name="UserText" type_name="gh_string" type_code="10">ariasD[0] = 1;
ariasD[n_Integer?Positive] := ariasD[n] = Sum[2^((k (k - 1) - n (n - 1))/2) ariasD[k]/(n - k + 1)!, {k, 0, n - 1}]/(2^n - 1);
iFabiusF[x_]:=Module[{prec=Precision[x],n,p,q,s,tol,w,y,z},If[x&lt;0,Return[0,Module]];tol=10^(-prec);
z=SetPrecision[x,Infinity];s=1;y=0;
z=If[0&lt;=z&lt;=2,1-Abs[1-z],q=Quotient[z,2];
If[ThueMorse[q]==1,s=-1];
1-Abs[1-z+2 q]];
While[z&gt;0,n=-Floor[RealExponent[z,2]];p=2^n;
z-=1/p;w=1;
Do[w=ariasD[m]+p z w/(n-m+1);p/=2,{m,n}];
y=w-y;
If[Abs[w]&lt;Abs[y] tol,Break[]]];
SetPrecision[s Abs[y],prec]];
FabiusF[Infinity] = Interval[{-1, 1}];
FabiusF[x_?NumberQ] /; If[Im[x] == 0, TrueQ[Composition[BitAnd[#, # - 1] &amp;, Denominator][x] == 0], False] := iFabiusF[x];
Derivative[n_Integer][FabiusF] := 2^(n (n + 1)/2) FabiusF[2^n #] &amp;;
SetAttributes[FabiusF, {NumericFunction, Listable}];//Timing//AbsoluteTiming;
ToString[DecimalForm[N[Table[{ToString[DecimalForm[N[t],256]],ToString[DecimalForm[N[FabiusF[t]],256]],ToString[DecimalForm[N[0],256]]},{t,0,N[1],N[1/32]}]],256]]</item>
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<X>-260</X>
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<W>200</W>
<H>289</H>
</item>
<item name="MarginLeft" type_name="gh_int32" type_code="3">0</item>
<item name="MarginRight" type_name="gh_int32" type_code="3">0</item>
<item name="MarginTop" type_name="gh_int32" type_code="3">0</item>
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<X>-259.466</X>
<Y>521.5567</Y>
</item>
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<chunk name="PanelProperties">
<items count="7">
<item name="Colour" type_name="gh_drawing_color" type_code="36">
<ARGB>255;255;255;255</ARGB>
</item>
<item name="DrawIndices" type_name="gh_bool" type_code="1">true</item>
<item name="DrawPaths" type_name="gh_bool" type_code="1">false</item>
<item name="Multiline" type_name="gh_bool" type_code="1">true</item>
<item name="SpecialCodes" type_name="gh_bool" type_code="1">false</item>
<item name="Stream" type_name="gh_bool" type_code="1">false</item>
<item name="Wrap" type_name="gh_bool" type_code="1">true</item>
</items>
</chunk>
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<item name="Name" type_name="gh_string" type_code="10">Replace Text</item>
</items>
<chunks count="1">
<chunk name="Container">
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<item name="Description" type_name="gh_string" type_code="10">Replace all occurences of a specific text fragment with another</item>
<item name="InstanceGuid" type_name="gh_guid" type_code="9">cc216dbe-7368-4ad0-b361-9576424dcc24</item>
<item name="Name" type_name="gh_string" type_code="10">Replace Text</item>
<item name="NickName" type_name="gh_string" type_code="10">Replace Text</item>
<item name="RecursiveReplace" type_name="gh_bool" type_code="1">false</item>
</items>
<chunks count="5">
<chunk name="Attributes">
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<X>288</X>
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</item>
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<X>341</X>
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</item>
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</chunk>
<chunk name="param_input" index="0">
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<item name="Description" type_name="gh_string" type_code="10">Text to operate on.</item>
<item name="InstanceGuid" type_name="gh_guid" type_code="9">5cd71bb6-669e-4d72-a523-2cdb216701d2</item>
<item name="Name" type_name="gh_string" type_code="10">Text</item>
<item name="NickName" type_name="gh_string" type_code="10">Text</item>
<item name="Optional" type_name="gh_bool" type_code="1">false</item>
<item name="Source" index="0" type_name="gh_guid" type_code="9">3f3d8116-c897-4cc1-8f26-d9cfbf2afd3a</item>
<item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
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<chunk name="param_input" index="1">
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<item name="Description" type_name="gh_string" type_code="10">Fragment to replace.</item>
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<item name="Optional" type_name="gh_bool" type_code="1">true</item>
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<item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
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</chunk>
<chunk name="PersistentData">
<items count="1">
<item name="Count" type_name="gh_int32" type_code="3">1</item>
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<chunks count="1">
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<chunk name="param_input" index="2">
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<item name="Description" type_name="gh_string" type_code="10">Optional fragment to replace with. If blank, all occurences of F will be removed.</item>
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</chunks>
</chunk>
</chunks>
</chunk>
<chunk name="param_output" index="0">
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<item name="InstanceGuid" type_name="gh_guid" type_code="9">61005a47-bf72-44ac-b2ee-58fe4593ead5</item>
<item name="Name" type_name="gh_string" type_code="10">Result</item>
<item name="NickName" type_name="gh_string" type_code="10">Result</item>
<item name="Optional" type_name="gh_bool" type_code="1">false</item>
<item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
</items>
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</item>
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<item name="NickName" type_name="gh_string" type_code="10">Replace Text</item>
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<item name="Description" type_name="gh_string" type_code="10">Fragment to replace.</item>
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<items count="1">
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</bitmap>
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